Atomic charges and charge flux

Atomic Charges and Charge Flux Parameters from the Atomic Multipolar Tensors. The Planar Case... 

The atomic charges and charge flux parameters are thus all contained in the atomic polar tensor, and are readily available from ab initio calculations. 

ATOMIC CHARGES AND CHARGE FLUX PARAMETERS FROM THE ATOMIC MULTIPOLAR TENSORS. THE PLANAR CASE... 

Equation (18) is a quantum mechanical expression for the force on a nucleus in a planar molecule due to a homogeneous electric field. The expression is accurate to first order (i.e., polarizability is neglected) and, in view of the definitions (equations 16 and 17) of atomic charge and charge flux, is nothing else than equation (2). The latter, as already stated, underlies the empirical force field calculations. This further demonstrates the self-consistency of the present approach. 

Similar formulation, based on representing a molecular difKile moment in terms of effective atomic charges, has been put forward by Aleksanyan el al. [107,110]. Basically the treatment refers to analogous intensity parameters. These are effective atomic charges and atomic charge fluxes expressed in the space of atonuc Cartesian displacement... 

According to this treatment, repulsive interaction at the hydrogen atoms produces a flux of negative charge toward the carbon atom concerned and thereby... 

Let us discuss an L matrix transformation for isothermal and isobaric atomic fluxes when there is one additional electronic species present. We start with the flux equations in which the index j denotes the atomic species and e denotes the electric charge carriers (eg., electrons). 

According to the AIM theory, an atom is defined as a region of space bounded by a surface that is not crossed by any gradient vectors of p(r) (the so-called zero-flux property) [45]. A molecular system is thus partitioned into atomic basins whose boundaries are such surfaces. Integration of the electron density over an atomic basin A gives its total electron population Na so that the net atomic charge is q = — Na- Koch and Popelier proposed the use of... 

R. L. A. Haiduke, R. E. Bruns. An atomic charge-charge flux-dipole flux atom-in-molecule decomposition for molecular dipole-moment derivatives and infrared fundamental intensities. J. Phys. Chem. A-, 109, 2680-2688 (2005). 

The largest difference between force fields is probably how they handle electrostatics. Each force field uses its own definition of what functions and data should be used. The well-known MM2 force field describes all electrostatic interactions by bond dipoles (4), but most other force fields utilize atomic point charges. The charges may in turn be obtained from fragment matching (34), from bond-type-dependent charge flux (35), or from more complex schemes that can also respond to the environment (36). 

We may draw the following conclusions at this point. Forces on nuclei are determined not only by the atomic charges, but include terms from the charge flux. As can be seen from the example of water, it appears that the charge flux may be fairly significant. In water, the neglect of charge flux causes an 80% error in the in-plane forces. Additional research is under way to further characterize these effects and their importance. 

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 ... 

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