Generalized atomic polar tensor charges

The derivative of the dipole moment with respect to the nuclear coordinates determines intensities of IR absorptions (Section 10.1.5). A central quantity in this respect is the Atomic Polar Tensor (APT), which for a given atom is defined in 

Such a matrix is not independent of the coordinate system, but the trace is. J. Cioslowski has proposed a definition of atomic charges as one-third of the trace over the APT, denoted Generalized Atomic Polar Tensor (GAPT) charges. The charge on atom A is defined in eq. (9.18). 

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GAPT (generalized atomic polar tensor) a charge calculation method GB/SA (generalized Born/surface area) method for computing solvation effects... 

Generalized Atomic Polar Tensor (GAPT), for Hiickel theory, 93, 94 atomic charges. 226... 

Analysis of the derivatives of dipole moments with respect to nuclear displacements (the atomic polar tensors) gives rise to yet another definition of atomic charges. The GAPT (generalized atomic polar tensor) atomic charges ate... 

Cioslowski J, 8ay PJ, Ritchie IP (1990) Charge distributions and effective ateutuc charges in transition-metal complexes using generalized atomic polar tensors and topological analysis. J... 

For planar molecules the perpendicular charge fluxes are zero by symmetry, and the atomic charge may be extracted from the perpendicular elements of the atomic polar tensor. The definition given above for the oxygen charge is thus quite general namely, for planar molecules ... 

So far we have seen that the APT representation of infrared absorption intensities offers a mathematically efficient way of reducing the experimental data to quantities associated with motions of individual atoms in molecules. In general terms such a rationalization of intensity data appears acceptable since intramolecular charge distribution may be approximately expressed in teims of partial atomic charges provided, of course, that an effective way is found to relate the charge distribution with atomic polar tensors. 

In the present section a theoretical framework for analysis of vibrational intensities recendy developed by Galabov et al. [146] is presented. Fully corrected for rotational contributions atomic polar tensors are transformed into quantities termed effective bond charges. The effective bond charges are expected to reflect in a generalized manner, polar properties of the valence bonds in molecules. Aside from die usual harmonic approximation no other constraints are imposed on the dipole moment functirm. 

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