This is an overview of some of the important, challenging, and problematic issues in contemporary electron transfer research. After a qualitative discussion of electron transfer, its time and distance scales, energy curves, and basic parabolic energy models are introduced to define the electron transfer process. Application of transition state theory leads to the standard Marcus formulation of electron transfer rate constants. Electron transfer in solution is coupled to solvent polarization effects, and relaxation processes can contribute to and even control electron transfer. The inverted region, in which electron transfer rate constants decrease with increasing exoergicity, is one of the most striking phenomena in electron transfer chemistry. It is predicted by both semiclassical and quantum mechanical models, with the latter appropriate if there are coupled high- or medium-frequency vibrations. The intramolecular reorganizational energy has different contributions from different vibrational modes, whic...

Contemporary Issues in Electron Transfer Research

The transition of PbS from molecular to bulk form has been observed in polymer films. As the particle size decreases the band gap shifts to the blue and eventually approaches the transition energy of the first allowed excited state, X→A, of a PbS molecule. Discrete absorption bands also appear. The electron‐hole‐in‐a‐box model with effective mass approximation cannot explain the observed size dependence. We have developed two theoretical models, both including the effect of band nonparabolicity, that successfully explain the observed size dependence down to about 25 A.

PbS in polymers. From molecules to bulk solids

The field of cluster research can trace its origins back to the mid-nineteenth century when early studies of colloids, aerosols, and nucleation phenomena were reported. The field underwent a resurgence of interest several decades ago when well-defined clusters were observed in supersonic expansions that could be investigated using mass spectrometers. The advent of the laser provided a new dimension, enabling detailed spectroscopic observations through the probing of systems of varying size and degree of solvation. Modern interest derives from recognition that interrogating clusters provides a way of studying the energetics and dynamics of intermediate states of matter as cluster systems evolve from the gas toward the condensed state. Herein, we endeavor to highlight some of the significant advances which have been made during the past several decades that have led to a nearly explosive growth of interest in the field of cluster science. Finally, we conclude that the field will continue to expand through i...

Clusters: Structure, Energetics, and Dynamics of Intermediate States of Matter

The Panel was charged with assessing the present scientific understanding of the size-dependent physical and chemical properties of clusters, the methods of synthesis of macroscopic amounts of size-selected clusters with desired properties, and most importantly, the possibility of their controlled assembly into new materials with novel properties. The Panel was composed of both academic and industrial scientists from the physics, chemistry, and materials science communities, and met in January 1988.In materials (insulators, semiconductors, and metals) with strong chemical bonding, there is extensive spatial delocalization of valence electrons, and therefore the bulk physical properties which depend upon these electrons develop only gradually with cluster size. Recent research using supersonic-jet, gas-aggregation, colloidal, and chemical-synthetic methods indeed clearly establishes that intermediate size clusters have novel and hybrid properties, between the molecular and bulk solid-state limits. A scientific understanding of these transitions in properties has only been partially achieved, and the Panel believes that this interdisciplinary area of science is at the very heart of the basic nature of materials. In Sec. V (Future Challenges and Opportunities), a series of basic questions for future research are detailed. Each question has an obvious impact on our potential ability to create new materials.Present methods for the synthesis of useful amounts of size-selected clusters, with surface chemical properties purposefully controlled and/or modified, are almost nonexistent, and these fundamentally limit our ability to explore the assembly of clusters into potentially novel materials. While elegant spectroscopic and chemisorption studies of size-selected clusters have been carried out using molecular-beam technologies, there are no demonstrated methods for recovery and accumulation of such samples. Within the past year, the first reports of the chemical synthesis of clusters with surfaces chemically modified have been reported for limited classes of materials. Apparatus for the accumulation and consolidation of nanophase materials have been developed, and the first promising studies of their physical properties are appearing. In both the chemical and nanophase synthesis areas, clusters with a distribution of sizes and shapes are being studied. Progress on macroscopic synthetic methods for size-selected clusters of controlled surface properties is the most important immediate goal recognized by the Panel. Simultaneous improvement in physical characterization will be necessary to guide synthesis research.Assuming such progress will occur, the Panel suggests that self-assembly of clusters into new elemental polymorphs and new types of nanoscale heterogeneous materials offers an area of intriguing technological promise. The electrical and optical properties of such heterogeneous materials could be tailored in very specific ways. Such ideas are quite speculative at this time; their implementation critically depends upon controlled modification of cluster surfaces, and upon development of characterization and theoretical tools to guide experiments.The Panel concluded that a number of genuinely novel ideas had been enunciated, and that in its opinion some would surely lead to exciting new science and important new materials.

