Advances in research on clusters of transition metal atoms

Surface Science 156 (1985) 8-35 North-Holland. Amsterdam

ADVANCES ATOMS

fN RESEARCH

R.L. WHETTEN,

ON CLUSTERS

D.M. COX, D.J. TREVOR

OF TRANSITION

and A. KALDOR

Corporate Research - Scrence Laboratories, Exxon Research and Engineering East. Clinton Township, Annandale, New Jersey 08801. USA

Received

10 August

1984; accepted

for publication

METAL

6 September

Company,

Route 22

1984

This article reviews research on the physical and chemical properties of clusters of transition metal atoms, with special emphasis on recent advances made through the new molecular beam and flow techniques. Following our introductory section describing motivation for the study of metal clusters, we outline the major synthetic techniques: Matrix isolation or suspension and free-jet or cold flow condensation of laser-vaporization plasmas. Before discussing the new experiments based on these methods, we review physical and chemical models of transition metal clusters. These models are adaptations of bulk or molecular descriptions of metals or metal containing compounds, and are concerned with the prediction of electronic structure and elementary excitation in clusters, magnetic order and structural rigidity, or chemical reactivity and perturbations. Within this framework we survey recent experimental measurements and their interpretations. Highlighted examples include: (1) the precision measurement of rovibronic or magnetic properties of dimers and trimers as tests of computational electronic structure approximations, (2) measurements of electron binding energies of Fe and Ni clusters as a probe of the molecular versus bulk behavior of these systems, (3) the current status of experiments on the optical properties of small metallic particles, (4) magnetic moment measurements on Fe clusters as critical tests of the molecular theory of metallic and magnetic behavior, (5) discussion of possible effects of cluster melting, and the melting of Au clusters, (6) the facile size-selected reactions of free Fe and Ni clusters with H,, 0, and CO, and (7) the evidence for new chemistry in the adsorption of hydrocarbons on free Pt. Ir and Ru clusters.

1. Infliction TechnologicaI advances in the last decade have made possible the intensive exploration of a new realm of matter, one which has now aroused widespread attention for a variety of reasons. This realm is given various names: clusters, small particles, microcrystals, depending on one’s point of view. As motivation it suffices here to mention that our new ability to explore this intermediate range of matter causes us to reassess our understanding of its limiting forms, molecules or atoms versus bulk solids and liquids. In particular, to some extent the molecular or atomic sciences and condensed-matter sciences have devel-

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oped independently; in many ways the central ideas of these fields have not been reconciled and are presently in collision. Their reconciliation or unification is essential for further significant advances. Current cluster research offers an opportunity to resolve this situation by “seeing both ends from the middle”; from this effort we expect to undeistand and predict not only the immediate cluster behavior, which is considered of great technological significance in its own right [l], but also to obtain a clarification of the relationships between molecular and condensed matter. This implicit goal has stimulated many research programs in recent years. As an example, the recent synthesis of a molecular view of melting (and, conversely, an extended matter view of molecular fluxionality) through cluster models is an indication of what may be achieved [2]. The subject of this review is recent research on clusters (defined [3] as having < lo3 atoms, or approximately < 25 A diameter) of transition metal atoms, or sub-microscopic fragments of bulk d-block metals. At the risk of stating the obvious, it is useful to summarize why transition metal clusters are of sufficiently special interest to deserve a classification of their own. This is certainly not the result of experimental knowledge of the properties of the isolated clusters; such knowledge has been virtually nonexistent until recently and remains very sparse even at present. Rather the special interest derives from expectations based on the unique role played by d-block elements in molecular, surface and solid state sciences. This relationship may be viewed as follows. (I) Organo-transition metal chemistry or ligated clusters. The past two decades has seen an explosion of interest in the properties of inorganic and especially organometallic transition metal complexes, which are distinguished by their highly variable oxidation states or modes of bonding and special optical and photochemical properties [4]. This variable oxidation state behavior is of critical importance in biochemistry [5]. More recently, a large effort has been made to synthesize and characterize ligated clusters of metal atoms, the analog of which are essentially unknown in main-group elements [6]. (2) Surfaces and thin films. The bulk surfaces of transition metals have long been noted for their uniquely high and metal-specific catalytic activity for transformations of organic molecules [7]. They are also well known for their optical properties, although with limited exceptions these are shared by mainblock metals [8]. In addition one must take note of discoveries on the electronic properties of transition metal thin films [9], and also the large enhancement of certain chemical and optical activity of roughened or finely dispersed surfaces [lo], both of which point to unusual properties of small transition metal clusters. (3) Bulk metals, their complexes and alloys. Elemental ferro- and anti-ferromagnetism are the properties only of certain d- and f-block metals [ll]. Many other interesting bulk phenomena, such as superconductivity, are found not to

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be the exclusive domain of transition metals, but see their fullest range among these materials and their complexes and alloys. On the basis of these observations it is thus highly reasonable to expect that the study of transition metal clusters will play a unique role in the emerging cluster sciences. We here describe some new results already suggesting the fulfillment of this promise. This article therefore has the following scope. We first (section 2) review the synthesis of isolated metal clusters. These techniques lead to complementary classes of physical and chemical measurements. We then list some of the guiding predictions or hypotheses (section 3); this should not be construed as a theory of transition metal clusters but rather as a set of more-or-less well-defined and mutually exclusive models based on guesses about what underlying physical constraints will be most important in determining cluster properties. These working hypotheses can then be tested against the still-limited experimental results, which are discussed in section 4. This leads to a summary of the current status of transition-metal cluster research and one possible prospectus for the near future.

2. Synthesis of transition metal clusters There exist several methods for the preparation of transition metal clusters. each having a greater or lesser degree of generality, specificity and resulting product isolation. This last feature of the synthetic method in particular often determines what measurements may be performed and can even play a role in their outcome. It may first be asked to what extent a ligated cluster having internal metal-to-metal bonds resembles a free or surface-supported metal cluster. Much attention has been given to the suggestions put forth most notably by Muetterties and co-workers that such large organo-transition metal clusters be regarded as models for transition metal surfaces [12,13]. This has led to some exploration, but thus far the results must be skeptically viewed as unencouraging [14]; one explanation for this is the large difference in electronic structure of the (l&electron-type) closed-shell, low-multiplicity ligated clusters as compared with the anticipated very open-shell and high state-multiplicity of bare clusters [15]. Thus at present one must regard the electronic, structural and chemical properties, in short the very nature of bare metal clusters and nearly-saturated ligated clusters as unlikely to be similar, with greater similarity the higher the degree of unsaturation. Since work on ligated clusters is quite well reviewed [16,6], it is not further discussed here. Also worthy of mention are techniques for thermodynamic measurements on small clusters, which have accumulated a large and useful body of information on bond energies [17]. Of particular note are the pioneering efforts of

