Rare gas,

Fig. Ill-13. (a) Plots of molecular density versus distance normal to the interface a is molecular diameter. Upper plot a dielectric liquid. Lower plot as calculated for liquid mercury. (From Ref. 122.) (b) Equilibrium density profiles for atoms A and B in a rare-gas-like mixmre for which o,bb/ o,aa = 0.4 and q,ab is given by Eq. III-56. Atoms A and B have the same a (of Eq. m-46) and the same molecular weight of SO g/mol the solution mole fraction is jcb = 0.047. Note the strong adsorption of B at the interface. [Reprinted with permission from D. J. Lee, M. M. Telo de Gama, and K. E. Gubbins, J. Phys. Chem., 89, 1514 (1985) (Ref. 88). Copyright 1985, American Chemical Society.]...

It was noted in connection with Eq. III-56 that molecular dynamics calculations can be made for a liquid mixture of rare gas-like atoms to obtain surface tension versus composition. The same calculation also gives the variation of density for each species across the interface [88], as illustrated in Fig. Ill-13b. The density profiles allow a calculation, of course, of the surface excess quantities. 

Fig. VII-4. Interactions across a dividing surface for a rare-gas crystal. (From Ref. 43.)...

A related approach carries out lattice sums using a suitable interatomic potential, much as has been done for rare gas crystals [82]. One may also obtain the dispersion component to E by estimating the Hamaker constant A by means of the Lifshitz theory (Eq. VI-30), but again using lattice sums [83]. Thus for a FCC crystal the dispersion contributions are... 

LEIS Low-energy ion scattering [155-157] A monoenergetic beam of rare-gas ions is scattered elastically by surface atoms Surface composition... 

A few ab initio calculations are the main source of our current, very meagre knowledge of non-additive contributions to the short-range energy [91], It is unclear whether the short-range non-additivity is more or less important than the long-range, dispersion non-additivity in the rare-gas solids [28, 92],... 

This simple model is adequate for some properties of rare gas fluids. When it is combined with an accurate description of the electrostatic interactions, it can rationalize the structures of a large variety of van der Waals... 

The potential fiinctions for the mteractions between pairs of rare-gas atoms are known to a high degree of accuracy [125]. Flowever, many of them use ad hoc fiinctional fonns parametrized to give the best possible fit to a wide range of experimental data. They will not be considered because it is more instmctive to consider representations that are more finnly rooted in theory and could be used for a wide range of interactions with confidence. 

Thakkar A J, Hettema H and Wormer P E S 1992 Ab initio dispersion coefficients for interactions involving rare-gas atoms J. Chem. Phys. 97 3252... 

Perez-Jordy J M and Becke A D 1995 A density functional study of van der Waals forces rare gas diatomics Chem. Phys. Lett. 233 134... 

Rokni M and Jaoob J FI 1982 Rare-gas halide lasers Applied Atomic Collision Physics, Vol 3, Gas Lasers ed FI S W Massey, E W MoDaniel, B Bederson and W L Nighan (New York Aoademio)... 

For example, energy transfer in molecule-surface collisions is best studied in nom-eactive systems, such as the scattering and trapping of rare-gas atoms or simple molecules at metal surfaces. We follow a similar approach below, discussing the dynamics of the different elementary processes separately. The surface must also be simplified compared to technologically relevant systems. To develop a detailed understanding, we must know exactly what the surface looks like and of what it is composed. This requires the use of surface science tools (section B 1.19-26) to prepare very well-characterized, atomically clean and ordered substrates on which reactions can be studied under ultrahigh vacuum conditions. The most accurate and specific experiments also employ molecular beam teclmiques, discussed in section B2.3. 

The first two of these we can readily approach with the knowledge gained from the studies of trappmg and sticking of rare-gas atoms, but the long timescales involved in the third process may perhaps more usefiilly be addressed by kinetics and transition state theory [35]. 

In addition to the dependence of the intennolecular potential energy surface on monomer vibrational level, the red-shifting of the monomer absorption as a fiinction of the number of rare gas atoms in the cluster has been studied. The band origin for the Vppp = 1 -t— 0 vibration in a series of clusters Ar -HF, with 0 < n < 5, was measured and compared to the HF vibrational frequency in an Ar matrix (n = oo). The monomer vibrational frequency Vp p red shifts monotonically, but highly nonlinearly, towards the matrix value as sequential Ar atoms are added. Indeed, roughly 50% of the shift is already accounted for by n = 3. 

The fonnation of clusters in the gas phase involves condensation of the vapour of the constituents, with the exception of the electrospray source [6], where ion-solvent clusters are produced directly from a liquid solution. For rare gas or molecular clusters, supersonic beams are used to initiate cluster fonnation. For nonvolatile materials, the vapours can be produced in one of several ways including laser vaporization, thennal evaporation and sputtering. 

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... 

Tunable visible and ultraviolet lasers were available well before tunable infrared and far-infrared lasers. There are many complexes that contain monomers with visible and near-UV spectra. The earliest experiments to give detailed dynamical infonnation on complexes were in fact those of Smalley et al [22], who observed laser-induced fluorescence (LIF) spectra of He-l2 complexes. They excited the complex in the I2 B <—A band, and were able to produce excited-state complexes containing 5-state I2 in a wide range of vibrational states. From line w idths and dispersed fluorescence spectra, they were able to study the rates and pathways of dissociation. Such work was subsequently extended to many other systems, including the rare gas-Cl2 systems, and has given quite detailed infonnation on potential energy surfaces [231. 

The homonuclear rare gas pairs are of special interest as models for intennolecular forces, but they are quite difficult to study spectroscopically. They have no microwave or infrared spectmm. However, their vibration-rotation energy levels can be detennined from their electronic absorjDtion spectra, which he in the vacuum ultraviolet (VUV) region of the spectmm. In the most recent work, Hennan et al [24] have measured vibrational and rotational frequencies to great precision. In the case of Ar-Ar, the results have been incoriDorated into a multiproperty analysis by Aziz [25] to develop a highly accurate pair potential. 

Rank D H, Rao B S and Wiggins T A 1963 Absorption speotra of hydrogen haiide-rare gas mixtures J. Chem. Phys. 37 2511-15... 

MoKeiiar A R W and Weish H L 1971 Anisotropio intermoieouiar foroe effeots in speotra of H2- and D2-rare gas oompiexes J. Chem. Phys. 55 595-609... 

MoKeiiar A R W 1982 infrared speotra of hydrogen-rare gas Van der Waais moieouies Faraday Discuss. Chem. Soc. 73 89-108... 

Rohrbaoher A, Williams J and Janda K C 1999 Rare gas-dihalogen potential energy surfaoes PCCP 1 5263-76... 

Hutson J M and Howard B J 1982 Anisotropio intermoleoular foroes II Rare gas-hydrogen ohioride systems Mol. Phys. 45 769-90... 

Fraser G T and Pine A S 1986 Van der Waals potentials from the infrared speotra of rare gas-HF oomplexes J. Chem. Phys. 85 2502-15... 

In rare gas crystals [77] and liquids [78], diatomic molecule vibrational and vibronic relaxation have been studied. In crystals, VER occurs by multiphonon emission. Everything else held constant, the VER rate should decrease exponentially with the number of emitted phonons (exponential gap law) [79, 80] The number of emitted phonons scales as, and should be close to, the ratio O/mQ, where is the Debye frequency. A possible complication is the perturbation of the local phonon density of states by the diatomic molecule guest [77]. 

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