Photochemistry of van der Waals Complexes and Small Clusters

In a chemical reaction, the shape of the potential energy surface (PES) dictates the reaction rate and energy disposal in the products. Not only does the dynamics depend crucially upon the features of the surface, but, ultimately one seeks to influence the course of the reaction by preparing selectively certain regions of the surface. For harpooning reactions, the propensity rules for energy disposal in the products (influence of the entrance kinetic energy, effect of the early or late barrier) have been established by Polanyi (1972) and have been used later as guidelines. Here, the surface may easily be modeled in simple terms using long-range electrostatic interaction in the entrance valley. There was, then, need of an experimental method which allows the possibility of observing directly the characteristic regions of this potential energy surface, but also to investigate precisely the surface in other types of reaction. The study of the reactivity of van der Waals complexes is intended to fulfil this purpose. In classical experiments, the surface is obtained by inversion of the experimental data which are differential cross sections and internal energy distribution of the products. This procedure is difficult and not unambiguous. The first step is to determine the correlation between the entrance channel's parameters (kinetic energy, internal energy, angular momentum) and the final states of the products (kinetic energy, internal energy, angular distribution). This requires a precise control of the entrance channel. Therefore, the goal of many experiments is to reduce the initial states to a small subset, and to measure the energy disposal in the products with the greatest accuracy. This was first achieved by controlling the kinetic energy of the reactants in crossed beam experiments. Later, a certain control of the collision geometry was obtained by orienting the molecules or the atomic orbitals in crossed beam experiments or by using prealigned systems in a van der Waals complex: this subject is discussed in Buelow et al. (1986).

Reaction Dynamics in Femtosecond and Microsecond Time Windows: Ammonia Clusters as a Paradigm

The last decade has seen tremendous growth in the study of gas phase clusters. Some areas of cluster research which have received considerable attention in this regard include solvation (Lee et al. 1980), (Armirav et al. 1982), and reactivity (Dantus et al. 1991; Khudkar and Zewail 1990; Rosker et al. 1988; Scherer et al. 1987). In particular, studies of the dynamics of formation and dissociation, and the changing properties of clusters at successively higher degrees of aggregation, enable an investigation of the basic mechanisms of nucleation and the continuous transformation of matter from the gas phase to the condensed phase to be probed at the molecular level (Castleman and Keesee 1986a, 1988). In this context, the progressive clustering of a molecule involves energy transfer and redistribution within the molecular system, with attendant processes of unimolecular dissociation taking place between growth steps (Kay and Castleman 1983). Related processes of energy transfer, proton transfer, and dissociation are also operative during the reorientation of molecules about ions produced during the primary ionization event required in detecting clusters via mass spectrometry (Castleman and Keesee 1986b), providing further motivation for studies of the reaction dynamics of clusters (Begemann et al. 1986; Boesl et al 1992; Castleman and Keesee 1987; Echt et al. 1985; Levine and Bernstein 1987; Lifshitz et al. 1990; Lifshitz and Louage 1989, 1990; Märk 1987; Märk and Castleman 1984, 1986; Morgan and Castleman 1989; Stace and Moore 1983; Wei et al. 1990a,b). The real-time probing of cluster reaction dynamics is a facilitating research field through femtosecond pump-probe techniques pioneered by Zewail and coworkers (Dantus et al. 1991; Khundkar and Zewail 1990; Rosker et al. 1988; Scherer et al. 1987). Some real-time investigations have been performed on metal, van der Waals, and hydrogen-bonded clusters by employing these pump-probe spectroscopic techniques. For example, the photoionization and fragmentation of sodium clusters have been investigated by ion mass spectrometry and zero kinetic energy photoelectron spectroscopy in both picosecond (Schreiber et al. 1992) and femtosecond (Baumert et al. 1992, 1993; Bühler et al. 1992) time domains. Studies have also been made to elucidate the effect of solvation on intracluster reactions.

