Experimental Studies on Cluster Ions

ADVANCES IN ATOMIC AND MOLECULAR PHYSICS.VOL. 20

EXPERIMENTAL STUDIES ON CLUSTER IONS T. D . MARK* and A . W. CASTLEMAN, JR . Department of Chemistry The Pennsylvania State University University Park. Pennsylvania

I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Experimental. . . . . . . . . . . . . . . . . . . . . . . . . . . A . Molecular Beam Ionization Technique . . . . . . . . . . . . . B. High-pressure and Drift Cell Techniques . . . . . . . . . . . . C. Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Formation of Cluster Ions . . . . . . . . . . . . . . . . . . . . . A . Ionization of Neutral Clusters . . . . . . . . . . . . . . . . . B. Association Reactions . . . . . . . . . . . . . . . . . . . . . IV . Dissociation of Cluster Ions . . . . . . . . . . . . . . . . . . . . A . Unimolecular (Metastable) Dissociations . . . . . . . . . . . . B . Collision-Induced Dissociations. . . . . . . . . . . . . . . . . C. Photodissociation . . . . . . . . . . . . . . . . . . . . . . . V . Thermochemical Properties . . . . . . . . . . . . . . . . . . . . A . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . B. Equilibrium Measurements. . . . . . . . . . . . . . . . . . . C. Entropies . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Bonding to Positive Ions . . . . . . . . . . . . . . . . . . . . E . Solvation . . . . . . . . . . . . . . . . . . . . . . . . . . . F . Some Structural Considerations. . . . . . . . . . . . . . . . . G . Systems Containing an Organic Constituent . . . . . . . . . . . H . Bonding to Negative Ions . . . . . . . . . . . . . . . . . . . VI . Other Properties . . . . . . . . . . . . . . . . . . . . . . . . . A . Reactivity . . . . . . . . . . . . . . . . . . . . . . . . . . B. Recombination . . . . . . . . . . . . . . . . . . . . . . . . C. Transport Properties . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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* Visiting Professorofchemistry (1983)in the Department ofchemistry. The Pennsylvania State University. Permanent address: Institut f i r Experimentalphysik.Leopold Franzens Universiat. A-6020 Innsbruck. Austria. 65 Copyright 0 1985 by Academic Press. Inc. All rights of reproductionin any form reSeNed.

ISBN 0- 12-003820-X

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T. D. Mark and A . W. Castleman, Jr.

I. Introduction The last decade has been marked by a rapidly growing increase of interest in the properties of both neutral and ionic clusters (e.g., see reviews by Kebarle, 1968, 1972a,b, 1974, 1977;Zettlemoyer, 1969; Milne and Greene, 1968, 1969; Narcisi and Roth, 1970; Ewing, 1972, 1975, 1976; Wegener, 1974; Klemperer, 1974, 1977; Knof, 1974; Good, 1975; Blaney and Ewing, 1976; Christophorou, 1976; Sinfelt, 1977; Muetterties, 1977; Smirnov, 1977; Smalley et al., 1977; Hoare, 1979; Ferguson et al., 1979; Stein, 1979; Castleman, 1973a, 1974, 1979a- d, 1982a,b,d- f; Castleman and Keesee, 1983a,b, 1984; Castleman et al., 1982a,b; Muetterties et al., 1979; Castleman and Mark, 1980; Geoffroy, 1980; Gingerich, 1980a,b; Smith and Adams, 1980, 1983b; Hamilton, 1980; Levy, 1980, 1981;van der Avoird et al., 1980;Perenboom et al., 1981;Beswick and Jortner, 1981;Hagena, 1981; Gspann, 1982; Sattler, 1982; Ferguson, 1982; Mark, 1982a,b; Mots, 1982; Bohme, 1982; Lewis and Green, 1982; Ng, 1983; Martin, 1983; Dehmer, 1983; Buttet and Borel, 1983; Friedel, 1983; Geraedts et al., 1983a). This interest is due to the many faceted aspects ofcluster research which pertain to important questions of both a fundamental, as well as an applied nature. Cluster ions comprise a nonrigid assembly of components having properties between those of large gas phase molecules and the bulk condensed state and many of the studies have provided data which serve to bridge the gap between atomic and molecular physics on one hand, and condensed matter physics on the other. Additionally, it is well recognized that research on the properties of cluster ions is valuable in obtaining a more complete understanding of the forces between ions and neutral atoms or molecules, where, for example, data on energetics provide a direct measure of the depth of the potential well of interaction between the ion and the collection of neutral molecules. Work on increasingly higher degrees of aggregation has had a direct bearing on the field of interphase physics which is concerned with elucidating the molecular details of the collective effects responsible for phase transformations (nucleation phenomena), the development of surfaces, and ultimately solvation phenomena and the formation of the condensed state. A natural extension ofwork on large gas phase ion clusters is the attempt of various investigatorsto connect their properties to those of ions in liquids or solids. Such research enables a further understanding of bonding and reactivity of complexes known to exist in the solution phase that have gas phase analogies. For instance, exciting new results and experiments involving both ions and neutral clusters suggest that relatively few molecules must be coclustered for either the ion or the neutral system to begin to display properties normally associated with the condensed phase (Castleman, 1979a,

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1982a-d,f, 1983; Castleman et al., 1978a,b, 1981c, 1982a,b; Kay et al., 1981; Castleman and Keesee, 1981a, 1983a,b, 1984; Lee et al., 1980a,b; Keesee et al., 1979a, 1980; Holland and Castleman, 1982a,b).Furthermore, studies of the attachment of electrons to neutral clusters provide a technique for investigating the solvated electron which is a specific example of the general class of systems termed polarons (Emin, 1982). Systems composed of metal atoms are beginning to draw the attention of theoreticians interested in theories of nonmetallic- metallic transitions and the onset of metallic conductivity. In other areas of physical chemistry cluster research is being utilized to unravel important problems pertaining to energy transfer and energy redistribution within molecules; the results are expected to have an important bearing on the further development of statistical theories of reaction rates and unimolecular decomposition. Finally, the surface-cluster analogy has drawn the particular attention of inorganic chemists who are beginning to lay the foundation for interpreting the molecular details of catalytic processes (Messmer, 1979; Shustorovich and Baetzold, 1983; Muetterties, 1977; Muetterties et al., 1979; Block and Schmidt, 1975; Beauchamp, 1983; Somorjai, 1981) and to lay a physical basis for understanding catalysis. Furthermore, both ion and fast atom bombardment techniques are utilized in surface chemistry and solid state physics to investigate surfaces and reactivity of surface sites. Data on gas phase cluster ions are useful in interpreting the results. Also, small clusters are currently being used as prototypes of surface sites in theoretical efforts to model electronic states and properties of the surface state (Gatos, 1981). In terms of applied fields, examples of the importance of cluster research are legion. The existence and role of cluster ions in the upper atmosphere have been recognized for many years and have drawn the attention of numerous researchers (Ferguson et al., 1979; Castleman and Keesee, 198lb; Keesee and Castleman, 1982; Arnold and Joos, 1979; Arnold and Fabian, 1980; Arnold et al., 1982; Bohringer and Arnold, 1981; Arijs, 1983; Arijs et al., 1982, 1983a-d; Mohnen, 1971a,b;Turco et al., 1982). Recognition of their potential role in the lower atmosphere is becoming increasinglyevident as the result of recent observations of positive and negative cluster ions below the troposphere by Arnold ( 1983) and suggestions due to Ferguson (1977), Castleman (1 980), Castleman and Keesee ( 1981b), Keesee and Castleman (1 982), and Arnold ( 1980). A general view of the earth’s environment, consisting of a weakly ionizing plasma surrounding the globe is given by Smith and Adams ( 1980).Cluster ions are known to exist throughout most of the earth’s atmosphere (Ferguson et al., 1979) and are implicated as being important in maintaining the charge balance as well as potentially effecting certain nucleation processes leading to aerosol particle formation (Castleman and Keesee, 1981b; Keesee and Castleman, 1982). Additionally, the

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formation of interstellar molecules has been suggested to be initiated via radiative stabilization involving ion clusters (Smith and Adams, 198la; Villinger et al., 1983).Other applied areas to which cluster ion research contributes include combustion science, where ion clusters are also known to form during combustion processes, and they have been suggested as playing a role in soot formation, radiation chemistry, biochemistry, electrochemistry, analytical detection of trace species, and the transport of fission products in nuclear reactors, and even mechanisms of corrosion in high-temperature systems (see for example Franck, 1978; Pitzer, 1983). Others have suggested the use of cluster ions for fuel injection into fusion reactors (Henkes, 1964) and cluster ions are also present in other high-temperature systems such as those designed as sources of energy employing magnets, hydrodynamics, and others too numerous to mention. In a general sense a cluster (or, as they are sometimes referred to, a microcluster) is defined as an aggregate of atoms, ions, and molecules so small that an appreciable number of the constituents are present on its surface at any give time, i.e., setting an upper limit in the region of lo4- los constituents/ microcluster (Hoare, 1979). In the present article, only a selected class of clusters, i.e., the ionic clusters, will be treated. They can be categorized into two groups, one consisting of cluster ions formed by the attachment of neutrals, L, to preexisting ions, I+, (I+ * L,, n = 1,2, . . .), and one consisting of ionized van der Waals molecules (A:, AB:; n = 1, 2, . . .). There are three types of experimental approaches to produce and study these cluster ions depending on different degrees of physical isolation, i.e., clusters moving freely in space (gas phase studies), clusters supported upon a substrate surface, and clusters existing in solids and liquids. In part because excellent reviews are available (Ozin, 1977, 1980; Hoare, 1979; Moskovits, 1979; Muetterties et al., 1979; Miller and Andrew, 1980; Hamilton, 1980; Perenboom et al., 1981; Lewis and Green, 1982) and in part to keep the present review article to manageable proportions, herein attention is given to the more limited subject of gas phase cluster ions. As a prelude to a discussion of the known properties of cluster ions, some of the main types of experiments now available for the production and analysis of cluster ions will be selectively reviewed first. Following this will be a discussion of their production, loss, and properties in the gas phase.

11. Experimental Generally, a cluster ion experimental system consists of a suitable cluster ion source coupled to a conventional apparatus designed for the study of ion

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properties. Since these apparatus have been characterized previously, or are available commercially, only brief mention of them will be made where necessary. Therefore, attention is given to a description of the pertinent details of the cluster ion source, with the inclusion of a discussion of those cases where cluster ion production is part of the experimental setup itself. A. MOLECULAR BEAMIONIZATIONTECHNIQUE Although the existence of condensation in high-velocity expanding jets has been known since at least 1942 (Oswatitsch, 1942), it is only recently (after some pioneering studies by Becker et al., 1956, 1962; Becker and Henkes, 1956;Bentley, 1961;Henkes, 1961,1962) that this fact has been put to use with the advance of mass spectrometry (e.g., Gspann and Korting, 1973; Beuhler and Friedman, 1980; Sattler et al., 1980; Stace and Shukla, 1980;Stephanetal., 1980a, 1983a;DietzetaL 1980;HelmetaZ., 1981;Echt ef al., 1984) and the advent of an array of supersonic nozzle designs, i.e., ranging from the use of a simple hole (Klemperer, 1974; Helm et al., 1979; Dehmer and Poliakoff, 1981) to the use of more sophisticated designs employing differential pumping, seeding, various nozzle shapes, multiexpansion, laser vaporization, and/or pulsed operation (e.g., Becker and Henkes, 1956; Hagena, 1963, 1974, 1981; Hagena and Obert, 1972; Larsen et al., 1974;Gentry and Giese, 1977, 1978;Behlen et al., 1979;DeBoer et al., 1979; Liverman ef al., 1979, and earlier references therein; Otis and Johnson, 1980; Beuhler and Friedman, 1980; Levy, 1980; Brutschy and Haberland, 1980; Bowles ef al., 1981; Saenger, 1981; Dietz et al., 1981; Cross and Valentini, 1982; Kay et al., 1982; Reyes-Flotte et al., 1982; Kappes et al., 1982a; Kappes and Schumacher, 1983; Delacretaz et al., 1983a; Peterson et al., 1983, 1984a). In principle, careful control ofthe nozzle and stagnation chamber parameters (ie., pressure, gas mixture, temperature) can lead to the production of quite high concentrations of bound neutral clusters (van der Waals molecules) from the dimer upward to the n = lo8 range (see also reviews on supersonic nozzle beams by Anderson et al., 1966; Milne and Green, 1968, 1969; Andres, 1969; Anderson, 1974; Hagena, 1974, 1981). This neutral cluster production has been studied (and/or used) with a variety of experimental techniques, i.e., ionization detector with retarding Jield (Bauchert and Hagena, 1965; Hagena and Henkes, 1965; Falter et al., 1970; Hagena and Obert, 1972;Hagena and von Wedel, 1974;Obert, 1977,1979), electron diflaction (Audit, 1969; Stein and Armstrong, 1973; Raoult and Farges, 1973; Farges ef al., 1973, 1977, 1981, 1983; Yokozeki and Stein, 1978; DeBoer et al., 1979; DeBoer and Stein, 1981; Bartell et al., 1983; Heenan et al., 1983; Buttet and Borel, 1983, and references therein), light scattering

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(Stein and Wegener, 1967; Stein, 1969; Klingelhofer and Moser, 1972; Wegener and Wu, 1976; Wu et al., 1978a,b; Konig et al., 1982; Godfried and Silvera, 1983), electric and magnetic deflection (with mass spectrometry) (Gordon et al., 1971; Dyke et al., 1972a,b; Dyke and Muentner, 1972; Novick et al., 1972; Klemperer, 1974, 1977, and references therein; Knight etal., 1978;Odutolaetal., 1979;Bartonetal., 1979;Castlemanetal., 1981a, 1983c; Kremens et al., 1984; Sievert et al., 1983; Sievert and Castleman, 1984; Keesee et al., 1984; Knight, 1983), beam scattering with or without mass spectrometry (Becker et al., 1962; Burghoff and Gspann, 1967; Van Deurson et al., 1975; Herschbach, 1976; Van Deursen and Reuss, 1977; Buck and Meyer, 1983),single and multiphoton ionization mass spectrometry(Robbins et al., 1967;Fosterer al., 1969;Feldman et al., 1977;Herrmann et al., 1977, 1978a,b, 1979; Mathur et al., 1978, 1979; Rothe et al., 1978; Cook and Taylor, 1979a,b, 1980; Cook et al., 1980; Leutwyler et al., 1980, 1981, 1982a,b;Hopkinsetal., 1981, 1983;WaltersandBlais, 1981;Dehmer andpoliakoff, 1981;Dietzetal., 1981;Fungetal., 1981;Duncanetal., 1981; Ono and Ng, I982a,b; Dehmer, 1982; Dehmer and Pratt, 1982a,b; Pratt and Dehmer 1982a-c, 1983; Delacretaz et al., 1982a,b, 1983a,b; Eisel and Demtroder, 1982; Martin et al., 1982; Kappes et al., 1982a; Michalopoulos et al., 1982;Powers et al., 1982, 1983; Shinohara andNishi, 1982;references summarized by Ng, 1983;Kappes and Schumacher, 1983; Rademann et al., 1983; Bronner et al., 1983; Haberland et al., 1983a; Choo et al., 1983; Rohlfing et a)., 1983; Stanley et al., 1983a,b;Castleman et al., 1983d;Shinohara, 1983;McGeoch and Schlier, 1983; Peterson et al., 1983, 1984a,b; Dao et al., 1984; Echt et al., 1984), photoelectron spectroscopy and electronelectron spectroscopy (Mathis and Vroom, 1975; Dehmer and Dehmer, 1977, 1978a,b;Carnovale et al., 1979, 1980; Kubota et al., 1981; Yencha et al., 1981; Poliakoff et al., 1981, 1982; Tomoda et al., 1982, 1983; Tomada and Kimura, I983), electron impact ionization mass spectrometry (sometimes combined with additional diagnostic tools, such as lasers, velocity selectors, etc.) [Greene and Milne, 1963, 1966; Leckenby et al., 1964; Cuthbert et al., 1965; Leckenby and Robbins, 1966; Milne and Greene, 1967a,b; Buchheit and Henkes, 1968; Knof and Maiwald, 1968; Golomb and Good, 1968; Tay and Dawson, 1970; Tay et al., 1970; Golomb et al., 1970, 1972; Henkes and Isenberg, 1970; Harbour, 1971; Milne et al., 1972; Fricke et al., 1972; Yealland et al.. 1972; Gspann and Korting, 1973; Dorfield and Hudson, 1973a,b;Lin, 1973;Larson et al., 1974; Gspann and Krieg, 1974; Calo, 1974; Van Deursen and Reuss, 1973, 1975, 1977; Henkes and Mikosch, 1974; Van Deursen et al., 1975; Henkes et al., 1977; Lee and Fenn, 1978; Stephan et al., 1978, 1980a,b, 1981, 1982a-c, 1983a-c,e, 1984; Gough et al., 1978; Herrmann et al., 1978b, 1982; Helm et al., 1979, 1980a,b, 1981; Market al., 1980a, 1982, 1983;Castleman et al., 1980a,b, 198lb,e; Dun and

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Stevenson, 1980; Stace and Shukla, 1980, 1982a-c; Gspann and Vollmar, l980,198l;CookandTaylor,1980;Cabaudetal., 1980;Buelowetal., 1981; Futrell et al., 1981a,b, 1982; Kay et al., 1981; Geraedts et al., 1981, 1982, 1983b; Casassa et al., 1981; Lisy et al., 1981; Yamashita et al., 1981; Hoareauetal., 1981;Gspann, 1981;Sattleretal., 1981;Echtetal., l981,1982a,b; Stephan and Mark, 1982a-c, 1983; Gough and Miller, 1982; Vernon et al., 1982,1983; StaceandMoore, l982,1983;Soleretal., 1982(seealsoHagena, 1983); Saito et al., 1982, 1983; Dreyfuss and Wachman, 1982; Kay and Castleman, 1983;Haberland et al., 1983a; Labastie et al., 1983;Muller et al., 1983; Ding and Hesslich, 1983a,b; Stace, 1983a,b;Bomse et al., 19831, and electron attachment to van der Waalspolymers (Gspann and KOrting, 1973; Klots and Compton, 1977, 1978a,b; Klots, 1979; Bowen et al., 1979, 1983; Armbruster et al., 1981; Haberland et al., 1983b; Stephan et al., 1983d). The extent of condensation in a supersonic expansion depends upon the time scale of expansion (Hagena and Obert, 1972)and the degree of cooling in the expansion, which scales with the stagnation pressure,po,nozzle diameter, D, and nozzle-stagnation temperature, To.Obert (1979) has reported a scaling law for hydrogen clusters p o . DI.5 . T-2.4 = constant (1) The practical limit to production of neutral clusters is the requirement of sufficient pumping capacity to handle the gas load discharged through the nozzle. Besides the use of larger and larger pumps (combined with the differential pumping stages), there have been introduced recently several other techniques, i.e., pulsed nozzles and laser vaporization within the nozzle (see references above). Translational temperatures down to 0.00 15 K have been predicted (Toennies and Winkelmann, 1977) and almost achieved (Levy, 1980).The ultimate temperatures achieved in a given supersonic expansion due to the fact that the density usually follow the order TmS < T,, < Tvibr, of the gas drops as the expansion proceeds and vibrational (and rotational) cooling is less facile than translational, requiring far more collisions. Because condensation is a much slower process than rotational or even vibrational relaxation, extensive cooling of the internal degrees of freedom can be achieved before condensation takes place, i.e., rotational distributions corresponding to less than 0.2 K and vibrational temperature of down to 20 K have been observed ( e g , Levy, 1981, and references therein). Since condensation involves the production of clusters via statistical processes, it is generally difficult to obtain narrow size cluster distributions. However, the production of a relatively narrow distribution has been achieved with a special source design ( e g , Bowles et al., 1981). It is sometimes desirable to minimize the production of clusters heavier than a particular one under study. A pressure- temperature relationship given by Van Deursen and Reuss ( 1977)

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T. D.Mark and A . W. Castleman, Jr.

can be used to select conditions that serve to cut offthe production of heavier clusters, but usually this can only be applied to separate dimers and trimers from heavier clusters (Ng, 1983; see also Dehmer and Pratt, 1982b). Finally, it should be mentioned that thus far parameterized studies of factors influencing cluster distributions have been largely confined to those with species which are gaseous or have substantial vapor pressures at room temperatures. However, Schumacher and co-workers (e.g., Herrmann et al., 1978a,b; Kappes et al., 1982a) have investigated the influence of the nature of the carrier gas mass on alkali clusters, and other highly refractory compounds have been recently clustered (e.g., Preuss et al., 1979, and references therein; Dietz ef al., 198 1; Michaloupoulos et al., 1982; Powers et al., 1982, 1983; Hopkins et al., 1983; Rohlfing ef al., 1983). In principle, a cluster ion can be produced from any of these neutral cluster beams with an ionizing agent of sufficient energy and intensity. Although different ionization (electron, single and multiple photon, Penning ionization, heavy particle impact) and detection techniques have been used, the basic features of virtually all molecular beam ionization mass spectrometers are similar. Two examples are described in what follows to provide the reader with some information about the actual design ofsuch an apparatus. Figure 1 shows a detailed cross section of the molecular beam production section, ionization region, and ion optics in front of a modified commercial double-focusing mass spectrometer used in our Innsbruck laboratory (Stephan et al., 1982a-c, 1983a). The gas (mixture) under study (gaseous atoms and/or molecules) is expanded from a high-pressure (up to 10 bar) variable temperature (down to 100 K) stagnation reservoir through an aperture nozzle (10- to 50-pm diameter) located 4 cm from the electron beam which intersects the molecular supersonic jet at 90”.The molecular beam isdefined by the nozzle and a collimator (5-mm diameter) in front of the ionization chamber. A 500 liter/sec turbo pump is used to evacuate the open ion source chamber and to handle the gas load imposed by the supersonic jet (giving a Torr, depending on the stagnabackground pressure between and tion pressure and gas mixture). The ion source is isolated from the mass spectrometer by the mass spectrometer entrance slit ( S , ) , serving as a differential pumping aperture. Ions produced by electron impact ionization are extracted at right angles (“off line detection”) from the ionization region by an electric field penetrating into the ionization chamber (penetrating field extraction, see Stephan et al., 1980~).Special deflection plates (deflection mass spectrometry, see Stephan et af., 1980c) in the ion optics between the ion source (commercial, Nier type) and the mass spectrometer entrance slit serve to sweep the extracted ion beam across the mass spectrometer entrance slit, thus allowing ions formed by cluster ionization to be distinguished from

73

EXPERIMENTAL STUDIES ON CLUSTER IONS

ELECTRON BEAM

MASS

ROMETER

F

FIG. I . Schematic view of supersonic molecular beam electron impact ionization mass spectrometer after Stephan et al. (1982a-c, 1983a). Nozzle N is a m dia. pinhole located 4 cm from the electron beam crossing region. S is the stagnation chamber and A an aperture. Electrode L, , plate P and chamber C are at common source potential, while electrode L, produces a field penetration extraction field. Beam centering plates L3, L, locate the extracted ion beam on a defining aperture D, whereas the earth slit, L,, constitutes the end of the accelerating region. Deflection plates L6,, and L, and L, centerthe beam on the mass spectrometer entrance slit, S, , or sweep the beam across S, . Beam flag F is used to interrupt the beam diagnostically.

background ions with the same m/z (Helm ef al., 1979, 1981; Stephan ef al., 1982b,c, 1983a;see also Stace and Shukla, 1980). This simple experimental set-up allows the production of atomic and molecular clusters up to n = 50 with sufficient intensity for (also high-resolution) mass spectrometric studies, i.e., measurement of appearance energies, study of metastable decay, etc. Figure 2 shows an overview of another, rather novel, technique involving pulsed laser vaporization within a pulsed supersonic nozzle and (subsequent) mass-selective resonant two-photon laser ionization (Dietz et al., 1980, I98 1;Michalopoulos ef al., 1982; Powers ez al., 1982, 1983; Hopkins et al., 1983). Generation of ultracold metal clusters (e.g., for Mo, T,,, < 6 K, Trot- 5 K, TYib - 325 K; Hopkins et al., 1983) is achieved by the followingtechnique. The vaporization laser (Nd :YAG second harmonic) hits a rotating target rod within the throat ofa pulsed supersonic He expansion. As the vapor cools in the high-density He gas, clustering of metal atoms within the exit channel of the expansion begins to occur and further clustering and cooling occur as the gas freely expands into the vacuum. The length of the exit channel controls the extent of cluster production, i.e., producing up to n = 30 clusters of Cu, Fe, Ni, W, and Mo at 8 atm He stagnation pressure, 1-mm orifice, an extension channel of 2.5-mm length and 3-mm diameter, 10-Hz pulsed operation, and typical base pressures with pulsed beam-on of

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T. D.Murk and A . W. Castleman, Jr. V4fQRRATlON LASER

\

PROBE LASER

MOLECULAR BEAM

FIG.2. Schematic view of supersonic molecular beam two-photon ionization mass spectrometer after Dietz ef al. (1980), Powers ef al. ( 1 982), Hopkins ef af.( I 983). ( I ) Main chamber containing pulsed nozzle with laser vaporization; (11) probe chamber, (111) detection chamber containing time of flight mass spectrometer; (A) repeller plate; (B) draw-out grid; (C) flight tube grid; (D)deflection plates; (E) flight tube; (F) support rods; (G) copper cryoshield; (H) stainless steel liquid nitrogen Dewar.