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Bauer and co-workers on the nucleation kinetics of small metal particles [18]. Inasmuch as these methods do not lead to measurements of other cluster properties, they are not regarded as preparation techniques here. The remaining synthetic techniques, those which have allowed the highest information content experiments, may be characterized by three main criteria: (i) generality, the extent to which the technique can produce clusters of any transition metal, and any size cluster desired; (ii) specificity, the extent to which one an select a narrow distribution of cluster sizes (the ultimate being the “pure” case where each cluster has the same number of atoms); specificity may also be taken to refer to the range of internal energies of the clusters, with low or controlled temperature most desirable; and (iii) degree of isolation, referring primarily to the chemical inertness of the cluster environment. No technique yet developed is successful on all counts; in particular it has been difficult to devise a general but specific technique. Still, this problem is partially overcome by making only cluster-size-specific measurements and determining additionally the distribution of cluster sizes. The synthetic techniques are divided into three classes: (1) Matrix isolation. The matrix isolation technique [19] typically codeposits hot metal atoms and an inert gas on a cold window. The embedded atoms aggregate when the matrix is irradiated or slightly thawed. This method is general, because metal atoms are easily produced, and by controlled irradiation a range of size distributions can be produced. Because the matrix is optically transparent a variety of optical measurements (but usually absorption and resonance-Raman spectroscopy) can be performed. By codepositing a reactant gas it has been demonstrated that chemical reactions can be studied by this technique [20]. A disadvantage has been that, while possible in principle, no measurements of the actual size distribution of clusters has been achieved. Closely related techniques involve embedding larger clusters in a porous material such as zeolites [21], or in a gel [22]. It appears that these techniques are capable of narrow size distributions relative to the mean size produced. In the case of a gel, the actual (dimensional) size distribution of large clusters (and small particles) has been characterized by transmission electron microscopy [22]. A major concern of these methods is the relatively unknown chemical inertness of the support. (2) Metal cluster beams and gaseous flows. The systematic application of gas-phase and molecular beam techniques in transition-metal cluster research is quite new, but derives from the earlier developments of Schumacher and co-workers [23] at Beme (see also the note of Knight et al. [24]) on the volatile alkali metal clusters. These efforts produced first effusive and later cooled supersonic beams of clusters which were size-specifically characterized by the mass-resolved photoionization technique. The remaining obstacle to producing transition metal cluster beams and flows was to somehow combine intense sputtering sources to vaporize these refractory metals with a means of cooling

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and condensing the resulting plasma. This problem was solved at about the same time by Dietz et al. [25] and Bondybey and English [26]. The former used the pre-expansion region of a high-pressure pulsed nozzle to quench the laser-produced metal atom plasma and form a metal cluster free jet, while the latter technique is identical except that the high-pressure inert gas flow is continuous and confined. The former technique yields an intense beam of metaf clusters amenable to characterization as described by Schumacher et al. [23]. Mass-specific information from the confined flow technique requires passing the flow into the inlet of a mass-spectrometer source chamber as described by Riley et al. [27]. The production of intense collimated beams of transition metal clusters represents an immense advance, because it allows the application of powerful molecular beam techniques to the study of these unique systems [28]. A number of problems remain, however, since many measurements require either a pure sample or limited size distribution. In principle this distribution could be controlled by the sputtering and quenching conditions, but this has up to now given only rough variations. In addition the question has been raised whether the larger metal clusters so produced are internally cold [29]; it should be noted that a large heat of formation must be removed to leave cold clusters. It appears that both beam and flow synthetic techniques are readily adaptable to studies of chemical reactions of metal clusters, and preliminary reports have appeared describing these methods [30,31]. (3) Substrate-supported clusters. Many of the methods used to study extended material systems, including those which directly measure cluster geometry and electron densities, are not presently suitable for molecular beam methods, and some have vacuum requirements incompatible with matrix isolation synthesis. An alternative is to prepare the clusters on relatively inert nonvolatile surfaces under vacuum. Unfortunately the simplest method, that of atomic deposition and aggregation, produces a wide size distribution of clusters and particles, i.e. this is not yet a selective synthetic method [32]. Nonetheless, a series of investigations of the photoemission spectra of large Pt 1 and Pd, clusters has been reported, with results on the evolution of band structure in these small metallic systems [33]. This method has thus shown its usefulness, and will undoubtedly see significant improvements in selectivity. This cursory discussion of synthetic techniques illustrates the advances accomplished and remaining difficulties in the development of a general but selective method for the preparation of isolated transition metal clusters. While it may be that eventually one class of synthetic methods will emerge and surpass all others, for the present it is evident that the techniques have complementary limitations. Thus while a certain cluster may be perturbed by its rare gas matrix relative to the gas phase, the variation of this perturbation with rare gas host may provide invaluable information on its physisorption characteristics, an important electronic property. Its matrix resonance-Raman

R. L. Whetten et al. / Advances in research on clusters

spectrum may be at present the only information on its vibrational but a beam measurement will be required to measure its ionization and magnetic moment, and a flow system may be best to learn chemical reaction rates.

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binding, potential about its

3. Models for describing transition metal clusters In formulating models for the description of transition metal clusters it should be realized that because of their complexity and diversity, specific agreement with ab initio theory cannot be a goal. It is much better that different semi-empirical schemes based on physical and chemical models with well-defined assumptions be developed for direct contact with experimental results, leaving ab initio methods to eventually rationalize the success of a semi-empirical model. Yet when one faces the current wave of experimental measurements, it is found that a large number of models exist with which to compare; some are qualitative, but most have varying levels of quantitative complexity. And each is based on some assumption about which of the many possible physical factors underlying anticipated cluster behavior is of overriding importance. It is worthwhile to consider briefly the origin of these models: We know that as clusters become large the effects of the edges or surfaces becomes negligible; thus we expect large clusters to show characteristics of bulk behavior of the corresponding metal or alloy. On the other hand, even large clusters of hundreds of atoms must have most atoms at or very near the surface, so assuming the cluster is thick enough and that the effect of surface curvature is sufficiently small, we expect the cluster properties to resemble that of the corresponding surface. At the opposite extreme, one expects the chemical behavior of the smallest clusters to be governed by the effects determining the stability of organo-transition metal complexes, i.e. a tendency toward saturation of open coordination sites [4]. The electronic properties of small clusters may be thought of as related to thin films, governed by large quantum size effects [9]. Finally, on dissociating the cluster one obtains the corresponding atomic system, with its relatively complicated valence electron system serving as a basis for the cluster’s electronic and magnetic properties. Each of these limits or asymptotes is already described by some model, which, when the cluster is sufficiently near it, may be taken as given or with slight modifications to explain metal cluster behavior. In particular, most quantitative models applied thus far are adapted from solid state theory with the assumption that if the cluster has the same phase or geometry, then its properties will converge to those of the corresponding bulk material. Thus many of the computational papers written thus far on transition metal clusters have been concerned with the criteria for and the rate of this convergence [34].

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In this way it is hoped to learn at what stage the bulk metal or surface can be used as a model for clusters; turning this question around yields a problem considered by others to be of greater importance, namely, at what stage can a cluster be used to model a bulk metal, so that one can speak of a “molecular theory of metals” [35]? We will not survey all possible approaches to modelling cluster behavior: instead we will discuss those general and strong predictions which can be tested by experiments. These predictions are divided into three classes: (1) electronic structure and elementary excitations; (2) magnetic properties and structural rigidity, and (3) chemical reactivity and perturbability. 3.1. Electronic structure and elementarv excitutions The largest number of theoretical models of transition metal clusters naturally are concerned primarily with electronic structure and binding; one can cite an array of techniques used ranging from simplest semi-empirical extended-Huckel or neglect-of-overlap models [36,37] through SCF-HF [38] and SCF-X(Y-SW [39] approaches and finally for smaller clusters to SCF-HF-CI [40] and density-functional [41] methods which in principle can be made exact. In practice, the large number of valence electrons makes drastic approximations necessary for all but the dimers. In the absence of definitive experimental results calculations could be carried out largely without regard for which approximations could be safely made in treating a real cluster. Recently, a better understanding of the effect of these approximations has been achieved. A uniform prediction of all methods is that many aspects of bulk metallic behavior, in particular the formation and characteristics of a band structure. should be realized for quite small clusters (4-20 atoms) [42]. Two approaches have been used to obtain these results: (i) calculate the total electronic energy at several internuclear configurations to determine the equilibrium geometrical structure, or (ii) assume the bulk geometry and calculate the band structure for a number of closed-shell sizes. In either case the characteristic electronic structure of the bulk is said to appear by 10 atoms, and this would presumably result accordingly in recognizable photoemission spectra. Aside from this overall point of agreement, the rates of convergence of different properties are not necessarily the same; as an example Upton and Goddard’s calculations on Ni clusters indicate that while the work function or first ionization threshold converges rapidly to the bulk value, the electron affinity is much more slowly converged (far from bulk even for 87 atoms) [43]. For individual clusters, the computational methods differ most depending on the extent to which they successfully treat electron correlation; thus it is now widely assumed that independent-electron models such as molecularorbital approaches at or below the Hartree-Fock level are quite inadequate for predicting absolute electronic structure parameters [44], but it remains unclear

