Reactions and properties of clusters

International Journal of Mass Spectrometry and Ion Processes, 118/119 (1992) 1 6 7 - 1 8 9

167

Elsevier Science P u b l i s h e r s B.V., A m s t e r d a m

Reactions and properties of clusters* A.W. Castleman, Jr. Department of Chemistry, PennsylvamaState University, Umversity Park, PA 16802 (USA) (Received 26 August 1991)

ABSTRACT The elucidation from a molecular point of view of the differences and similarities in the properties and reactivity of matter in the gaseous compared to the condensed state is a subject of considerable current interest One of the promising approaches to this problem is to utlhze mass spectrometry m conjunction with laser spectroscopy and fast-flow reaction devices to mvestigate the changing properties, structure and reactivity of clusters as a function of the degree of solvation under well-controlled c o n d m o n s In this regard, an investigation of molecular cluster ions has provided considerable new insight into the basic mechanisms of ion reactions within a cluster, and this paper reviews some of the recent advances in cluster production, the origin of magic numbers and relationship to cluster ion stablhtles, and solvatlon effects on reactions There have been some notable advances In the production of large cluster ions under thermal reaction conditions, enabhng a systematic study of the influence of solvatlon on reactions to be carried out These and other new studies of magic numbers have traced their ongln to the thermochemical stability of cluster ions There are several classes of reaction where solvaUon has a notable influence on reactivity. A particularly interesting example comes from recent studies of the reactions of the hydroxyl anion with CO 2 and SO2, studied as a function of the degree of hydration of OH Both reactions are highly exothermlc, yet the differences in reactivity are dramatic In the case of SO2, the reaction occurs at near the collision rate By contrast, CO2 reactivity plummets dramatically for clusters having more than four water molecules The slow rate is in accord with observations in the liquid phase

INTRODUCTION

Cluster science has undergone an explosive growth in activity during the last few years [1-11]. In view of the large number of basic problems to which a study of clusters may provide new insight, and because of the vast array of applied areas to which clusters relate, the field has become very broad. Hence it is no longer practical to give an overview of the entire subject. Herein, we confine ourselves mainly to the area of cluster ions, with attention to hydrogen-bonded systems. One of the main basic thrusts of current activities in cluster science is toward connecting the gaseous and the condensed states. This paper is directed * P a p e r p r e s e n t e d a t t h e 12th I n t e r n a t i o n a l M a s s S p e c t r o m e t r y C o n f e r e n c e , A m s t e r d a m , T h e N e t h e r l a n d s , 2 6 - 3 0 A u g u s t 1991. 0168-1176/92/$05.00

© 1992 Elsevier Sctence P u b h s h e r s B V. All r i g h t s r e s e r v e d .

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to elucidating the interrelationships of cluster ion structure, properties and reactivity as influenced by the degree of aggregation, namely the influence of solvation. There has been considerable progress in this area during the last few years owing to advances on several fronts. First, as expected, some of these are due to improved instrumentation. As discussed herein, improvements in the reflectron technique, in conjunction with theoretical concepts of the evaporative ensemble, now enable thermochemical properties to be deduced for cluster ions of much larger size than those that could be studied with previous techniques. From another aspect, the newly proven interrelationship between magic numbers, discontinuities observed in otherwise smoothly varying mass spectral distributions of cluster ions, with thermochemical stability and cluster stucture now enables new insight to be gained regarding the nature of the ion core in solvated systems. These concepts have led to the development of new "titration" techniques which also assist in unraveling cluster structure. Another area that has undergone significant advancement in the last few years is the method of producing large cluster ions under thermal reaction conditions. In conjunction with the well-developed flowing afterglow technique, the availability of thermalized clusters in this size regime now enables the influence of solvation on reactivity to be probed in detail at the molecular level. CLUSTER ION PRODUCTION AND STUDY There are two general experimental techniques that are utilized in the studies discussed in this paper. One of these involves multiphoton ionization of clusters produced in supersonic expansion and investigated using molecular beam time-of-flight techniques. The second is fast-flow reactor in which thermal energy rate constants of large clusters can be measured under welldefined reaction conditions. Investigations of cluster ion unimolecular and collision-induced dissociation are further contributing to an understanding of dynamical processes involved in energy transfer and reactivity [12-19]. In addition, ab initio calculations are contributing to an understanding of the structure and bonding of both strongly and weakly bound cluster ions. Molecular beam photoionization time-of-flight mass spectrometry The time-of-flight (TOF) mass spectrometer technique is experiencing a resurgence in popularity owing to the advent of pulsed lasers, which supply short durations of light and thereby lead to efficient ionization in a small volume, and improved fast-timing electronic circuitry. In a typical TOF mass spectrometer, either a two-element or alternatively a single-element accelerating field may be used in the region of ionization. This is followed by a field-free drift region, whereafter the ions are detected. Using the conventional TOF method,

