Clusters Van der Waals

Clusters may be held together by a variety of different forces, strong enough to hold the atoms together, but weak enough to allow some flexibility in the interatomic angles, which allows further atoms to be added to the system. If clusters are characterised by their stackability, not all binding forces are suitable to build up a cluster sequence. 

One of the simplest types of cluster is formed by packing together atoms which are chemically inert. They are then held together by the van der Waals forces between neutral atoms, which impose no particular bond orientation and which do not change the electronic configuration on each site, so that infinite stackability is, in principle, readily achieved. The structure of van der Waals clusters is illustrated schematically in fig. 12.2. 

As pointed out above, there are two extreme situations involving localised and delocalised valence electrons in cluster physics at one end of the scale, the noble gases possess valence electrons which remain localised on individual atomic sites, while, at the other, the alkalis possess delocalised valence electrons which can wander over the cluster and resemble the conduction electrons of a metallic solid. 

Between these two extremes lie clusters of atoms more stable than the alkalis, but less so than rare gases, and which may actually effect a transition from van der Waals to metallic behaviour as a function of the cluster size N. A good example is provided by Hg clusters Hg atoms have a closed 6s2 subshell, and a resonably high ionisation potential. The small clusters (up to about 10 or 15 atoms) exhbit a van der Waals behaviour with quasiatomic 5d — 6p transitions, while a conduction band appears for larger N [662] as the aggregates become metallic. 

The structure of a van der Waals cluster is similar to that of an insulating solid in that the nature of the atoms remains unaltered, i.e. each atom inside the cluster carries the same number of electrons as the corresponding free atom. It is no surprise that rare gases, which have high ionisation energies, should form clusters of this type. 

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One method to study energy-selected ions is threshold ionization, in which ions with precisely defined energy contents are produced. These ions can then be used to study unimolecular fragmentation, ion-molecule reactions, van der Waals clusters, and hydrogen-bonded clusters [62]. 

There have been a number of theoretical investigations of the structure and dynamics of heterogeneous clusters in which a single atom or molecule interacts with a rare-gas cluster Pair potentials are often a good candidate for providing a simplified treatment for the ground state of extended systems such as small van der Waals clusters like NaAr HgArn or Li Arn... 

Extension to many dimensions provides insight into more sophisticated aspects of the method and into the nature of molecular interactions. In the second stage of this unit, the students perform molecular dynamics simulations of 3-D van der Waals clusters of 125 atoms (or molecules). The interactions between atoms are modeled using the Lennard-Jones potentials with tabulated parameters. Only pairwise interactions are included in the force field. This potential is physically realistic and permits straightforward programming in the Mathcad environment. The entire program is approximately 50 lines of code, with about half simply setting the initial parameters. Thus the method of calculation is transparent to the student. 

The calculations of g(r) and C(t) are performed for a variety of temperatures ranging from the very low temperatures where the atoms oscillate around the ground state minimum to temperatures where the average energy is above the dissociation limit and the cluster fragments. In the course of these calculations the students explore both the distinctions between solid-like and liquid-like behavior. Typical radial distribution functions and velocity autocorrelation functions are plotted in Figure 6 for a van der Waals cluster at two different temperatures. Evaluation of the structure in the radial distribution functions allows for discussion of the transition from solid-like to liquid-like behavior. The velocity autocorrelation function leads to insight into diffusion processes and into atomic motion in different systems as a function of temperature. 

Van der Waals clusters (N2) (C02) noble gas clusters Molecular clusters (L2)n clusters of organic molecules H-bonding clusters (H20) ... 

The most important conclusions of these dynamical studies is that van der Waals clusters behave in a statistical manner and that IVR/VP kinetics are given by standard vibrational relaxation theories (Beswick and Jortner 1981 Jortner et al. 1988 Lin 1980 Mukamel and Jortner 1977) and unimolecular dissociation theories (Forst 1973 Gilbert and Smith 1990 Kelley and Bernstein 1986 Levine and Bernstein 1987 Pritchard 1984 Robinson and Holbrook 1972 Steinfeld et al. 1989). One can even arrive at a prediction for final chromophore product state distributions based on low energy chromophore modes. If rIVR tvp [4EA(Ar)i], a statistical distribution of cluster states is not achieved and vibrational population of the cluster does not reflect an internal equilibrium distribution of vibrational energy between vdW and chromophore states. If tvp rIVR, and internal vibrational equilibrium between the vibrational modes is established, and the relative intensities of the Ar = 0 torsional sequence bands of the bare chromophore following IVR/VP can be accurately calculated. A statisticsl sequential IVR/VP model readily explains the data set (i.e., rates, intensities, final product state distributions) for these clusters. 

I trust that this book gives the flavor of the pace, excitement, and accomplishments of the last few years of cluster research. For me, the most surprising and important feature of this volume is the breadth that this new area of physical chemistry demonstrates. The various experimental chapters cover ionic chemistry, hot atom chemistry, photochemistry, neutral molecule chemistry, electron and proton transfer chemistry, chemistry of radicals and other transient species, and vibrational dynamics and cluster dissociation. Of at least equal importance is that theoretical potential energy surface studies are not accessible for cluster systems and are being pursued. All of us associated with this project have tried to convey the fresh insights and contributions that van der Waals cluster research has brought to physical chemistry. 

Chalasinski G, Szczesniak MM (1994) Origins of structure and energetics of Van der Waals clusters from ab initio calculations. Chem Rev 94 1723-1765... 

Chalasinski, G. and Szczesniak M.M., Origins of Structure and Energetics of van der Waals Clusters from ab Initio Calculations. Chem. Rev. (1994) 94 1723—1765. 

Wanna J, Menapace JA, Bernstein ER (1986) Hydrogen bonded and non-hydrogen bonded van der Waals clusters Comparison between clusters of pyrazine, pyrimidine, and benzene with various solvents. Journal of Chemical Physics 85 1795-1805. 

Fig. 9. Experimentally determined dissociation energies of mercury clusters ions (open circles) and calculated dissociation energies of neutral van der Waals clusters, scaled to the Hg, dissociation energy.

The first is the choice of fairly large, finite-sized van der Waals clusters for the environment of the chemical reaction (10 -10 atoms or molecules in our case). At such sizes, the number of surface atoms is relatively important compared with the number of atoms staying inside the cluster, and in our case the reactants deposited on the clusters stay at the surface, but are free to migrate, to collide with each other and eventually to react. 

The fluorescence spectroscopy of the 2 state of coronene has been examined in the solid state, as isolated molecules, and also in van der Waals clusters 39, fluorescence of... 

Calculations on the gas phase interactions of most pairs (or small clusters) of molecules have been possible using ORIENT for some time. This program is available on request from the author s web site (http //fandango.ch.cam.ac.uk/). The latest version ORIENT3 not only can determine the minimum energy structures of van der Waals clusters, their transition states, and other stationary points, it also can calculate their vibrational modes, and it has the ability to use anisotropic repulsion, dispersion, and induction energy models. 

D J. Chartrand, J.C. Shelley, R.J. LeRoy, Pulling, packing, and stacking structural proclivities of SFg-(rare gas)jj van der Waals clusters. Journal of Physical Chemistry, 95 (1991) 8310. 

The second part of the chapter (Section III) deals with the time-dependent self-consistent-field (TDSCF) method for studying intramolecular vibrational energy transfer in time. The focus is both on methodological aspects and on the application to models of van der Waals cluster systems, which exhibit non-RRKM type of behavior. Both Sections II and III review recent results. However, some of the examples and the theoretical aspects are presented here for the first time. 

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