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how well one can rely on information on trends in properties from such approaches. It is also convenient to distinguish the results of methods which specifically address spin polarization, such as the approximate density-functional methods, from those which do so only with much greater difficulty, such as the usual configuration interaction schemes. The testing ground for the molecular-orbital methods has been the dimers, and even here the approximate methods diverge in their predictions. Of overriding concern here is the description of bonding in terms of s and d atomic orbitals, and the extent to which (n + 1)s and nd electrons may be regarded as independent. Thus it is anticipated that small clusters of contracted d-block atoms (especially d”s noble and d9s coinage) will bond mainly through s electrons to form weak, more isotropic bonds. The extent to which this changes as one moves toward the center of the d-block, however, has been a matter of concern, with most approaches, including the highly-correlated generalized valence bond (GVB) method [45], yielding relatively weak, a-bonding for Cr, and MO,, in stark contrast to the most recent results from local density-functional methods (LD) predicting an ultra-short, strong bond involving substrantial 7~- and b-bonding contributions [46,47]. Thus the GVB method paradoxically predicts more bulk-like bonding than do LD results. Investigation of the appropriateness of the assumptions underlying these models and approximations derived from them has been stimulated by the new availability of unambiguous experimental information (see below). For larger clusters, usually at assumed bulk geometries, the Xa-SW approach shows high correspondence to known bulk band structure, with certain important exceptions such as an enhanced electronegativity of central versus surface atoms. Thus at the extreme of larger clusters it appears reasonable to apply solid-state and bulk-surface models to the clusters’ electronic properties. A set of approximations have been reviewed by Schumacher et al. [29]. A particularly important property is the work function of the clusters and its convergence for large clusters to the bulk work function. In extrapolating from the bulk value it is important, assuming band structure to remain essentially identical, to correct for the size of the cluster and specifically for the curvature of its surface. The classical droplet model encompasses these corrections and predicts a smooth increase in work function with decreasing cluster size [48]. Any specific deviations from this curve may thus be taken as evidence for uniqueness of certain cluster sizes, while systematic deviations might suggest more serious errors in the assumption of bulk band structure or a conducting sphere. Theoretical predictions of elementary excitations in metal clusters have been reviewed by Bennemann and Reindl [49] and the optical properties of metal clusters, within the so-called jellium model [50], have been of growing interest in the past two or three years, particularly with respect to predictions of large enhancements of radiation-matter interaction and the surface-enhanced Ra-

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man probing of the local fields at small-particle surfaces. While predictions on these effects are of significance to transition-metal cluster work, for the purposes of this review only bare cluster optical properties are considered. For smallest clusters it is only necessary to point out that the density of low-lying electronic excited states will typically be very high (in comparison to molecules having the same number of electrons) and nonuniform [51]. These cluster electronic states have their analog in molecules as intravalence excitations. while in extended matter they would be regarded as electron-hole excitations. The nature of the transition from this description to a bulk one is unknown, and at present all strong predictions are based on extrapolations from bulk metals and surfaces. These predictions may be enumerated as follows: (i) At optical frequencies the strongest absorption-interaction feature for larger clusters is the (collective) surface plasmon resonance, which broadens and red-shifts with decreasing particle size. The disintegration of this excitation, which has no molecular analog, in favor of electron-hole excitations is a particularly important phenomenon yet to be thoroughly studied. (ii) Photoemission spectra of core levels are altered strongly by final-state effects, again shifting and asymmetrically broadening resonances [52]. (iii) In the infrared, absorption increases as w2 and strengthens sharply with increasing cluster size [53]. The first and last predictions in particular have been the subjects of recent investigations, and both these and the striking results of the spherical jellium model will undoubtedly be the object of future experimental tests, especially for the simpler alkali and noble transition metals. 3.2. Magnetic properties

and structural rigidit,

The discussion of electronic properties just given remains incomplete because for transition metal clusters two additional factors must be considered in any successful description: (i) the ordinarily small effects of spin on bonding and electronic structure are known to be critically influential especially in the first-row transition metals [54], and thus the analogous effects require investigation in clusters of all sizes; (ii) the effects of vibrational motion on bulk electronic properties is additionally known to be very significant in explaining such features as the temperature dependence of conductivity and metal-insulator and metal-superconductor transitions; and so the nonrigidity or melting of clusters is of particular importance. There is no a priori way of telling when spin and vibration effects will be critical: in fact, order of magnitude estimates of the characteristic level spacing of spin, electronic, and vibrational states of clusters would indicate that all three lie in the same range for some sizes, and thus would be strongly mixed. In this case one would necessarily regard such clusters as intrinsically complex systems, for which a statistical or thermodynamic approach might yield more meaningful agreement with experiment than any precise calculation of unmixed electronic states [55].

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Perhaps the most striking predictions yet made for transition metal clusters are those concerning the magnetic ordering of first-row clusters [37,56-581. Using the Xa approximation for electronic exchange and correlation, Yang and Johnson 1561,Massmer and Salahub and co-workers [57,58] calculated the electronic structure of first-row transition metals with and without spin polarization, and obtained a uniform and simple overall picture with considerable experimental implications. This picture can be illustrated as follows: the bulk ferromagnetism of Fe, for example, has its analog in small Fe clusters with very high magnetic moments and large exchange splittings, while the anti-ferromagnetic and nonmagnetic behavior of Cr and V, respectively, similarly find analogous or precursor behavior in their small metallic clusters. This result can evidently be understood in terms of the ground-state electronic wavefunctions of these systems, which are said to be very similar (when the breaking of translational symmetry is ignored) to those for the bulk metal, and show the correct Fermi level orbitals to serve as precursors for ferroma~etic, anti-ferromagnetic and superconducting systems. A number of these results are reviewed in the recent paper of Johnson and Messmer 1351,who claim these results form the core of a real-space molecular theory of metallic and superconducting systems, pending experimental observations demonstrating the correctness of this description of clusters. In light of these calculations it would seem that a correct description of the spin degrees of freedom in a metal cluster system is essential to predicting the properties of the cluster. These predictions are now open to experimental verification via magnetic measurements, but it should be remembered that the calculations refer to T = 0 K at the bulk geometry. This leads us finally to consider the question of the rigidity of clusters and the possibility of cluster melting. The problem of cluster nonrigidity and its relationship to bulk melting has attracted a sustained effort in recent years [59]. Although most computational work has assumed fairly shallow atom-atom pair potentials, the study of cluster nonrigidity, far from being totally removed from metal clusters, has actually been stimulated by suggestions that small alkali (and probably noble transition) metal clusters may be melted at sub-room-temperature internal energies [60). The general observation in simulations of lower melting temperature with decreasing cluster size would seem to have far-reaching implications in the study of transition metal clusters since it is unlikely that T = 0 K electronic properties and magnetic ordering could survive such a transition. Simulations of cluster melting have led to a search for general laws underlying this phenomenon, and one has recently emerged [2]. If the cluster in its solid form can be regarded as rigid within the small-vibrations approximation, and the liquid form regarded as sufficiently expanded such that only pair interactions are important, then the cluster rigorously exhibits different but sharp melting and freezing temperatures between which the two phases co-ex-

