Rare-gas clusters

C1.1.6 RARE-GAS CLUSTERS AND OTHER WEAKLY BONDED MOLECULAR CLUSTERS... 

Rare-gas clusters can be produced easily using supersonic expansion. They are attractive to study theoretically because the interaction potentials are relatively simple and dominated by the van der Waals interactions. The Lennard-Jones pair potential describes the stmctures of the rare-gas clusters well and predicts magic clusters with icosahedral stmctures [139, 140]. The first five icosahedral clusters occur at 13, 55, 147, 309 and 561 atoms and are observed in experiments of Ar, Kr and Xe clusters [1411. Small helium clusters are difficult to produce because of the extremely weak interactions between helium atoms. Due to the large zero-point energy, bulk helium is a quantum fluid and does not solidify under standard pressure. Large helium clusters, which are liquid-like, have been produced and studied by Toennies and coworkers [142]. Recent experiments have provided evidence of... 

Miehle W, Kandler O, Leisner T and Echt O 1989 Mass spectrometric evidence for icosahedral structure in large rare gas clusters Ar, Kr, Xe J. Chem. Phys. 91 5940... 

Elucidating the origin of magic numbers has been a problem of long-standing interest, made accessible through the use of the laser-based reflectron TOF technique and evaporative ensemble theory. Three test cases are considered, first protonated ammonia clusters where (NH3)4 NHj has been found to be especially prominent, and then two other cases are considered, one involving water cluster ions and another rare gas clusters. 

The spectroscopy of elementaiy systems such as atoms / molecules trapped in the volume or at the surface of small rare-gas clusters is a subject of continuous... 

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... 

As shown in previous publications relative to absorption spectroscopy and ground-state equilibrium geometries, the sodium atom in a 3s state prefers to bind on the surface of a rare-gas cluster. This stems from the fact that the NaAr diatomics have a smaller bonding energy at a longer intemuclear distance than ArAr, in concordance with the rather large size of the isotropic 3 s orbital. 

The first experimental evidence for the existence of magic numbers was reported by Recknagel and coworkers (Echt et al. 1981). Since then, a number of experimental and theoretical studies of magic numbers in rare gas clusters have been published (Buck and Meyer 1986 Carnovale et al. 1989 Castleman et al. 

Dehmer and Pratt were one of the earliest groups to observe resonance structures in the photoionization efficiency (PIE) curves of small argon ions and mixed rare gas cluster ions (Dehmer and Pratt 1982 Pratt and Dehmer 1982). The structures in the PIE curves of small argon cluster ions were attributed to interband transitions while the features observed in the PIE curves of mixed rare gas cluster ions were suggested to arise from autoionizing states. Walters et al. (1985) also observed similar resonances in the PIE curves of C6H6/HC1... 

The purpose of our work was to examine whether the compressed hot cluster provides an effective medium for reactions with high barriers. In the simplest case of cluster impact experiments, the reactants are embedded inside a rare gas cluster, and this cold droplet is incident on an inert surface at various velocities. Two classes of reactions were examined in detail using standard molecular dynamics simulations the dissociation of halogen molecules and four-center reactions. ... 

The high relative velocities following impact of a cluster on a surface suggests that such dissociation processes can readily take place when a diatomic molecule embedded inside the cluster is activated by a collision. Molecular dynamics simulations show that beyond a threshold, the yield of dissociation of halogen molecules solvated in a rare gas cluster is a rapidly increasing function of the collision velocity and can reach 100%, see Fig. 6. This, unlike the surface impact induced dissociation of unclustered, cold, halogen molecules where the yield reaches a plateau of below 40%. ° ... 

Diatomic molecules embedded in rare gas cluster can dissociate in one of two ways a heterogeneous dissociation of the molecule on the surface and a homogeneous mechanism where dissociation takes place inside the cluster without the molecule reaching the surface. The sudden collision regime insures that an effective vibrational excitation of the diatomic molecule will occur due to a collision between the diatomic molecule and the rare gas atoms of the cluster. Yet, the size of the cluster and the identity of the rare gas atoms influence the yield of dissociation. 

On the other hand, heavier rare gases are not acting as effectively in removing energy from the internally hot, nascent, molecular products. The yield of stable molecular products is favored in lighter rare gases (cf. Fig. 14) where the reactive yield is plotted for Ne and Ar rare gas clusters on a reduced energy scale. 

Fig. 13. The yield of all rearrangement processes following a bimolecular N2 + O2 collision vs. the collision energy in kcalmol . (The energy is computed from the velocity of impact using the reduced mass of the reactants.) The results shown are for the reactants embedded in a 125 atoms rare gas cluster where the identity of the rare gas is indicated in the inset (for more details about the energy scaling, see Ref. 82).

In the previous section we showed that molecular dynamic simulations and an information theory analysis predicted similar results for the fragmentation process of impact heated rare gas clusters, results which soon thereafter have been confirmed experimentally. In this section we compare the results from both methods on the study of the impact of clusters containing several N2 and O2 molecules and clusters containing only N2 and O2 molecules. We still have no definitive results for this particular experiment but we hope that this challenge will be taken up soon. Other four-center reactions have, as we write this chapter, been observed. 

The reason we employ two rather distinct methods of inquiry is that neither, by itself, is free of open methodological issues. The method of molecular dynamics has been extensively applied, inter alia, to cluster impact. However, there are two problems. One is that the results are only as reliable as the potential energy function that is used as input. For a problem containing many open shell reactive atoms, one does not have well tested semiempirical approximations for the potential. We used the many body potential which we used for the reactive system in our earlier studies on rare gas clusters containing several N2/O2 molecules (see Sec. 3.4). The other limitation of the MD simulation is that it fails to incorporate the possibility of electronic excitation. This will be discussed fmther below. The second method that we used is, in many ways, complementary to MD. It does not require the potential as an input and it can readily allow for electronically excited as well as for charged products. It seeks to compute that distribution of products which is of maximal entropy subject to the constraints on the system (conservation of chemical elements, charge and... 

Dissociation Dynamics of Diatomic Molecules Embedded in Impact Heated Rare Gas Clusters, T. Raz, I. Schek, M. Ben-Nun, U. Even, J- Jortner and R. D. Levine, J. Chem. Phys. 101, 8606 (1994). 

A. Ulitski, R. Elber, The thermal equilibrium aspects of the time dependent Hartree and the locally enhanced sapling approximations Formal properties, a correction, and computational examples for rare gas clusters, J. Chem. Phys. 98 (1993), 3380. 

Mixed molecular clusters can be prepared by two different techniciues (i) by a co-expansion, where a mixture of the dopant with a rare gas is expanded into fhe vacuum, or (ii) by a pick-up procedure, in which case the neat rare gas clusters prepared by a supersonic expansion travel through a chamber with a dopant and a buffer gas. For solid systems one is thus able to prepare clusters with the dopants... 

Figure 2. Size dependence of the DMC calculated ground vibrational (librational) wavefunction for HI on Ar , (n = 1 — 6, corresponding with labels a) to f)). Wavefunction is depicted as a function of cos 0 where 0 is the angle between the cluster center of mass and the center of mass of the dopant. Note the flip of the H wavefunction towartls the rare gas clusters upon increasing cluster size seen for the calculations in reduced dimensionalitv is no more observed.

Early work on the structure and dynamics of rare-gas clusters followed two main routes. Hoare and searching for the most stable structures,... 

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