Intermolecular Dynamics and Bimolecular Reactions

The study of clusters has taken the path that is quite typical in physical chemistry research for a newly discovered system or state of matter: (1) elucidation of energy eigenstates, both experimentally and theoretically, (2) elucidation of structure through experiments and calculations of various degrees of sophistication, (3) exploration of system dynamics, and (4) explorations of chemical reactivity within the new system. Indeed, previous review volumes covering cluster research have dealt mostly with eigenstates and structure, with some attention given to the dynamics and reactions of clusters (Bernstein 1990; Halberstadt and Janda 1990; Jena et al. 1987; Weber 1987). The study of all aspects of cluster energy levels, structure, and behavior is both important and useful on a number of different levels. First, cluster research is performed because clusters themselves are a fascinating system in which to study intermolecular interactions and solvation behavior. Second, and perhaps more useful, cluster investigations can lead to a far better understanding of condensed phase and surface systems. With regard to condensed phase dynamics and chemical reactions, clusters provide three very important components for the basic data set: (1) clusters can generate the minimum irreducible set required for a dynamical event or reaction to occur, (2) clusters provide an excellent proving ground for the comparison between experiment and theory because both sets of results can be based on exactly the same systems, and (3) an isolated cluster of minimum size with regard to a dynamical event or reaction is an ideal entity in which to investigate a dynamical or reaction coordinate, its dimensionality, and its dependence on system properties. Of course, clusters are not simply small condensed phase systems: they can express behavior quite different from condensed phase systems. For example, reactions that occur in condensed phases may not occur in clusters; however, these differences can be understood and related to the different properties of the two systems.

Magic Numbers, Reactivity, and lonization Mechanisms in ArnXm Heteroclusters

During the past decade, there has been an enormous increase in experimental and theoretical studies directed toward obtaining a fundamental understanding of the properties of van der Waals (vdW) clusters (Castleman 1990; Castleman and Keesee 1986b, 1988b; Garvey et al. 1991; Goyal et al. 1993; Janda 1985; Jortner 1984; Levy 1981; Märk 1987; Märk and Castleman 1985; Ng 1983; Stace 1992). As the term "cluster" is frequently used in the scientific community with different connations, it would be appropriate to define "cluster" in the context of this field. Gas phase clusters are defined as finite gas phase aggregates composed of two to several million components (i.e., atoms or molecules). These species are held together by different types of forces, ranging from the weak van der Waals forces all the way up to strong electrostatic forces. A techique of classifying clusters based on the type of the binding forces has been developed. Another convenient basis for the classification of clusters is according to the size, such that clusters with n = 2-10 or 13 have been termed microclusters, clusters with n = 10-102 have been referred to as small clusters, and aggregates with n ≥ 102 are called large clusters (Jortner 1984). Clusters composed of a few molecules can be treated, to a first approximation, as isolated gas phase species, while clusters with sizes n > 103 begin to exhibit properties resembling those of condensed or bulk materials. Between these two extremes lies the regime where cluster systems cannot be adequately treated by either the molecular concepts or the conventional solid-state approach. Thus, clusters have previously been described as the conceptual bridge linking the gas and the condensed phases (bulk liquids or solids) (Castleman 1990; Castleman and Keesee 1986b, 1988b; Garvey et al. 1991; Goyal et al. 1993; Janda 1985; Jortner 1984; Levy 1981; Märk 1987; Märk and Castleman 1985; Ng 1983; Stace 1992).

Weakly Bound Molecular Complexes as Model Systems for Understanding Chemical Reactions

An issue of central importance in chemical reaction dynamics is the nature of the energy transfer processes within and between reactants and products. At a fundamental level, bond rupture and formation can be understood in terms of the transfer of energy into the reaction coordinate, causing a bond to break, and then relaxation of the energy away from the newly formed bonds in the product molecules to the other degrees of freedom of the system. By their very nature, these processes are highly anharmonic, making their detailed characterization a formidable challenge. In recent years, spectroscopists have taken on the challenge of trying to characterize the quantum states of a molecule at the high vibrational energies corresponding to the chemically interesting regime. At these energies, the density of states becomes extremely high and the coupling between the states very strong, the result being that the vibrations can no longer be characterized in terms of simple isolated local or normal modes. In the extreme limit, where RRKM theory (Wardlaw and Marcus 1987) applies, there is rapid energy redistribution that, at least approximately, samples the available states statistically, allowing us to overlook many of the fine details. Although we are still far from having a complete understanding of the quantum state dynamics of systems in this regime, the recent progress that has been made in both experiment (Felker and Zewail, 1985; Go et al., 1990; Parameter 1982, 1983; Smalley 1982) and theory (Stuchebrukhov and Marcus 1993; Uzer 1991) is helping to better define the important processes. Ultimately, the detailed characterization of all the intramolecular couplings in a molecule would provide us with a basis for understanding the chemistry at a fundamental level, in both the statistical and nonstatistical regimes. After all, energy transfer from one vibrational mode of a molecule to another is determined by the intermode couplings, which, in the ground electronic states of molecules, are predominantly due to anharmonic and/or coriolis effects. Of course, the problem becomes even more challenging when one moves from the realm of isolated molecules to solvated systems.