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ist. If this model, or one similar but with weaker assumptions. is valid for metals, then one might expect melting or nonrigidity to play an important role in cluster behavior at temperatures far below the bulk melting point. Certain experimental evidence for this behavior is discussed below. Aside from these rather destructive effects of vibrational motion, the vibrations of transition metal clusters may be of interest with respect to their role in the molecular-orbital model of superconductivity recently described by Johnson and Messmer [35]. Future experiments on superconducting metals may aim to test this cluster model by observing the highly interactive modes implicated. It will be seen that the molecular beam techniques described above are highly suitable to measurements discussed in this section. 3.3. Chemical reactivity and perturbability The final category of predictions or cluster models are those concerned with chemical properties or the interaction of clusters with molecules and non-metal atoms. While the models of the last section were motivated by the potential connection between cluster properties and those of bulk solids and liquids, the motivation for chemical reaction models is to explore the connections between cluster and bulk surface properties. Thus it is hoped that a correct description of just a few cluster surface atoms will be sufficient for the modelling of reactions of small molecules on metal surfaces. This supposition is the basis of the popular surface cluster model [61]. With the development of matrix methods and beam techniques for the study of chemisorption a systematic examination of the models is now possible. An essential question of chemisorption is the number of nearby metal atoms in the cluster needed to bind and transform a substrate molecule [62]. Finely dispersed small particles supported on surfaces are widely known to have very high catalytic activity, so it is of interest to learn what the minimal geometrical and valence requirements of such a system are. The simplest qualitative models of valence, such as those used in explaining organo-transition metal catalysis, provide an answer to these questions, but it is not clear that these ideas will provide a unique answer when the cluster is highly unsaturated. For this reason extensive calculations have been undertaken to investigate possible modes of bonding and the number of active surface sites required. The results of these calculations have been summarized [61,63] and therefore it suffices here to mention that most studies agree on the existence of specific binding requirements, which may be regarded as potential analogs of the tested valence rules governing organo-transition metal chemistry. In particular our expectations about transition-metal cluster chemistry are shaped by experience or knowledge of the ligated metal complexes at one extreme and the metal surfaces at the other. thus one expects high valence and a number of surface oxidation states or bonding modes from clusters of Ta or

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MO, and simple non-charge-transfer bonding from the noble metals [16]. The activity of Mn, Fe, Co and Ni cluster groups would lie somewhere in between, and higher chemical activity should be exhibited by 4d and 5d metals. Similarly, analogous to surface reactivity, one expects Pt clusters to readily form carbides, Fe clusters to form oxides, and Au clusters to be fairly inert. Finally, the perturbability or physisorption properties of transition metal clusters is of interest, if only because one wishes to know how the cluster environment affects measurements of cluster properties in matrix environments. Although there have not been calculations of these effects, a reasonable guide is obtained by considering the effect of matrices on metal atomic absorption lines [64], the complexing of rare gas atoms by unsaturated transition metal complexes [65], or the effect on work function of a physisorbed gas [66]. Regardless of the criterion the effect may be very large, shifting atomic lines, metal complex absorption maxima or work functions typically by 0.2-0.5 eV (note that these are all difference measurements, so the shift of a particular orbital could be larger).

4. New results on transition metal clusters In the preceding section we presented an overview of models which represent a framework for interpreting experiments on transition metal clusters. In some cases these models take the form of specific predictions about a class or size of cluster; in other cases they are merely alternative sets of expectations based on large extrapolations from the behavior of related materials. The new experiments on metal clusters address these models, and so are grouped in the same way as the last section. This review of results is not comprehensive, and discriminates against matrix isolation work done before 1983, which is quite well reviewed [19], and against high-temperature experiments on surface supports, where most measurements are on particles (> lo3 atoms or > 50 A). Instead it is hoped that the description of these new experiments will illustrate how their individual extent of generality and specificity allow critical measurements to be made. 4. I. Results on electronic structure and elementary

excitations

In the past two years several types of new experiments have been performed to probe the electronic structure and elementary excitations of clusters and small metal particles. The method chosen. and hence the type of results obtained, depends mainly on the size of the cluster; therefore the discussion here is ordered by method and by increasing cluster size. The most detailed test of electronic structure calculations on transition metal clusters has been for the dimers and trimers (but see below on the

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electronic-magnetic structure of larger clusters of 4-50 atoms). It is likely that with these new experimental results a picture will emerge on what factors are necessary for a correct description of these molecule-size clusters. Until recently, however, almost no experimental information was available on dimers and trimers other than thermodynamic properties and ground-state vibrational frequencies from matrix resonance-Raman studies. With the advent of molecular beam and cold flow techniques this situation has been altered considerably. Thus one has had in rapid succession the bond lengths, and ground- and some excited-state symmetry information for a number of dimers, determined to high precision by rovibronic absorption spectra taken with either laser-induced fluorescence or resonance-enhanced two-photon ionization methods. The progress of this work through the end of 1983 has been reviewed by Morse and Smalley [28], and it suffices here to illustrate the impact of this work. For this purpose the examples of Cr, and MO, are ideal. Following earlier transient flash-photolysis studies of these dimers and the characterization of a number of inorganic complexes containing metal-metal bonds, all of which implicated strong cr. 7~ and even 6 participation in an ultrashort Cr, bond (< 1.9 A), several electronic structure calculations were carried out with the aim of discovering what features are necessary to reproduce such bonding. (For a brief history of Cr, calculations, see Kok and Hall [67].) While lower-level calculations appeared promising, the most comprehensive calculations using the multi-configuration GVB scheme predicted little or no chemical binding [45]. Because of the difficulty in describing the evidently intricate and very non-bulk-like bonding in Cr,, these authors further suggested that the local density method, which is based on exchange potential data taken from bulk metallic properties, would fail as well. At this critical juncture the rather tentative assignments of transient absorption spectra were dramatically extended and confirmed in detail by the almost simultaneously reported spectra from three laboratories using the new beam or flow cluster synthesis techniques, all supporting a ‘Ez ground state having equilibrium bond length 1.68 A [68-701. The predictions of Goodgame and Goddard [45], combined with the new existence of reliable information, were not to go untested for long. Two independent computations [46,47] within the local-density method indicated that it is eminently capable of an accurate description of the electronic structure and multiple bonding in Cr, and MO, (see table of ref. [47]), as demonstrated by agreement in bond length, harmonic vibrational frequency and total binding energy. This’result is interpreted as a success for the local density theory in its spin-density form [46], but, more importantly, it suggests that an exact description of the electron correlation (such as provided by the GVB method with many configurations) among a few valence electrons is less important than uniformly treating the correlation among many electrons (i.e. a larger initial basis) even if the latter necessitates a simplified description of the correlation.

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These results, combined with similar measurements for V, [71], Ni, [72], and Cu, [73] confirm the simple qualitative picture of decreased involvement of d electrons in binding with contraction of the atomic 3d shell. Results consistent with this picture have also been obtained for Fe, by magnetic moment [74] (SternGerlach) and ionization potential [75] (photoionization) measurements in combination with Xa-SW calculations. Here the additional electrons play an antibonding role at small internuclear distances, and are said to show the high degree of localization and spin alignment characteristic of incipient fe~oma~etism (see below). For metal clusters larger than dimers detailed spectroscopic studies have not yet appeared, with the exception of diffuse matrix spectra of noble metals, a resonance-Raman spectrum of Ni 3, and both jet and vapor spectra of Cu, [76]. The Ni, spectrum was interpreted by Moscovitz and DiLella [77] in terms of an obtuse isosceles geometry with a fairly flat bending potential, in disagreement with the calculations of Newton [78]. This again can be viewed as a question of how large a role the d-shell electrons play in bonding, with experiment here suggesting a very small role, so that the electronic structure resembles that of Cu, and Na,, and calculations portraying a significant role such that Ni, is more rigidly linear. In the extreme case of Cu, both calculations [79] and experiment agree on exclusively s-p~ticipation leading to a very floppy alkali-like cluster. For larger transition metal clusters geometrical characterization and electronic symmetry designation is expected to be much more difficult to arrive at by optical rovibronic spectroscopy, and therefore different experimental properties come to the fore. Among the most important parameters of electronic structure is the binding energy of valence electrons as measured by t~eshoId photoionization or photoelectron spectroscopy. These values are well known for atoms, and for bulk metals as the work function. It has very recently become possible to examine these properties for a large range of small clusters (< lo* atoms) by molecular beam photoionization spectroscopy [80]. In a series of experiments [81,82] Rohlfing, Cox and Kaldor have measured or bounded (within a few tenths of an electron volt) the io~zation potentials of small and intermediate-size metallic and nonmetallic clusters, among these the transition metals Fe and Ni. Aside from the importance of individual measurements for comparison with calculations, an essential question concerns the manner in which the ionization potentials or Fermi electron binding energies vary between atomic and bulk external values. The striking answer for both small Ni and Fe clusters 181,821is that a highly nonmonotonic decrease in ionization potential toward the work function is obtained, and these oscillations are additionally not centered around the values of the classical droplet model (see fig. 1). For both Ni and Fe the lowest electron binding energy drops very rapidly toward the work function. It is notable that, in contrast to results on carbon [83] and Pb 1841clusters, each