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dissociation which occurs with rates in the neighborhood of 105-108 s -t can be investigated by either of two methods. One involves analyzing the peak shape (arrival spectrum) of ions created in a dual field accelerating Wiley-McLaren mass spectrometer [20]. In this situation a knee is observed [21] because the ions spend far more time in the first low-field region where ionization is initiated than in the second high-field region where the bulk of the acceleration occurs. An alternative method is to operate under single-field conditions and deduce rates from the shape of the late-arriving tail of the peak [22,23]. The most useful method of studying metastable cluster ion dissociation arising from evaporative dissociation employs a reflecting electrical field (reflectron). Although originally designed to enhance the resolution of the TOF method [24], a reflectron can also be employed to investigate dissociation in the field-free drift region, so that slower dissociation processes may be observed. Such experiments are performed by subjecting the cluster beam to multiphoton ionization, often using a tunable dye laser with various optical components that provide desired wavelength selection capabilities. The ions are accelerated in the accelerating field to several kiloelectronvolts, whereafter they enter a field-free region and then are electrically reflected and detected in a manner depicted in Fig. 1. With appropriate potentials applied to the reflectron grids, non-dissociating parent ions can be separated from those that dissociate while within the field-free region. A unique identification of these daughter ions can be accomplished by the time separation and by an energy analysis made with the reflectron. The separation of the parent and daughter ions is possible as a result of the loss in kinetic energy with essentially no change in velocity of the cluster ion packet upon dissociation; the parent species with greater kinetic energy have a longer path to the detector than do the daughter (dissociation) products. Supersonic expansion techniques including both continuous sources as well as pulsed jets are commonly used to produce beams of neutral clusters. In both cases cooling of the beam is accomplished through the conversion of the random thermal energy of a high pressure source gas into a directed beam velocity [25]. Since the latent heat of condensation, which is released during the clustering process, leads to internal vibrational and rotational heating of the aggregate, clusters do not generally attain temperatures as low as unclustered species. However, cooling collisions with an inert gas serve to reduce the internal temperature of the cluster and enable clusters to be produced that have sufficiently long lifetimes to be experimentally investigated. Fast f l o w reactors f o r study&g reaction kinetics

The flowing afterglow technique [26] and other related flow reactors such as the selected-ion flow tube [27] have provided a wealth of data on general

A.W. Castleman, Jr.~Int. J. Mass Spectrom. Ion Processes 118/119 (1992) 167-189

170

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A.W. Castleman, Jr.~Int. J. Mass Spectrom. Ion Processes 118/119 (1992) 167-189

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ion/molecule reactions [28,29], with some attention to ion clusters. A typical fast-flow apparatus is shown in Fig. 2; the flow tube is generally about 1 m long and 8 c m in diameter. Flow velocities are on the order of 102ms -~ and pressures in the reactor region are typically around 0.5 Torr. While most of the gas is pumped away, a small fraction is sampled through an orifice where the ions are mass identified and counted. Reactant gases are added uniformly into the flow, so kinetic data (or the approach to equilibrium) can be determined by varying the position, the rate of reactant addition into the tube, or the bulk flow velocity. Ions or cluster ions produced in a suitable source are introduced into the flow tube where they are thermalized by collisions with an inert carrier gas. Neutral reactant gas is added through a reactant gas inlet at an appropriate location downstream in the flow tube and allowed to react with the ions. Ions on the flow tube axis are sampled through a small orifice where they are mass analyzed with a quadrupole mass spectrometer and detected. A large-volume mechanical p u m p is used to maintain the flow velocity and p u m p away the bulk of the carrier gas exiting the flow tube. Rate coefficients, k, are determined by establishing pseudo-first-order reaction conditions in which the reactant ion concentration is small compared with that of the reactant neutral. Bimolecular rate coefficients are then obtained from the slope of the natural logarithm of the measured signal intensity I of the the reactant ion vs. the flow rate QB of reactant gas [26,30,31]:

I) In Too -

kz QB P v~ac kBT

(1)

Here I 0 is the reactant ion intensity at QB equal to zero (no reactant gas flow) and is usually constant over the course of an experiment, z is the reaction distance (from reactant gas inlet to sampling orifice), Qc the carrier gas flow rate, P the average pressure (or number density) in the flow tube, V~ the measured ion velocity, K B the Boltzmann constant, and T the absolute temperature. The velocity can be determined by applying a pulsed potential on the reactant gas inlet and measuring the arrival time of the resulting disturbance in the ion intensity. Where appropriate, termolecular rate coefficients [31] are determined from the slope of the apparent bimolecular rate coefficient plotted vs. the pressure P. THE STRUCTURES AND STABILITIES OF CLUSTER IONS