Theoretical Approaches to the Reaction Dynamics of Clusters

The theoretical treatment of cluster kinetics borrows most of its concepts and techniques from studies of smaller and larger systems. Some of the methods used for such smaller and larger systems are more useful than others for application to cluster kinetics and dynamics, however. This chapter is a review of specific approaches that have found fruitful use in theoretical and computational studies of cluster dynamics to date. The review includes some discussion of methodology; it also discusses examples of what has been learned from the various approaches, and it compares theory to experiment. A special emphasis is on microsolvated reactions—that is, reactions where one or a few solvent molecules are clustered onto gas-phase reactants and hence typically onto the transition state as well. Both analytic theory and computer simulations are included, and we note that the latter play an especially important role in understanding cluster reactions. Simulations not only provide quantitative results, but they provide insight into the dominant causes of observed behavior, and they can provide likelihood estimates for assessing qualitatively distinct mechanisms that can be used to explain the same experimental data. Simulations can also lead to a greater understanding of dynamical processes occurring in clusters by calculating details which cannot be observed experimentally. One interesting challenge that reactions in van der Waals and hydrogenbonded clusters offer is the possibility of studying specifically how weak interactions or microsolvation bonds affect a chemical reaction or dissociation process. In that sense, theoretical studies of weakly bound clusters have proved to be useful in learning about the "crossover" in behavior from that of an isolated nonsolvated molecule in the gas phase to that for a molecule in a liquid or solid solvent. It is very common to begin reviews with a disclaimer as to completeness. Such a disclaimer is, we hope, not required for this chapter because it is not a comprehensive review but a limited-scope discussion of selected work that illustrates some issues that we perceive to be especially important. The chapter is divided into three parts. Section 1.2 discusses collisional and statistical theories for cluster reactions.

Dynamics of Ground State Bimolecular Reactions

During the past decade, the study of photoinitiated reactive and inelastic processes within weakly bound gaseous complexes has evolved into an active area of research in the field of chemical physics. Such specialized microscopic environments offer a number of unique opportunities which enable scientists to examine regiospecific interactions at a level of detail and precision that invites rigorous comparisons between experiment and theory. Specifically, many issues that lie at the heart of physical chemistry, such as reaction probabilities, chemical branching ratios, rates and dynamics of elementary chemical processes, curve crossings, caging, recombination, vibrational redistribution and predissociation, etc., can be studied at the state-to-state level and in real time. Inevitably, understanding the photophysics and photochemistry of weakly bound complexes lends insight into corresponding processes in less rarefied surroundings, for example, molecules physisorbed on crystalline insulator and metal surfaces, molecules residing on the surfaces of various ices, and molecules weakly solvated in liquids. However, such ties to the real world are not the main driving force behind studies of photoinitiated reactions in complexed gaseous media. Rather, it is the lure of going a step beyond the more common molecular environments. Theoretical modeling, which in many areas purports to challenge experiment, must rise to the occasion here if it is to offer predictive capability for even the simplest of such microcosms. Subtleties abound. Roughly speaking, two disparate regimes can be identified which are accessible experimentally and which correspond to qualitatively different kinds of chemical transformations. These are distinguished by their reactants: electronically excited versus ground state. For example, it is possible to study the chemical selectivity that derives from the alignment and orientation of excited electronic orbitals, albeit at restricted sets of nuclear coordinates. This is achieved by electronically exciting a complexed moiety, such as a metal atom, which then undergoes chemical transformations that depend on the geometric properties of the electronic orbitals such as their alignments and orientations relative to the other moiety (or moieties) in the complex.