R. L. Whetten et al. / Advances tn research on clusters

22

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Fig. 1. (a) Variation in the observed ionization threshold of Fe clusters as a function of cluster size. The highly nonmonotonic curve indicated by the rectangles is from the photoionization data of ref. [Sl], and is to be contrasted with previously known values for the atomic ionization potential and bulk Fe work function. The pronounced oscillations for Fe, between x = 2 and x = 20 are not predicted by any current model of metal clusters; in particular they represent a significant deviation from the simple droplet model used to explain trends for Na and Ag clusters (see text), as can be readily seen through comparison with the smooth curves calculated using that model. (The curves use the formula of ref. f48j with the work function of Fe taken as 4.8 eV; the upper and lower curves represent two extreme choices of cluster radius, taking it to be proportional to the diatomic radius of 0.95 A or the bulk lattice radius of 1.39 A, respectively [75].) (b) Photoionization yields as a function of photon energy for selected Fe clusters showing relatively sharp rises at threshold. Trends in thresholds are taken to be reflections of changes in the binding energy of Fermi electrons. Note that the large shifts from Fez and Fee, to Fets in threshold energy represent most of the energy difference between the IP of the smallest clusters and the reported work function.

showing pronounced abundance or “magic number” oscillations, the IP oscillations in Fe and Ni are not accompanied by such effects. It would thus appear that, in contrast to results on Na [29] and Ag [48], which are interpretable using the droplet model, the transition metal electronic structure presents deeper problems of interpretation, and it will be interesting to compare these results to those for other metals as they become available. At present one cannot rule out any of several explanations for oscillations in the Fermi electron binding energies: (i) This behavior could result from large differences in small cluster topology with number of atoms; for example it is tempting to ascribe binding maxima as resulting from filled packing shells [82], although much more dramatic geometrical changes (for example, from favoring linear over two- or three-dimensional structures) have also been suggested [77].

R. L. Whetten et al. / Advances in research on clusters

23

(ii) A model definitely predicting oscillations is based on the quantum size effects observed in thin films and also expected for metallic spheres, although these ideas are evidently formulated for results on larger clusters or small particles, where changes in structural packing are presumably less important [85]. This latter explanation may be considered the more complex manifestation of purely electronic shell filling such as has been recently observed as stability magic numbers for carbon clusters (3-30 atoms) [83], or for Na clusters (2-100) [85]. Although the latter authors considered only the effects of total cluster stability within a spherical jellium model, the somewhat earlier predictions [50] of the self-consistent spherical jellium model model reveal a pronounced alteration in the work function attributed to the same cause. In any case the simplest jellium model is not expected to be as applicable in describing the more localized d-shell electrons, so that even assuming an isotropic distribution of nuclei one does not expect identical predictions for shell-filling patterns or magic numbers. For larger clusters of small noble metallic particles (20-100 A or lo*-lo3 atoms), it has been possible to perform a variety of experiments to investigate spin resonance [86] or such optical properties as infrared and ultraviolet-visible absorption resonances [19] and the photoionization quantum yield (photoyield). The measurements were made on matrix-isolated or gel- or smoke-suspended clusters, and results through mid-1983 have been reviewed by Bennemann and Reindl[49] and compared to solid-state predictions or extrapolations for small spherical particles. At that point it could be stated that, while the shifts and broadening of surface plasmons for Ag particles could be understood, the large enhancement of photoyield and infrared absorption were then inexplicable in terms of current theoretical models. Since that time, however, it has been reported [22] that small Ag particles (= 50 A) in a gel show little or no anomalous enhancement of infrared absorption over the predictions of classical models. Evidently the earlier measurements were affected by an unknown amount of agglomeration to much larger particles having very high absorption cross sections. Thus with the exception of the photoyield [49], which is now being calculated within the self-consistent spherical jellium model [50], it appears that the small sphere model is capable of accounting for the gross optical features of Ag particles measured thus far. It will be of great interest to learn whether tight-binding adaptions of these models will be similarly successful in predicting properties of the main transition metal small clusters. All this points to rapid but nonmonotonic convergence of small cluster electronic structure properties toward bulk values, so that many more investigations of the unique 4-100 atom range may be expected. 4.2. Results on magnetic order and melting The sweeping predictions of Salahub, Messmer, Johnson and their coworkers on magnetic behavior in 3d transition metals are currently under

24

R.L. Whetren et al. / Advances wz research on clusters

experimental investigation in a series [87,88] of supersonic cluster beam Stern-Gerlach experiments with mass-resolved photoionization detection, with striking and contrasting results now available for Fe and the IIIA metal Al. For each metal detailed predictions by spin-polarized X&SW or local spin density techniques have been made, and early experimental results appear well in line with these predictions. Thus for Fe even the dimer shows the high-spin ferromagnetic alignment predicted (fig. 2) and for higher clusters the spreading of clusters in the inhomogeneous magnetic field scales linearly with cluster size, implicating continuing high magnetic moments or precursor ferromagnetic states. In contrast, most small Al clusters show very little or zero magnetic moments, which is said to be consistent with the precursor superconducting state predicted for Al clusters. These measurements therefore provide preliminary support for the attractive analog models of cluster behavior, and continuing tests across the 3d row are essential. The requisite conditions for the measurement of large magnetic moments of Fe clusters may be of some interest. Specifically they are consistent only with a relatively large uncoupling of the excess spin degrees of freedom from internal motions and external rotations of the cluster, as found for example in the diatom&’ Hund’s case-b behavior; otherwise the rigid-structure predictions of magnetic moments would be diluted by such mixing or coupling. The Fe results are thus consistent with a simple physical picture, in contrast with the “intrinsically complex” notion above, in which very strong spin ordering and large exchange splittings govern the electronic structure, which may be regarded as relatively uncoupled from the nuclear or ionic motions. In addition it may be noted that the predicted cluster magnetic moments wereregarded as very sensitive to cluster geometry [89], so that the preliminary Fe results may be tentatively taken as reassuringly consistent with well-behaved cluster growth characterized by rigid structures at low temperatures [90]. In light then of the expected consequences of melting on electronic and magnetic ordering, these preliminary results are indicative of the production of relatively cold clusters by the supersonic jet condensation synthetic method, in answer to the questions raised by Schumacher et al. [29]. In fact, a sharp reduction in magnetic moment with increasing temperature might provide clues on the melting of transition metal clusters. Until now the most definitive results on metal cluster melting have been for supported Au small particles in the 20-50 A range [91]. This report shows a smooth drop in melting temperature with decreasing cluster size from the = 1200 K bulk value to less than 300 K for 20 A Au clusters (order of lo2 atoms) and is consistent with the phenomenological theoretical models at that time. Assuming that the melting temperature is the lower T, of ref. [2] (the temperature below which the liquid form cannot coexist), then for the presumably more strongly bound Fe clusters sub-room-temperature internal energies might allow even smallest clusters to remain rigid or frozen. Clearly, further effort for the smaller clusters

R.L. Whetten et ai. / Advances in research on clusters

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26

R.L.