Techniquefor deducing cluster ion bond energiesfrom studies of dissociation dynamics The general versatility of the evaporative ensemble approach [32] for

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172

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deducing bond energies was first demonstrated [13,14] for ammonia cluster ions, though it is a technique of general applicability. Following laser ionization of neutral clusters, ammonia for example, internal ion/molecule reactions lead to ion clusters containing excess internal energy. These species, which comprise protonated ammonia in the example under discussion, undergo dissociation in the drift region of a TOF spectrometer through the process of evaporative cooling. A general cluster ion evaporative dissociation process can be expressed as IL, ~ IL,_ x + xL

(2)

Here, I designates the ion core (NH~- in the case of ammonia) and L the clustering ligand (e.g. NH3). The intensity and width of the metastable ion peaks carry information on the internal energy of the parent cluster ions. In the measurement of decay fractions of dissociating cluster ions, the parent and daughter ions are decelerated in the first region and reflected in the second field of the reflectron (see Fig. 1). As a result of metastable decomposition, the daughter ions have an energy of Ud = (MJMp)Uo (Uo is the birth potential and Md and Mp are the masses of the daughter and parent respectively); hence they do not penetrate into the reflective field as deeply as the corresponding parent ions. A critical aspect of deducing accurate kinetic energy release and rate measurements is to vary potential settings on the second and last grids of the reflectron to cause parent and daughter ions to follow the same flight paths. The integrated intensities of the peaks are then used to compute the decay fraction of the original parent cluster. The evaporative ensemble [13,14,32] approach assumes that each cluster ion has undergone at least one evaporation before entering the field-free region of the TOF mass spectrometer. The evaporative ensemble predicts that the normalized population of daughter ions at time t is given by D = (C,/72) In {t/[t o + (t - to) exp (-- ~2/C,)]}

(3)

where C, is the heat capacity of the cluster ion (in units of Boltzmann constant kB), and 7 is the Gspann parameter; it has been determined to be about 25, independent of cluster size [I 3,14,32]; to is defined as the flight time that the parent ion spends from the point of ionization to the last TOF lens, whereas t is the flight time that the parent ion spends from the last TOF lens to the first grid of the reflectron unit. At time t, the remaining population of dissociating cluster ions is given by P = P0 - D, where P0 is the population of parent ions at time to and D is the population of daughter ions at time t. For smaller clusters, however, the Gspann parameter requires modifications: 7'2 = 72/[1 - (7/2C,) 2]

(4)

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Replacing 7 with the modified Gspann parameter ?' leads to D = (Cn/7'E)ln {t/It o + ( t - to)exp(-?'2/Cn)]}

(5)

For systems comprising non-linear molecules, the heat capactiy of the cluster ion of size n is chosen to be 6(n - 1) (in units of the Boltzmann constant) by considering (only) the cluster modes. The binding energy of a molecule in a cluster ion of size n can be calculated using the equation

AE, = 7(Er)/[1 - (7/2C,)]

(6)

We have recently demonstrated [13,14,36] through a detailed investigation of ammonia clusters, whose bonding is well known from other measurements, that a T O F mass spectrometer equipped with a laser-based ionization system and reflectron enable quantification of the metastable decay fractions, the average kinetic energy released upon dissociation (in good agreement with that measured by other techniques [34]), and a determination of the thermochemical bond energies for the cluster ions as a function of size. Various statistical theories can be used to treat the data including those developed by Engelking (see ref. 13) and the others formulated by Klots. Employing other considerations due to Klots [35] for the case of larger clusters, we have demonstrated through more extensive studies of ammonia clusters [33] and xenon clusters [36] that the relative bonding energies of neighboring clusters can be deduced directly from measurements of the dissociation fractions employing the following relationships: D = 1 - (~W.)-Jln[1 + (exp(~W.) -- 1)to/t]

(7)

where

~W. = ~2(W./AE.)/[C.(1 - ~,/2C. + (?/C.)2/12...)2]

(8)

IV. = AE.{1 + [(dE/dAE.) k - 1](AE. - AE._,)/AE.}

(9)

(dE/dAE.), = (C./?)(1 + ?/2C. + (7/C.)2/12...)

(10)

A determination of the ratio AE./AE.+~ follows from application of these equations. Whereas for the case of very small ions the resulting values are somewhat sensitive to the choice of parameters in the equations, for those m excess of n = 10 the deduced bond energy ratios are insensitive to the choices of heat capacity and the Gspann parameter. The heat capacity C. is estimated from the bulk heat capacity and the required time ratio to/t is deduced experimentally.