8X 1 X lod, and 4 X lo-* Torr in chambers 1-111, respectively. The clusters are detected by a time-of-flight mass spectrometer (a vertical cross section is shown in Fig. 2) 1 18 cm downstream from the nozzle. The clusters are interrogated using two-color ionization by scanning a Nd :YAG pulsed dye laser and using a second color of sufficient energy (provided by a Nd :YAG harmonic or excimer laser) to ionize the excited clusters. Again, ions are extracted at right angles into the mass spectrometer and deflection plates have to be used to counteract the translational velocity of the molecular beam. In ending this discourse on supersonic expansions (the most commonly used technique for generating neutral clusters), it is interesting to note two other techniques for both neutral and ionized cluster production, i.e., the expansion of ionized gas (Dole et al., 1968; Mack et al., 1970; Searcy and Fenn, 1974;Armbruster et al., 1981;Udseth et al., 1981; Beuhler and Friedman, 1982a,b; Yamashita and Fenn, 1983; Haberland et a/., 1983b) and inert gas (“cold bath”) condensation (“quench flow”) of evaporated metals, etc. (Pfund, 1930a,b;earlier references in Perenboom et al., 1981; Duthler et

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al., 197 1; Mann and Broida, 1973; Eversole and Broida, 1974; West et a/.,

1975; Nishida and Kimoto, 1975;Granqvist and Buhrmann, 1976;Kimoto and Nishida, 1977; Knight et al., 1978; Schulze and Abe, 1980; Kimoto et al., 1980; Sattler et al., 1980a,b, 1981, 1982; Bondybey and English, 19811983; Bondybey, 1982; Sattler, 1982; Muhlbach et al., 1982a,b; Pfau et al., 1982a,b; Riley et al., 1982;Gole et al., 1982; Heaven et al., 1982a;Martin et al., 1983; Bondybey et al., 1983). The latter technique has been particularly successful in producing refractory metal clusters (also in combination with laser evaporation). As pointed out by Riley et al. (1982),generallythese latter sources will not result in clusters as cold internally as do supersonic expansions. B. HIGH-PRESSURE AND DRIFTCELLTECHNIQUES Although early observations of ion clusters were obtained in ion sources operated in the neighborhood of lo4 Torr, equilibrium conditions were generally not attainable with the few collisions taking place and thermodynamic parameters usually could not be measured with confidence. Early attempts by Field ( 196l), Melton and Rudolf (1 960), and Wexler and Marshall ( 1 964) were made using essentially conventional mass spectrometric ion sources but with small ion exit slits and improved pumping. These new methods enabled reactions requiring a third body for stabilization to be observed, but it was generally impossible to ensure that complete thermalization ofthe ions and the attainment ofion equilibrium had occurred. Major developments were made by Kebarle and co-workers during the 1960s and early 1970s that have led to the investigation of bonding and reaction for a number of clustering sequences (see sections devoted to thermochemistry and association reactions). Kebarle and his group have used several different types of high-pressure mass spectrometers, including a high-pressure alpha particle instrument capable of operating at pressures up to several hundred Torr, a 100-keV proton beam mass spectrometer, and a 4-keV pulsed electron beam apparatus (Kebarle, 1972b, 1975). Important data have been derived from these techniques by Kebarle and by many others who have adapted similar devices. Related high-pressure instruments operate as drift cells and employ internal electrodes that function to move the ion clusters from the point of production to a suitable sampling orifice. There, the ions effuse into vacuum and are introduced into a mass spectrometer for identification and quantitative measurement of requisite intensities. In the limit of zero field, the two apparatuses are identical, but as operated in actual practice the latter do potentially impart some field energy to the ions being investigated. The drift

76

T. D. Mark and A . W. Castleman, Jr

field techniques generally do have the advantage of providing relatively high ion intensities at pressures of several Torr, but it is important that measurements be made as a function of field energy ( E / N ) to establish that true equilibrium is being achieved (see for instance Castleman et al., 1978a). The general high-pressure technique is adaptable to two configurations, one in which the ions are injected at a constant flux and the other where the beam is pulsed and the evolution of the cluster reactions is followed as a function of time. With suitable corrections for loss at the boundaries of the apparatus and electrodes, the ion ratio at long times can be taken as proportional to the equilibrium ratios (Kebarle, 1972). Deriving exact correction methods to account for the diffusion and loss of ions and separating these from the equations pertaining to cluster evolution as a result of sequential clustering reactions has introduced some approximations and thereby uncertainties. However, within experimental error, studies by the two techniques have led to basically the same thermodynamic parameters. The high-pressure pulsed electron beam apparatus used in the laboratories of Kebarle is shown in Fig. 3. It is composed of an electron filament, suitable electrodes for electrostatic focusing of the beam, deflection electrodes, and magnetic and electrostatic shielding for the electron beam region. Appropriate carrier and clustering gases are introduced into the ion source through an entrance port. The electron gun is constructed with conventional cathode ray focusing geometry and is provided with a deflection plate for the positioning of the beam. Suitable electrodes enable the ions to be focused and directed into the mass spectrometer for identification. Ion source temperatures of - 20 to 600 "Ccan be achieved with the heating coils and cooling channels located in the copper mantle. During operation, the electron beam enters the ion source through a slit of X 4 mm and has an intensity of about lo-' A when operated continuously. The ions exit the ion source through a narrow slit constructed of X stainless steel razor blades that has an approximate dimension of 3 mm. In operation, a pulsing sequence is initiated in which the electron beam is on for a short period of time. After an appropriate delay time, an ion gate is opened for another short period (generally a few microseconds) and the ions, after having resided a specific number of microseconds in the ion source, are collected over a specified differential time duration. (In other versions of operation, the apparatus does not utilize an ion gate but the current is collected continuously.) The ion source is field free and the ions created in the electron beam diffuse throughout the cell and through the ion exit slit. In pulsed operation, the total ion intensity at first increases, then reaches a maximum, and thereafter gradually decreases to zero. Reaction conditions must be selected such that the ion concentration changes due to reactions are

+

EXPERIMENTAL STUDIES ON CLUSTER IONS

77

FIG. 3. Electron beam, high-pressure ion source after Kebarle (1972b). (1) Electron filament; (2)-(6) electrodes for electrostatic focusing of electron beam; (7),(8) deflection electrodes; (9) magnetic and electrostatic shielding of electron beam; (10) ion source with copper heating mantle; ( 1 I ) electrostatic wire mesh screen with high pumping conductance for shielding of ions and efficient pump out of neutrals; (1 2) electron entrance slit; (1 3) electron trap; (14) copper lid holding ion exit slit flange; ( 1 5 ) gas in- and outlet; (16)-( 18)ion source supports and insulation; (19)-(26) ion beam acceleration and focusing; (27) mass spectrometer tube to 90" magnetic sector; (28) 84x1. pumping lead leading to 6-in. baffle and diffusion pump; (29)gas line heaters.

much faster than the decrease of total ion concentration caused by diffusion of the ions to the walls (Kebarle, 1972). The data composed of normalized ion intensities are analyzed as if they represented concentration changes for a homogeneous reaction system in which, at time zero, a unit concentration of primary ions is created. The ions are then considered to react in a pseudo

78

T. D. Mark and A . W. Castleman, Jr.

first-order fashion with the total ion concentration remaining constant. The treatment assumes equal diffusion coefficients for all ions, and also the absence of reactions which are second order in ion concentration. Modifications of this apparatus have been made which enable the production of positive metal-like ions using thermionic source techniques (see for instance Searles and Kebarle, 1969). Field and co-workers (e.g., Beggs and Field, 1971a), Conway and coworkers (e.g., Conway and Janik, 1970), Pack and Phelps (1966, 1971), Puckett and Teague ( 197la), Keller and Beyer ( 197la), Rakshit and Warneck (1979), Castleman and co-workers (Castleman et al., 1978a; Keesee et al., 1980), Meot-Ner and co-workers (e.g., 1978, and Meot-Ner and Sieck, 1983),and Wince1and co- workers (e.g., Wlodek et al., 1980),among others, have used adaptations of the high-pressure technique sometimes in conjunction with the drift cell method. A typical ion source and mass spectrometer arrangement is shown in Fig. 4. In the case of positive ions, a thermionic emission source is employed with the application of a positive voltage to a heated filament on which the source material is dispersed. In the case of negative ions, the thermionic source is replaced with a platinum filament on which a barium zirconium material is dispersed; the heated filament then becomes a copious source of electrons. In this case a negative voltage is applied to the filament. The ions are focused by means ofa repeller assembly, the potential of which is set a few volts below that of the filament. Ion energies are further controlled by means of two electrodes placed before and just after the reaction cell. The potential of the “top gate” is adjusted to ensure field-free conditions in the reaction cell where clustering reactions and the final equilibrium process take place. The temperature of the high thermal conductivity (gold-plated copper block) reaction cell is established by a combination of electrical heating and cooling jacket surrounding the high-pressure vessel. Appropriate thermocouples are located throughout the system and a temperature within 0.5 “C of the same value is established on all of them. The high-pressure vessel is mounted inside a vacuum chamber (---); see Fig. 4. A 10-in. diffusion pump plus liquid nitrogen cold trap is used to maintain pressures less than 1 X 10-6 Torr in this chamber. Ions and ion clusters diffuse through a 50- to 75-pm hole in a platinum disk into the vacuum chamber. There they pass through suitable ion optics for focusing the ionic species into the mass spectrometer for quantitative determination of intensities using pulsecounting techniques. A crucial feature of this apparatus is its ability to operate at moderate pressures (typically 5 -25 Torr) and, more importantly, to ensure the acquisition of equilibrium. Measurements of apparent equilibrium constants are made as a function of both nature and pressure of the carrier gas and of the electric field parameters in the ion source (with particu-

------------1

r-

I I

I I

I

I

OUADRUPOLE

I

I

ION COUNTING EOUIPMENT

CMNNELTRON MULTIPLIER

I

I I I

79

EXPERIMENTAL STUDIES ON CLUSTER IONS

I

ocl 50

I I

I

I I

OUTER JACKET

I

I I I I I I

SCALE 1

1u

u

CAPACITANCE MANOMETER

FIG.4. Schematic ofthe ion clusteringapparatus, after Castleman ef a/.(1978a). The figure isdrawn approximately to scale, with internal supportsomitted forclanty. ---,A region ofhigh vacuum. For further discussion refer to the text.

80

T. 11. Miirk uncl A . M '. Castleman. J r

lar attention to the top gate potential). A plateau region in the plot of apparent equilibrium constant versus E / N (where E is the electric field and N is number density) is sought to ensure that field penetration from elsewhere in the ion source is not imparting significant energy to the ions above thermal and thereby influencing the equilibrium measurements.

C. OTHERS In addition to the above-mentioned techniques for the production of cluster ions in the gas phase, there is a number of methods where the production process involves the transfer of energy to the surface of a sample and the subsequent emission of neutral and/or ionized (singly and multiply) clusters. Within the space available in this article, it is not possible to give a detailed description of these techniques; however, the reader is referred to some recent papers and reviews on these methods, e.g., evuporatron (direct or Knudsen) (Drowart and Goldfinger, 1967, and earlier references therein; Margrave, 1968; Gingerich, 197 1, 1980a,b; Gutbier, 196 1; Lin and Kant, 1969; Donovan and Strachan, 197 1 ;Gingerich and Finkbeiner, 197 1; Emelyanov ct ul., 197 1 ; Marr and Wherrett, 1972; Evans et al., 1972; Brundle et a / , 1972; Schaaf and Gregory, 1972; Wagner and Grimley, 1972; Piacente and Gingerich, 1972; Neckel and Sodeck, 1972; Cocke and Gingerich. 1972, 1974: Hildenbrand, 1972; Guido and Balducchi, 1972; Boschi and Schmidt, 1973; Stearns and Kohl, 1973a,b, and references therein; Kordis and Gingerich, 1973a,b, 1977; Cabaud et al., 1973, and references therein; Dehmer et uI , 1973; Gingerich et ul., 1974; Potts et a/., 1974; Wagner and Grimley, 1974; Berkowitz, 1975; Ihle and Wu, 1975; Richardson and Weinberger, 1975; Cocke et a/., 1975: Streets and Berkowitz, 1976a.b; Wu, 1976, 1979, 1983; Potts and Price, 1977; Drowart ef a/., 1977; Smets ef a/., 1977: Smoes r" u I , 1977; Zmbov et a/., 1977; Grimley ct a / , 1978; Kingcade ef a1 , 1978; Biefeld, 1978; Potts and Lyns, 1978; Gupta and Gingerich, 1978a,b, 1979; Neubert, 1978; Gingerich and Cocke, 1979; Wu el ul., 1979; Potts and Lee, 1979; Hilpert, 1979; MacNaughton et a/., 1980; Berkowitz et a/., 1980; Pitterniann and Weil, 1980, and references therein; Hilpert and Gingerich, 1983; Rosinger ef a/ , 1983),fie/cI &sorption (also including the electrohydrodynamic and electrospraying techniques) (Beckey, 1960; Schmidt, 1964, and earlier references therein: Dole et al., 1968; Mahoney et al., 1969: Anway, 1969; Mack ef al., 1970; Huberman, 1970; Evans and Hendricks, 1972: Colby and Evans, 1973; Simons ef ul., 1974, and references therein; Heinen et ul., 1974; Rollgen and Schulten, 1975a,b; Schulten and Rollgen, 1975; Block and Schmidt, 1975; Iribarne and Thomson, 1976; Stimpson et a/., 1978; Rollgen and Ott, 1978; Rollgen e/ a/., 1978, 1980; Sudraud et ul.,

EXPERIMENTAL STUDIES ON CLUSTER IONS

81

1979; Thomson and Iribarne, 1979; Culbertson et al., 1980; Waugh, 1980; Dixon et al., 1981a,b; Block, 1982a,b; Moller and Helm, 1983; Helm and Moller, 1983a,b; Yamashita and Fenn, 1983), laser evaporation (see also above, and Berkowitz and Chupka, 1964; Bykovskii et al., 1971;Fiirstenau et al., 1979; Fiirstenau and Hillenkamp, 198I), laser-inducedjield evaporation(Kellogg, 1981, 1982;Jentschetal., 1981, 1982;Block, 1982a;Drachsel et al., 1982; Tsong et al., 1983), spark evaporation (Mattauch et al., 1943; Sasaki et al., 1959; Dornenburg et al., 1961; Franzen and Hintenberger, 1961; Hintenberger et al., 1963; Cornides and Morvay, 1983; Becker and Dietze, 1983),Penning ion source evaporation (Kaiser et al., 197l), sputtering (Honig, 1958, and earlier references therein; Krohn, 1962; Hortig and Miiller, 1969; Clampitt and Jefferies, 1970; Joyes, 1971; Tantsyrev and Nikolaev, 197 1, 1972;Staudenmaier, 1972; Leleyter and Joyes, 1973, 1975; Herzog et al., 1973; Richards and Kelly, 1973; Honda et al., 1978, 1979; Szymonski et al., 1978; Taylor and Rabalais, 1978; Wittmaack, 1979; Lancaster et al., 1979a,b;Jonkman andMich1, 1979, 1981;Leleyter et al., 1981; Orth et a/., 1981a,b, 1982a,b; Devienne et al., 1981; Pedrys et al., 1981; Campanaef al., 1981, 1983; Barlaketal., 1981, 1982;Leleyter, 1982;Standing et al., 1982;Devienne and Roustan, 1982,and referencestherein; Winograd et al., 1982; Kimock et al., 1983; Ens et al., 1983; Joyes and Leleyter, 1983; Stulik et al., 1983; Michl, 1983), and electron-induced desorption (Clampitt and Gowland, 1969; Floyd and Prince, 1972). Furthermore, cluster ions have been observed and studied in various types of discharges and ion traps (e.g., Narcisi and Roth, 1970; Loeb, 1973, and references therein; Colby and Evans, 1974; Schwarz, 1978; Mathur and 1980)and in the atmosphere and ionosphere Hasted, 1979; Kaufman el d., (e.g., see Ferguson and Fehsenfeld, 1969; Narcisi and Roth, 1970; Sechrist and Geller, 1972; Loeb, 1973; Meyerett et al., 1980; Carlon, 1980, 1983; Ferguson and Arnold, 1981; Arijs, 1983).

111. Formation of Cluster Ions A. IONIZATIONOF NEUTRALCLUSTERS

1. Ionization Processes und Mechanisms

If the energy of an electron, photon, or beam of ions (or fast neutrals) colliding with a gas phase cluster target is greater than a critical value (ionization energy or appearance energy), some of the neutral clusters, depending

82

T. D.A4iirk mil ‘4. W. Casileman, Jr.

on the corresponding ionization cross section, will be ionized resulting in the production of an ion (and sometimes a neutral) and the ejection of one (or more) electrons (e).As the energy of the electrons (or photons) is increased, the abundance and variety of the resulting ions will increase (e.g., see Rosenstock rt al., 1977; Mark, 1982c,d, 1984a,b). The ionization process (and concomitant changes in vibrational and rotational excitation) is governed by the Franck-Condon principle (and the selection rules) and may proceed via different reaction channels, i.e., for the simple case of a dimer .4,

+ h v ( e ) - .A: + e(+e) --A$+ + 2r(+ e )

single ionization double ionization

e(+e)

autoionization

+A’(+(>)

predissociation

-,4:(+e)-’4:+ --A

-AA:*+e(+e)-,il++A

-

-

/I+

.4:+ ‘4;

+e(+~)

+ 2e(+e) + e + hv’(+e)

+ A + e(+ e)

fragmentation autoionization radiative transition dissociative ionization ion pair forination

Moreover, in addition to being produced by ion pair formation (lo), negative ions may be produced by two other generalized processes: .-I2

+ e - .4;*

-

/I-

+ /I

resonance capture

(1 1)

dissociative resonance capture

(12)

The A;* ion in reaction ( I I ) is unstable and stabilization must occur by radiation emission before it decomposes by autodetachment. Furthermore the endoergic charge transfer process

+A;

(13) can be used (with X a fast alkali beam) as a relatively gentle electron attachment to weakly bound clusters (e.g., Bowen et al., 1983). Reactions (2), ( 3 ) , (9), (lo), and (12) can be classified as direct ionization processes, whereas reactions (4)- (8) can be categorized as two-step processes. Photon ionization cross sections of rare gas and alkali dimers have been found to show only autoionization lines (due to molecular states; see X + A,--rX+

EXPERIMENTAL STUDIES ON CLUSTER IONS

83

also Carlson ef al., 1980, 1981) near the first ionization threshold and virtually no contribution from direct ionization due to a poor Franck-Condon overlap between the neutral and the lowest vibrational states of the ion (e.g., Ng el al., 1976, 1977a,b;Dehmer and Poliakoff, 1981; Dehmer, 1982; Leutwyler et al., 1981, 1982a; Pratt and Dehmer, 1982a,c; Dehmer and Pratt, 1982a,b; Martin et al., 1982). Observed autoionization lines corresponding to the optical allowed atomic Rydberg series have been attributed to associative ionization reactions occurring in the ionization region via interaction of excited monomers and background gas monomers (e.g., Dehmer, 1982, and references therein). Conversely, Ng et af. (1977~)have reported for nitric oxide dimers that the dominant ionization mechanism is direct ionization such that only one of the NO molecules in the dimer is excited to different vibrational states of NO+ (XIZ+)forming an NO-NO+ (lZ+u’) complex (for other examples see also Linn et al., 198la,b; Erickson and Ng, 1981). Moreover, molecular dimers may be ionized either directly or via a vibrational autoionization process in one of the moieties as described by Anderson et af. (1980) for (H2), H,-H,

+ hu -,H,-H:(n,o)

-,H,-HI(u’)

+e+

H:

+H +e

(14)

(see also Tiedemann et af., 1979;Ono eta/., 1980;Linn and Ng, 1981) or via an autoionization process involving association ionization of loosely bound molecules, sometimes termed chemiionization and studied in detail by Gress et af. (1980) and Ono et af. (198 la,b), i.e., determining the relative reaction probabilities of various product channels of the chemiionization processes as a function of n

+ CS + e, -,S: + 2CS + e, -+C,S: + S + e, -,CS: + C + e,

CS:( V,n) - CS, + CS:

-

(CS,): + e,

Similar to the last step in reaction (14) a number of cases have been reported where ionization of a cluster involves an internal ion molecule half reaction, e.g., producing such ions as H30+from (H,O), (Milne et af., 1970; Ng el al., 1977d), H,O+(H,O), from (H,O), (Hermann et af., 1982), OH-(H,O), from (H,O), and NO-(N,O), from (N,O), (Mots and Compton, 1978a,b),N H t from (NH3)2 (Ceyer et af.,1979a; Stephan et al., 1982c; Choo et al., 1983),NHt(NH,), from (NH,), (Stanley et af., 1983a; Echt et al., 1984),C,H: or C,Hf from (C2H4),(Ceyer et af., 1979b),Of,,,from 0; (a 4111,,u) - (O,), (Linn et af., 1981b), C,Of from (CO,), (Stephan et al.,