Whetten et ai. / Advances

tn research on ciusters

is required on this interesting problem. In this regard it may be noted that experiments on Ni, and both experiments and calculations on Cu, indicate very flat bending potentials indicative of complete floppiness or nonrigidity even near the zero-point level. This work is thus of fundamental interest both to molecular physics and to cluster science. 4.3. Chemical reactions of free metal clusters Because much of the technological interest in transition metal clusters is the consequence of expectations about their unique chemical properties in selectively binding, transforming, and releasing organic molecules, it is apparent that a virtually unlimited number of studies will be performed now that new synthetic techniques are available. An example of the excitement generated by this possibility is the series of novel “chemisorption” complexes prepared in cryogenic matrices. The reactivity of these clusters is attested to by their ability to chemically bind with even such an inert molecule as N, [92]. The matrix method is additionally well-suited to the determination of changes in substrate bonding upon adsorption through vibrational frequency measurements. For measurements of cluster reaction yields, however, the molecular beam cluster sources coupled to flow reactors have important advantages over matrix techniques both in terms of the breadth of chemistry accessible and through the analytical tools available to probe reaction products. Recently work has been undertaken at a number of laboratories to exploit these. In fact, the versatility of the new synthetic methods in producing novel “micro-materials” makes it possible for fundamental cluster research to initiate new approaches into catalytic chemistry. Fig. 3 shows the distribution of “alloy clusters” readily produced by the molecular beam method [93]. The near statistical nature of the distribution is suggestive of a stepwise aggregation process which could trivially lead to the synthesis of heretofore unknown mixed-metal or compound clusters [94]. Riley et al. [30] combined the laser vaporization, cold flow method with downstream injection of reactant and photoionization mass spectrometry to study the reactions of Fe and Ni clusters with small inorganic molecules. With

spin-polarized structure calculations. According to this model, magnetic electrons are localized by their occupation of highly anti-bonding orbitals at the highest-occupied (Fermi) level. The energy of the electrons is then lowered by strong ferromagnetic coupling. (b) This diagram of cluster abundances (from photoionization mass spectrometry) is evidence for a near-linear increase in magnetic moment with increasing number of Fe atoms. The high-field spectrum above, recorded under otherwise identical conditions, shows the uniform depletion of clusters on the beam axis. if any size cluster had a small magnetic moment then it would appear with the same strength at both zero and high field, and would thus appear much stronger relative to its neighbors in the upper spectrum. This result may therefore be taken to indicate that free Fe clusters are highly and uniformly magnetic from the dimer to the bulk.

R.L. Whetten et al. / Advances in research on clusters

27

25

Mass (AMU)

Fig. 3. The formation of Ni-Cr alloy clusters foreshadows attempts to synthesize and study microscopic entities haying unique chemical properties. This diagram of cluster abundances, as determined by photoionization mass spectrometry, can be understood in terms of a statistical model (lower spectrum) assuming equal probability of Ni and Cr atom addition during condensation and free-jet expansion.

0, the high reaction rates of Ni, and Fe, were studied and larger clusters were found to form nearly stoichiometric complexes Fe,,,0 and NiO,,,,. These results were interpreted in terms of a correspondence to bulk nonstoichiometric solids. By contrast, with HZ/D, a wide range of adsorption numbers is found, and in addition both isotope effects and H-D exchange reactions are observed. Finally, the injection of CO causes a tremendous depletion of detected clusters. These interesting early results promise a large number of extensive studies to follow. In another series of experiments, the reactions of Pt, Ir, and Ru clusters with a number of saturated and aromatic hydrocarbons have been the subject of a preliminary study by Trevor et al. Let us focus on the reactions of benzene and normal hexane with Pt clusters [31]. In these experiments a reactor channel is appended to the condensation region of a pulsed metal cluster beam source and reagents are added at low concentration (lo-50 ppm) to the helium carrier gas. In more recent experi-

R. L. Whetren et al. / Advances in research on clusiers

Pt&,ZD;Z_,x=2-l Pt 5C 12D+ 12-xx=2-8 Pt 4C12D+ 12-xx=0-6 Pt,C,,D;,_,x=O-2

400

600

/

I

I Pt;

800

1000

1200

rnass (arnu) Fig. 4. Time-of-flight mass spectrum of platinum clusters reacted with benzene-d, detected by two-photon ionization with an ArF laser (6.4 eV, = 0.4 mJ pulse energy, cylindrically focused with a 25 cm lens). No complex is detected on the metal atom. The di-benzene-d, di-platinum parent ion is observed strongly. For the trimer, Pt,, the big complex appears to be partially dehydrogenated, which appears as a peak representing a dist~bution of species, with deute~um tosses of x = O-2 atoms. The Iarger metal clusters even further dehydrogenate the dibenzene adducts as indicated in the figure, where x represents the deuterium atom loss. Note also the observation of the species Pt z,sC6D4. Adjacent to each bare cluster peak are extensive carbide sequences, Pt,C, (M = l-4), on all metal clusters. The degree of carbidization increases slowly with the number of metal atoms in the cluster. In addition, for Pt,, n > 3, some deuterium is retained in the metal cluster as indicated by the peaks Pt,_,C,D,,, where _v= O-4.

ments an additional pulsed valve is used for better control to directly inject the reactant gases only into the reaction channel. A photoionization mass spectrometer using an ArF laser (6.4 eV) is used for detection of the species produced. This series of experiments provides new insight into the chemical species produced in the reaction of naked transition metal clusters with hydrocarbons. As shown in fig. 4, it is found qualitatively that there is prolific chemistry to abstract hydrogen and to produce platinum carbides and partially dehydrogenated species; in fact, the larger the number of metal atoms in the cluster the greater the dehydrogenation activity towards species such as benzene. However very small clusters. such as Pt ?, form a parent molecular ion of Ptz-dibenzene, a species previously not observed. Assuming that fragmentation and ionization cross-section effects are negligible, then one can say that with

R.L. whetten et al. / Advances in researchon cksters

ZOO

400

600

mass

800

1000

29

-I 200

(amu)

Fig. 5. This pair of photoion~tion mass spectra reveals a surprising similarity between the adducts formed from reaction of small Pt clusters with hexane (upper trace) and with benzene (lower trace). In particular note the greater extent of dehydrogenation of di-hydrocarbon complexes for hexane tban for benzene, with the result that the peaks nearly line up, as indicated by the vertical lines. These spectra are consistent with the idea that dehydrogenation an bare metal clusters tends toward certain stable products. However, note that if fragmentation effects are negligible, as assumed, then these results imply that clusters as small as Pt, are capable of extensive dehydrogenation of hexane.

Pt, unlike with Ni [SS], there is no observable parent ion of a Pt-hydr~rbon complex. It should be noted, that ions of Pt, and Pt, clusters complexed with C,r>, are detected as well as ions of Pt, and larger clusters complexed with C,D,., y = l-3. These are believed to be parent ions of respective neutral precursors; however, there is evidence that the carbide clusters prevalent in figs. 4 and 5 are the result of fragmentation following ionization, rather than being intrinsic to Pt/hydrocarbon chemistry. The chemistry associated with the benzene/platinum-cluster system is even more interesting when contrasted with results on normal hexane (fig. 5). Here the carbide formation, as well as the formation of d&hydrocarbon adducts to the platinum clusters, qualitatively mimics that observed for benzene, from Pt z up. Once again dehydrogenation activity is rampant, but note the close overlap of the mass spectra with that of benzene. Qualitatively it appears that normal hexane is aromatized by metal clusters as small as Pt 2. Of course, to demonstrate this result conclusively structural information is required.

30

R.L. Whetten et al. / Advances in research on clusters

Currently further experiments are underway to better characterize these early results and to confirm trends as a function of the hydrocarbons and the transition metals involved. These early results are encouraging evidence, however, that a connection between molecular and metal-like behavior in this “molecular surface” regime can be explored from chemical as well as physical viewpoints.