Magic numbers The subject of magic numbers in clusters has been one of long-standing interest since early observation of pronounced intensity anomolies seen in the

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mass spectral distributions of molecular and atomic systems [1-3,7,37-44]. There have been extensive disagreements over the origin of these pronounced anomalies seen in the mass spectral distributions of clusters, with explanations ranging from transient intermediates and frozen-in fragments formed in a molecular beam, to especially stable neutral or ionic species. In this paper we draw on several examples from work conducted in our own laboratory which point to the origin of magic numbers in several important solvated systems. Applying these methods to the xenon system has been particularly revealing [36]. The results have shown a one-to-one correspondence between magic numbers observed in cluster mass spectra and the relative stabilities of the clusters in terms of their binding energies. This detailed study has for the first time established the origin of magic numbers, also showing that they appear at sizes slightly displaced from those of largest thermodynamic stability if a second nearest-neighboring cluster size is one which is particularly strongly bound. More recent studies of the ammonia system show that the protonated pentamer of ammonia appears as a magic number owing to its stability (see Fig. 3).

Influence of solvation on the composition of core ions Studies of ion solvation, structure and stability are also possible using the reflectron T O F mass spectrometer technique. In small hydrogen-bonded cluster ions, it is known that stability is due to the nature and location of the ligand molecules which bond to the central proton or protonated species, for example, (CH3COCH3)2 H+ [45], (CHaOCH3)aH3 O+ [46] and (NHa)4NH + [33,47,48]. It is interesting to consider the location of the proton in the general case for systems of widely varying proton affinity [17,19,49-53]. Let us consider, for example, a situation where the proton affinity of molecule X in a mixed cluster ion (NH3)n(X)m H+ is less than that of another such as ammonia, and compare it with the alternative case where the proton affinity of molecule X is larger than that of ammonia. The proton affinity of ammonia is 204.0 cal mol-1 and those of C H 3C O C H 3 , C H 3CN and CH 3CHO are 196.7 cal mol - ~, 188.4 cal mol - t and 186.6 cal mol - t respectively [54]. In all three mixed cluster ion systems, the intensity distributions show [52] that there is a maximum at n + m = 5. Results of metastable decomposition studies [53] of the mixed cluster ions were determined to be (NH3),(X)mH + ~ (NH3)~(X)m_~H + + X (NH3)~(X)m H+ ~ (NH3),_I (X),,H ÷ + NH 3

for n = 1 for n/> 2

(11) (12)

The results clearly indicate that NH~- is the core ion; this is as expected in view

176

A. W Castleman, Jr.~Int. J. Mass Spectrom. Ion Processes 118/119 (1992) 167-189 24 22

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Fig. 3. Relatwe binding energies for (NHs)nH+ deduced from a study of the metastable decay fractions and employingthe evaporative ensemble approach (see text). The literature values are taken from R.G. Keesee and A W. Castleman, Jr., J Phys. Chem. Ref. Data, 15 (1986) 1011. of their relative proton affinities. The four available hydrogen-bonding sites become occupied in order for the first solvation shell to become completed. The four ligands can include any combination o f ammonia and molecule X. The loss of an ammonia molecule resulting from the metastable decomposition for n ~> 2 indicates that X is more strongly bonded to the NH~- than is another N H 3. This is not surprising since all molecules considered here have higher dipole moments and polarizabilities than ammonia, which leads to them having a greater ion-dipole and ion-induced dipole interaction. Next, let us consider the case of pyridine (C5HsN) and trimethylamine (TMA) (CH3)3N [55] whose proton affinities are 220.Scalmol -l and 225.1 cal m o l - ~respectively, and larger than that of ammonia [54]. Metastable decomposition studies of NH3(CsHsN)m H÷ ( m - - 1-5) yield the following results: NH3(CsHsN),,H + ~ (CsHsN)m H+ + N H 3

for m < 4

NH3(CsHsN)m H+ ~ N H 3 ( C s H 5 N ) m _ I H + + CsHsN

(13) for m/> 4

(14)

For m < 4, the higher proton affinity of pyridine leads to its stronger bonding to the proton, whereby the a m m o n i a molecule is lost upon metastable dis-