84

T. D.Mark and A . W. Castleman,Jr.

1982b), CO$.O, from (CO,), (Stephan et al., 1983d), CHf(CH,), from (CH,), (Ding and Hesslich, 1983b). In some cases (depending on reaction energetics and dynamics) this leads to a situation where the protonated cluster ions are by far the dominant ions appearing in a mass spectrum, whereas the unprotonated cluster ions are either not detectable or order of magnitudes smaller (Fricke et a!., 1972;Lin, 1973; Van Deursen and Reuss, 1973; Ng et al., 1977; Ceyer et al., 1979a; Tiedemann et al., 1979; Anderson et al., 1980; Castleman et al., 1981e; Stephan et al., 1982c; Hermann et al., 1982; Dreyfuss and Wachman, 1982; Shinohara, 1983).Obviously, such an internal ion molecule reaction can be viewed in terms of an initial rearrangement within the cluster ion and a subsequent unimolecular decomposition. It is interesting in this conjunction to point out recent fragmentation studies by Ono and Ng (1 982a,b), Stace and Shukla (1982c), Stace and Moore (1982), and Stace (1983a,b). Moreover, Biermann and Morton (1 982) have studied the production of protonbound dimers via unimolecular decomposition of molecules following photoionization. Lifetimes with respect to unimolecular decomposition have been estimated from measured and calculated reaction rate constants for dimerization and trimerization reactions involving protonated species (e.g., see Olmstead et al., 1977; Davidson et al., 1977; Neilson et al., 1978; D. Smith et al., 1982; Adams et al., 1982, and references therein). The observation of multiply charged cluster ions (e.g., Domenburg et a!., 1961; Dole et al., 1968; Henkes and Isenberg, 1970; Gspann and Korting, 1973; Simons et al., 1974; Henkes et al., 1977; Stimpson et al., 1978; Sudraud et al., 1979;Mark et al., 1980a; Helm et al., 1980a, 1981;Dixon et al., 1981b; Kellogg, 1981, 1982; Sattler el al., 1981; Stephan el al., 1982a; Jentsch et al., 1981, 1982; Echt et al., 1982a;Dreyfuss and Wachman, 1982; Ding and Hesslich, 1983a; Becker and Dietze, 1983; Drachsel et al., 1982; Cornides and Morvay, 1983; Tsong et al., 1983) raises an interesting point about their production and stability. According to experimental evidence and calculations presented by Helm et al. (1 98 1) and Stephan el al. (1 982a), doubly ionized heteroatomic rare gas dimers are produced by direct ionization from the ground state to either weakly bound attractive potential curves lying below the dissociation limits of the respective atomic ions (e.g., see potential energy curves of NeXe2+in Fig. 5) or to quasi-bound molecular levels (e.g., ArXe2+,Neb2+).The existence of stable mononuclear trimers (like Ni:+, Au:+, and W;+) has been explained by Jentsch et al. (1982) by a simple empirical rule relating neutral bond energy to the Coulomb energy (see also observation of PtHe$+by Tsong et al., 1983). Henkes and Isenberg ( 1970)reported the existence of very large, multiply charged N, clusters (also produced by multielectron ionization) and explained their stability by the fact that multiply charged clusters (with the exception of very small clusters

EXPERIMENTAL STUDIES ON CLUSTER IONS 6

h

2 z e -5 .-m 5

v

-

B

1

1

1

1

1

1

85

I

4-

3-

21-

01

2

3

4

5

6

(A) FIG.5. Qualitative potential energy curves for low lying states of NeXez+ after Helm et al. (1981). (a) Xe2+(1So)+ Ne(’S,); (b) Xe2+(’D,) + Ne(lS,); ( c ) Xe+(2Pl/2)+ Ne+(,P); (d) Xe2+(3P,) Ne(lS,); (e) Xe2+(’P,) + Ne(’S,); ( f ) Xe+(2P,,,) Ne+(,P); (g) Xe2+(’P,) Ne( IS,). Internuclear separation

+

+

+

as discussed above) are only stable if their size exceeds a certain critical value, where the repulsive Coulomb energy (minimized by distributing the charges uniformly on the surface) is smaller than the binding energy (see also an earlier prediction by Henkes, 1962, and later studies on critical sizes by Gspann and Korting, 1973; Henkes et al., 1977; Sattler et al., 1981, 1983; Echt et al., 1982a; and Ding and Hesslich, 1983a, on Pb, NaI, Kr, Xe, H,, N,, CO, and N,O clusters). See also the occurrence of multiply charged small clusters of polystyrene (Dole et al., 1968) and doubly charged Fee G,, and (Mg.G,) clusters, where G is glycerol (Simons et al., 1974; Stimpson et al., 1978). As a possible production mechanism for triply charged dimers of W, Mo, Re, and Ir observed by field evaporation by Kellogg (1981, 1982) postionization of singly charged dimers has been proposed. Another excitation (ionization) mechanism, used recently quite successfully for detailed information on the ionization process (i.e., fragmentation), on autoionizing Rydberg states (threshold spectroscopy) and intermediate states (excitation spectroscopy)is multiphoton excitation (ionization) (Feldman et al., 1977; Herrmann eta]., 1977, 1978a,b, 1979; Rothe et al., 1978; Mathur et al., 1978a,b; Leutwyler et al., 1980, 1981, 1982a,b; Fung et al., 1981;Hopkinsetal., 1981, 1983;Michalopoulosetal., 1982;Shinoharaand Nishi, 1982; van Raan et al., 1982, and references therein; Martin et a!., 1982; Eisel and Demtroder, 1982; Riley et al., 1982; Delacretaz et a!., 1982a,b; Powers et al., 1982, 1983; Bernheim et al., 1983; Rademann et al., 1983;Stanley et al., 1983;Shinohara, 1983;Choo et al., 1983;McGeoch and Schlier, 1983). Depending on the type of information desired, either one or

86

T. D. Mark and A . W. Castleman, Jr.

two color, resonant or nonresonant, two photon or multiphoton, mass selective photoionization has been employed. Henmann et al. (1977, 1978b), Rothe et al. (1978), and Leutwyler et al. (1980) have discussed in detail the corresponding ionization mechanisms and photon lunetics (including the respective power dependencies).

2. Ionization Cross Sections and Appearance Energies Ionization of neutral clusters as a function of the energy of the ionizing agent is described in quantitative terms by the ionization cross section function, i.e., partial, total (charge production), counting (ion production), and effective (total divided by number of units in the cluster) cross sections (for a definition see Mark, 1982d, 1984a,b). Although these cross sections (in particular partial cross sections) are an indispensible prerequisite for the quantitative detection of clusters (see also Section III,A,3), unfortunately, little is known about their absolute magnitude and/or fragmentation yields (partial cross section ratios). This is mainly due to the facts that (1) it is not possible to produce targets of neutral clusters of known density and definite cluster size and (2) fragment ions ( e g , from atomic clusters) appear in the mass spectrometer at mass to charge ratios of smaller clusters. In the following section we will discuss first total and counting ionization cross sections, then partial ionization cross sections and ratios, and finally threshold studies leading to the determination of appearance energies and molecular levels.

a. Total and counting ionization cross sections. For the determination of these cross sections no mass analysis of the product ions is necessary, thus facilitating the experimental task. However, no total cross sections for a specific cluster size have been measured to date, only cross sections for certain cluster size distributions (usually not very well characterized and only measured after ionization!). Studies performed for large clusters include absolute and relative effective electron impact ionization cross sections for CO, clusters (Hagena and Henkes, 1965; Falter et al., 1970), absolute effective electron impact ionization cross sections for H, (Henkes and Mikosch, 1974, see Fig. 6), and absolute electron impact counting ionization cross sections for H, (Tay et al., 1970). In all of these experiments a shift of the maximum to higher electron energies with larger cluster distributions has been observed (e.g., see Fig. 6). Moreover, the effective ionization cross section appears to decrease, indicating that, at least for large clusters, no simple additivity rule ( e g , see for normal molecules Otvos and Stevenson, 1956; Lampe et al., 1957; Stevenson and Schissler, 1961; Batabyal et al., 1965; Hamson et al., 1966; Pottie, 1966; Beran and Kevan, 1969; Grosse

EXPERlMENTAL STUDIES ON CLUSTER IONS

87

Electron energy (eV)

-

FIG.6. Absolute effective electron ionization cross sections as a function of electron energy for various H2 cluster size distributions (H,)" e ions (with n the mean cluster size); (a) n = l,(b)n = 340,(c)n = 1700,(d)n = 8750,(e)n = 48,00O,(f)n= 85,00O(afterHenkesand Mikosch, 1974). Also shown for comparison is the total ionization cross section function for H, measured by Rapp and Englander-Golden (1965).

+

and Bothe, 1970;Alberti et af.,1974;Bartmess and Georgiadis, 1983)can be used.

b. Partial ionization cross sections. Relative partial ionization cross section functions (i.e., giving the general shape of the ionization efficiency) have been measured for a number of cluster systems for both electron impact ionization (Leckenby and Robbins, 1966 [Arf and (CO,)f]; Milne et al., 1970 [(H,O),,H+]; Gspann and Korting, 1973, (N2)g((n=11838) and (H,)S+(n= 65132) with z = 1 to 4; Herrmann et al., 1978b (Na;); Helm et al., 1979 (Art, Krf,Xef, ArKr', and KrXe+);Castleman et al., 1981e, and Hermann el al., 1982 [(H,O),H+)]) and photoionization (e.g., Robbins et al., 1967 (Nat); Ng et af.,1977 (XeKr+, XeAr+, and KrAr+); Herrmann ef af.,1978a,b (Na:, K:); Jones and Taylor, 1978 [(CO,):]; Ono ef al., 1980, 1981a,b [(CS,):, OCS:]; Walters and Blais, 1981 [(H2S):]; Dehmer and Pratt, 1982b (Ar:); Ono and Ng, 1982a,b [(C,H,):]; Peterson et al., 1984 (Na,+)I. Because of the reasons mentioned above, no absolute partial ionization cross sections have been measured. Moreover, some of the relative functions may be falsified by contributions from higher clusters (e.g., see studies of Ar, photon ionization cross sections as a function of stagnation gas pressure by Dehmer and Pratt, 1982b). To calibrate mass spectrometric detection, the additivity rule mentioned above has sometimes been applied, i.e., the usual

88

T. D.Mark and A . W. Castleman. Jr.

working rule has been that, for example, the neutral dimer-to-monomer ratio is half the ratio of the dimer-to-monomer ion current measured by the mass spectrometer (e.g., see Leckenby and Robbins, 1966; Milne and Greene, 1967a-c; Yealland et al., 1972; Dorfeld and Hudson, 1973a; Lee and Fenn, 1978; Pittermann and Weil, 1980; Cook and Taylor, 1980).This working rule tacitly assumes that there is no fragmentation of the clusters

-200 -150 -100 - 5 0

0

-200 -150 -100 -50

0

RELATIVE FREQUENCY (ern-')

50

RELATIVE FREQUENCY ( cm-'

FIG.7. (a) One-color resonant two-photon ionization spectrum ofa benzene cluster beam monitoring the photoion signal in the benzene dimer channel after Hopkins et al. (1 98 1). The frequency scale is relative to the monomer origin at 38086. I/cm. Note by comparison to (b) that most spectral features in this scan result from fragmentation of the trimer into the dimer signal channel. (b) Two-color resonant two-photon ionization scan (after Hopkins cf al., 198 1 ) ofthe absorption bands ofthe benzene dimer, trimer, and tetramer in the region of the lB,,(nnl*) + 'A, origin of benzene monomer. The intensity for each spectrum has been normalized here to a constant level. Actually, the two-color observed peak photoion signals were in the ratio 1 :0.05 :0.03 for dimer :trimer :tetramer, respectively. The zero of the relative frequency scale is set to the position ofthe forbidden origin ofthe benzene monomer at 38086. I/cm. The red shifts ofthe most prominent features from the monomer origin are - 40, - I 15, and - I49/cm for the dimer. trimer, and tetramer, respectively. The strong features in the trimer spectrum centered 22 and 40/cm to the blue ofthe origin are due to progression activity in the van der Waals modes of the cluster.

EXPERIMENTAL STUDIES ON CLUSTER IONS

89

during ionization, which has recently been shown to be incorrect (see below). Helm et al. ( 1979) and Mark (1982c,d) have recently proposed for rare gas dimers a modified additivity rule theoretically taking into account the dissociative channels (see also Drowart and Goldfinger, 1967; Stafford, 1971; and Gingerich, 1980b). c. Partial ionization cross-section ratios. Partial ionization cross sections and their ratios will play an important role, if the ionization process leads to more than one ion, e.g., either multiply charged ions and/or fragment ions. Cross section ratios (or measured ion current ratios) have been reported for various multiply charged cluster ions produced by electron impact (Gspann and Korting, 1973; Helm et al., 1981; Sattler et al., 1981; Stephan et al., 1982a; Echt et al., 1982a; Dreyfuss and Wachman, 1982) and range from 0.1% (ArXe2+/ArXe+,Helm et al., 1981)to 100%[(CO,):+/(CO,):, Echt et al., 1982al.Conversely, there is only very little information on cross section ratios between fragment ions and their respective cluster parent ion (i.e., fragmentation ratios). Determination of this ratio necessitates the unambiguous identification and quantitative analysis of fragment and parent ions. The task is also complicated by the fact (see Sections III,A,3 and IV,B) that part of the fragmentation may take place after the ions have exited the source region. Moreover, fragmentation of some molecular clusters has been easily verified (i.e., via dissociative channels leading to an ion with different mass than the neutral clusters). While fragmentation of atomic and/or molecular clusters has been found to be negligible or ruled out for some systems (e.g., Milne and Greene, 1967a; Yealland, et al., 1972; Walters and Blais, 1981; Lisy et al., 1981; Kappes et al., 1982a; Dreyfuss and Wachmann, 1982), it was recently possible via improved experimental detection techniques to demonstrate beyond a doubt that in the case of others (at least for small clusters) considerable fragmentation is occurring upon electron or photon impact' sometimes already several tenths of an electron volt above threshold [e.g., Henkes, 1962; Milne et al., 1972; Wagner and Grimley, 1972, 1974; Van Deursen and Reuss, 1975, 1977; Smets et al., 1977; Herrmann et al., 1978b; Jones and Taylor, 1978; Lee and Fenn, 1978 (see also Helm et al., 1979; Gentry, 1982); Grimley et al., 1978; Lisy et al., 1981; Duncan el al., 1981; Hopkins et al., 1981 (e.g., see Fig. 7); Vernon et al., 1982, 1983; I As Mark (1 982d, 1984a,b)has recently pointed out, there is, in contrast with general belief, no large difference in fragmentation yields between electron and photon ionization threshold spectra.This should be true also for clustersand warrants further investigation. In this conjunction it is interestingto point out that Hoareau et al. (198 1) were able to detect Nazclusters up to n = 20 despite the fact that Herrmann ef al. (1978b) could only observe Na,+clustersup to n = 3 by electron ionization. See also results by Cook and Taylor (1980), Riley ef al. (1982). and Haberland ef al. (1 983a).

90

T. D. Mark and A . W. Castleman, Jr.

Poliakoffet al., 1982; Dehmer and Pratt, 1982b;Dehmer, 1982; Riley et al., 1982;Ono and Ng, 1982a,b;Delacretaz etal., 1982a,b;Geraedts et al., 1982, 1983; Gough and Miller, 1982; Haberland et al., 1983a; Buck and Meyer, 1983; Ding, 1983; Peterson et al., 19841. This question, however, is still a matter of dispute (see also discussion by Echt et al., 1982b; Hermann et al., 1982;Haberland etal., 1983a; and Section III,A,3), although it appears at the moment that at least for most ofthe small clusters appreciable fragmentation does occur (e.g., for large clusters see studies by Gspann and Korting, 1973; Gspann and Vollmar, 1980, 1981; Echt et al., 1982b; Sattler, 1983a,b). Moreover, there exist three recent sophisticated studies reporting the determination of absolute cross section ratios (Gough and Miller, 1982;Geraedts et al., 1982; Buck and Meyer, 1983), e.g., yielding at an electron energy O f 100 eV a[CO+/(CO)2]/a[(CO)z/(CO),] = 0.8 5/0.25 ; a[SF f / ( sF6 )2 ]/ a[sFf'SF~j/(SF6)2] 100, a [ S F ~ / ( S F 6 ) , ] / a [ S F f ( S F 6 ) z / ( S F 6 ) ,a] 150, a[SFf / ( s F 6 ) 3]/a[ SFfSF6/ (SF, ), ] 3 15; and a(Ar+/Ar,)/a(Ar f/Ar, ) = 0.70/0.30, a(Ar+/Ar,)/o(Arz/Ar,) = 0.6 1/0.38 [with a(Ar:/Ar,) 01(preliminary results), respectively. In addition, Wagner and Grimley (1 974) and Grimley et al. ( 1978)have reported electron impact fragmentation ratios for Bin and (LiF), , Hermann el al. ( 1982) apparent fragmentation ratios for (H,O), (n = 3 to 10)as a function of electron energy and stagnation conditions, and Ono and Ng (1982a,b) have recently reported fragmentation photoionization and a clastogram for the (C,H,), phoratios for (C2H2)3 toionization in the wavelength region between 1200 and 600 A.

-

d. Threshold studies. The importance of low-energy ionization studies of clusters produced in expanding jets has been recognized first by Lee and co-workers and Dehmer and co-workers with emphasis toward determination of adiabatic and vertical ionization (appearance) energies and elucidation of the respective potential energy curves and electronic levels. This subject has been recently reviewed in great detail for single photon ionization by Ng (1983) and for electron impact ionization by Mark (1982a,b), both including literature up to the end of 1981 (see also compilation by Levin and Lias, 1982). Ng (1983) has not included work in the area of multiphoton ionization. Moreover, both authors have not included the measurement of appearance energies by mass spectrometry of high-temperature systems (e.g., see reviews by Drowart and Goldfinger, 1967; Berkowitz, 197 1, 1979; Gingerich, 1980a,b;and other recent studies by Lin and Kant, 1969; Donovan and Strachan, 1971;Gingerich and Finkbeiner, 1971;Gingerich, 197 1; Emelyanov et al., 1971; Marr and Wherrett, 1972; Schaaf and Gregory, 1972; Wagner and Grimley, 1972; Piacente and Gingerich, 1972; Neckel and Sodeck, 1972; Cocke and Gingerich, 1972, 1974; Hildenbrand, 1972; Stearns and Kohl, 1972a,b, and references therein; Kordis and Gingerich,

EXPERIMENTAL STUDIES ON CLUSTER IONS

91

1973a,b, 1977; Cabaud et al., 1973, and references therein; Gingerich et al., 1974;WagnerandGrimley, 1974;Cockeetal., 1975;Wu, 1976,1979,1983; Drowart et al., 1977; Smets et al., 1977; Smoes et al., 1977; Zmbov et al., 1977; Grimley et al., 1978; Kingcade et al., 1978; Biefeld, 1978; Gupta and Gingerich, 1978, 1979a,b;Neubert, 1978; Gingerich and Cocke, 1979; Wu et al., 1979; Hilpert, 1979; Pittermann and Weil, 1980, and references therein; Hilpert and Gingerich, 1983; Rosinger el al., 1983). In the following we will as an example briefly review the new literature on single-impact ionization and in addition the studies employing multiphotoionization employing supersonic expansions (for older appearance energies see also Rosenstock et al., 1977). In contrast with the above-mentioned studies on the absolute magnitude of the ionization cross section functions, in threshold ionization studies it is only necessary to obtain accurate energy dependencies of the relative ionization cross section functions. Clearly, photoionization and in particular molecular beam laser multiphoton ionization gives more accurate threshold energies than electron impact studies. On the other hand, electron ionization is simple (and can be quite accurate if appropriate electron monochromators are used, in particular for the determination of the double-ionization threshold not accessible by direct photon ionization) and it has been demonstrated that there is good agreement between thermochemical values (binding energies, proton affinities) derived from electron impact threshold energies and those deduced in high-pressure mass spectrometry or drift cell studies (see Section V). Newer studies (not included in the review of Mark, 1982a,b) include rare gases, CO, ,ArCOZ,NH, ,N, ,Pb, NayI, Hg, clusters (Harbour, 1971; Cabaud et al., 1980; Hoareau eta)., 1981; Stephan et al., 1982a-c, 1983a,d, 1984; Mark et al., 1982a, 1983; Saito et al., 1982). A similar good agreement has been noted for photoionization threshold energies (Ng, 1983). It should be mentioned, however, that these comparisons are only meaningful if the obtained appearance energies correspond to the adiabatic threshold (Anderson et al., 1980; Dehmer and Poliakoff, 1981) and the AH values correspond to the same temperature, i.e., correcting for heat capacity changes from translational, vibrational, and rotational degrees of freedom (e.g., see Conway and Janik, 1970; Teng and Conway, 1973; Castleman et al., 1982a). Single photoionization thresholds have been determined for rare gases, NO, 0, , HF, HCl, HBr, HI, COYN2, H2, CS2, OCS, COz,N,O, SOz, HzO, NH,, C2H2,C2H4,and acetone clusters (as reviewed by Ng, 1983) and in addition for rare gases, alkali, oxidized alkali, ArCO, ,H2S,Na,Cl, Cu, CuBr, and acetic acid clusters (Hudson, 1965; Robbins et al., 1967; Foster et al., 1969;Herrmann et al., 1978a,b;Cook and Taylor, 1979b;Waltersand Blais, 1981;Pratt and Dehmer, 1982a,c, 1983;Dehmer and Pratt, 1982a,b;Powers

92

T. D. Mark and A . W. Castleman, Jr.

et al., 1983; Martin et al., 1983; Castleman et a!., 1983d; Peterson et a/., 1983, 1984; Dao et al., 1984). For some cases it was possible to measure a

whole sequence of ionization energies, e.g., from the monomer up to Fe25 (Rohlfing et al., 1983), to (H2S), (Walters and Blais, 1981) to Na,, and K, (Herrmann et al., 1978a,b), and to Na, (Robbins et al., 1967; Castleman et al., 1983d; Peterson et al., 1984a) and recently for N%5(Kappes and Schumacher, 1983).The results on Nanhave been compared to theoretical calculations, and are in fair agreement (see discussion by Peterson et al., 1984a) with the classical description of the work function of a spherical metal drop (see also the electron ionization results of Saito et al., 1982a,b, for Pb, up to n = 7 and of Neubert, 1978, for Ten up to n = 7), e.g., see Fig. 8. But the agreement can be improved by a different choice of radius (see Kappes and Schumacher, 1983). 2.5

I

1

-2

-3

I

I

I

I

I

4

5

6

7

8

1

--

a 3 4.0-

4.5

-

5.0

1

n (otomr/clurter)

FIG.8. Plot of work function versus number of atoms in a Na cluster using W(R)= W ,

+

3 e2/R,where W represents the work function, R the radius of equivalent sphere, and e the

elementary charge. The conversion between number and equivalent spherical size was made using (a) R = 1.86 A for the nearest neighbor distance, (b) R = 1.54 A based on the covalent radius (Demitras et al., 1972), and (c) R = 2.1 I A based on the bulk density. (0)Experimental results of Peterson et al. (1984a). The polycrystalline work function ( W, = 2.75 eV) was taken from Whitefield and Brady (1971); note that the results for different crystal faces range from 2.65 to 3.10 eV.