5. Summary and prospects The culmination of technological advances in the synthesis of metal clusters in beams and cold flows has been quickly put to use in performing a growing range of physical and chemical measurements on isolated transition metal clusters. These results, combined with those obtained by the older matrix isolation techniques, have begun to challenge a number of models at all levels of complexity. At this early stage all measurements appear significant, but as techniques progress it is likely that experiments which are rich and specific in the information they provide will be necessary to push forward significantly our understanding and predictive ability. A number of these cases have already appeared and were cited here: the nature of bonding in Cr, and MO, as a challenge to the local density functional description of small cluster bonding, the magnetic moments of Fe clusters as a test for the predictions of magnetic order in transition metal clusters, and the evidence of limited dehydrogenation of saturated and unsaturated hydrocarbons on small Pt clusters. In addition one must mention the nonmonotonic trends in cluster work function for Ni and Fe; it is a challenging question whether these should be attributed to quantum size effects or to geometrical factors. These experiments will undoubtedly generate further development and winnowing of cluster models, but it is even more likely that they will stimulate new exploratory experiments aimed at elucidating the range of transition metal cluster behavior and putting into better perspective our current knowledge. While the study of dimers and trimers may continue to attract the greatest number of physical measurements, the investigation of chemical properties can now be usefully performed for any-size small cluster, and it is clear that one must in the future critically choose questions for such high-information experiments. It is also likely that this first generation of beam experiments will be superseded by further technological developments permitting much better control of cluster size distributions, which would permit use of such techniques as photoelectron or photoemission spectroscopy. The deposition of size-selected beams on demonstrably inert supports would additionally enable one to use well-developed vacuum-surface techniques for geometrical and electronic structure characterization as well as initiating the complete study of the chemical

R. L. Wheften et al. / Advances in research on clusters

31

reactions (including desorbed products) of transition metal clusters. Thus the investigation of transition metal clusters may be expected to play a unique role in the cluster sciences as they build bridges between our knowledge of molecular and condensed matter.

Note added in proof

During the elapsed time since this manuscript was written, two developments have occurred which necessitate comment here: (1) Improvements in chemical-reactor technology have led to a burst of ~~-quality data on the kinetics and reactive processes of transition-Mets clusters [96-983. In several cases, reaction rates were shown to be critically dependent on cluster size, and for Fe, reactions with hydrogen the relative rates closely follow variations (fig. 1) in cluster IP [99]. (2) An exhaustive review of quantitative data on small transition metal clusters has appeared [loo]; this article includes an important discussion of recent ESR experiments on matrix-isolated clusters, a topic omitted here.

References [l] E.L. Muetterties. T.N. Rhodin, E. Band, CF. Brucker and W.R. Pretzer, Chem. Rev. 79 (1979) 91; K. Bittler and W. Gstertag, Angew. Chem. 19 (1980) 190; J.R. Anderson, The Structure of Metallic Catalysts (Academic Press, New York, 1975). [2] R.S. Berry, J. Jellinek and G. Natanson, Phys. Rev. A30 (1984) 919; Cl. Natanson, F. Amar and R.S. Berry, J. Chem. Phys. 78 (1983) 399. [3] J. Jortner. Ber. Bunsenges. Physik. Chem. 88 (1984) 188. We will roughly refer to small clusters (loo-IO’ atoms), intermediate clusters (lo’-lo*), large clusters (lo*-lo”), and particles, both small or fine (lo’-10”) and large (lOh-109). (4) J.P. Collman and L.S. Hegedus, Principles and Applications of Organotransition Metal Chemistry (University Science Books, Mill Valley, CA, 1980); G.L. Geoffrey and MS. Wrighton. Organometallic Photochemistry (Academic Press, New York, 1979). [5] See for example: J.E. Hueey, Inorganic Chemistry, 2nd ed. (Harper and Row, New York. 1978). [6] F.A. Cotton, Accounts Chem. Res. 11 (1978) 225; R.D. Adams, Accounts Chem. Res. 16 (1983) 67; E.L. Muetterties, R.R. Burch and A.M. Stolzenburg, Ann. Rev. Phys. Chem. 33 (1982) 89. [7] For references, see: T.E. Madley. J.T. Yates, D.R. Sandstorm and R.J. Voorhoeve, Treatise Solid State Chem. 6B (1976) 1. [S] N.W. Ashroft and N.D. Mermin. Solid State Physics (Saunders College, Philadelphia, 1976); J. Perenboom, P. Wyler and F. Meier, Phys. Rept. 78 (1981) 174. [9] F.K. Schulte, Surface Sci. 55 (1976) 427. For references to analogous theoretical predictions for small metal particles, see: R. Kubo, A. Kawabata and S. Kobayashi, Ann. Rev. Meter. Sci. 14 (1984) 49.

32 [lo]

R. L. Whetten et al. / Advances m research on clurters

R.K. Chang and T.E. Furtak, Ed%, Surface Enhanced Raman Scattering (Plenum, New York, 1982). [ll] Specifically, only 3d elements Cr through Ni show bulk magnetic ordering among d-block metals. See for example table 34.1 of ref. [S], and accompanying references. [12] E.L. Muetterties, Bull. Sot. Chim. Beiges 84 (1975) 959; 85 (1976) 451. [13] E.L. Muetterties, T.N. Rhodin, E. Band, C.F. Brucker and W.R. Pretzer, Chem. Rev. 79 (1979) 91. A similar early view is put forth by G.A. Ozin, Catal. Rev. 16 (1977) 191. v41 M. Moscovits, Accounts Chem. Res. 12 (1979) 229; E. Borella, Intern. J. Quantum Chem. 19 (1981) 1065. have = lo* electronic 1151 As examples, contrast the dimers of Fe and Co, which uncomplexed states within the first eV above the zero point, with Fe,(CO), and the Co,(CO)s, each of which has only one. Even with removal of one or two carbonyls the cluster state density would remain very low. Metal Clusters, Ed B.F.G. Johnson (Wiley, New York, 1980). WI R.G. Wooley, in: Transition [I71 K.A. Gingerich, Faraday Symp. Chem. Sot. 14 (1980) 109. The author and co-workers used Knudsen cell techniques to measure bond strengths of a number of transition and non-transition metal small clusters. WI H. Bauer and D.J. Frurip, J. Phys. Chem. 81 (1977) 1015, and references therein. of these techniques with numerous references, see G.A. Ozin, Faraday [I91 For a description Symp. Chem. Sot. 14 (1980) 7. A further improvement in the cell matrix technique is the use of gas aggregation and condensation into vacuum. See: W. Schulze, F. Frank, K.-P. Charle and B. Tesche, Ber. Bunsenges. Physik. Chem. 88 (1984) 263. PO1 G.A. Ozin, Accounts Chem. Res. 10 (1977) 21, and references therein. WI For example, see: K.J. Klabunde and Y. Tanaka, J. Mol. Catal. 21 (1983) 57. WI R.P. Devaty and A.J. Sievers, Phys. Rev. Letters 52 (1984) 1344. L. Wbste and E. Schumacher, Chem. Phys. 48 (1980) 253; 1231 S. Leutwyler, A. Herrmann, M.M. Kappes, R.W. Kunz and E. Schumacher, Chem. Phys. Letters 91 (1982) 413. See also G. Delacretaz, J.D. Ganiere, R. Monot and L. Woste, Appl. Phys. B29 (1982) 55. v41 W.D. Knight, R. Monot, E.R. Dietz and A.R. George, Phys. Rev. Letters 40 (1978) 1324. 1251T.G. Dietz, M.A. Duncan, D.E. Powers and R.E. Smalley, J. Chem. Phys. 74 (1981) 6511; D.E. Powers, S.G. Hansen, M.E. Geusic, A.C. Puiu, J.B. Hopkins, T.G. Dietz, M.A. Duncan and R.E. Smalley, J. Phys. Chem. 86 (1982) 2556. WI V.E. Bondybey and J.H. English, J. Chem. Phys. 76 (1982) 2165. v71 S.J. Riley, E.K. Parks, C.-R. Mao, L.G. Pobo and S. Wexler, J. Phys. Chem. 86 (1982) 3911. PI M.D. Morse and R.E. Smalley, Ber. Bunsenges. Physik. Chem. 88 (1984) 228; R.E. Smalley, Laser Chem. 2, (1983) 167. M. Kappes, K. Marti, P. Radi, M. Schar and B. Schmidhalter. Ber. v91 E. Schumacher, Bunsenges. Physik. Chem. 88 (1984) 220. [301 S.J. Riley, E.K. Parks, L.G. Pobo and S. Wexler, Ber. Bunsenges. Physik. Chem. 88 (1984) 287. 1311 D.J. Trevor, R.L. Whetten, D.M. Cox and A. Kaldor, J. Am. Chem. Sot. 107 (1985) 518. of sizes produces the measured 1321Typically experiments are performed in which a distribution results. Example: J. Colbert, A. Zangwill, M. Strong in and S. Krummacher, Phys. Rev. B27 (1983) 1378. [331T.T.P. Cheung, Surface Sci. 127 (1983) L129; 140 (1984) 151, and references therein. [341J. Demuynck, M. Rohmer, A. Strich and A. Veillard, J. Chem. Phys. 75 (1981) 3445. See also: 0. Sinanoglu, Chem. Phys. Letters 81 (1981) 188. I351 K.H. Johnson and R.P. Messmer, Synthetic Metals 5. (1983) 151. results is given by A.B. Anderson, J. Chem. Phys. [361A critical discussion of extended-Huckel 68 (1978) 1744.