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sociation. The loss of pyridine in the case of m >1 4 can be accounted for by the fact that a central NH4+ core ion is formed which provides four sites for hydrogen bonding to the ligands. Hence the structure is dictated by the net energetics of bonding. This finding is consistent with the previous proposed stable structure for the cluster ion (NH3) n(x)m H+ . Extensive studies conducted on mixed protonated clusters of ammonia and T M A show that the ion intensity distributions of (NH3),(TMA)m H+ [55,56] display local maxima at (n, m) = (1,4), (2, 3), (2, 6), (3, 2) and (3, 8). As before, the fact that the maximum ion intensity occurs at (n, m) = (1, 4), (2, 3) and (3, 2) indicates that a solvation shell is formed around the NH~- ion with four ligands of any combination of ammonia and T M A molecules. In the situation where the maximum of the ion intensity occurs at (n, m) = (2, 6) and (3, 8), the experimental results suggest that another solvation shell results which contains the core ions [H 3N-H-NH3] ÷ (with six available hydrogen-bonding sites) and [H3N-H(NH2)H-NH3] + (with eight available hydrogen-bonding sites). The observed metastable unimolecular decomposition processes [55] support the above solvation model. Through studies of the ternary systems comprising the foregoing bound with water, additional observations revealed the general validity of these concepts. Some structures pertinent to the present considerations are shown in Fig. 4. Of course, account must be taken of the fact that these systems are very floppy and one should not expect them to display a rigid structure. Studies of these systems made at higher degrees of aggregation have provided strong evidence [56] for ring-like structures for mixed neutral clusters (A)n" (M)m (m is both the proton donor and acceptor such as ammonia and water; M is only a proton acceptor such as acetone, pyridine and trimethylamine). For example, under a wide variety of experimental conditions, mixed cluster ions display a maximum intensity at m = 2(n + 1) when n ~< 5 for (NH3)n • (M)mH + , and m = n + 2 when n ~< 4 for (H20)n. (M)m H+ . These findings reveal that the cluster ions with these compositions have stable closed shell structures as discussed above. Despite the consistent trends, deviations are observed at certain cluster sizes. For example, a breakdown of the pattern occurs at n > 5 for the ammonia system and n > 4 for the water system, with the most intense peaks occurring for species with one molecule less than the expected pattern, i.e. m = 2 ( n + 1 ) - 1 when n = 6 for (NH3) . . ( M ) , . H + and m = ( n + 2 ) 1 when n = 5 for (H20), • (M)m H÷ • These results are compatible with suggestions that hydrogen-bonded ring structures form. As the clusters grow to larger and larger sizes, the structures evidently are more stable when they undergo rearrangement or ring closure.

d.W. Castleman, Jr./lnt. J. Mass Spectrom. Ion Processes 118/119 (1992) 167-189

178

÷

TMA :

TMA

H

I

/H"

T M & .... t I - - N - -

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I

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T T Ftg. 4. Structures compatible with the observed magic n u m b e r c o r r e s p o n d i n g to (A) H + (NH3)(H20)2((CH3)3N)6, (B) (NH3)5 • (TMA)12 • H + , (C) (H20)4 • (TMA)6 • H + .

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Studies of the structures of water cluster ions The encagement of ions by molecules is a well-known phenomenon in the condensed phase as shown by the pioneering work of Cram and Lehn [57] on ions interacting with crown ethers and cryptands. In the case of the gas phase clusters, heretofore there have been only three known examples where structures of well-defined geometry can enclose ions, namely water molecules encaging N H ~ , H3 O + and O H - . The "solvation" of NH~ by water clusters has been conjectured [58] on the basis of magic numbers observed in the mass spectra of mixed water-ammonia coexpansions. More extensive interest and attention has been given to studies of the encagement of H30 + by 20 water molecules, investigations which have extended over many years [37,44,59,60]. However, the structure of this species was only recently revealed [61] through titration experiments of the exposed hydrogen atoms which extend outward from the clathrate cage. Recently, we investigated [61] the structure of pure water clusters. Particularly interesting species in this regard are H ÷ (H20)20 and H ÷ (H20)21, the latter being the very prominent magic number in the water system. The first direct experimental evidence for clathrate structures of (H2 O), H ÷ (n = 20, 2 I) was obtained on the basis of a technique similar to the one described above which also allows the number of non-hydrogen-bonded surface hydrogen atoms to be counted. Neutral clusters (H20),. ((CH3)3N)m , prepared in a pulsed nozzle supersonic expansion, were ionized by multiphoton ionization and investigated with a reflectron TOF mass spectrometry technique. The magic numbers (n, m) in the ion intensity distributions of ( H 2 0 ) n " ( ( C H 3 ) 3 N ) m " H + served to reveal the stable hydrogen-bonding structures. For the mixed cluster ion (H20)20 • ( ( C H 3 ) 3 N ) m " H + , the intensity distribution was found to display an abrupt intensity drop after the magic number at (20, 11), while for (H20)21 • ( ( c n 3 ) 3 N ) m • H + the magic number appeared at (21,10). The findings gave experimental evidence for a stable clathrate structure (H20)20 H÷, being a pentagonal dodecahedron with the proton residing on the surface, while for (H2 O)21H +, the H 30 + ion is encaged inside the clathrate structure of (H2 0)20; the latter structure provides a total of ten hydrogen-bonding sites for (CH3)3N. An analogous anion species is inferred for clusters of O H - with water [60], and this also shows prominent magic numbers for the 20-mer. Recently we reported [62] what we believe to be the first known example of the encagement of an atomic ion in a cluster to form a gas-phase clathrate, in particular Cs ÷ contained with a complex composed of 20 water molecules. During the course of the studies, evidence was also acquired for the encagement of Cs ÷ by other (distorted) clathrates involving 18, 22, 24, 27 and 29 water molecules.