EXPERIMENTAL STUDIES ON CLUSTER IONS

93

Even more accurate determination of ionization energies (and/or dissociation energies) is possible by sequential two-photon ionization and/or optical - optical double-resonancespectroscopy of Liz, Na, ,Na, ,K2,NaK, Cu,, fluorobenzene,benzene-Ar (Herrmann et a/., 1978a,b, 1979; Mathur etal., 1978b;Leutwyleretal., 1980, 1981, 1982a;Fungetal., 1981;Eiseland Demtroder, 1982; Martin et al., 1982;Powers et al., 1983; Rademann et al., 1983;Delacretaz et al., 1983b;Bernheim et al., 1983;McGeoch and Schlier, 1983). In the case of two-color two-photon ionization, the whole FranckCondon accessible range of the intermediate rovibronic statesis mapped out by the subsequent ionization steps, thus assisting the determination of the adiabatic ionization energies. This may explain the slight but significant differences between single- and two-photon ionization results (i.e., see also recent three-photon ionization results by Delacretaz et al., 1983b). According to Martin eta/. (1982), however, the true ionization potential can only be deduced by extrapolation of Rydberg states, because ionization threshold methods lead to slightly different results dependent upon the experimental condition (see also Eisel and Demtroder, 1982; Leutwyler et a/., 1982a; Delacretaz et al., 1983b). Complementary information to that gained from the methods discussed above can be obtained by photoelectron spectroscopic studies. The photoelectron spectrum gives direct information on the vertical appearance energy, and relative vertical transition strengths (if the excitation is nonresonant, i.e., see Ref. 3 in Poliakoff et al., 1982)and indirect information on the structure from Franck - Condon envelopes. Studies include photoelectron spectra of Ar,, Kr,,. Xe,, (H,O),, methanol dimers, formic, acetic, and trifluoroaceticacid dimers in supersonic expansions (Dehmer and Dehmer, 1977, 1978a,b; Carnovale et al., 1979, 1980; Tomoda et al., 1982, 1983; Tomoda and Kimara, 1983), and of high-temperature vapors (e.g., Berkowitz, 1971, 1975, 1979; Evans et al., 1972; Brundle et al., 1972; Dehmer et al., 1973; Boschi and Schmidt, 1973; Potts et al., 1974; Richardson and Weinberger, 1975; Streets and Berkowitz, 1976a,b; Potts and Price, 1977; Potts and Lyus, 1978; Potts and Lee, 1979; MacNaughton et al., 1980; Berkowitz et al., 1980). Since the methods of neutral cluster production (see above) generally result in a distribution of cluster sizes and the spectral features of these different clusters are frequently overlapping, conventional photoelectron spectroscopyis not unambiguous. Poliakoff et al. (198 1,1982)have recently shown for the case of Xe, that mass analysis of the ion cluster in coincidence with the photoelectron spectrum removes these problems. Moreover, this photoelectron- photoion coincidence technique has been helpful in assessing fragmentation of the cluster under study (Poliakoff et al., 1982). (For comparison there are photoemission spectroscopic studies of the electronic

94

T. D. Mark and A . W. Castleman, Jr.

structure of supported clusters, e.g., see Kubota et al., 1981; Yencha et al., 1981 ; Lee et al., 1981; Mason, 1983, and references therein.) Finally, it is interesting to point out that there exist some studies on cross sections for electron attachment to clusters (H,O, N,O, NO2, CO,, SO,, H,S, C1,) and their respective electron affinities (Dillard, 1973; Mots and Compton, 1977, 1978a,b; Mots, 1979; Bowen et al., 1979, 1983; Stephan et al., 1983d; Quitevas and Herschbach, 1983).

3. Mass Spectra of Cluster Distributions A large number of cluster studies has been concerned with either the distribution of neutral clusters produced in supersonic expansions, inert gas condensation, etc. (see above), and detected by ionization mass spectrometry, or the distribution of ionic clusters as, for instance, ejected from surfaces by ion bombardment (e.g., see references given in Section 11, A and C). For both cases observed anomalies (“magic numbers”) were interpreted and/or correlated with particularly stable or unstable cluster geometries (structures) often under the assumption that these anomalies arose in the primary cluster production process. In light of some recent findings, i.e., fragmentation and metastability (e.g., see Sections III,A,2 and IV,B), such interpretations should be accepted with some caution and treated on a very individual basis, i.e., some of the measured distributions (especially for very large clusters) may reflect the actual distribution before the detection process, whereas in other cases the measured distribution is strongly distorted by secondary processes introduced by the detection process (e.g., see discussions by Echt et al., 1982b; Sattler, 1983a,b; Haberland, 1983). In the following we will discuss, out of the vast amount of systems studied, well-documented examples of particular interest, including an atomic, molecular, and metallic cluster species.

a. Ar, cluster distributions. Argon cluster mass spectra have been recorded by a number of groups (Greene and Milne, 1963; Milne and Greene, 1967a; Worsnop et al., 1981; Dreyfuss and Wachman, 1982; Ding and Hesslich, 1983a). In each case neutral clusters are produced in a supersonic nozzle expansion. The detection has been achieved by electron impact ionization (with electrons at least several electron volts above threshold) with subsequent mass spectrometric analysis. Intensity variations have been observed in the mass spectra as a function of cluster size at various expansion conditions. Similar irregularities have been reported for water clusters (see below) and other rare gas clusters (Echt et al., 1981; Ding and Hesslich, 1983a), although it should be pointed out that there are distinct differences, i.e., the first magic numbers [corresponding to complete shell icosahedra (Hoare,

EXPERIMENTAL STUDIES ON CLUSTER IONS

95

1979)], 13 and 5 5 , observed in Xe, are not observed in Ar or Kr expansions. Conversely, the magic number 19 appears to be common to all three rare gases and has also been observed in most studies. Milne and Greene ( 1967a) ascribe these anomalies, due to kinetic processes during “nucleation,” to lower stability of the neutrals, or to differing behavior of the ions, whereas Ding and Hesslich (1983a) (following the approach of Echt et al., 1981, 1982b)concluded that the observed structure in the mass spectra mirrors the abundance of the neutral cluster distribution. (Recent studies also suggest some contribution to magic numbers following ionization; Ding, 1983.) However, it seems that from the mass spectra alone (and also from changes in the expansion conditions and in the electron energy, unless all the way down to the appearance energy) it is not possible to establish the origin of these variations. Recent studies (see also Sections III,A,2 and IV,B) on the direct fragmentation of Ar, and Ar, upon electron impact (Buck and Meyer, 1983),on the direct fragmentation of Ar, clusters with n > 5 upon electron, photon, or Penning ionization (Haberland ef al., 1983a), on the metastable decay of Ar ;(Stephan and Mark, 1982b, 1983),and on the metastable decay of Ar:(Stace and Moore, 1983; Mark et al., 1984) cast serious doubt concerning the interpretation of these intensity distributions in terms of structure and stability of the neutral clusters.

b. (H,O), cluster distributions. Again, several groups reported measurements of the relative intensities of clusters of water molecules detected by mass spectrometry in supersonic expansions of water vapor (Lin, 1973; Holland and Castleman, 1980b; Castleman et al., 1981e; Hermann et al., 1982; Dreyfuss and Wachmann, 1982). There are intensity variations, the most prominent of which occurs at (H20)21H+.Due to the fact that this irregularity at n = 2 1 is observed at the same cluster size n = 2 1 whether ( Hz0)21H+ are produced by electron impact ionization on neutral clusters present in the expansion of water vapor (see above references) and in atmospheric air (Carlonand Harden, 1980;Carlon, I98 1) in studiesof the growth of water clusters formed during the coexpansion of water vapor and protons in a supersonicexpansion(Searcyand Fenn, 1974;Burke, 1978;Beuhler and Friedman, 1982b),or during studies of the secondaryion mass spectra of ice (Lancaster et al., 1979a), Hermann et al. (1982) (see also discussion in Searcy, 1975; Kassner and Hagen, 1976;Searcy and Fenn, 1976)concluded that this discontinuity observed in the neutral expansion studies originates after the ionization process. These conclusionsare supported by recent findings on fragmentation (Vernon et al., 1982), metastable decay (Stace and Moore, 1983) and the stability of (H20)!1H+ via dodecahedra1 clathrate structure where an “excess” proton remains in the cage structure and an unbonded H,O is trapped in the center (Holland and Castleman, 1980b). It

96

T. D. Mark and A . W. Castleman, Jr.

is interesting to note in this conjunction the reported existence of stable ion structures in hydrogen bonded ion clusters (Stace and Moore, 1982), preferential solvation of protons in mixed clusters as detected by monitoring the competitive decomposition processes via metastable peak intensities (Stace and Shukla, 1982b)and the fact that Kay et al. (198 1) have recently reported some indirect evidence of solvated ion pair formation for aqueous nitric acid clusters by electron impact mass spectrometry [see also Herschbach, 1976, for solvation in the scattering of HI from (NH3),,].

c. (CsI), cluster distributions. This is another interesting case where it has been recently demonstrated that measured cluster ion distributions have been modified prior to detection by metastable decay: Secondary cluster ions ejected from alkali- halide surfacesby energetic Xe+ion bombardment have beenobservedwithSIMS(Campanaetal., 198l;Barlaketal., 1981,1982).It was found that the ion intensity showed distinct anomalies, i.e., the most prominent of which occurs at (CsI),,Cs+.These anomalies were correlated to particularly symmetrical cubic-like structures. Similarly, Sattler et al. (see Martin, 1983) related anomalies observed in mass spectra of alkali- halide clusters produced by supersaturation of the vapor in cold He gas to a multiring structure of the neutral clusters. However, very recent studies by Standing et al. (1982) and Ens et al. (1983) (see also Campana et al., 1983) have clearly demonstrated that the anomalies observed by SIMS studies are due to unimolecular decay after the ion formation, i.e., the yield of cluster ions decreases smoothly with n when observed at very short effective times after ion formation (e.g., Fig. 9). Because secondary ion clusters (CsI),Cs+ with n > 7 produced by 8 keV Cs+bombardment were found to be mainly metastable, with lifetimes << lOOpsec, the cluster distribution observed at an effective time of 70 psec showed a pronounced increase of the n = 13 cluster ion in agreement with recent theoretical findings (Martin, 1978, 1980, 1983).

-

REACTIONS B. ASSOCIATION The vast majority of association reactions has been investigated using either the flowing afterglow, or SIFT modification thereof, or the high-pressure pulsed mass spectrometer technique (see Section 11,B). The field of ion - molecule association reactions comprises a very large subset of the general subject of ion - molecule reactions and has been the subject of several recent major reviews. In particular, the reader is referred to collected data of all reaction rate constants measured in flow reactors through 1977 (Albritton, 1978). Good (1975) has prepared a comprehensive discussion and re-

97

EXPERIMENTAL STUDIES O N CLUSTER IONS

-5.OA

10

20 n

30

1

41

FIG.9. Relative yields of secondary ion clusters (CsI),Cs+(W)as measured by Campana ef al. (1981), Barlak ef al. (1981, 1982), and (0) by Ens ef al. (1982), both normalized to n = 1 (after Ens et al., 1982).

view of third-order ion -molecule clustering reactions through the end of 1973 including some updates of data for 1974. Another review dealing with association reactions covering the same time period has been published by Lias and Ausloos ( 1975). Another somewhat earlier, but comprehensive review, is that by Parker and Lehrle (197 1). Similarly, Smirnov (1977) has prepared a review of the literature through 1976, with emphasis on cluster ions of interest in the atmosphere, and Smith and Adams reviewed thirdorder ternary ion - molecule reactions of atmospheric interest through 1979 (see Smith and Adams, 1980). Additionally, Meot-Ner (1979) has discussed the temperature and pressure effects of association reactions and surveyed literature through the late 1970s. Finally, Adams and Smith (1983) have just completed the most recent review of ternary association reactions, covering the period through mid-1983. Since this subject has obviously been well reviewed, we treat herein a few recent findings which are especially germane to the main theme of our review article dealing with the dynamics and properties of cluster ions. The basic mechanisms of ion - molecule association reactions are well

98

T. D.Mark and A . W. Castleman, Jr.

understood (Ferguson, 1972, 1975).The reactions are visualized to proceed via an intermediate complex (AL)* which has a lifetime, T,, against unimolecular decomposition back to the reactants A and L. A may be taken to represent the reactant ion, perhaps already containing some cluster subunits, and L the next associating molecule. Collision with a third body, My can either remove excess energy from the complex and result in the formation of a stable entity, or it can provide collisional energy necessary for dissociation back to the original reactants as follows: A (AL)*

k +L= (AL)* kr

+ M k' AL + M

A+L~".AL

and AL

+ M "(AL)* k,

(AL)* L A

+M

+L

(17)

AL~"-A+L

the rate Taking kcto represent the rate ofclustering, k, (proportional to 1 /q), of dissociation of the complex, and k,, the rate of stabilization of the complex by a third body (M), a steady-state treatment for the complex (AL)* leads to the following equation for the overall forward rate, kfo, kfo =

kck, [MI k, k, [MI

+

Likewise, the overall reverse rate is given by k, as follows:

As seen from the above equations, the reactions can be written in terms of a

low- and high-pressure limit, respectively,

kfo = kc

EXPERIMENTAL STUDIES O N CLUSTER IONS

99

Although the basic mechanisms of cluster formation are well understood, the details are still a subject of intense investigation and some controversy. The major problems of interest concern the extent of statistical energy redistribution in the intermediate excited complex, its lifetime against dissociation into the original parent reactants (see Section IV,A, devoted to unimolecular decomposition), and the extent to which the collisions are effective in removing energy or reactivating stable clusters to the energy level sufficient for dissociation. Related to this is the question ofthe pressure dependence of the association reactions, discussed by Meot-Ner (1979), and the temperature dependencies discussed by Adams and Smith (1 98 1 1983), Kebarle (1975), Porter (1975), Jennings ef al. (1982), Headley el al. (1982a,b), van Koppen and Bowers (1983), Johnsen et al. (1983), Bohringer el al. (1983ac), Bohringer and Arnold ( l982,1983a,b), Bates (1979a,b, 1980),and Herbst ( 1979, 1980). Based on an RRK formalism (Robinson and Holbrook, 1972; Forst, 1973), as discussed by Meot-Ner (1979), the reverse reaction of the excited complex has an energy dependence of the form k, = rRT/[(D" rRT)]$-* (22) where D is the dissociation energy and Y is the number of square terms that contribute to the internal energy. As discussed by Mautner (1979),where D is much greater than rRT, this leads to ¶

+

O

k, - T" (23) whereby k , becomes proportional to T-". The T-" form is used by most workers to correlate data, and Bates (1 979a,b, 1980)has developed a theoretical basis for assessing the expected range ofthe parameter n. In particular, he showed that it is related to (1/2 S), where I is the number of rotational degrees of freedom in the separated reactants and 6is the temperature coefficient associated with the temperature coefficient of the collisional stabilization efficiency. This relationship is obtained where there is little vibrational contribution to the temperature dependence through low-frequency modes in the association complex (Bohringer et al., 1983a,b;Bohringer and Arnold, 1982). The accuracy with which n can be determined from experiments depends largely on two factors, one having to do with the measurements being made at a limiting value ofpressure rather than in the transition region between the high- and low-pressure limits, and the second on the range over which the temperature measurements are made. In many cases the range is insufficient for determining an accurate value of n and much controversy has arisen in the literature about the values of coefficients reported for measurements made over very narrow ranges of temperature.

+

100

T. D. Mark and A . W. Castleman, Jr.

The reviews of Adams and Smith ( 1983)and Meot-Ner (1979) list a rather extensive set of n values from measurements reported in the literature. Adams and Smith have shown that the vast majority of these are rather consistent with the theories of Bates (1979, 1980) and Herbst ( 1979, 1980). For certain reactions, the expected linear dependence of log k versus log T has been reported to be invalid, especially for the association of CO with CO+, where CO is the third body, for CO with HCO+ with hydrogen and CO as the third body, and for N: with N,, with N2 as the third body (see Meot-Ner, 1979). Jennings et al. (1982) and Headley et al. (1982a) have N, , one of reported unexpectedly large values of n for the reaction of N: which has been the subject of intensive investigation by a number of researchers. Recent findings by Bohringer et al. ( 1983a- c) and Bohringer and Arnold (1982, 1983a,b) shed some light on the discrepancies. In particular, their results demonstrate that in the case where nitrogen is both the clustering molecule and the one serving as the third body, the complex (Na)* may be stabilized by switching of an N, molecule out of the excited complex rather than via a superelastic collision (which presumably occurs when other gases such as helium are used as third body). To further study this reaction, Rowe et al. (1983a,b) have used a unique technique involving a very large supersonicjet apparatus that enables the maintenance of a uniform density for up to 40 cm following expansion. This has permitted measurement of the N: N, reaction down to 20 K. Their data fit an extrapolation of the data of Bohringer and Arnold (1983b) and Smith and Adams (1982) showing a linear relationship (constant value of n ) over the full temperature range from 20 to 400 K. The functional form of the temperature dependence based on RRK theory also predicts that k, should vary inversely relative to D oand thus kf, should be related directly to D o .Meot-Ner (1979) has pointed out that such a relationship has been observed in the case of a number of systems of varying complexity. The magnitude of k, has also been observed to decrease with increasing number of degrees of freedom in the excited complex as would be expected from simple considerations. The discussion of temperature coefficients considers the forward and backward rates for data taken in the lowpressure regime. Furthermore, they are based on a very simple formalism; a more appropriate one is that based on RRKM theory (see Robinson and Holbrook, 1972; Forst, 1973), but this has not been applied in a detailed treatment of the temperature coefficient of these reactions. Olmstead et al. (1977) and Jasinski et al. (1979) have employed RRKM theory to a treatment of ion - molecule complex (cluster) formation for several systems including proton-bound dimers of H,O and H,S, the formation of the benzene dimer cation (C6H6): and proton-bound dimers of

+

+

EXPERIMENTAL STUDIES ON CLUSTER IONS

101

ammonia, CH,NH,, and (CH,),NH. As with RRK theory, the application of RRKM theory hinges on the crucial assumption of randomization of internal energy within the collision complex. The authors have made approximate estimates of stretching and bending frequencies for the complexes based on values for the neutrals; the only adjustable parameter involved was fitting the entropy of the complex. Using this procedure, the calculated values of k , and the temperature dependence for the overall reactions were found to be in good agreement with the experimental results considered. Most of the treatments usually do employ strong collision assumptions, and this is subject to question as discussed by Meot-Ner (1 979). Recently, Chang and Golden (198 I) have made a careful reanalysis of the kinetics for ion - molecule association reactions using a model similar to RRKM theory as an extension of the general formalisms of Troe (1977), which enable a treatment of the so-called fall-off region in association kinetics. Their computations were constrained to reaching limited values corresponding to ADO (Su and Bowers, 1973) or Langevin (see McDaniel el al., 1970) collision frequenciesat the high-pressurelimit and the strong collision energy transfer rate constant at the low-pressure limit. Chang and Golden (1981) showed that for reactions at the low-pressure limit, the requisite information is the density of states of the association complex, which is related to entropy. Detailed calculations were made for the low-pressureand fall-off regime of these association reactions, showing very good accord with experimental measurements. The particular usefulness of thermochemical information in interpreting the kinetics of association has been demonstrated and emphasized. They reconsidered one particular reaction in the association reaction of the ion C,Hfwith CH,Cl (CH, as third-body) and showed that at pressures as low as 4 Torr the reaction is still at nearly the high-pressure limit. This demonstrates one ofthe major problems which has been inherent in study of ion -molecule association reactions, namely where measurements of the temperature dependence of the reactions have usually been made at the fixed pressure rather than number density. When the measurements are not at the true limiting low-pressure limit, erroneous determinations of the temperature coefficient can easily result. According to Chang and Golden ( I 98 l), the preferred method is to first compute the low-pressure limit rate constant in the unimolecular direction for a complex AL using ADO theory (Su and Bowers, 1973; Bass et al., 1975; see also Hsieh and Castleman, 198 1; Castleman et al., 1983b) and a simple harmonic oscillator model followed by a few correction factors which account for anharmonicity, energy dependence of the density of states, overall rotation, and internal rotation. Thereby, the low-pressure decomposition rate constant is readily calculated and in cases where thermochemical data are available, the forward one can be computed directly from the equilib-

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rium constant of the reaction. A filled RRKM curve is then used to treat the fall-off region. Comparison of experiment and theory has shown the validity of the model and especially of the assumption of a strong collision for small clusters, but has demonstrated that the strong collision assumption breaks down for the case of large ones where small molecules serve as the third body. The authors conclude that uncertainties in enthalpies for ion - molecule complexes have a relatively small influence on the calculated rate constants compared to their sensitivity to entropic properties. Few attempts have been made to study association reactions in expanding beams except for the work for Rowe et al. (1983a,b) and another one by Searcy and Fenn ( 1974). Generally, deriving kinetic information requires deconvoluting changes in a very complex mixture of ion clusters. For this reason and the fact that temperature is rarely uniform during a flow expansion, the SIFT technique and pulsed reaction cells [see also low-temperature ( <20 K) Penning ion trap studies by Luine and Dunn, 19821 have distinct advantages for study of the kinetics of association reactions and are to be preferred. A need for detailed information on the energy dependence of cluster reactions has come from several recent studies. Ferguson and co-workers (Ferguson, 1983; Durup-Ferguson et al., 1983a,b; Bohringer et al., 1983d; Dobler et al., 1983a,b) have made some very important new measurements on vibrational relaxation of ions, attributing the process partly to the formation (and dissociation) of intermediate ion - molecule cluster complexes. Their findings point out the need for investigations of association reactions not only as a function of temperature but also as a function of electric field. Preliminary measurements in this new area of investigation have been made by Smith and Adams (1983a) for the N f N, reaction to form Na with both N, and He as a third body, and for CO, H,, O,, and N, association to CHf with He buffer gas (also, see Meisels et al., 1974; Schummers et al., 1973;and Barassin et al., 1980). The findings suggest that the temperature and center of mass kinetic energy dependencies differ by unit, i.e., T-" compared to E-"+I. One can expect major new advances in this field in the near future.

