Atomic polar tensor charges

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

Such a matrix is not independent on the coordinate system, but the trace is. 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 as... 

Rotational and Dipole Strength Calculations for the CH-Stretching Vibrations of L-alanine Using the Localized Molecular Orbital, Nonlocalized Molecular Orbital, Atomic Polar Tensor, and Fixed Partial Charge Models ... 

Because the intensity of a given vibrational mode is connected with the changing molecular dipole moment associated with that particular motion of the atoms, analysis of these intensities offers valuable insights into charge redistributions within the system. One can partition the dipole changes into contributions from various atoms using an atomic polar tensor (APT) formalism - " which is defined for an atom a as... 

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

It is clear that the above results are contrary to the simple and common model of fixed atomic point charges that predicts an isotropic response to an external field. The source of the problem is that the atomic polar tensor is not isotropic. This tensor has nine elements (for each nucleus), corresponding to the derivatives of each component of the dipole moment with respect to the three Cartesian coordinates of the nucleus. The properties of these tensors and their interpretation as atomic charges have been extensively discussed in the literature in connection with infrared intensities.It is well known that the anisotropy of these tensors can be explained as follows. If we write the total molecular dipole moment as formed from point charges, then a typical element of the atomic polar tensor is, for example. 

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 ... 

In the same way that atomic charges are definable by the atomic polar tensor, higher order atomic multipoles can be defined in terms of higher-order atomic multipolar tensors.Specifically, atomic dipoles and quadrupoles, and for diatomics and linear molecules even atomic octupoles, can be calculated. For example, atomic dipoles are given by... 

Recently, two other methods for determining atomic charge have been developed, neither of which makes reference either to orbitals or to the space associated with a given atom. Instead, one method involves the calculation of the atomic polar tensor, and the second fits the elearostatic potential to an expansion of charges at the atomic nuclei. 

In an entirely different approach, Cioslowski has defined atomic charge based on the atomic polar tensor.This method makes no recourse to the nature of the atomic orbitals or the volume of an atom in a molecule. The method makes use of the dipole moment and the derivatives of the dipole moment, which are obtained from the wavefunction. 

The total charge of a molecule Q is the sum of the atomic charges Q, and Q is the trace of the atomic polar tensor of rank one ... 

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