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INFLUENCE OF SOLVATION ON KINETICS

There are several classes of reaction where solvation influences reactivity. These include (a) site-specific solvation blocking, (b) solvation effects on the nature of the core ion reaction site, (c) solvation effects on exothermicity (or exoergicity), and (d) solvation influences on the energy barrier to reaction. Investigations of the influence of clustering on the sites of energy absorption and the ensuing reaction mechanisms are particularly pertinent in further elucidating these classes. Some specific examples are given for the first two in what follows.

Site-specific solvation blocking of a reaction site It has been recognized for a long time that, following the ionization of one moiety within either a single component or mixed cluster system, internal reactions proceed whose study can often facilitate the unraveling of similar processes in the condensed phase. The observed mechanisms also frequently bear direct analogy to those observed for isolated gas-phase ion/molecule reactions; indeed, this analogy has provided a useful starting point for predicting the possible stable product ions resulting during the course of the dynamical events. In beam experiments, evaporative dissociation typically dominates at long times and current interest centers on the dynamical role discussed in an earlier section. Most cluster systems comprising (at least partially) hydrogen-bonded constituents undergo evaporative dissociation processes following ionization, but some display other rather interesting solvation-driven competitive reaction channels [63-70]. Let us consider, for example, the case of clusters composed of methanol. Following multiphoton ionization (MPI), neutral methanol clusters are also found [63-65] to undergo a well-known ion/molecule reaction which leads to the production of protonated clusters and the evolution of C H 3 0 . In accord with observations for most other systems, these clusters undergo metastable evaporation rates which decrease with time after the initial ionization event and, for a given observational time window, display an increase in rate with cluster size. The cluster ions, H ÷ (CH3OH)n, also undergo other intracluster reaction pathways, some of which show a dependence on the degree of aggregation. For example, the following reaction has been identified for n >~ 7: [H + (CH3OH)n]* --* H + ( H 2 0 ) ( C H 3 O H ) . 3 "hI- (CH3)20 -1- CH3OH

(15)

while the loss of water from the protonated methanol dimer ion occurs via the dehydration reaction H + (CH3OH)2 --. (CH3)2OH + + H 2 0

(16)

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a process requiring an induction time of at least several tenths of a microsecond [64]. Analogous water elimination reactions are not observed for the parent cluster ions larger than n = 2. Interestingly, recently reaction (15) has been found to occur also for n/> 7 in thermal reaction experiments [71] and is evidently due to solvation effects. In the case of these large clusters, H3 O+ is solvated more strongly by methanol than is protonated dimethyl ether, (CH3)2 OH +. A significant difference in reactivity with cluster size is observed; methanol clusters for sizes n = 4-9 lose dimethyl ether on a longer time scale while clusters with n >/7 also undergo prompt loss of C2 H 6 0 u p o n ionization. Most surprisingly, some analogous reactions also occur in the presence of alkali metal ions [72,73]. Some direct evidence of how the presence of a solvent can influence a reaction has been obtained from data for the acetone system, where the presence of an H 2 0 solvent can dramatically affect the course of one of the (dehydration) reaction channels [66]. Observed major cluster ions resulting from prompt fragmentation following multiphoton ionization include [ ( C H 3 ) z C O ] m - H +, m = 1-15, [ ( C H 3 ) z C O ] m . C2H3 O + , m = 1-17, and [(CH3)2CO]m • CH3~, m = 1-10. In a time window of a few tens of microseconds, all these three classes of cluster ions unimolecularly decompose, losing only one acetone monomer. Interestingly, a reaction corresponding to the dehydration of [(CH3)2CO]m " H + and leading to the production of [(CH3)2CO]m_ 2 • C 6 H l l O + is observed for m = 2-6. The,most striking finding is that the presence of water molecules in a cluster suppresses this dehydration reaction. Experiments conducted to study the influence of the presence of water in the cluster on the dehydration reaction were very revealing [66]. The findings strongly suggested that the presence of water inhibits the dehydration mechanism of [(CH3)2CO],," H + cluster ions. This finding not only clarifies the probable reason for the discrepancy between several earlier studies, but most importantly, provides evidence of another example for the influence of a solvent on ionic reactions in clusters. Influence of solvation on ion core reaction sites

Thermal reaction techniques enable a quantification of the influence of solvatlon on reactivlties [67,74-78]. One particular reaction which is a good example of how solvation can affect the nature of a core ion reaction site comes from a study [74] of the interaction of O H - with CO2. The gasphase reaction between the individual species is very exothermic (AH°= - 88 kcal m o l - 1) and can only take place by a three-body association mechanism. The reaction proceeds very slowly in the liquid phase and has been calculated [79] to have a barrier of about 13 kcal m o l - i. In biological systems,

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182 1

2

.