+

IV. Dissociation of Cluster Ions If cluster ions are produced in an excited state they may decay via unimolecular dissociation into a fragment ion and one or more ligand units. On the

other hand, stable cluster ions may be dissociated by collisions involving electronic, vibrational and/or rotational excitation followed by immediate fragmentation. In case the collision is with a molecular target this process is termed collision-activated dissociation (sometimes also called collision-in-

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duced dissociation),in case of a photon photodissociation.The mechanisms, dynamics, and implications of these three loss processes will be discussed in the following. Some of the information gained from studies on cluster dissociations include the stability, structure, and electronic properties of cluster ions. A. UNIMOLECULAR (METASTABLE) DISSOCIATIONS

One area of rapid development in unimolecular ion chemistry has been the study of metastable ions (Cooks et af., 1973; Levsen, 1978), which are those ions which have lifetimes 3 psec (Lifshitz, 1983). (Note that prompt unimolecular fragmentation has been discussed already in Section 111,A.) The existence and importance of metastable cluster ions has been established only very recently, despite the fact that unimolecular decay was to be expected and series of cluster ions constitute an ideal testing ground for statistical unimolecular decay theories (such as QET), because ions within such a series have progressive numbers of vibrational degrees of freedom, but very similar chemical properties (Stace and Shukla, 1982a; Stephan and Mark, 1982b). The first evidence of metastable cluster ions appears to have been reported for positively charged droplets of glycerol doped with NaI by Huberman (1970) and Simons et al. (1974), for Ag,Clf cluster ions by Wagner and Grimley (1 972), and for unidentified negative SO, cluster ions by Stamatovic (1974; see also Maksic et al., 1973; Stamatovic and Miletic, 1982). By now metastable ions (with lifetimes up to 100 psec) have been observed by electron impact ionization of free jet clusters or high-temperature vapors (Wagner and Grimley, 1972; Stace and Shukla, 1980; Stephan et af.,1981, 1983a-c, e;Futrell etaf.,1981a,b, 1982;StephanandMark, 1982a-c, 1983; Mark, 1982a,b; Stace and Shukla, 1982a-c; Stace and Moore, 1982, 1983; Mark et al., 1984), by photoionization of free jet clusters (Delacretaz et af., 1982a,b;Echt et al., 1984),for cluster ions effusing from a high-pressure (up to several Torr) drift cell (Sunner and Kebarle, 1981; Hunton et al., 1984a), for cluster ions extracted from a monoplasmatron or a high-pressure (up to lo-' Torr) EI/CI ion source (Maas et al., 1976; Flamme et al., 1980; McLuckey et af.,1981;Illies et al., 1983a,b), and cluster ions produced by ion sputtering (Ens et af., 1983; Campana et al., 1983) or field evaporation (Huberman, 1970; Simons et al., 1974; Stimpson et al., 1978). Quantitative studies have revealed several interesting results on the stability and electronic properties of cluster ions, including measurements of the metastable yield as a function of neutral precursor properties (Stephan and Mark, 1982b, 1983;Stace, 1983b), measurements ofthe metastable yield asa

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function of electron or photon energy (Stephan and Mark, 1982a, 1983; Delacretaz et al., 1982a; Stephan et al., 1983c),measurements of the metastable yield as a function of cluster size (Stimpson et al., 1978; Sunner and Kebarle, 198 1; Stephan and Mark, 1982c, 1983; Stephan et al., 1983a;Stace and Shukla, 1982b; Stace and Moore, 1983; Echt et al., 1984; Hunton et al., 1984a), measurements of the average kinetic energy released during metastable decay as a function of cluster size (Stace and Shukla, 1982c), and measurements of the kinetic energy release distribution for molecular dimer cluster ions (Illies et al., 1983b).The measured average kinetic energies are in disagreement with a simple classical RRK model (Stace and Shukla, 1982c), whereas the measured kinetic energy distributions are in excellent agreement with statistical phase space theory calculations (Illies et al., 1983b), supporting the hypothesis that observed metastables of ion - molecule clusters are due to statistical (vibrational) predissociation [see also RRKM calculations and measurements on the metastable decay of K+(H,O), clusters by Sunner and Kebarle (198 l)]. On the other hand, the existence of small atomic (or pseudoatomic) cluster ions (e.g., He:, Art, Arf, ArNf, Na) has been rationalized as being due to (rotational) barrier penetration or electronic predissociation (Maas et al., 1976; Flamme et al., 1980; Stephan and Mark, 1982a-c, 1983;Stephan et al., 1983b,c,e).Moreover, electron impact upon (He), clusters with n up to lo7 has been found to result in metastable states of more than 1 msec lifetime and the ejection of small ionized clusters with n up to 70 (Gspann and Vollmar, 1980, 1981; Gspann, 1981).

B. COLLISION-INDUCED DISSOCIATIONS Experimental information on collision-induced dissociation (CID) of cluster ions is scarce and limited to a few cluster ions (Van Lumig and Reuss, 1977, 1978; Rollgen et al., 1978, 1980; Van Lumig et al., 1979; Stace and Shukla, 1980; McLuckey et al., 1981;Sunner and Kebarle, 1981;Futrell et al., 1981a,b, 1982; Stephan et al., 1981, 1983a-c,e; Udseth et al., 1981; Stephanand Mark, 1982a-c, 1983;Lauetal., 1982;Dawson, 1982;Hunton etal., 1983a, 1984a;Illiesetal., 1983a,b;IlliesandBowers, 1983;Ervinetal., 1983; Henkes and Pfeiffer, 1983; Echt et al., 1984). Some of these studies provide collision cross sections (Van Lumig and Reuss, 1977, 1978; Van Lumigetal., 1979;SunnerandKebarle, 198l;Udsethetal., 198l;Lauetal., 1982;Dawson, 1982;Futrell et al., 1982;Stephan et al., 1983b,e;Ervin et al., 1983). Sunner and Kebarle (198 1) and Lau et al. (1982) have demonstrated that CID cross sections increase rapidly with the number of cluster ligands (see also Dawson, 1982),with the internal energy ofthe cluster ions, and with decrease of the dissociation energy. From these results it is concluded that

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the small scattering angle collisions producing the observed dissociations (see also Dawson, 1982) induce only small excitation energies in the cluster ions. Udseth ef al. (198 1) have studied the interaction of heavy-water cluster ions as a function of interaction energy and target gas. A very thorough and systematic study of the collision dynamics as a function of collision energy, cluster size, and fragmentation channel has been performed by Van Lumig and Reuss (1978) (e.g., see Fig. 10).Moreover, Van Lumig et a/. (1 979) have also measured double differential fragmentation cross sections of Hln+I with 1

I

I

I

1

I

I

I

i

1000

100

-2 z

Y

E

b’

10

10

01

5 7 9 11 13 15 17 19 Z1 23 25 27 29 31 33 35 37 39 H[amu]

FIG. 10. Fragmentation cross sections for hydrogen cluster ions with He as scattering partner versus parent mass M, after Van Lumig and Reuss (1978). The fragment masses are indicated on top of the curves. The thin lines correspond to Am = 4 and Am = 16 fragmentations, a,,,,,= 100 corresponds to 0.35 A*.For parent masses heavier than a 15 amu and also for fragmentation loss of more than one H,, a,,,,is energy-independent.

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T. D. Mark and A . W. Castleman, Jr.

n < 7 to elucidate the reaction mechanism and kinematics, finding that elastic scattering is unimportant. Recently, Ervin et al. (1983) measured the CID cross section as a function of the kinetic energy for the dimanganese cluster ion. The measured threshold energy was used to obtain an adiabatic ionization potential for Mn, . In another study of the CID mechanism Illies and Bowers (1983) have measured kinetic energy relase distributions in agreement with calculated excess energies. McLuckey et al. (198 1) have determined proton affinities of proton-bound dimers from observed (metastable) or CID abundance ratios, using a kinetic approach to study the energetics of cluster ions. In general, according to McLuckey et al. (1981), proton affinities obtained by this method agree within 0.3 kcal/mol with values obtained by conventional methods.

C. PHOTODISSOCIATION 1. Introduction

Studies of the interactions of photons with molecular ions are of both fundamental and practical interest and, although work in this field is relatively scarce, it is growing at an ever increasing rate. High-resolution studies can provide information about the location, shape, and symmetry of the ground and excited states of the ions. Furthermore, information on molecular bond energies, and in some cases the electron affinity of the parent neutral, is obtained. Additionally, where kinetic energy release measurements are made, the results provide information on energy transfer and on the dissociation dynamics of ion clusters. With regard to practical applications, photodissociation cross sections are used in modeling calculations of the atmosphere, of magnetohydrodynamic generators, and the development of gas discharge lasers, in modeling combustion processes, and in interpreting the study of photo-induced chemical reactions. Although there is a wealth of information for the electron photodetachment spectroscopy of atoms and molecular ions (Corderman and Lineberger, 1979; see also Lineberger, 1982)and the photodissociation of molecular positive ions (Richardson, 1976;Moseley, 1982a,b),there are only limited data for cluster ions. For an interesting discussion of the infrared absorption of some molecule ions in matrices, the reader is referred to Andrews (1983). Finally, Woodin et al. (1978) have investigated the multiphoton dissociation of the dimer ion H+(Et20),in the infrared.

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2. Positive Cluster Ions Among the simple systems which have been studied are the rare gas dimer ions Arf, Nef (Vestal and Mauclaire, 1976), A r t (Moseley et a/., 1977), Net, Arf, K r f , and Xef (Lee and Smith, 1979b), Hef (Flamme et al., 1980), and Art, Krf,and Xet (Vanderhoff, 1978a). In conducting their studies, Vestal and Mauclaire (1976) employed a tandem quadrupole photodissociation mass spectrometer and obtained absolute values of photodissociation cross section over the wavelength range 580 to 620 nm. The cross sections for photodissociation of Arf were found to exhibit a strong dependence on ion source pressures, with cross sections varying from 2 X lo-'* cm2 at 0.1 Torr to 6 X cm2 at 0.5 TOK.In earlier studies Miller et al. ( 1976) studied the photodissociation of Arf and Net over the wavelength range 565 to 695 nm. In their work much smaller cross sections were found for the photodissociation of Arf and Nef was not observed to photodissociate indicating a cross section of less than 7 X cm2. Carrington et d. (1 976) also investigated the photodissociation of Art. In the work of Moseley et al. (1977), photofragment energy distributions were measured for the process Arf(o:) hv +Ar+ Ar and transitions to the dissociative states 2 ~ and g '0: were observed due to the effects of the spin orbit interaction in Art. Photodissociation cross sections of Net, Art, Krf, and Xet measured by Lee and Smith (1979b) provide information on photodissociation cross sections from 350.0 to 500.0 nm. Both Net and Arf cross sections were observed to vary with effective kinetic temperature which was changed by increasing the ion drift velocity in the experiments. The alterations were attributed to vibrational excitation of the ions. Ultraviolet absorption bands of rare gas dimer ions were found to be red shifted with increasing atomic number in accordance with theoretical calculations (Wadt et al., 1977). Vanderhoff ( 1978a)also measured photodissociation cross sections for A r t , Krf, and Xef at 3.0 and 3.5 eV. The results show that theabsorption shifts to lower photon energies for heavier rare gas ions. The laser-induced photodissociation of Hef measured by Flamme et al. (1 980) provided information on momentum distributions of He+ fragments over the range of approximately 570 to 585 nm. Photodissociation spectra were only observed when the polarization direction of the light was parallel to the ion beam. The data showed discrete structure in the He+ photofragment energy distributions that were in excellentagreement with the theoretically calculated structure for He; applying the ground state potential energy curve of Maas et al. ( 1976). In a review paper Moseley ( 1982b)has reported unpublished work of Camngton, Buttonshaw, and Kennedy for Hf,the

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T. D. Mark and A . W. Castleman. Jr.

simplest triatomic molecule. Measurements in the infrared were made in a single one cm-' scan in which 108 transitions were apparently observed. The next most simple cluster ion which has been investigated is Csz (Helm and Moller, 1983a; and Helm et al., 1983) which was studied in a fast ion beam photofragment spectrometer. Bound - free transitions were observed in the wavelength range 406.7 to 950.0 nm. Three photodissociation channels were identified. At the longest wavelength studied, photodissociation was found to produce ground state atoms Cs(6s), while in the energy range 530.9 to 454.5, excited state atoms Cs(6p) were produced. At 457.9 nm photodissociation leading to the formation of both the 6p and 5dstates were observed. The measurements established a lower limit for the bond energy of Cslof 0.59 f 0.06 eV, in fair agreement with the accepted value of 0.70 eV (see Berkowitz, 1971). Moller and Helm (1983) and Helm and Mdller (1983b) have extended their work (Helm and Moller, 1983a; Helm et al., 1983) to clusters containing up to 9 cesium atoms. The wavelength dependence for the dissociation was determined in the range 950 to 410 nm, observing both angular and kinetic energy distribution of the photofragments. In the case of the larger ion clusters, complex fragmentation patterns were found. For Csi, dissociation into excited atomic and molecular states has been resolved, leading to a dissociation energy of Csi equal to 1.3 eV. In the case of studies of clusters containing from 3 to 7 atoms, the presence of the fragment ions at energies corresponding to 4,&,4,$, and 4 of the primary beam energy was taken by the authors as a clear indication of the occurrence of photodissociation to the atomic ions and neutrals, although whether the neutral product is an atomic or molecular form could not be ascertained from the measurements. In preliminary studies, the researchers have observed fragmentation of Cst to Cst, Csg to Cst, Cst to both the ionized tetramer and timer, and C$ to the tetramer. The breadths of the kinetic energy distributions for the various photofragments were found to be significantlydifferent, reflecting the difference in energy release in the photodissociation process. Burke and Wayne ( 1977)measured the photodissociation of a number of positive ions relative to the photodissociation cross section of Oz(HzO) at a wavelength of 514.5 nm for the species N;, Ni, Oa, Of(H,O), O;(H20),, NO+(NO), NO+(NO),, NO+(NO)(NO,), and NO:. At a wavelength of 337.1 nm they measured the relative photodissociation cross sections with respect to N t for the species in Nf, O z , O;, Oz(H,O), Of(H,O),, NO+(NO), NO+(NO)(NO,), NO+(H,O), NO:, and for H+(H,O),, 2 S x 6 5. No measureable values were found in the ultraviolet for O t , the second hydrate of O z , NO+(NO), or for the proton hydrates. In the case of O f hydrates, the observed cross sections were about three to four times smaller than those measured by Beyer and Vanderhoff (1976). With regard

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to proton hydrates, Henderson and Schmeltekopf (1972) set upper limits for the photodissociation cross sections of proton hydrates in the wavelength range from 580 to 610 nm. Beyer and Vanderhoff (1976) also failed to observe the photodissociation of proton hydrates up to the x = 4 species in the energy range 1.83 to 2.7 1 eV. Vanderhoff (1977) also studied the photodissociation for NO+(NO) and NO+(H20)spanningaphoton wavelength range from 799 to 350 nm. In the case of NO+(H,O) the photodissociation cross sections were observed to be very small or zero for the photon energies studied. The absolute photodissociation cross sections for NO+(NO)were found to vary smoothly with photon energy attaining a maximum value of 2 X cm2 at approximately 650 nm. However, the photodissociation cross sections were observed to vary with both laser power and the electric field in the ion source-photodissociation drift section of the apparatus. It was concluded that the photodissociation of an ion formed through an intermediate ion of large photodissociation cross section can be misleading because of the inhibition of reactions linking the two ions. Studies by Hodges and Vanderhoff (1980) of 0 2 ( S 0 2 ) + showed structureless bands indicative of dissociation through a repulsive state. Very recently, Jarrold et al. (1983) have investigated the dynamics and energy disposal in the photodissociation of (NO); over the range 660 to 488 nm. Kinetic energy distributionsfor the product ion NO+ were derived, including information about the angular distributions.The product angular distributions were well fitted with a simple relationship characteristic of dissociation occumng on a repulsive surface. The fraction of the available energy partitioned into relative kinetic energy was found to increase from 22Yo at 659 nm to 32%at 488 nm. The data indicate that photodissociation occurs by a transition to an excited state which has a negligible lifetime compared to that of rotational period. Smith and Lee (1 978) measured absolute photodissociation cross sections from a number of homomolecular clusters including Ot,N,Ot, NZ, and (CO,):. As pointed out by Moseley (1983), the cross sections generally resemble those for direct association of a homonuclear diatomic ion. Moseley ( 1983) has also reviewed results for Cot,showingthat the repulsive state apparently consistently correlates with the higher dissociation limit. As an example, CO$ is found to dissociate into Cot 0, which is 1.7 1 eV above the channel 0; CO,. Vestal and Mauclaire (1977) also studied the photodissociation spectrum of (CO,): for the visible spectrum 580-620 nm. A cm2was observed. large photodissociation cross section of 2 X Beyer and Vanderhoff (1976) also studied the photodissociation cross sections of 0: (CO,)and Of(H,O) finding that the photodissociation cross sections were similar. However, they observed the Ot(C0,) to exhibit a

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T, D. Mark and A . W. Castleman, Jr.

threshold in the energy range of 2 eV that was not observed in the case of the other species. At a threshold of 2.16 eV, Ot(C0,) was observed to photodissociate to C o t , suggesting that the photon energy absorption was sufficient to reach an Oz-CO: dissociation curve. These observations led to the conclusion that the existence of a photon-assisted charge transfer reaction was operative. The investigators were unable to study the production of 0: photofragments because of the presence of other 0; ions in the spectrum. Considering O t (HzO)z,the photodissociation cross section for the second hydrate was substantially less than that for the first over most of the energy range studied ( 1.83 to 2.7 eV). Studies of the dissociation of OZ(0,) suggested transition to an Ot-Oz repulsive state, giving rise to features in photodissociation cross sections attributable to the relative shapes of the bound and repulsive potential curves.

3. Negative Cluster Ions The most extensive set of measurements for the photodissociation of cluster ions has been reported by Moseley and co-workers (Cosby and Moseley, 1975;Moseley et al., 1975a, 1976;Cosby el al., 1975, 1976, 1978; Smith et al., 1978, 1979a,b;Lee and Smith, 1979).Considerable attention has been focused on the laser photodissociation of COT, not generally considered a cluster ion, Early data reported by Moseley and co-workers (Cosby and Moseley, 1975; Moseley el al., 1975a, 1976; Cosby et al., 1976) suggested a single-photon process leading to a bond dissociation energy for 0 - and COz of approximately 1.8 eV. Other measurements in combination with data from the laboratory of Ferguson (Dotan et al., 1977b)established the dissociation energy in the neighborhood of approximately 2.3 eV, raising considerable controversy (see discussion in Hiller and Vestal, 1980).Burt ( 1972)also made photodetachment cross section measurements for COT and its first hydrate where it was concluded that the threshold energy is 1.8 eV for COT and 2.1 eV for CO,.H,O in contradiction to other experiments. Studies of the photodissociation cross sections for COY were also made by Beyer and Vanderhoff (1 976) in a high-pressure drift tube. The results and conclusions from the work were generally similar to those of Moseley and co-workers. More recent work by Vestal and co-workers (Vestal and Mauclaire, 1977; Hiller and Vestal, 1980) is in disagreement. The suggestion of Hiller and Vestal ( 1980) that a two-photon process might be involved was consistent with the results of a power study which indicated the likelihood of an intermediate bond electronic excited state. More recent measurements by Castleman and co-workers (Castleman et d., 198lf, 1982b, 1983a) and Hunton ez

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al. (1983b, 1984b) established a strong influence of electric field on vibrational excitation in the parent ions. An energy analysis (Hunton et a/., 1983a) of the photofragment 0- ions produced in the photodissociation identified two distinct 0- production mechanisms; a two-photon absorption via an intermediate bound electronic state and a collision-assisted single-photon process via a long-lived excited state. The collision-assistedstate was found to have a radiative lifetime exceeding 1 psec and a collisional dissociation cross section measurably higher than that for the ground state. Experiments have also been conducted on the photodissociation of CO; water hydrates (Moseley et al., 1975a; Cosby et al., 1976; Smith et al., 1978, 1979a).Castleman and co-workers (Castleman et al., 198If, 1982b, 1983c; Hunton et al., 1983b, 1984b)observed that the same intermediate state was apparently responsible for CO; hydrate photodissociation for one, two, and three water clusters leading to CO;, as for the bare ion photodissociation process leading to 0-. The studies established that virtually no energy was transferred to translational energy and the cross section for water loss was approximately two orders of magnitude larger than that for the case of the bare ion. The experiments showed that all water molecules are lost simultaneously upon absorption of the photon, providing good evidence for rapid vibrational energy distribution within the parent ion as the mechanism for photodissociation of the cluster hydrates. Photodissociation cross sections for O;, O;.H20, 0 3 - H 2 0 , COT and were NO~~H20 CO,*H,O, HC0;-H20, O ~ ~ N O a n d 0 ~ ~ N O ~ H 2 0 , a n d studied (Moseley et al., 1975a;Cosby et al., 1975, 1976, 198;Lee and Smith, 1979a; Smith et al., 1978, 1979a,b; Smith and Lee, 1979) using a drift tube mass spectrometer and tunable dye laser. Many of the ions did not dissociate cm2were established from the work. or detach and upper limits of 1 X In the case of photodetachment studies of ion clusters, very few definitive data have been reported. Hong et al. (1977) have investigated photodetachment from CO;. In measurements of OH(H20)- by Golub and Steiner ( 1968),it was observed that there is a monotonic rise ofthe cross section over the full 1-eV range above the threshold of 2.95 f 0.15 eV. The photodestruction cross section of 0;.H20 had also been measured by Vanderhoff (1978b). Lee and Smith (1979a) found the wavelength dependence to be qualitatively similar to the photodetachment cross section of 0 ; except for a blue shift. This led to the conclusion that the photodestruction process of 0, - H 2 0 is most likely dominated by the dissociative photodetachment process. In the case of O;-H20, the photodissociation process leading to 0, and 0- was believed to dominate over the detachment because the photodetachment of 0, was found to be small compared to photodissociation (Lee and

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T. D. Mark and A . W. Castleman. Jr

Smith, 1979a; see also Cosby et al., 1978). The photodissociation cross section of 0;.H20 and 0;.(H20),, measured over the range 630 to 5 12 nm (Cosby et al., 1978), showed structure resembling that of O;, but progressively blue shifted and less structured with the addition of each water ligand. The major product ion was found to be 0 7 , although the photodissociation channel leading to 0- as the product could not be totally ruled out from the measurements. Studies were also conducted by Moseley et al. (1975a) on the photodissociation of HCO;. H 2 0but no photodissociation was observed in the energy range between 2.35 and 2.71 eV. Cosby et al. (1976) found the total photodestruction cross section for HCO:-H20 at 514.5 nm to be less than cm2.In the case of COT, cross sections of less than 3 X 7X cm2 between 690 and 550 nm were found. However, small but nonzero cross sections were measured at 520 and 514.5 nm. The photofragments of COTcould not be observed and it is not known whether the photodestruction of this ion is due to photodetachment or photodissociation. Vestal and Mauclaire ( 1 977) also investigated the photodissociation of CO;. Both 0; and COT were found to be products at 305 nm in approximately equal amounts, but CO; was more than a factor of 10 less at 365 nm and the 0 5 channel dominated. A threshold of 3.25 k 0.15 eV was found for the dissociation to COT, with a threshold of 1.1 k 0.2 eV for the product 0;. Vanderhoff and co-workers (Vanderhoff, 1978; Beyer and Vanderhoff, 1976) also investigated the photodestruction cross sections of CO; at energies ranging from 695 to 799.3 nm and at 4 13.1 and 4 15.4 nm. Their results show that the photodissociation of CO; has a cross section of 1.5 X 10- cm2 or less. Smith and Lee ( 1979) reinvestigated the photodissociation spectroscopy of 0 ; H 2 0 between 4 I7 and 470 nm, finding cross sections ranging from 5.64 k 0.85 to 6.50 k 1.44 X cm2, with little detailed structure. The behavior was somewhat similar to that found between 450 and 500 nm (Lee and Smith, 1979a) and to the very diffuse structure observed at longer wavelengths (Cosby et al., 1978). At high-proton energies the absorption structure was apparently smoothed out by the influence of the water hydration on the ozonide chromaphore. Cosby et al. (1 975) studied the photodestruction cross section for 0 ; over the energy range 1.93 to 2.7 I eV, while structure was observed with cross cm2. The 0 ; photodestruction sections varying from 1.0 to 2.2 X cross sections were observed to be similar to the 0; photodetachment cross sections, with at least two broad maxima at photon energies between 1.94 and 2.7 1 eV observed. The pressure range ofthe experimental apparatus was not sufficiently high to ensure that the 0 ; ions were in a thermal distribution

