Polarizability invariants

Recently, Rizzo and collaborators reported ab initio calculations of the polarizability invariants for the helium318 319, neon320, and argon318 319 dimers, followed by quantum-statistical and classical calculations of the dielectric second... 

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]. 

P. D. Dacre and L. Frommhold. Spectroscopic examination of ab initio neon diatom polarizability invariants. J. Chem. Phys., 75 4159-4160 (1981),... 

Here each independent molecular polarizability invariant is explicitly defined as... 

Recently, the sapt approach has been applied (32) to compute the interaction-induced polarizability for the helium diatom. The computed polarizability invariants have been analytically fitted, and used in quantum-dynamical calculations of the binary collision-induced Raman spectra. The results of the dynamical calculations are summarized in Fig. 1. 

Fig. 4.1 The interaction polarizability invariants Aa(R) of the complexes Xe-Xe (a) and He-He (b) (firstly printed in our work [59]). Solid lines— analytical calculations taking into account the exchange polarizability dashed lines—analytical calculations without considering the exchange polarizabihty circles— ab initio calculation [112] squares—ab initio calculation [62]. All values are in a.u...

The interaction-induced (hyper)polarizability of two Kr atoms was calculated with a [8s7p6d5f] basis set at the SCF and MP2 levels of theory. At R/ao = 4, the MP2 values of the interaction (hyper)polarizability invariants are (SCF values in parentheses) a = 3.6127 (2.4113) and Aa = 24.8369 (21.8086) e ao Eii The interaction mean second hyperpolarizability at the same distance is y = 17837.0 (11719.3) e" ao" Eii . The electron correlation effects are important for all properties at short separations. The R-depen-dence of the polarizability invariants and the Cartesian components and the mean of the second hyperpolarizability are shown in Figs. 5 and 6, respectively. In both cases, the strong anisotropic character of the (hyper)polar-izability for short separations is very much obvious. 

Fig. 5 R-dependence of the interaction-induced polarizability invariants of two Kr atoms.

The interaction electric properties of the HCN-HF and HNC-HF complexes was reported by Li et al Their final-field calculations were performed with large augmented correlation-consistent basis sets. At the CCSD(T) level of theory a large d-aug-cc-pVTZ basis set yields the following values for the dipole moment and (hyper)polarizability invariants of HCN-HF (HNC-HF values are given in parentheses, in italics) p = 2.2918 (2.5335) eao, a = 23.186(24.353) and Aa= 14.393 (74.575) e Eh", =-6.03 (7.60) y = 2553.4 (3049.3) e ao Et l Notice the... 

Thus, the respective absolute trace and anisotropy Raman differential cross sections are functions of a single polarizability invariant derivative only... 

Eq. (8.45) shows that for an ordinary Raman experiment the absolute differential Raman scattering cross sections can be expressed in terms of derivatives of the molecular polarizability invariants a and y with respect to normal coordinates. These derivatives contain valuable information about the variation of molecular polarizability with vibrational motion. Gas-phase Raman scattering cross sections are most suited for intensity analysis since at low partial pressure of the sampling gas these quantities are not influenced by effects of intermolecular interactions, thus reflecting properties of individual molecules. 

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