Research opportunities on clusters and cluster-assembled materials—A Department of Energy, Council on Materials Science Panel Report

The geometries and energies of small silicon clusters have been investigated in a systematic manner by means of accurate ab initio calculations. The effects of polarization functions and electron correlation have been included in these calculations. Several geometrical arrangements and electronic states have been considered for each cluster. All the geometries considered have been completely optimized within the given symmetry constraints with several basis sets at the Hartree–Fock level of theory. Single point calculations have been performed at these geometries using complete fourth‐order perturbation theory with the polarized 6‐31G* basis set. The effects of larger basis sets including multiple sets of polarization functions have been considered for Si2 and Si3. Singlet ground states are found for Si3–Si7 with the associated geometries corresponding to a triangle, a planar rhombus, a trigonal bipyramid, an edge‐capped trigonal bipyramid, and a tricapped tetrahedron, respectively. The best calculated structure for Si10 corresponds to a tetracapped octahedral arrangement where alternate faces of the octahedron have been capped to yield a structure with overall tetrahedral symmetry. All the geometries are considerably different from those derived from microcrystal fragments. Binding energies have been computed for all clusters and used to interpret the distribution and fragmentation patterns of small silicon cluster ions observed recently.

Theoretical study of small silicon clusters: Equilibrium geometries and electronic structures of Sin (n=2–7,10)

The kinetics of the gas phase reactions of hydrogen and deuterium with iron clusters in the range Fe6 to Fe68 have been investigated. It is found that reaction rate constants are a strong function of cluster size, varying by more than five orders of magnitude in this size range. The largest rate constants correspond to approximately 3% of a hard sphere cross section. Abrupt changes in the rate constant from one cluster to the next are seen. Qualitative temperature dependencies of cluster reactivity have been determined. The more reactive clusters show decreased reactivity with increased tempeature, while the least reactive clusters become more reactive. Strong isotope effects are seen only in the Fe10 to Fe14 size range. Mechanisms for the reactions of H2 and D2 with iron clusters are discussed in light of these observations.

Gas phase reactions of iron clusters with hydrogen. I. Kinetics

Evidence is presented for structural changes in iron clusters in the Fe13 to Fe23 size range. Abrupt changes with cluster size are found for several chemical properties, including reactivity with hydrogen and binding energies of ammonia and water. These changes often come at the same cluster sizes, pointing to a common origin—fundamental changes in the structure of the bare iron clusters. In addition, changes in structure as a consequence of adsorbate binding are suggested. The experimental observations leading to these conclusions are detailed, and possible structures for clusters in this size range are proposed.

Chemical probes of metal cluster structure: Reactions of iron clusters with hydrogen, ammonia, and water

Reactions of iron clusters with an excess of hydrogen are found to yield fully hydrogenated products FenHm whose compositions remain fixed over a wide range of hydrogen pressures. For n=6 to 131, the observed m values are always even, have narrow ranges, and for many clusters are unique. Up to n=30, nearly stoichiometric 1:1 ratios of m to n are found. Above 30, cluster hydride compositions are consistent with a monolayer of chemisorbed hydrogen on the cluster surfaces. At sufficiently high hydrogen pressures additional hydrogens bind to the clusters, most likely as a second, physisorbed layer. The experimental results are discussed in terms of cluster structure and the relation to bulk iron behavior.

Reactions of iron clusters with hydrogen. II. Composition of the fully hydrogenated products

Generation of continuous beams of clusters of refractory metals by a thermal flow surce is described. The source consists of a high-temperature (up to 2000/sup 0/C) oven for metal vaporization and a liquid-nitrogen-cooled quench cell for condensation and cluster growth. Various flow gases are used to vary the distribution of clusters produced. The operation of the source and the characterization of cluster beams of Al, Cr, Ni, Cu, and Ag are discussed.

Generation of continuous beams of refractory metal clusters

Studies are described of the chemisorption of ammonia on isolated neutral iron clusters Fen for 2≤n≤165. Clusters are generated by laser vaporization in a continuous‐flow‐tube reactor, and reaction products are detected by laser‐ionization time‐of‐flight mass spectrometry. Ammonia is found to chemisorb nondissociatively on cluster surfaces on the 1 ms time scale of these experiments. Measurements of ammonia uptake provide information on adsorption kinetics and on the number and nature of the binding sites. The ammonia binding energy is found to decrease with increasing cluster coverage. For chemically saturated clusters, the ratio of adsorbed NH3 molecules to surface iron atoms is found to decrease with increasing cluster size, going from >1/3 for small clusters to 100. Ammonia chemisorption is accompanied by a large decrease in cluster ionization potentials, as much as 2 eV for saturated clusters. At sufficiently high exposure the beginning of the formation of a second, physisorbed layer of molecules is seen. Detailed measurements of product composition under different exposure conditions give evidence for numerous changes in cluster structure throughout the growth sequence from small to large clusters. Often these structural changes involve particularly stable reaction products. Evidence for the existence of metastable structures is presented. Several possibilities for cluster structure are suggested.

L. G. Pobo

Papers

Gas phase reactions of iron clusters with hydrogen. I. Kinetics

Chemical probes of metal cluster structure: Reactions of iron clusters with hydrogen, ammonia, and water

Reactions of iron clusters with hydrogen. II. Composition of the fully hydrogenated products

Generation of continuous beams of refractory metal clusters

The reaction of iron clusters with ammonia. I. Compositions of the ammoniated products and their implications for cluster structure