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of internal energy states and efforts to observe the photofragment ions were unsuccessful. Photodissociation measurements have also been made by Smith and coworkers (Smith et al., 1978; Lee and Smith, 1979a), for 0 6 . The product channel was found to be 0;. Burt (1972) reported the average photodetachment cross section of 0 7 at 450 nm to be 9 X cm2, a value which exceeded the work of Lee and Smith (1979a) by approximately a factor of four. It was also concluded that 0 ; may be photodestroyed by dissociative attachment. Smith et af. (1979b) also investigated the total photodestruction cross sections for NO,.H2O, NO7.H2O, O,.NO, and 0 ; - N 0 . H 2 0 at wavelengths between 350 and 825 nm. It was concluded that the isomer of the NO;, 0, * NO, and its hydrate have large photodissociationcross sections at wavelengthsshorter than 550 nm. In the case ofNO;.H,O, a threshold near 4 13.1 nm was evident and the cross section was found to be nearly one-half that of the parent NO: at 350 nm. The products of photodestruction could not be experimentally established because of the presence of a large excess of NO; in the drift tube. It was speculated that dissociative photodetachment was the observed process, consistent with the observed blue shift in the hydrate threshold with respect to NO,. In the studies by Smith el al. (1979b), the photodestruction cross section for Oy - NO showed a gradually increasing cross section with little detailed structure. Sizable Oy photofragment signals were observed at 530 and 440 nm indicating photodissociation to 0, and NO as the major process throughout the wavelength range. The findings suggest that a single electronic transition may be responsible. The ion 0 ; - N 2 0 was found to have a cmz slowly increasing photodestruction cross section of 0.8 to 1.0 X from 640 to 530 nm. In the case of the ion O;-NO.H,O, large amounts of 0,NO were detected as the principal photodissociation product. The work of photodissociation cross sections and reactions to form the various isomer ions suggested that the isomer 0 NO is apparently more easily hydrated than NO; and that 0;"0.H20 is apparently not really converted to NO 3 * H,O. Several other ions have been proposed to exist in isomeric structures, in particular, having a peroxy form. For instance, evidence from photodetachment threshold measurements had suggested peroxy form of NO, as well as the normal form (see Richardson el af.,1974b;Pearson et af.,1974;Dunbar, 1979)but a reexamination of this ion (Huber, 1977a,b) provided evidence that a single-ion structure with varying degrees of vibrational excitation is more likely as an explanation of the observations. The earlier suggestion of a peroxy form of CO ; (Burt, 1972)is also no longer accepted but evidence still

-

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T. D.Mark and A . W. Castleman. Jr.

persists for peroxy forms of SO; (Dunbar, 1979; Fehsenfeld and Ferguson, 1974; Fehsenfeld, 1975). More recently, Hodges and Vanderhoff ( 1980) measured the photodestruction cross sections for six ions containing SO2over the photon energy range 1.55 to 3.5 eV. It was found that the cross section for SO;- increased smoothly with photon energy from about 0.9 to 2.4 X lo-'* cm2.The photodestruction cross section for SO:(SO2) was found to consist of broad structureless bands with direct dissociation through repulsive excited states being indicated. In the case of O:(SO2),N02(S02)-, and NO,(SO,)-cross sections different from zero were found only at the upper end of the photon energy range studied. In the case of N02(S02)-a measureable photodissociation cross section was found at 2.6 eV, while in the case of N03(S0,)photodestruction was only observed at 3.5 eV. Dunbar and Hutchinson ( 1974) have observed photodisappearancespectra for 10 transition metal carbonyl anions using an ion cyclotron resonance technique and a xenon arc light source including narrow band interference filters and a monochromator. The ion disappearance mechanism was believed to be photodissociation, although electron photodetachment was not ruled out. Comparison of the spectra showed that for both increasing values of n or for species containing metals of higher atomic number, the optical absorption of the species M(C0); shifted toward the blue in a continuous fashion. The case of the nickel carbonyl trimer was the only exception. The optical transitionsare attributed to a charge transfer process carrying a metal 3d-type electron into a higher ligand orbital. A comparison of the tetramer carbonyl of cobalt was found to be consistent with the solution properties of the ion. The photodisappearance spectra of all the anions were similar, showing a well-defined threshold followed by a more or less well-defined peak. Investigations were extended to Mn(CO),, Co(CO),,, 3 , Fe(CO);, Cr(CO);, Mn(CO);, V(CO);, Ni(CO);, and Cr(CO):,d 3 . Photodisappearance was not reproducibly observed for Mn(CO), between 800 and 300 nm and it was concluded that this ion may not have a photodisappearancecross section comparable in magnitude to the others studied. Similar evidence that Fe(CO), and Fe(CO), undergo photodissociation rather than photodetachment of electronshas been obtained by Richardson et al. ( 1974a).Experiments with plain polarized light demonstrated that the Fe(C0)y appearance was preferentially enhanced when the optical E vector was parallel to the magnetic field in the ICR; but the disappearance of Fe(C0); was not influenced by the optical E vector. This implied a nonisotropic scattering of the FeCO; and CO in the photodissociation process, giving evidence that the product ion must be formed with appreciable kinetic energy. These observations are consistent with an expected nontetrahedral

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geometry for Fe(C0);. Evidence was obtained that Fe(C0): further photodissociates to yield Fe(C0):. For additional details on species of the type Fe(CO);, see EngelkingandLineberger (1979) and Compton and Stockdale ( I 976). 4. Comparison to the Condensed Phase

One of the nicest examplesof the photodissociation data in understanding the condensed phase is provided by the results of Freiser and Beauchamp (1977; see also Freiser et al., 1976)on the photodissociation of a number of clusters bound to H+ and Li+: for C6H5X,where X = H, CN, NH,, CHO, COCH,, NO2, OCH,, 0-, and S- and with pyridine and ferrocene. In particular, these data have provided information on the changing bond energy of electronically excited ion complexes. A comparison of excitation energies of the base B with the corresponding acid -base complex AB, has provided information on the excited state basicity of B. Other comparisons of the excitation energies of a chromaphoricacid A with the complex AB has yielded information about the excited state acidity of A. In a few instances photodissociationspectra of solvated acid - base complexesof the type B2Li+ have also been obtained, providing information on the effects of further solvation on the excitation spectra of these complexes. Studies of the second type are also presented using the reference base H- with the acids C6H5CO+ and C6H5CHOH+.Comparison of the above data with liquid phase absorption spectra has shown interesting similarities. The first reported laser-induced fluorescence spectra of free jet cooled ion - inert gas clusters has been reported by Heaven et al. ( 1982a).The laser excitation spectrum of C6F5H+expanded in a mixture of 1090argon and helium was obtained at stagnation pressures of 1.3, 2.7, and 4.0 atm. The observations are consistent with a red-shifted spectrum increasing with the degree of clustering to argon. The laser excitation spectrum of C6F5H+in a solid argon matrix has been reported, enabling a comparison. At high backing pressures, the cluster cation spectrum turns into a continuum totally unlike that of the matrix. It is suggested that because of a balance between collisional cooling and heating caused by complex formation, large clusters may not be as cold as the argon matrix experiments. Further advances can certainly be expected in studies derived from both photodissociationstudies of mass-selected cluster ions and investigations of fluorescence. One of the objectives of such studies is elucidating changes occurring during the continuous course from the gaseous to the condensed phase. It is evident that techniques are now available, enabling this goal to be reached.

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V. Thermochemical Properties A. INTRODUCTION

The area which has received by far the greatest attention in the field of cluster ions is the one devoted to experimental studies of their therrnochemical properties. Several early reviews have been written on this subject, three general ones by Kebarle (1972a,b, 1977) covering the period up through 1976 and several others representing an extensive review of each author’s own works, but those with some attention to the general field include Kebarle ( 1974, 1979, Castleman (1979a,b), Castleman and Keesee (198 1a), Castleman et al. (1982a), and Keesee and Castleman ( 1984). Other general reviews containing information related to this topic include Tafi (1 975a,b), Aue and Bowers (1979), Beauchamp (1971), Lias and Ausloos (1975), Friedman and Reuben (197 l), Schuster et al. (1977), Wiegand (1982), and Franklin and Harland (1974). A tabulation of all known thermodynamic values of cluster ions through mid- 1983 has been made by Castleman and Keesee (1984). The classes of cluster ions, being either anions or cations, can be further subdivided into ones composed of simple inorganic constituents and those containing organic ligands and/or organic ions. While both categories are discussed, herein major attention is given to the inorganic species having bond energies less than 3 eV. The subject of proton affinities is not covered and the interested reader is referred to other references (e.g., see Aue and Bowers, 1979; Lias et al., 1984; Taft, 1975a,b; also see Friedman and Reuben, 1971; Kebarle, 1977). Chupka (1959), using a Knudsen cell technique, made one of the first direct measurements ofa bond energy for a cluster ion (K+ H,O). However, the majority of the thermochemical properties of cluster ions have been derived using one of six other principal techniques. High-pressure mass spectrometry (including various drift cell variations), pioneered by Kebarle and co-workers (e.g., see Kebarle, 1972), has been utilized extensively by Kebarle and co-workers (Searles and Kebarle, 1968, 1969; Good et al., 1970a,b; Hiraoka et al., 1972,1973, 1979; Hogg et al., 1965, 1966; Payzant and Kebarle, 1970;Lau and Kebarle, 1981;Durden et al., 1969;Hiraoka and Kebarle, 1975a-d, 1976, 1977a-c; Payzant et al., 1971, 1972, 1973; Kebarle et al., 1967a-c, 1968, 1969, 1972, 1976, 1977; Kebarle, 1968, 1970, 1972b, 1974, 1975; Cunningham et al., 1972; Lau et al., 1980, 1981, 1982; Davidson et al., 1977, 1978, 1979a,b; Davidson and Kebarle, 1976a-c; Yamdagni and Kebarle, 1973a,b, 1971, l972,1974a,b, 1976; Gimsrud and Kebarle, 1973; Yamdagni et al., 1973; Dzidic and Kebarle, 1970; Kebarle

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and Godbole, 1963; Kebarle and Hogg, 1965), Castleman and co-workers (Tang and Castleman, 1972, 1974, 1975; Castleman and Tang, 1971, 1972a,b;Castleman and Keesee, 198la, 1983a,b; Lee er al., 1980b;Holland and Castleman, 1980; Peterson et al., 1984; Tang et al., 1971, 1976; Castleman, 1976a, 1978, 1979a,b, 1980, 1982a-c, 1983; Castleman et al., 1971, 1978a, 1981b, 1982a,b, 1983a,e; Keesee et al., 1979a, 1980; Miirk et al., 1980b; Keesee and Castleman, 1980a,b; Upschulte et al., 1983), Field and Meot-Ner (Mautner) and co-workers (Bennett and Field, 1972a-d; Field, 1969; Field et al., 1969; Beggs and Field, 1971a,b; Field and Beggs, 1971; Meot-Ner and Field, 1974a,b, 1975, 1977a,b; Meol-Ner and Sieck, 1983; Meot-Ner, 1978a,b, 1979, 1980, 1983; Meot-Ner et al., 1978, 1979), and Conway and co-workers (Turner and Conway, 1976, 1979; Conway and Janik, 1970;Janik and Conway, 1967; Conway and Nesbitt, 1968; Liu and Conway, 1975; Conway and Yang, 1965; Wlodek et al., 1980, 1983a,b; Wincel, 1972; Luczynski et al., 1974, 1978; Luczynski and Wincel, 1974). The flowing afterglow, the newer SIFT extension of this technique, and the ICR method have all been used to acquire thermochemical information by following the forward and reverse rates of association reactions (e.g., Fehsenfeld et al., 1971a,b, 1975, 1978; Fehsenfeld and Ferguson, 1973, 1974; Dotan et al., 1977b, 1978; Howard et al., 1971, 1972; Bierbaum etal., 1976; Woodin and Beauchamp, 1978; Larson and McMahon, 1983; Staley and Beauchamp, 1975; Haartz and McDaniel, 1973;Jones and Staley, 1982a,b; Uppal and Staley, 1982a,b;Kappes and Staley, 1982a,b;Reents and Freiser, 1981; also see Beauchamp, 1971, and references contained therein). Well depths for the systems F--Xe and Cl--Xe have also been reported (Thackston et al., 1980; DeVreugd et al., 1979). Positive ion cluster bond energies have also been derived from a number of appearance potential measurements. Some examples include the bonding of rare gas atoms to gas ions, CO, to C o t , for NO to NO+, CO to CO+, N, to Nt, 0, to 0: and 0+,HC1 to HCP, HBr to HBr+, HF to HF+, CS, to CSZ, OCS to OCS+, OCS to CSt, N,O to N20+and NO+, SO, to SO; and SO+, C2H, to C,H$, and C2H, to C,Ha,C,Hf, C,Htand C,H$, and the bond energy for ArCOt (Erickson and Ng, 1981; Linn and Ng, 1981; Linn et al., 1981a,b;Ng, 1983;Ngetal., 1976,1977a-d;Onoetal., 1980, 1981a,b;Ono and Ng, 1982a,b; Stephan et al., 1982b, 1983a, 1984; Dehmer and Pratt, 1982;Pratt and Dehmer, 1983;Horton et al., 1975). Related measurements have also been reported for CS, onto CS:, HIS onto H2S+,and acetone onto the ion (Walters and Blais, 1981; Trott et al., 1978, 1979). Similarly, the bonding of C1 to Nat, and NaO to Na+ has also been derived from appearance potential measurements, employing data for the bond energy of NaCl to Na+ derived by Chupka (1959) from studies of the photoionization of Na,Cl and Na,O (Peterson et al., 1983). For some spectroscopically deter-

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T. D. Mark and A . W. Castleman. Jr.

mined values of rare gases bound to rare gas ions the reader is referred to Huber and Herzberg (1979). Using thermodynamics, desired information on bond energies can be derived from measurements of appearance potentials if it is assumed that adiabatic potentials are obtained from the measurements, and information is available for the bonding of the neutral precursors. The bonding of ammonia to NH; has been derived from the photoionization of ammonia clusters (Ceyer et al., 1979a),where similar measurements have been determined by Stephan et al. ( 1982c, 1983a) using electron impact ionization. Within the relatively large limits of error reported for the two appearance potential measurements, the bond energies are in moderately good agreement but in the cases where there is “internal” reaction following ionization, the values differ significantly from those derived by high-pressure mass spectrometric techniques. Yet another method is to observe the exchange reactions of species with a cluster ion, the thermochemical properties ofwhich are well known, and by a series of bracketing measurements thereby obtain the thermochemical properties for the desired species under investigation. This technique has been explored by Ferguson and co-workers (see Albritton and Fehsenfeld, 1982) to derive information on electron affinities and bond energies for certain negative ion clusters. Two final methods which have sometimes been useful include studies of the photodissociation of cluster ions, which provide information on the upper limit of bond energy (e.g., Helm and Mtiller, 1983a; Moseley et al., 1976, 1977, 1981; Abouaf et al., 1978; Cosby et al., 1978; Beyer and Vanderhoff, 1976). Finally, measurements of the threshold for collisional dissociation are sometimes used (e.g., Wu et al., 1977; Wu and Tiernan, 1981;DePaz et al., 1969).Interestingly, the formation of H,O- has required an excess energy of collision (Paulson and Henchman, 1982; see also Kleingeld and Nibbering, 1983). B. EQUILIBRIUM MEASUREMENTS The high-pressure mass spectrometer techniques (discussed in detail in Section II,B) depend on the acquisition of equilibrium at high pressure and the measurement of appropriate determination of the relative concentrations of the cluster ions whose thermodynamic properties are being determined. I.L,+L+M=I.L,+,

+M

(24)

Here, I designates a positive or negative ion, L the clustering neutral (ligand), and M the third body necessary for collisional stabilization of the complex.

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119

Taking the standard state to be 1 atm, and making the usual assumptions (e.g., Castleman et al., 1978a)concerning ideal gas behavior and the proportionality of the chemical activity of an ion cluster to its measured intensity, the equilibrium constant Kn,,+Iis given by

,

Here, C,,+ and C,, represent the respective measured ion intensities, P, the pressure (in atmospheres) of clustering molecules L, AGi,n+l, and the standard Gibbs free energy, enthalpy, and entropy changes, respectively, R the gas law constant, and T absolute temperature. The technique permits clustering to be investigated sequentially, whereby details of the enthalpy of clusteringcan be obtained from slopes of van’t Hoff plots and entropies from appropriate intercepts. A typical van’t Hoff plot is shown in Fig. 1 1 for the clustering of ammonia onto Li+. The above method provides values of enthalpies rather than energies of clustering. Enthalpies, which are typically reported as constants, are in fact weakly dependent on temperature and the reported values are derived from the assumption that the data are representable as straight lines over a moderate temperature range. Precisely, the enthalpy of a given reaction at one temperature is related to that at another through an expression involving both absolute temperature and the difference in the heat capacities between the products and reactants. But, it has become commonplace in the literature to discuss measured enthalpies in terms of “bond energies,” especially by those individuals who are comparing experiment to theory. Nevertheless, enthalpy is only equal to bond energy at 0 K and in a few cases authors have made good estimates of heat capacities for the systems which are required to correct the enthalpy measurements so that they can be reported as actual bond energy values. The corrections typically range from 0.5 to 2 kcal/mol. For an example of the magnitude of the corrections, the reader is referred to Turner and Conway ( 1976) and Janik and Conway (1967). A further potential problem in deriving the desired values from experiments has been pointed out by Sunner et al. (1 98 1). They emphasize that measurements made on large clusters at moderate temperatures may be somewhat influenced by unimolecular decomposition of the cluster ions following their exit from the high-pressure reaction cell and entrance into the mass spectrometer. While the influence is not expected to be large, they estimate that up to 1 or 2 kcal/mol of error might result. By extrapolation to the intercept, van’t Hoff plots also enable a determination of the entropy for each individual association reaction. The entropy is also rigorously dependent on temperature, although only weakly so. An alternative approach sometimes used to ascertain AH values is one which

T. D.Mark and A . W. Castleman, Jr.

120 lo(

I

I

I

I

1 22

I 26

30

I

1

a

lo5

-+

lo4

c Y 10’

102

101

1

I

18

1

1

34

I 38

I

42

(I/T x IO’)/K

FIG. I 1. A van’t Hoff plot, natural logarithm of the equilibrium constant versus reciprocal absolute temperature, for Li+(NH,), NH, * Li+(NH,),+, , after Castleman eta/. (1978a). (a) K,,*;(b) (4 (4L;(e) K,,6

+

depends on measuring the AG value at one temperature and using a calculated value of A S to obtain AH. This technique is most often employed when data are available at only one temperature, and has been commonly used to derive AHand A S values from early flowing afterglow measurements which were confined to operation around room temperature. In this regard, it is instructive to ascertain the degree to which A S can be calculated with confidence and this point is discussed in the next section. C. ENTROPIES Most, although not all, investigators who utilize the high-pressure mass spectrometer and related drift cell techniques report experimentally determined values of entropy along with enthalpy. Although both are derived

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from the same measurements and subjected to the same precision, ASvalues are generally known with less accuracy due to the nature of the measurements. While AH is determined from a slope, any inherent bias in the determination of ion ratios or partial pressures of the clustering gas directly influences the A S calculated from the intercept of a van’t Hoff plot. Hence mass discriminatioh effects in the sampling or in the mass spectrometer, imprecise knowledge ofthe concentrations of the clustering ligands, or possible fragmentation and unimolecular decomposition processes (Sunner et af., 198 l), can lead to a more serious effect on AS. In principle, AScan be determined by application of the Sackur-Tetrode equation ( McQuarrie, 1976)

j- I

- In( 1 - e-%/T)

1

where the equation is written for nonlinear molecules and rn is molecular weight, V volume, N number of molecules, €Iithe characteristic rotational temperatures, and 8, the characteristic vibrational temperatures. The first term on the right, associated with translational effects, is readily calculated. The second and third terms depend on knowledge of structure and vibrational frequencies since the second term involves a knowledge of the moment of inertia, and the third information on the contribution of vibrations to the entropy. Hence, since clusters frequently have very low frequency vibrational modes, neglecting these contributions to entropy can lead to very serious errors. A determination of entropies requires knowledge of both the structure, to determine moments of inertia, as well as the vibrational frequencies since there are both rotational and vibrational contributions. Castleman et af. ( 1978b) employed simple statistical mechanical computational techniques for estimating A S contributions due to translation and rotation for K+(H,O),. From the data of Dzidic and Kebarle (1970) they were able to determine by comparison the extent of vibrational contributions in the clusters. The major difference between the entropy change for an association reaction involving an atomic rather than a molecular ion is that the rotational entropy contributions are of opposite sign. For example, in the abovementioned case, for the first cluster the relative magnitudes were -36.7, 8.7, and 6.6 e.u., respectively, for translation, rotation, and vibration compared to -37.0, -9.5, and +22.3 e.u. for the second. Of the 22.3 e.u. associated with internal motion (vibration), approximately 4.0 e.u. is due to

+

+

122

T. D. Mark and A . W. Castleman, Jr.

internal rotation of the molecules, 6.6 e.u. to the stretching frequencies, and 1 1.7 e.u. to contributions arising from two bending modes with frequencies of approximately 1.7 X 10l2/sec.Similar contributions were deduced from consideration of the clustering of water to C1- and NO, (Castleman et al., 1982a). The contribution due to translation is always large compared to the values for rotation and vibration. For instance, using estimated C1-0 separations and frequencies deduced from molecular orbital calculations of Kistenmacher et al. (1973b, 1974) the entropy contributions at 470 K were estimated to be - 35.6 e.u. for translation, 10.2 for rotation, and 6.3 for vibration. These estimates led to a total calculated entropy change of - 19.1 e.u. compared to - 19.7 determined experimentally. Although it is evident that fairly reasonable estimations of entropy changes can be based on calculations, the vibrational contribution is rather significant due to the low-frequency modes present in ion clusters. Values from molecular orbital calculations are approximate but generally adequate for purposes of evaluating the requisite contribution. However, rarely do these numbers exist for clusters larger than one or two molecules to the central ion. Since the vibrational contribution is of a fairly large magnitude, it is evident that the preferred method for deducing A H o values for sequential clustering reactions is to derive these from van? Hoff plots made over a fairly wide range of temperatures rather than using estimated entropy values and a measured AG at one temperature. Insufficient attention has been focused on methods for deriving better entropy values. Such data would enhance knowledge of cluster structure and would also contribute to other areas such as in the development of models of ion-induced nucleation (see Castleman and Keesee, 198lb, 1983; Castleman ef al., 1978a,b, 1974, 1976a-c, 1978b, 1981d; Castleman, 1979a-d, 1980, 1982a-f; Lee ef al., 1980a,b; Holland and Castleman, 1982a; Castleman and Tang, 1972a,b; Keesee and Castleman, 1982, 1983) and the kinetics of association reactions (Chang and Golden, 1981). A consideration (Castleman et al., 1978b; Castleman, 1979a; Holland and Castleman, 1982a) of the experimental entropy values in terms of the usual classical equation for nucleation (Abraham, 1974) shows that the actual trends are not in agreement with predictions. The problem is that the simple classical model assumes a random liquid-like disordered structure, while in actual fact the entropies pass through a maximum negative value before becoming increasingly positive (toward the limiting value for the case ofa liquid). In the region between, the trends are greatly influenced by cluster structure that is not accounted for by the simple models. Ligand-ligand steric effects and crowding of the solvation shells at very small degrees of clustering greatly influence entropy values. The importance with regard to kinetics is discussed in Section II1,B.