0

I

1

.

0

,oop\ 9op ¢ 8.oi'-/

b

/

~

\

4.01-/

0

~

-~

2

4

6 8 I0 Cluster Size n

12

14

Fig. 5. Cluster size dependence of the rate constants for the reactions of CO2 with the large hydrated amons at T = 130 K: r-l, experimental values for O H - ( H 2 0 ) , ; - - , calculated values

for OH- • (H20).. the reaction rate is enhanced by about four orders of magnitude through the enzyme carbonic anhydrase. Recent studies carried out in our laboratory provide detailed information on the influence of hydration on the reaction kinetics, and are supportive of the suggested role played by the enzyme in facilitating this reaction which is so importap.t in respiration. Typically, hydration can have a pronounced effect on reaction thermodynamics, but in the case of O H - ( H 2 0 ) , the clustering of a number of water molecules is still insufficient to cause the reaction to become endothermic. In fact, owing to the formation of very stable products, namely HCO3 ( n 2 0 ) m , the reaction enthalpy is still very exothermic even if as many as three water ligands were to become replaced by one CO2 molecule. Thus an explanation for the discrepancy shown in Fig. 5 between the experimentally measured rate constants and theoretically predicted values based on a parameterized trajectory theory [80] must be attributable to the reaction kinetics. A general formulation of the reaction can be written [74] in terms of a Lindemann-type mechanism:

kt

CO2+ OH- (H20)..--~--- {OH-(H20).(CO2)}*

(17)

{OH-(H20).(CO2)}* + He k,, OH-(H20).(CO2) + He

(18)

{OH-(H20),(CO2)}*

(19)

kr, HCO3 (H20)m + (n - m)(H20)

The intermediate reaction complexes can undergo unimolecular dissociation (k_,) back to the original reactants, collisional stabilization (ks) via a third-

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183

body, and intermolecular reaction (kr) t o form stable products HCOj-(H 20)m with the concomitant displacement of water molecules. By using a steady state approximation on the concentration of {OH-(H20),COz}*, the experimentally measured rate constant, kexp, can be related to the rate constants of the elementary steps by the following equation: kex p = k I {ks[He] + kr}/{k_ 1 + ks[He] + kr}

(20)

Equation (20) can be simplified according to four possible limiting situations, but for the experimental conditions used, the following applies [74]: k i >> kr and ks[He], and k r >> ks[He], then kexp = klkr/k_~

(21)

The experimental findings are of value in unraveling the details of the enzymatic hydrolysis dynamics of CO2. In the basic solution, CO2 can react directly with CO2 to form HCO3 : CO2(aq) + O H - ( a q ) ko. , HCO3 (aq)

(22)

The second-order rate constant ko._ has been measured to be 8.5 × 103 M -~ s -~ [81], while the rate constant for the enzymatic hydrolysis of CO2 has been measured to be 7.5 × 107 M - t s- l [82], or 1.2 × 10- ~3cm 3s- ~in the units employed by gas-phase chemists, which is about four orders of magnitude larger than ko._. By contrast, the gas-phase collision limit for CO2 with a large anion is about 10-t°cm3s -1 and the experimentally observed value decreases with increased hydration. It has been found [83] that the key aspect of the enzyme catalysis is the presence of a zinc atom which breaks a water molecule into H + and O H - that can then react rapidly with CO2 to form HCO3. It is interesting to compare the reactions of CO2 and water clusters of O H with the results of the analogous reactions involving SOz [78]. Both reactions are highly exothermic. Trends in hydration are not much different from that for the CO2 case, at least for small clusters. Nevertheless, as seen in Fig. 6, SO2 displays a very large reactivity vs. cluster size over the full range investigated. Indeed, the trends are in good accord with computations made employing results of trajectory studies made by Su and Chesnavich [80]. Measurements made in our laboratory, as well as those by others, reveal that SO2 interacts with bare O H - via an association reaction. However, the reaction mechanism changes from one of association to switching upon hydration: O H - (H20). + SO2 --* HSO3 (H20),. + (n - m)(H20)

n ~> 1

(23)

A.W. Cast&man, Jr.~Int. J Mass Spectrom. Ion Processes 118/119 (1992) 167-189

184 36

~

3.2

,nil 2.8 io24 -*20 o~

1.6

8 i.z

~os 04

0

2

4

6

8

I0

12

14

16

18

Cluster Size n

Fig. 6. Dependence o f rate constants o n cluster size for the reactions o f O H - ( H 2 0 ) . with SO2 at T = 135 K.

