Pair polarizabilities

Gelbart (1974) has reviewed a number of theories of the origins of the depolarized spectrum. One of the simplest models is the isolated binary collision (IBC) model of McTague and Bimbaum (1968). All effects due to the interaction of three or more particles are ignored, and the scattering is due only to diatomic collision processes. In the case that the interacting particles A and B are atoms or highly symmetrical molecules then there are only two unique components of the pair polarizability tensor, and attention focuses on the anisotropy and the incremental mean pair polarizability... 

The first ab initio smdy of an interaction polarizability was that of O Brien et al. (1973) on a pair of helium atoms. They obtained /0(r) for the range r = 3.5ao through lOao- The experimentally determined value of is negative, which suggests that the incremental mean pair polarizability must be negative around the minimum in the potential curve. 

A problem with studies on inert gas is that the interactions are so weak. Alkali halides are important commercial compounds because of their role in extractive metallurgy. A deal of effort has gone into corresponding calculations on alkali halides such as LiCl, with a view to understanding the structure and properties of ionic melts. Experience suggests that calculations at the Hartree-Fock level of theory are adequate, provided that a reasonable basis set is chosen. Figure 17.7 shows the variation of the anisotropy and incremental mean pair polarizability as a function of distance. 

Figure 17.7 Anisotropy (doited) and mean incremental pair polarizability...

Dacre, P. D., A calculation of the helium pair polarizability including correlation effects, Mol. Phys. 36, 541-551 (1978),... 

The simplest, and least realistic, method for including induced dipole interactions is to average the potential for pair-polarizable point dipoles over all relative orientations, in which case the induced energy is the well-known Debye component of the van der Waals potential ... 

Because not much is known experimentally about general interaction tensors, and especially not about their long range behaviour, we will not pursue this line of approach, but rather give a brief review of the existing work which has concentrated on two different tensors the pair dipole (order 1 tensor) and the pair polarizability (order 2 plus order 0 tensor). 

The influence of Van der Waals interactions on the polarizability of interacting molecules manifests itself in deviations from the Clausius-Mosotti equation in the Kerr effect and in collision induced li t scattering Ahhougji measurements of these effects are all performed on bulk systems in thermodynamical equilibrium and not on Van der Waals molecules per se, we will nevertheless say a few words about pair polarizabilities, because, just as in the case of the collision induced IR absorption, much can be learned about Van der Waals interactions from the comparison of experimental and computational results. 

Finally, it must be pointed out that theory and experiment are not yet in complete agreement with regard to the trace of the pair polarizability of HCj. The most... 

Previous Reviews. A general survey of the effects of molecular interactions on the optical properties of matter was recently given by Buckingham [435]. The work concerning ab initio and approximate computations of pair polarizabilities has recently been reviewed by Hunt [80] a careful comparison of the data available from various measurements reveals a high degree of consistency with the fundamental theory. Hunt has also reviewed the utility of the DID model and its limitations [79]. The results of measurements of the polarizability invariants of rare-gas pairs have been reviewed by one of the authors [271]. Substantial discussions of induced polarizabilities can be found in a number of review articles on CILS and dielectric properties [11,27, 143, 274, 343, 376]. 

Measurements. The anisotropy of the pair polarizability has been determined from three types of measurements depolarized CILS spectra, pressure dependent depolarization ratios, and second virial Kerr coefficients. 

Computations. Efforts to compute pair polarizabilities from first principles, using perturbation techniques or modern quantum chemical methods, have been known for many years and are reviewed by Hunt [80] in the desirable detail. Amos s review of ab initio methods applied to the computation of molecular properties considers supermolecular properties, too [2]. 

The helium pair polarizability increment has been studied extensively [19, 29, 39, 41, 48, 56, 57, 63]. We mention in particular the most recent work by Dacre [48], which includes a careful review of previous results. Systems such as H-H in the and states may be considered as tractable examples representative of various types of real collisional pairs [6,28,54, 55,66,74,85, 144, 145, 147]. Elaborate self-consistent field (SCF) calculations, supplemented by configuration interaction (Cl) corrections are also known for the neon diatom [50]. For atom pairs with more electrons, attempts have been made to correct the SCF data in some empirical fashion for Cl effects [47, 49]. Ab initio studies of molecular systems, such as H2-H2 and N2-N2 have been communicated [16, 18]. 

Theory. If the invariants of the pair polarizability are known, along with a refined model of the intermolecular interaction potential, the lineshapes of binary spectra can be computed quite rigorously [227, 231, 271], Lineshape computations based on exact or approximate classical trajectories are known [196, 264, 276, 316, 337]. Such computations generate spectral functions that are symmetric, g — co) = g((o). For massive pairs at high enough temperatures, such classical profiles are often sufficient at frequency shifts much smaller than the average thermal energy, ha> < kT, albeit special precaution is necessary when the system forms van der Waals dimers [302]. 

F. Barocchi, M. Neri, and M. Zoppi. Etetermination of the pair polarizability of argon from the two-body CILS spectrum. Chem. Phys. Lett., 79 537-540 (1978). 

A. D, Buckingham and K. L. Clarke-Hunt. The pair polarizability anisotropy of SF in the point-atom-polarizability approximation. Molec. Phys., 40 643-648 (1980). 

V. Chandrasekharan and G. C. Tabisz, Resonance and dispersion energies and the point-dipole model of atomic pair polarizability, Canad. J. Phys., 58 1420-1423 (1980). 

P. D. Dacre, A calculation of the neon pair polarizability including correlation effeets. Canad. J. Phys., 59 1439-1447 (1981). 

P. D. Dacre. Pair polarizabilities of the heavy inert gases II. SCF calculations of the pair polarizabilities of krypton and xenon. Molec. Phys., 47 193-208 (1982). 

D. B. DuPre and J. P. McTague. Pair polarizability of hydrogen atoms. Relation to collision induced light scattering and dielectric phenomena in rare gases. J. Chem. Phys., 50 2024-2028 (1969). 

P. R. Hilton and D. W. Oxtoby. Charge transfer in atomic collisions The pair polarizability anisotropy. J. Chem. Phys., 72 4Ti-4n (1980). 

N. Meinander, G. C. Tabisz, and M. Zoppi. Moment analysis in depolarized light scattering Determination of a single-parameter empirical pair polarizability anisotropy for Ne, Ar, Kr, Xe and CH. J. Chem. Phys., 54 3005-3013 (1986). 

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