+

O

+

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IONS D. BONDINGTO POSITIVE One impetus for studies of ion clustering is to quantify the potential of interaction between ions and neutral molecules, i.e., the well depth. In the case of alkali metal ions with rare gases, this has been accomplished through mobility measurements (see for instance Takebe, 1983). Studies ofthe properties of large clusters provide data which serve to bridge the gap between the gaseous and the condensed phase, and this is another reason why there has been increased attention paid to cluster ion research in recent years. Data for clustering to positive inorganic ions have been reported by Searles and Kebarle (1968, 1969),Good et al. (1970a,b), Hiraoka and Kebarle (1975a-d, 1977a-c), Upschulte et al. (1983), Hogg et al. (1966), Payzant and Kebarle ( 1970),Payzant et al. (1 973), Tang et al. ( 1976),Tang and Castleman ( 1972, 1974, 1975), Castleman et al. (1978a, 1980, 1981b, 1982a, 1983a,e), Holland and Castleman (1 980a, 1982a), Peterson et al. (1984b), Castleman (1978, 1979a), Luczynski and Herman (1979), Wince1 (1972), Meot-Ner and Field (1974a,b, 1977a,b), Stephan et al. (1982b,c, 1983a, 1984), Beggs and Field (197 la,b), Bennett and Field (1972a,d), Long and Franklin ( 1973, 1974), Franklin et al. (1958), Chong and Franklin (1971), French et a/. (1973), Fehsenfeld et al. (1971b), Arifov et al. (1971a-c, 1973a,b), Turner and Conway (1976, 1979), Janik and Conway (1967), Perry ef al. (1980), Spears and Fehsenfeld ( 1972),Conway and Janik ( 1970), Yang and Conway (1964), Adams et al. (1970), Conway and Nesbitt (1968), Fehsenfeld et al. (1978), Teng and Conway (1973), Liu and Conway (1975), Rowe et a/. (1982), Dotan et al. (1978), McKnight and Sarvina (1972,1973), McAdams and Bone ( 1972),Arshadi and Futrell ( 1974),Varney (1959,1968), Johnson et al. (1975, 1976), Saporoschenko (1965), Gatland et al. (1975), Beyer and Keller ( 1971), Colonna-Romano and Keller ( 1976), Keller and Beyer (197 la,b), Pack and Phelps (197 I), Elford and Milloy (1974), Paulson and Henchman ( 1982),Jennings et al. (1982), Headley et al. (1982a,b), Keller et al. ( 1973),Patterson ( 1968),Gusinow et al. (1970), Vanderhoff and Heimerl (1977), Helm (1976a,c), Howard et al. (1971, 1972), DePaz et al. (1968, 1969),Puckett and Teague (197 la,b), Bierbaum et al. (1976), Hiraoka et al. ( 1979),Speller et al. ( 1982a,b, 1983),Rakshit and Warneck (1980a,b, 198l), Wu (1979), Takebe (1983), Moseley et al. (1977, 1981), Hiller and Vestal (1981, 1982),Lifshitzetal. (1978), Wuetczl.(1977), WuandTiernan(1981), Cosby et al. (1978), Walters and Blais (198 I), Dehmer and Pratt (1982a,b), Pratt and Dehmer (1983), Abouaf et al. (1978), Ng et al. (1976, 1977a-d), Ceyer et al. (1979a), Linn et al. (198 la,b), Linn and Ng (198 l), Anderson et al. (1980), Tiedemann et czl. (1979), Erickson and Ng (198 l), Ono et al. ( 1980,198 1b), Samson and Cairns ( 1966), Lau et al. ( 1982),Cunningham et

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T. D. Mark and A . W. Castleman, Jr.

al. ( 1972),Kebarle et al. ( 1967c),Dzidic and Kebarle ( 1970), Davidson et al. ( 1979a),Haartz and McDaniel ( 1973),Davidson and Kebarle ( 1976a,c),and Speller et al. ( 1983).For the case of metal ion - hydrogen, metal ion - carbon, and metal ion -oxygen bond energies see Armentrout and Beauchamp (1980a,b, 1981) and Armentrout et al. (1981b). Comparing the relative bond strengths for a variety of ligands about a given positive ion, especially a spherically symmetric rare gaslike alkali metal ion structure, is very instructive in elucidating the role of the ligand. In this context, the most extensive data are available for sodium and, second, for potassium. A compilation of bond energies for a variety of molecules clustered to sodium has been made by Castleman et al. (1983a) (see also Castleman et al., 1978a; Peterson et al., 1980, 1981, 1984b; Castleman and Keesee, 1983b, 1984). A strong dependence on ion radius is observed upon comparing strengths measured for the first ligand-ion bonds. This would be expected for systems where electrostatic forces dominate the bonding. Since the sodium ion is a spherically closed shell entity of intermediate size, differences in the bonding of a variety of clustering ligands to this ion reflect properties intrinsic to the individual ligands. Data for molecules having a wide range of large permanent dipole moments, polarizabilities, and quadrupole moments are shown in Fig. 12. The corresponding electrostatic parameters for the molecules are given in Table I. Using simple electrostatic considerations, Spears (1972a,b) has been able to account for the hydration of simple ions, including Na+. Likewise, Diercksen and Kraemer ( 1977)and Clementi and co-workers (Kistenmacher et al., 1973a;Clementi, 197 1, 1976; Clementi and Popkie, 1972) performed ab initio SCF-MO calculations on the alkali ion hydrates and have shown that the bonding is almost purely electrostatic. For example, Mulliken electron population analysis by Clementi showed that the fractional transfer of a unit of charge for water to lithium, sodium, and potassium varied from a maximum of 0.0 18 to as little as 0.004. Using semiquantitative calculations, Castleman (1978) found that there was slightly more transfer of charge in the case of ammonia compared to water, but still found that the bonding is essentially electrostatic. Abraham et al. (1976; Abraham and Liszi, 1978) have extended their calculations to relatively large cluster sizes, showing a slight dependence on the radial distribution function of position within the first solvation shell with cluster size. These findings indicate a possible compressive effect, suggesting the possibility of a somewhat different gas phase ion cluster structure than that existing in the condensed phase. Referring to Fig. 12,it can be seen that the ordering ofthe ligand molecules with respect to the enthalpy change involved in forming the first cluster with Na+ follows the order DME (dimethoxyethane) >NH, > H,O > SO, > CO, > CO 3 HCI > N, 3 CH,. Additional considerations (Peter-

EXPERIMENTAL STUDIES ON CLUSTER IONS

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-AHy

+

FIG.12. -AH,,,+, versus cluster reaction, n,n 1, for (a) DME, (b) NH,, (c) H,O, (d) SO,, ( e ) CO,, (f) CO, (g) HCI, (h) N,, and (i) CH, clustered to Na+, after Castleman et al. (1983a).

son, 1982; Castleman et al., 1983b) suggest that DME forms a bidentate bond with Na+. Comparing the stronger bond for ammonia, compared to water in light of the electrostatic properties given in Table I, reveals the importance of the ion-induced dipole interaction in governing bond strength. Although ammonia has the smaller dipole moment, its much larger polarizability enhances its bonding at small cluster sizes. The role of the quadrupole moment is also seen by comparing the relative bonding of SOzto NH, . Both have approximately comparable values of dipole moments and polarizabilities, but the quadrupole moment of SOz leads to a repulsive interaction compared to the attractive one of NH,, consistent with the smaller bonding strength of SOz.The role of polarizability is further seen by comparing CO and HCl, where the latter has a larger dipole moment but both have significant polarizabilities. Molecules without permanent dipoles have comparatively low bond energies as seen for Nz and CH,; the relatively

TABLE I PROPERTIES OF SMALL MOLECULES"

Dipole moment

Quadrupole moment

Ligand

(Debye)

Dz

Polarkability %,a y , a,

(A3)

( 10-26esu/cm2)

H20

1.85 (a)

1.452, 1.651, 1.226 (b)

-0.13, -2.5, 2.63 (c)

12.6

SO2

1.63 (f)

2.653,4.273, 4.173 (f)

1.3,4.0, -5.3 (g)

12.34

166.7 (x) 169.3 (d) 133- 159 (h)

CO

0.1098(j)

2.601, 1.624, 1.624 (k)

-2.5, 1.25, 1.25 (I)

14.013

139.0 (d)

N2

0 (a)

2.39, 1.46, 1.46 (m)

- 1.2,0.6,0.6 (n)

15.769

113.769 (d)

Qzz,

QW9

8,

IP(a) (eV)

Proton affinity (kcal/mol)

AH,,,(exp) (kcal/mol) for attachment to Na+

BE, (kcal/mol) 0

-24 (e)

H

- 18.9 (i)

- 15.8

- 12.6"

-11.6

- 8.0 (i)

-7.7

/ \

H

O\ /O S C

II

0

N

II

N

0

co*

0 (a)

4.05, 1.95, 1.95 (0)

-4.32,2.16, 2.16 (p)

13.769

126.8 (d)

- 15.9"

II

C

II

0

CH,

0 (a)

2.56 (9)

0

12.6

128.2 (d)

NH,

1.47 (r)

2.388,2.1,2.1 (s)

-2.32, 1.16, 1.16(t)

10.2

202.3 (d)

-29.1 (u)

HCI

1.084 (a)

2.727, 2.477, 2.477 (v)

3.8, - 1.9, - 1.9 (1)

135 (w)

- 12.2 (i)

12.74

-11.1

- 7.2"

-2.75

H

" Table from Peterson (1982). Original source ofeach entry indicated by letter: (a)Handbook ofchemistry and Physics ( 1 974); (b) Liebmann and Moskowitz (197 1);(c) Verhoeven and Dymanus (1970); (d) Kebarle (1977); (e) Dddic and Kebarle (1970); (f) Patel er al. (1979); (8) Pochan er al. (1969); (h) Smith and Munson (1978); (i) Perry ef al. (1980); ( j ) Muenter (1975); (k) Hirschfelder ef al. (1964); (1) Stogryn and Stogryn (1966); (m) Trapy ef al. (1974);(n) Momson and Hay (1979); (0)Koide and Kihara (1974);(p)Barton er al. (1979);(9)Maryott and Buckley ( 1953);(r) McClellan (1962);(s) Koch ef al. (1962);(t)Kukolich (1970);(u) Castleman ef al. (1978a);(v) Gianturco and Guidott (1978);(w) Polley and Munson (1978);(x) Collyer and McMahon (1983).

EXPERIMENTAL STUDIES ON CLUSTER IONS

127

stronger bonding of CO, compared to N, and CH4is accountable in terms of the large polarizability of CO,. Another interesting trend is seen by comparing the binding of various ligands to K+and Li+(seeCastleman et al., 1978a;Woodin and Beauchamp, 1978). Interestingly, the bond strengths correlate inversely with differences in ionization potential between the respective ligand and the neutral metal. This approach is able to predict (Castleman el al., 1978a) the ordering of ion - ligand bond energies for many chemically similar systems, but fails in a few cases, for example, the bonding order of Li+ to methylamines where NH, < MeNH, < Me,NH, Me,N; but Me,N < Me,NH. The anomolous position of Me,N in this series most likely arises from repulsive interactions between Li+ and the methyl groups of the ligand, a factor not accounted for in the simple correlation with ionization potential differences (Woodin and Beauchamp, 1978). As pointed out by Kebarle (1977) alkali ion-molecule interactions can be considered in terms of a Lewis acid-base interaction, since there is so little electron transfer in these systems. However, the Lewis acid-base concept is not completely general. Rather convincing evidence that the bonding of molecules to certain ions does involve partial transfer of an electron comes from a number of experimental measurements which show that the bonding strengths exceed those expected on the basis of simple electrostatic considerations. In the case of metal ions, the first data suggestive of this fact were derived from measurements by Tang and Castleman (1972) for the bonding of water to Pb+, an ion having an electronic configuration 6sz 6p'. Despite the relatively large size of the ion (1.5 A, comparable to that of Rb+, 1.48 A) the bonding of the first water molecule has a AHvalue of 22.4 kcal/mol. This is closer to that of water bonded to sodium than to comparably sized closed shell ions. More recently, Castleman and co-workers (Tang and Castleman, 1974;Tang et al., 1976;Holland and Castleman, 1980a, 1982a)have shown similar behavior for water bound to other metal ions including Bi+ (6s26p2 valence shell), Sr+ (5s configuration) and for both water and ammonia bound to Ag+ and Cu+. In the case of each of these ions, the values were much larger than expected on the basis of electrostastic considerations. For Ag+ a AH value of 33.3 k 2.2 kcal/mol was obtained, while for Cu+ the value exceeded approximately 40 kcal/mol. Even the addition of the second ammonia ligand to Ag+ has a AH of 36.9 f 0.8 kcal/mol, also pointing to a bond energy for the first complex well in excess of 40 kcal/mol. Among the more interesting results are the stabilities of the cluster ions Na, 02,and (CO);, all of which are much greater than expected for ion-induced dipole interactions in the case of the first two, and ion - dipole interaction for the last species. It is suggested that bonding must arise due to the sharing of an electron by the two molecules (Conway, 1969, 1979 and

I28

T. D. Mark and A . W. Castleman, Jr.

Kebarle, 1977).Fehsenfeld et al. ( 1975)have suggested that the interaction of water with NO+ and NO: produces protonated nitrous and nitric acid, respectively. But the bond energies are within range of the usual values for small ions bound to water, i.e., 18.5 and approximately 21.2 kcal/mol (French el al., 1973; Fehsenfeld et al., 1975). Compared to studies of the binding of ligands of a single species to ions, relatively few multiligand complexes involving simple inorganic cations have been studied in the gas phase. In the case where both ligands are inorganic, data are available for the pairs H,O/NH, bound to H+ (Payzant et al., 1973), H,O/H,S to H+(Hiraokaand Kebarle, 1977a),and H 2 0 / C 0 2to Na+ (Peterson et al., 1984).Other data are available for a few systems where one or more ligands are organic (Hiraoka et al., 1972; see also Sunner et al., 1981 ;Yamdagni and Kebarle, 1976).Until now little attention has been paid to these systems, but it is slowly becoming recognized that the results are of value in understanding solvation (Peterson et al., 1984b; also see a related discussion in Arnett er al., 1972).

E. SOLVATION Kebarle ( 1972b, 1974), Kebarle et al. ( 1969,1977),and Kebarle and H o g (1965) were apparently the first to draw attention to the usefulness ofdata at successively larger degrees of clustering for gaining insight into the solvation of ions in the liquid phase. More recently, Lee et al. ( I 980a) and Holland and Castleman ( 1982b) have considered the ratio of the solvation energy in the liquid phase to the summed gas phase enthalpy values up to a given cluster size and shown a rather remarkable convergence with size for a wide variety of different cations clustered with both water and ammonia (see Fig. 13). Rather unexpectedly, at cluster sizes beyond five, the differencesin the ratios between a variety of both simple and complex ions are within experimental error. These findings lend confirmation to some of the very simple Born concepts (1920), albeit that they require corrections for surface tension effects (see Lee et al., 1980a; Holland and Castleman, 1982b).Klots ( 1981) has considered the role of the surface potential in similar relationships. Convergence of these ratios to approximately the same value is indicative of the fact that beyond the first solvation shell the majority of the contribution to solvation is from electrostatic interactions between the central ion cavity and the surrounding medium. However, in some cases (e.g., Sr+)for which there are no single-ion solvation results to compare, the AHvalues far exceed the heat of condensation of water to degrees of clustering far greater than expected (Tang et al., 1976).Although few data are available for ligands other than water, an ultimate limiting value of A H for very large cluster sizes,

7

a 6

I

1

1

I

I

5-

5 - p 5 A

4

s B om

0

=,

$12

3

4-

0

3-

2-

2

---_

I

I 2

I

3

I

4

n

I

5

I

6

Y

I-

OO

I

2

3

4

5

6

n

FIG.13. (a) Ratio of Randles’total enthalpy () of solvationto the partial gas phase enthalpy of hydration (25°C)for positive ionic cluster size n, after Lee et al. (1980a).Thomson’s drop (---). (b) Ratio of total enthalpy of solvationto the partial gas phase enthalpy of ammoniation(- 33°C) for Coulter (---), Li+ (A), Na+ (0),K+(V),Rb+ (0). positive ionic cluster size n, after Lee et al. (1980a). Senozan (mean) (---),

130

T. D. Mark and A . W. Castleman, Jr.

leveling off at a A H value corresponding to the heat of vaporization of the liquid is always indicated; and the approach is always evident at surprisingly small cluster sizes (e.g., see treatment of alkali metal solvation in ammonia, Lee et af., 1980a). Further evidence for the relationship ofcluster data to ion solvation comes from observations of discontinuities in otherwise smooth trends in A H with size. See, for instance, Kebarle et al. (1967c), Searles and Kebarle (1968), Davidson and Kebarle (1976a), Yamdagni and Kebarle (1972), Castleman et al. (1978, 1983d), and Holland and Castleman (1982a). For further discussions of the importance of ion clustering in understanding solvation, the reader is referred to Schuster ef al. (1 977), Schuster (1976), Abraham and Liszi ( 1978),Veillard ( 1977, 1978),Smith efal. ( 1982),and Clementi (1 976). The relationship to proton conductivity is discussed by Weidemann and Zundel ( 1970). F. SOMESTRUCTURAL CONSIDERATIONS Several experiments have indicated the existence of some particularly stable structures ofcluster ions, for instance, the eigenstmcture H,O+( H20), (Eigen and DeMaeyer, 1958; Fang et al., 1973)based on both experimental findings (Hermann et al., 1982) and theoretical computations (Newton, 1977). Yet, the thermodynamic measurements on the bonding of water to H,O+(DePazefal., 1968, 1969;Arifovefal., 1971a, 1973a;Bierbaumetal., 1976; Beggs and Field, 197la,b; Bennett and Field, 1972a; Cunningham ef al., 1972; Good et al., 1970a,b; Kebarle e?al., 1967; Lau ef al., 1982; MeotNer and Field, 1977; Puckett and Teague, 197la) fail to reveal a particularly dramatic change in bond energies for the addition of additional water molecules to the eigenstructure. Indirect evidence has also been reported (Searcy and Fenn, 1974;Holland and Castleman, 1980b;Castleman et al., 198la,c, 1983e;Castleman, 1979a, 1980; Hermann et al., 1982; Dreyfuss and Wachman, 1982; Stace and Moore, 1983; Kassner ef al., 1980; see also Kassner and Hagen, 1976; Lancaster el d.,1979a)for the unusual stability of H,0+(H20)20,But, there are no bond energy measurements for clusters of this size to support the inferences from the various experimental studies. More recently, Stanley et al. (1983a) and Echt et af. (1984) have gained some evidence for a special structure involving ammonia, namely NH:( NH,), , via multiphoton ionization studies of ammonia clusters. The species has an analog to the eigenstructure in the water system. The reported (Tang and Castleman, 1975;Arshadi and Futrell, 1974;Payzant et al., 1973; Searles and Kebarle, 1968; Stephan et al., 1982c, 1983a;Wincel, 1972;Hogg

EXPERIMENTAL STUDIES ON CLUSTER IONS

131

et al., 1966;Arifov ef al., 1973;Ceyer et al., 1979a;Fehsenfeld and Ferguson,

1973; Long and Franklin, 1973; Puckett and Teague, 1971; Luczynski and Herman, 1979) bond energy measurements do not provide conclusive evidence of a solvation shell at this cluster size. G. SYSTEMS CONTAINING AN ORGANIC CONSTITUENT

Despite the general thrust of this article to trends in small inorganic systems, there are several cases where those from organic ones can be generalized and are germane to the subject at hand. The influence of ligand size resulting in steric hindrance in subsequent ligand attachment was found in studies of the clustering of dimethoxyethane about the monovalent sodium ion (Peterson, 1982; Castleman et al., 1983a). Other systems where at least one component, either the ion or ligand, is inorganic and the other organic include Hiraoka and Kebarle ( 1975a,c, 1976, 1977b,c),Kebarle ( 1977), Lau and Kebarle (1981), Davidson et al. (1979b), Yamdagni and Kebarle (1973a), Gimsrud and Kebarle (1973), Lau et al. (1981), Kebarle et al. (1967a), Meot-Ner (1978a,b, 1983), Sunner ef al. (1981), Holland and Castleman ( 1982a),Peterson et al. ( 1984b),Castleman ef al. ( 1983e), Upschulte et al. (1983), Wlodek et al. (1983), Beggs and Field (197 lb), Meot-Ner and Sieck (1983), Meot-Ner and Field (1974a), Meot-Ner et al. (1978), Bennett and Field ( 1972b,c),Field and Beggs ( 197l), Davidson and Kebarle ( 1976ac), Field ( 1969),Speller ef al. ( 1982a,b),Davidson ef al. ( 1978, 1979a),Staley and Beauchamp (1979, Cordennan and Beauchamp (1976), and Reents and Freiser ( 1981). More recently, findings of rather large bond energies for the clustering of molecules of metal ions have been derived from the measurements of Staley and co-workers (Jones and Staley, 1982a-c; Kappes and Staley, 1982a,b; Kappes et al. 1982b; Uppal and Stelay, 1982a-c). They have investigated the attachment ofa number ofligands to Al+, Mg+, Mn+, Ag+, Cu+,Cr+, Ni+, and Fe+, all showing rather large relative binding energies to these ions of open electronic configuration. In terms ofatmospheric science, evidence ofthe importance ofthe binding of certain organic molecules to ions has come from the work of Bohringer and Arnold ( 1981) in studies made of water and methyl cyanide coclustered to protons. The results show that the hydration equilibrium constants for heteromolecular clusters containing ethyl cyanide molecules are generally lower than those for the corresponding proton hydrate ions; the values decrease with increasing number of methyl cyanide ligands contained in the complex. The data suggest that interaction between water and methyl cyanide, and among the methyl cyanide molecules, is weaker than that between

132

T. D. Mark and A . W. Castleman, Jr

water molecules. An exception in the general trends was found for H+(CH,CN),H,O, where it is the most stable ion containing four ligands in the system. The authors explain the high stability of this ion by a structural rearrangement in which H,O+ is expected to form the core ion and the methyl cyanide molecules are believed to symmetrically attach to the three hydrogen atoms sharing the positive charge. Among the ions with six ligands, a similarly enhanced stability was also found for the ion H+(CH,CH), ( H,O),. Evidently, when the charged site can switch upon ligand addition, rather different bonding effects are displayed. In the context of solvation effects, a rather interesting observation has come from the work of SenSharma and Kebarle (see Kebarle, 1977)regarding the bonding of water to the ion C2H,0Ht. Although not really conclusive, they have presented data which suggest that the binding energies of this system pass through a minimum, where at cluster size six the enthalpy value exceeds that for the fourth water molecule addition. This is taken as an indication ofthe deprotonation ofthe base C2H50H.Although C,H,OH isa relatively strong base in the absence of water, it is weak compared to water. These findings may be in accordance with the rather interesting observations of Stace and co-workers concerning the crossover in ion stabilities noted for mixed clusters (Stace and Shukla, 1982b). For certain organic systems, Davidson et al. (1979b) have also made a comparison of proton transfer free energies between the gaseous and solution phase. They concluded that the large attenuation due to the substituent effect in solution must result from an effect of the substituent on solvation that partially cancels the effect on the isolated molecule. For instance, an electron-withdrawing substituent-like CN, which increases the intrinsic acidity of a material like phenol, is expected to unfavorably affect the solvation of cyanophenoxide ion and thus reduce the acidity increase of cyanophenol in aqueous solution. Cluster ion research has a great deal to contribute to the field of solvation involving organic constituents, but further discussion is beyond the scope of this article.