With additional water ligands bound to the O H - , the reaction enthalpy becomes more positive owing to the net stabilization of O H - by water molecules. For example, in the case where all the water ligands are replaced by an S02 molecule during the reaction O H - (H20). +

SO 2 ~

HSO3 + n(H20)

(24)

the reaction enthalpy switches from being exothermic to being endothermic between n = 3 and n = 4. In hydrated clusters, only reactions leading to partial replacement of the water molecules maintain thermodynamic exoergicity: OH-

(H20)4

-k- S O 2 ~

HSO~- (H20) + 3(H20) + 46.6 k J m o l -j

(25)

Our observations are in accord with this fact. In the present experiment, even when n = 59, the anionic clusters O H - (H20), are still found to react very fast toward SOz, approaching the gas collision limit of about 10 - 9 c m 3 s - l . Since SO2 is a strong reductant in basic solution [84], no kinetics data are directly available for the reaction: SO2(aq) + O H - (aq) ~ HSO~- (aq)

(26)

However, the rate constant for the following reaction has been measured [85]: SO2(aq) + H 2 0 ( a q ) ~ HSO3 (aq) + H + (aq)

(27)

It is 3.4 x 106M-is -1 (5.6 x 10-15cm3s-1), which is about ten orders of magnitude faster than the comparable reaction with CO2. The rate constant for reaction (26) is expected to be larger than

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185

3.4 x 106M -I s -l, not only because reactions involving ions usually have much smaller activation energies than those involving only neutrals, but also because the very stable products HSO3 (H20)n are formed. The observation that association becomes the dominant reaction channel at large cluster sizes in the present experiments indicates the possibility of formation of the products OH-(H20)n(SO2). It is interesting to note that in solutions the SO2(OH-) form exists and the [SO2(OH-)]/[HSO3] ratio is about five at 20°C [86]. Usually, hydration of the negative ions will make the reactions more endothermic owing to the stabilization of the reactant ions. However, since the products of the reaction between SO2 and X - ( H 2 0 ) , are so stable, the reactions can maintain their negative enthalpies by "boiling off" a certain number of water molecules from the products. A factor which may contribute to the appreciable interaction between SO2 and the hydrated anion clusters is the large attractive quadrupole moment (Q,~ = 1.3 e.s. cm 2) [87] to the negative ions. CONCLUSION Multiphoton ionization studies of clusters utilizing a reflectron technique have enabled investigations of magic numbers, cluster metastability, energy release and bonding from which inferences of structure can be deduced. Recent investigations of mixed clusters of water and ammonia individually with a wide variety of molecules have provided insight into the solvation structure and the nature of the complexes formed upon proton solvation. The observed magic number patterns display expected ring closure at increased degrees of cluster aggregation. The findings have provided definitive information on the structure of water clusters, showing a cage-like pentagonal dodecahedron for 20 water molecules bound to a proton, with the proton "sitting" on the clathrate lattice. In the case ofn = 21, the H30 + ion becomes solvated at the center of the clathrate cage. The findings pertaining to the interrelationship of structure and reactivity make interesting comparisons and provide considerable new insight into evolutions from the gas to the condensed state. Recent advances in the production of large clusters under thermal reaction conditions now enable the changing reactivity of ions as a function of degree of aggregation to be investigated. Most importantly, it has been shown that work in this area can be used to elucidate the influence of solvation on reactivities. In other cases, where the role of the ions is only one of a spectator, we may expect that the clusters will be useful as prototype systems of value in unraveling the mechanisms of "surface" reactions. While small and medium sized clusters begin to exhibit properties associated

186

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with the condensed state, it is a mistake to expect that the observed reactions and properties of clusters and condensed matter will in most cases be identical. Indeed, clusters may be more appropriately viewed as a "new state of matter", termed the fifth state by some researchers. The investigation of trends in reactivity and property changes as a function of degree of aggregation serves to bridge an understanding of the gaseous and condensed phases, and new insight develops in cases where there are observed similarities as well as differences. From the perspective of cluster science, it is those cases where new and different behavior is displayed that are most interesting, providing new challenges to theorists and experimentalists alike. The field continues to expand and we can expect that it will remain an active one for many years to come. ACKNOWLEDGMENTS

Financial support by the U.S. Department of Energy, Grant Nos. DE-FGO2-88-ER60658 and DE-FGO2-88-ER60668, the National Science Foundation, Grant No. ATM-9015855, and the U.S. Environmental Protection Agency, Grant No. R-817437-01-0, is gratefully acknowledged. REFERENCES I 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

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