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[37] For example: G. Blyholder, Surface Sci. 42 (1974) 249;

A.B. Anderson, J. Chem. Phys. 64 (1976) 4046. [38] A. Wolf and H. Schmidtke, Intern. J. Quantum Chem. 18 (1980) 1187. [39] R.P. Messmer, S.K. Kundson, K.H. Johnson, J.B. Diamond and C.Y. Yang, Phys. Rev. B13 (1976) 1396. [40] F.A. Cotton and I. Shin, J. Am. Chem. Sot. 104 (1982) 7025, and references therein. [41] J. Keller, J. Mol. Struct. 93 (1983) 93. [42] R.P. Messmer, S.K. Knudson, K.H. Johnson, J.B. Diamond and C.Y. Yang, Phys. Rev. B13, (1976) 1396, for an early statement of this result. [43] T.H. Upton, W.A. Goddard and C.F. Melius, J. Vacuum Sci. Technol. 16 (1979) 351. The IP of 13-87 atom Ni clusters range from = 5 to 7.5 eV, while the electron affinity is at best more than 2 eV less, ranging from = 2.5 to 3.5 eV. [44] See for example: S.P. Walch and C.W. Bauschlicher, J. Chem. Phys. 79 (1983) 3590. [45] M.M. Goodgarne and W.A. Goddard, Phys. Rev. Letters 48 (1982) 135,; J. Phys. Chem. 85 (1981) 215. [46] B. Delley, A.J. Freeman and D.E. Ellis, Phys. Rev. Letters 50 (1983) 488. [47] J. Bemholc and N.A.W. Holzworth,. Phys. Rev. Letters 50 (1983) 1451. The fairly good agreement with bond energies here would seem to refute the statement of ref. [17] (“Approximate theoretical treatments, such as density functional theory, . . . have no useful predicting power as far as bond energies are concerned”). [48] D.M. Wood, Phys. Rev. Letters 46 (1981) 749; A. Herrmann, E. Schumacher and L. Waste, J. Chem. Phys. 68 (1978) 2327. The latest word on this model comes from: K.I. Peterson, P.D. Dao, R.W. Farley and A.W. Castleman, J. Chem. Phys. 80 (1984) 1780. [49] K.H. Bennemann and S. Reindl, Ber. Bunsenges. Physik. Chem. 88 (1984) 278. [50] W. Ekardt, Phys. Rev. Letters 52 (1984) 1925; Ber. Bunsenges. Physik. Chem. 88 (1984) 289. [51] By this it is meant that although electronic state densities may be very high, as for example in Ru, with a predicted 112 states in the lowest 0.6 eV [40], the distribution is neither smooth nor meaningfully structured (as for example a collective surface plasmon excitation). [52] For example: D. Schrneisser, K. Jacobi and D.M. Kolb, J. Chem. Phys. 75 (1981) 5300, and references therein. [53] D.B. Tanner, A.J. Sievers and R.A. Buhrman, Phys. Rev. Bll (1975) 1330. [54] The most obvious manifestation of this is the bulk ordering into magnetic domains [ll], but it is now believed that there generally exists a competition between bonding or delocalization and pararnagnetism (involving localization). See ref. [41] for further demonstration of this point. [55] Just such mixing is relatively common in the dynamics of nucleons in large nuclei and has also been found in the electronic spectra of complex atoms. See: T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey and S.S.M. Wong, Rev. Mod. Phys. 53 (1981) 385. Similarly, spectroscopic evidence for complete mixing in the vibrational states of a molecule was given for acetylene by E. Abramson, R.W. Field, D. Imre, K.K. Innes and J.L. Kinsey, J. Chem. Phys. 80 (1984) 2298. [56] C.Y. Yang, K.H. Johnson, D.R. Salahub, J. Kaspar and R.P. Messmer, Phys. Rev. B24 (1981) 5673. [57] D.R. Salahub and R.P. Messmer, Surface Sci. 106 (1981) 415. [58] K.H. Johnson, D.D. Vvedensky and R.P. Messmer, Phys. Rev. B19 (1979) 1519. [59] F.H. Stillinger and A. Weber, Phys. Rev. A25 (1972) 978; C.L. Briant and J.J. Burton, J. Chem. Phys. 63 (1975) 2045; R.D. Etters and J.B. Kaelber, J. Chem. Phys. 66 (1977) 5112. [60] See discussion of R.S. Berry, in: Quantum Dynamics of Molecules, Ed. R.G. Woolley (Plenum, New York, 1960).

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[87] D.M. Cox et al., to be published. [88] D.M. Cox, D.J. Trevor, R.L. Whetten, E.A. Rohlfing and A. Kaldor, submitted. For non-mass-resolved magnetization measurements of Fe, in zeolites, see F. Schmidt, U. Stapel and H. Walther, Ber. Bunsenges. Physik. Chem. 88 (1984) 310. [89] A. Pellegatti, B.N. McMaster and D.R. Salahub, Chem. Phys. 75 (1983) 83. [90] In support of this claim are measurements of the strong temperature dependence of the magnetization of surface-supported clusters nearing and even below the bulk Curie temperature: T.S. Cale, J.T. Richardson and J. Ginestra, Appl. Phys. Letters 42 (1983) 744. [91] Ph. Buffat and J-P. Borel, Phys. Rev. Al3 (1976) 2287; J-P. Borel, Surface Sci. 106 (1981) 1. [92] For review see: W.J. Power and G.A. Ozin, Advan. Inorg. Radiochem. 23 (1980) 80. [93] E.A. Rohlfing, D.M. Cox, R. Petkovic-Luton and A. Kaldor, J. Phys. Chem. 88 (1984) 6227. (941 J.H. Sinfelt. Bimetallic Catalysts (Wiley, New York, 1983). [95] R.E. Smalley, private communication. (96) R.L. Whetten, D.M. Cox, D.J. Trevor and A. Kaldor, J. Phys. Chem. 89 (1985) 566. [97] M.E. Geusic, M.D. Morse and R.E. Smalley, J. Chem. Phys. 82 (1985) 590. [98] SC. Richtsmeier, E.K. Parks, K. Liu, L.G. Pobo and S.J. Riley, J. Chem. Phys. 82 (1985). [99] R.L. Whetten, D.M. Cox, D.J. Trevor and A. Kaldor, Phys. Rev. Letters, in press. [lOO] W. Weltner and R.J. Van Zee, Ann. Rev. Phys. Chem. 35 (1984) 291.