H. BONDINGTO NEGATIVE IONS

Fewer data are available for the clustering of molecules to anions; systems composed of inorganic anions and ligands include those of Payzant and Kebarle ( 1972),Keesee and Castleman ( 1980b),Lee et al. ( 1980b),Keesee et al. (1979a, 1980c), Peterson et al. (1984b), Wlodek et al. (1980, 1983), Robbiani and Franklin (1979), Fehsenfeld and Ferguson (1974), Conway

EXPERIMENTAL STUDIES ON CLUSTER IONS

133

and Nesbitt (1968), Davidson et al. (1977), Spears and Ferguson (1973), Fehsenfeld et af. (1975), Kebarle et al. (1968, 1972), Castleman (1982a), Paulson and Henchman (1982), Pack and Phelps (1966, 197l), DePaz et al. ( 1970), Arshadi et al. ( 1970), Hiller and Vestal ( 1980, 198l), Lifshitz et al. ( 1978), Cosby el al. (1 978), Moseley et al. (1976), Wu and Tiernan (198 l), Arshadi and Kebarle (1 970), Larson and McMahon (1983), Yamdagni and Kebarle ( 1974b), Yamdagni et al. (1973), and Payzant et al. ( 1971, 1972). For some systems there is sufficient information to observe trends in factors governing cluster stability. As in the case of the positive ions, the most extensiveset of measurements is available for hydration. Also, considerable data are available for the clustering of HCl, SO,, MeCN, MeOH, and HCOOH to C1-. The same general tendency of the AH values to approach the AH of vaporization of the individual ligands at large cluster sizes is seen for these as with H20. Interestingly, however, data for MeCN bound to C1-, and water to I-, show that it is possible for a given bond energy to fall below the heat of vaporization at intermediate cluster sizes. This is understandable in the case of systems where the ion - ligand bond is comparatively weak and more than one binding site is available between ligands in the condensed phase. A rather interesting trend (Keesee et af.,1980c)in bond energies is seen for the case of the first ligand to a variety of ions where the trends for systems where data are available including SO,, water, and C02 show the inequality to be as follows: OH-> F - , O - > O ~ > N O ; > C l - > N O y > C O y > S O ~ = S O ~ = B r - > I -

(27)

The fact that the bromide ion is nearly equivalent to SO 3 is based on experimental hydration results (Arshadi and Kebarle, 1970) and is also supported by electrostatic calculations (Spears, 1972b, 1977;Keesee, 1979).The above inequality appears to parallel the order of gas phase basicity of the negative ions where the strongest bases exhibit the largest bond dissociation energies. Such a correlation has been suggested on the basis of similar studies of gas phase hydrogen-bonded complexes of the type A-. HR (Yamdagni and Kebarle, 197 1). In that work, the descending order of the heterolytic bond dissociation energies was found to correspond to the increasing order of the bond dissociation energies of A- - HR. On the basis of considerations in terms of acid -base concepts, the noted trend of negative ions appears to be a general one (Keesee et al., 1980c). An interesting comparison is that ofthe relative bond dissociation energies for a given ion with different ligands such as SO,, H20,and CO,. Hydrogen, sulfur, and carbon are the centers which are attracted to a negative charge. Water has a slightly larger dipole moment than sulfur dioxide but the quad-

134

T. D. Mark and A . W. Castleman,Jr.

rupole moment of water is repulsive when the dipole is attractive to a negative ion. Alternately, the quadrupole moment of SO, is attractive to a negative ion and carbon dioxide has no dipole but does have a significant quadrupole. Considering only charge - dipole or charge - multipole interactions, the bond strength for a ligand attached to a given ion would be expected to be in the order of H,O = SO,, but both being greater than CO, . For a weakly basic or large ion like I-, the order SO, > H,O > CO, is observed. However, as the ions become smaller or more basic, SO, bonds relatively more strongly than water. With 0: the enthalpy change for addition of CO, becomes comparable to that of H,O. Finally, for a small ion like 0-, the order SO, > CO, > HzO actually occurs. Interestingly, the mean polarizabilities for SO,, CO,, and HzOfollow the same order as their relative bind energies to small ions. Polarization energies are known to be relatively more important for smaller ions due to the ability of the neutral to closely approach the ion, and thereby become more influenced by the ionic electric field with the attendant result of a larger induced dipole. Qualitatively, consideration of the polarizabilities partially explains the increased bonding strength of SO, and CO, over that of water in clustering to smaller ions. In some cases, the bonds are strong enough to be considered as actual chemical ones instead of merely weak electrostatic effects. In other words, the bond may be of a covalent nature which is equivalent to stating that significant charge transfer occurs between the original ion and the clustering neutral. An example is OH-.CO, which is more properly considered as HCO,. Likewise, C1-.S02 has a rather strong bond energy for the first cluster addition, but a very weak one for the second addition, whereupon the first cluster addition may be thought of as forming a “molecule” over which the negative charge becomes relatively widely dispersed (Keesee and Castleman, 1980a,c). In terms of charge transfer, the electron affinity of the clustering neutral is a relevant factor to consider in assessing the relative bonding trends. SO, has an electron affinity of - 1 .O eV (Janousek and Brauman, 1979) and forms a stable gas phase negative ion, whereas the negative ion of water has not been observed (Caledonia, 1975).CO, has been detected in high-energy processes in which the linear neutral can be bent to form the ion although it is short lived and autodetaches (Paulson, 1970). Nevertheless, (CO,); is apparently stable (Hots and Compton, 1977; Stephan et al., 1983d; Rossi and Jordan, 1979).Collective effects are evidently important in the formation and stabilization of certain negative ion complexes. This point is further realized by recent observations of Haberland et al. (1983b), who have reported observations of the solvation of electrons by as few as 1 1 or 12 molecules. An examination of the bonding of neutral molecules onto ions has partic-

EXPERIMENTAL STUDIES ON CLUSTER IONS

135

ular value in elucidating the properties which govern stability. An interesting result is found by comparing the association of ammonia, water, sulfur dioxide, and carbon dioxide to both Na+ and C1-. The ion - dipole interaction is the most important electrostatically attractive force between an ion and a neutral molecule. Both sodium and chloride ions have closed electronic configurations and spherical symmetry, although the ionic radius of Na+ is considerably smaller. Consequently, with other factors being equal, a neutral molecule would be expected to bind more strongly to the smaller Na+. However, bonding and charge transfer are also important. Based on experimentally determined stepwise heats of association, it is evident (Castleman and Keesee, 1983b, 1984)that only sulfur dioxide binds more strongly to C1- than to Na+ for the first association step. Ammonia exhibits the largest difference between Na+ and C1-, with its binding being much weaker to the negative ion. The relative stability of the ion-molecule complexes for ammonia, water, and SO2are in reverse order for the two ions. In terms ofmagnitude, after the first ligand addition, the enthalpy change for the clustering of SO2onto C1- is much smaller than for Na+. Many of these trends are in agreement with expectations from electrostatic considerations. For instance water, sulfur dioxide, and ammonia have similar dipole moments. However, when the dipoles are aligned in the electrostatic field of the ion, the small quadrupole moments ofwater and the considerably larger one of ammonia are repulsive to a negative charge and attractive to a positive one. In the case of sulfur dioxide, the situation is reversed. Thus, the ion quadrupole interaction is consistent with the different ordering of the first bond energies for water, ammonia, and sulfur dioxide between the positive Na+ and the negative C1-. A number of authors have utilized thermochemical data to interpret trends and expectations concerning ions in liquids. The interested reader is referred to a few relevant references (see Schuster et a!., 1977;Kebarle, 1974; Castleman, 1979a, 1982a; Castleman et al., 1982a; Taft ef al., 1978; Watts and McGee, 1976; Murrell and Boucher, 1982). In the case of large clusters, a relationship has been observed for negative ions similar to that for positive ones, where the ratio of solvation enthalpy to the summed gas phase values of the cluster enthalpies is almost independent of systems beyond five or six molecule additions (Lee ef al., 1980a). The finding suggests that only five or six bond energies of a given ligand to an ion are needed to predict the solvation energy in the liquid phase. The importance of accounting for interaction among the ligands and solvent molecules was discussed in a recent article by Arnett ef al. (1972). Castleman ( 1979a) has considered this effect for the ion OH- solvated in water and clustered with CO, to form HCO,. Through a complete Born-

136

T. D. Mark and A . W. Castleman, Jr.

Haber cycle analysis, a direct analogy to the bond energies between OH- and CO, in the gas phase and interactions of OH- and CO, in the aqueous phase is made. A few Systems of cations bound to ligands have been investigated where one of the constituents composing the cluster is inorganic and the other is organic. The investigations include Larson and McMahon (1 983), Arshadi et al. ( 1970),Yamdagni et al. (1973e), Yamdagni and Kebarle ( 1971,1972), Wlodek et al. (1980, 1983a,b), Keesee et al. (1980c), Kebarle (1977), and Luczynski et al. (1978). As mentioned earlier, Kebarle (Davidson et al., 1979b; Yamdagni and Kebarle, 197 1) have reported a relationship between the basicity of A- and the hydrogen bond in the monohydrate A-.H,O complex which showed that the strength of the hydrogen bond increases with the gas phase basicity of A-. Similarly, it was found that the hydrogen bond in BH+.H20increases with the gas phase acidity of BH+. These relationships for the bonding of a water molecule in terms of the basicity of A- or the acidity of BH+ provided an explanation on a one-molecule solvation basis for the attenuation mechanisms observed in the solution phase. Thus, it was suggested that a substituent that increases the acidity of AH decreases the basicity of A- and therefore decreases the hydrogen bonding in A-.H,O. As with the cation clusters there is much to be learned about solutions of organic constituents.

VI. Other Properties It is outside the scope of this article to give a detailed review of some of the other gas phase properties of cluster ions, i.e., including reactivity, recombination, mobility, and diffusion. Therefore, this section will be only illustrative rather than exhaustive. Moreover, as indicated below, some of these properties have not been studied and much more work needs to be done before a general overview of the subject is warranted. A. REACTIVITY Association reactions, and their backward analog and declustering reactions (collision-induced dissociation), have been discussed already in Sections III,B and IV,B. Ligand switching reactions (see also Albritton, 1978; Dotan et al., 1978), in general (Bohme, 1982), proceed rapidly ( k 3 cm3/sec) when exothermic. Depending on the energetics of solvation, the successiveexchange may come to a halt at some intermediate stage of mixed

EXPERIMENTAL STUDIES ON CLUSTER IONS

137

solvation (e.g., see Smith er al., 1981). Here we will only consider reactive (cluster)ion - molecule reactions, including charge transfer, proton transfer, and ion - atom interchange processes. According to a recent review by Ferguson ( 1982), reactivity of cluster ions is an area in which very little research has been done. Studies have been reported by Good et al. (1970a,b), Puckett and Teague ( 197 1 a,b), Fehsenfeld et al. ( 197 1 a,b, 1976, 1978), Fehsenfeld and Ferguson ( 197 1,1973,1974),Young and Falconer ( 1972), Howard er al. (1974), Nestler et al. (1977), Smith etal. (1978b, 1980, 1981), Sieck (1978), Rakshit and Warneck (1979, 1980a,b, 1981), Bohme er al. (1979, 1982), Viggiano et al. ( 1 980), McCrumb et al. (1980), McCrumb and Warneck (1981), BohmeandMackay(l981),Hierl eral. (1981),Adamseral. (1982), Mackay et al. ( 1982), Fahey et al. ( 1982), Rowe et al. ( 1982), Kleingeld and Nibbering (1983), and Henchman er al. (1983). For information on the reactivity of Fe(C0): species, see Foster and Beauchamp (1975). The effect of clustering on the reactivity of ions is important for an understanding of ion chemistry in plasmas, as well as solvation chemistry in general (see McIver, 1980). Smith er al. (1978b) found that, for example, association of N, to N r does not seriously modify the reactivity of the N t except that it reduces somewhat the energy available for reaction. The most common mechanism apparently is direct charge transfer, usually followed by fragmentation with the nitrogen -nitrogen bonds in the reacting ions remaining intact [see also reactions of (CO,): observed by Rakshit and Warneck, 1979, 1980a, 198 11. Similarly, for ligand exchange (see above), some (nonresonant) charge transfer processes of OF(H,O), ,and reactions of hydrated hydronium ions, increased hydration of the reactant ion does not significantly decrease the reaction constant (Fehsenfeld et al., 1978; Viggiano er al., 1980; Fahey et al., 1982; Bohme, 1982). See also isotope exchange reactions studied by Smith et al. (1980) and Adams et al. (1982). In contrast, for some (resonant) charge transfer processes (Fahey el al., 1982) and in several ion-atom interchange and/or nucleophilic displacement reactions (Fehsenfeld and Ferguson, 1974; Fehsenfeld er al., 1976; Bohme and Mackay, 198 1; Hierl er al., 198 1; Mackay er al., 1982; Ferguson, 1982; Henchman et al., 1983), increased solvation of the reactant ion resulted in a significant decrease in reactivity (see also results obtained by Howard et al., 1974, for associative detachment of negative ions, in which Similarly, Bohme er the reactivities are also reduced by clusteringwith H20). al. ( 1979) found that stepwise hydration leads to a decrease of the reaction rate constant for proton transfer from H30+,e.g., to H,S with a concomitant change in AGO (see also Bohme, 1982; Bohme et al., 1982, for solvated proton transfer reactions). In case of nucleophilic displacement reactions (e.g., see Fig. 14) these striking results may be interpreted, according to Bohme and Mackay (198 I), and Henchman et al. (1983), in terms of the

138

10-0

T. D. Mark and A . W. Castleman, Jr.

I

1

1

1

I

1

I

1

\ n

I

I

I

n

FIG. 14. Reaction rate constants for gas phase nucleophilic displacement reactions of solvated anions with methyl chloride and methyl bromide as a function of the extent of solvation, after Bohme (1982).

qualitative model developed by Olmstead and Brauman ( 1977), and Pellerite and Brauman (1980). On the other hand, an enormous reactivity enhancement has been found by Rowe et al. (1982) for a new class of ion-catalyzed reactions between neutrals occumng in cluster ions in which the central ion does not form chemical bonds, e.g., the rate constant for the homogeneous gas phase reaction of N205with NO is smaller than cm2/sec,whereas the rate for this reaction on alkali ion cluster is increased at least seven orders of magnitude in the case of Na+ as central ion, and in excess of nine orders of magnitude in the case of Li+ (see also Kappes and Staley, 198lc). Other cluster ion reactions have been reviewed recently by Dillard ( I 973),

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Good (1 979, Smirnov (1 977), Smith and Adams (1980), Ferguson (1982), and Bohme (1982) (see also compilation of ion-neutral reaction rates by Albritton, 1978). See Cumming and Kebarle (1978) for a discussion of entropy changes in proton transfer reactions involving negative ions.

B. RECOMBINATION Although a large number of results is available concerning electron-ion and ion-ion recombination (Bardsley and Biondi, 1970; Mahan, 1973; Moseley et al., 1975b; Flannery, 1976; Smith and Adams, 1980; Brouillard and McGowan, 1983), until recently few reliable data were available on cluster ions. Smirnov ( 1977) and recently Smith and Adams (1980, 1982, 1983b) have reviewed ion cluster recombination data of environmental interest up to 1983. It was found by Smith and his colleagues (Smith et al., 1976, 1978a, 198lb; Smith and Church, 1977) that the binary rate coefficient for mutual neutralization is remarkably independent of the complexity of the recombining ions (- 6 X lo-* cm3/sec), more variation occurring with temperature than with size of the cluster ion. This is in contrast with electron - ion dissociative recombination (as studied for cluster ions by Kasner et al., 1961; Kasner and Biondi, 1965, 1968; Weller and Biondi, 1968; Gerard0 and Gusinow, 1971; Sauer and Mulac, 1971; Wilson and Armstrong, 1971;Plumber al., 1972; Leuet al., 1973a,b;Huanget al., 1976, 1978; Whitaker et al., 1981a,b; MacDonald et al., 1983) where, e.g., the results showed a marked increase in n for the cluster series H30+(H20) (reaching cm3/secat n = 6). Further data are required especially for large clusters. It is interesting to add here some recent studies on electron - Hirecombination yielding cross section functions for the electron-induced dissociation of H t and H; (Peart and Dolder, 1974; Mathur ef al., 1978, 1979). Moreover, E. E. Ferguson (personal communication) and, independently, Coffey and Mohnen ( 1971) have suggested that in some cases the product of the recombination of positive and negative cluster ions upon interaction might lead to zwitterions which would be electrically neutral overall, but have separated charges contained within. This proposal has been extended recently by Arnold and Fabian (1980) to include the growth of multiple ion clusters into a particle. Recent experimental results on clustering between nitric acid and water (Castleman et al., 198la; Kay et al.. 1981) indicate that ion pair formation does occur in a manner analogous to that anticipated by the above authors.

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Studies of the mobilities and diffusion coefficients of ions in gases are an important source of information on ion-neutral interactions, e.g., interaction potentials, collision frequencies, etc. Atomic and simple molecular ions have been extensively studied and results were reviewed some time ago by McDaniel and Mason (1973) and Loeb (1973). However, there is much less work on cluster ions, because the controlled production and detection of cluster ions require somewhat different experimental conditions than those usually available in drift tubes used for those studies. In addition, reactions occurring in the drift tube (e.g., clustering, declustering, switching) may obscure the true nature of the observed phenomenon [e.g., see for the case of (N,)f: Keller et al., 1965; Varney, 1968; Moseley et al., 1969; Varney et al., 1973; Sejkora and Mark, 1983; Sejkora et al., 1983; Mark and Mark, 19841. Recent cluster ion studies (available data up to 1973 have been reviewed by McDaniel and Mason, 1973, and by Loeb, 1973) on mobilities and diffusion coefficients include investigations by Young et al. (1970), Young and Falconer ( 1972), Bricard et al. (1 972, 1977), Elford and Milloy ( 1974), Huertas et al. (1974), Golden and Frain (1975), Burke and Frain ( 1975),Dee ( 1976),Bierbaum et al. ( 1976),Helm ( 1976a- c), Dotan et al. ( 1976, 1977a), Nestler and Warneck (1977), Nestler et al. (1977), Alger et al. (1978), Helm and Elford (1978), Rakshit and Warneck (1979), Hodges and Vanderhoff (1980), Takebe et al. (1981), Jowko and Armstrong (1982), Headley et al. (1982a), Sejkora et al. (1983), Girstmair et al. (1983), Schlager et al. ( 1983), Bohringer and Arnold (1983a), and Mark ( 1984c). As to be expected, mobilities (e.g., see Fig. 15) and diffusion coefficients decrease with the size of the cluster (see also Kilpatrick, 1971; Karasek et al., 1971), however, it should be pointed out that charge exchange reactions can reverse this trend [e.g., see results on (N,):for n = 1 and 2 by Varney, 1968; Moseley et al., 1969;Sejkoraetal., 1983;Girstmairetal., 1983)orresultson(He):forn= 1 to 4 by Helm (1976a). According to Schlager et al. (1983) and others, the observed zero-field mobilities of cluster ions are considerably smaller than the calculated Langevin mobilities. According to these authors this indicates that for cluster ions the polarization effects are relatively unimportant compared to elastic scattering processes (for a theoretical treatment see also Hagen et al., 1975). Moreover, according to Meyerett et al. (1980) and Keesee and Castleman ( 1983), not only the mass but also the effective radius of the ion is also expected to be a factor in determining mobility of large clusters. This could have implications on the common procedure (Bricard et al., 1977; Meyerett et al., 1980) of determining ion mass from mobility

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E /N (Td)

FIG.15. ReducedionmobilitiesofH,0+andH,0+-H20,(n = 0, 1,2)inHe(297K),after Dotan ef al. (1977a). 0.25 Torr (A&, 0.45 Tom (0,O).

spectra in the lower stratosphere(seealso ion mobility spectra measurements and size conversion by Hagen et al., 1975; Iribarne and Thomson, 1976; Northby and Akinci, 1978; Akinci and Northby, 1979; Akinci et al., 1980; Suck et al., 1983). Comprehensivereviews of the experimentaland theoretical work up to 1983 will be given in the forthcoming books by McDaniel and Mason ( 1984) and Lindinger et al. ( 1984).

ACKNOWLEDGMENTS This work was partially supported by the Fonds zur F6rderung der wissenschaftlichen Forschung (Austria). Moreover, the preparation of this articlewas made possibleby a sabbatical leave of T.D.M. as Visiting Professor in the Department ofchemistry, The Pennsylvania State University, with the support of the National Science Foundation, Grant ATM-82040 10. A.W.C. gratefully acknowledges the U.S. Department of Energy, Grant DE-AC02-82ER60055, the National ScienceFoundation, Grant ATM-8204010, and the Department of the Army, Grant DAAG29-82-K-0160,whose financial support enabled this article to be written. One of the authors (A.W.C) is especially indebted to Dr. Robert G. Keesee for helpful discussions during the course of writing this article, and both authors offer a special work of thanks to Ms. Barbara Itinger for the organizationofthe referencesand typing ofthis manuscript. T.D.M. gratefully acknowledgeshelpful discussions with Dr. Olof Echt, Univemitat Konstanz.

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