Bond charge parameter formulation

The bond charge parameter formulation developed by Van Straten and Smit [92] describes infi-ared intensities in terms of static bond charges and bond charge fluxes induced by vibrational distortions. In the mathematical procedure many common features with the )paratus of the valence-optical theory are present. 

In correlation studies over large numbers of crystal structures, the calculation of the lattice energy must be relatively fast, and it is very difficult, if not altogether impossible, to calculate accurate point charges or distributed dipoles for thousands of molecules. It is also impossible to analyze all the molecular structures to find the locations of specific charge sites such as lone pairs, bond dipoles, etc. the formulation must be a strictly atom-atom one, with all interaction centers located at easily recognizable atomic nuclear positions, and should either require no separate coulombic terms, or use a ready recipe for the approximate evaluation of atomic point charge parameters without ab initio molecular orbital calculations. 

Another model that can be applied to large-scale computations is the Williams force field (ref. [44], Chapter 4 see Table 8.4) with atomic point charge parameters calculated by the rescaled EHT approach (equation 4.12). This formulation (which we call here WqEHT) does not apply to hydrogen bonded crystals. The more refined forms of the Williams force field cannot be used, because of the difficulty of automatically allocating site charges far from atomic nuclei. 

Three types of intensity parameters oiter Eq. (6.59). These are die bond dipole moments Pk, die first derivatives of bond moments widi respect to internal coordinates, and second derivatives d pk/dR dR],. The latter quantities are termed electro-optical anharmonic parameters. These toms reflect the non-linear dependence of Pk on the vibrational coordinates Bj and are determined by die electrical anharmonicity of molecular vibrations. As in the charge flow formulation, harmonic terms miter the expressions for intensities of binary overtone and combination bands. 

In diis section a method for interpretation of Raman intensities based on further transformations of atomic polarizability tensors is presented. The formulation was recently proposed by Ehidev and Galabov [333], A new molecular quantity - effective induced bond charge, Ok introduced. The effective induced bond charges are obtained from rotation-free atomic polarizability tensors following the strate as outlined by Galabov, Dudev and nieva [146] in the infrared case (Section 4.IV). The Ok parameters are expected to be associated with polarizability properties of valence bonds. 

This perturbation-theoretic formulation of the dielectric susceptibility is most appropriate and will be used in the treatment of dielectric properties based upon pscudopotcntials in Chapter 18. However, for the calculation of higher-order susceptibilities, a more direct approach in terms of bond dipoles is more convenient. Because the two derivations are equivalent, the bond-dipole approach will also enable us to establish parameters for the bond dipoles and effective charges in terms of the parameters listed in Table 4-1. 

It should be emphasized that the charge-flux effects are implicidy included in electro-optical parameters of the type dpj dRj that appear in the first-order bond moment model [72]. Thus, in standard applications to various molecules it does not seem necessary to extend the original formulation since this would result in further increase in intensity parameters. 

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