Electrostatic potential polarization correction

Correction of Electrostatic Potentials for Polarization Application to Nucleophilic Attack in Aspartyl Proteases. ... 

Francl MM. Polarization corrections to electrostatic potentials. J Phys Chem 1985 89 428-433. 

The electrostatic potential V(r) is the first order contribution to the interaction energy. The second order contribution P(r), which is commonly referred to as a polarization correction to the electrostatic potential, is defined within the imcoupled Hartree-Fock perturbation theory by [41]... 

The i are the orbital energies and the c i are the molecular orbital expansion coefficients in terms of the atomic orbital basis set Xp- Contributions from terms greater than second order are generally small and can for most chemical applications be neglected [41, 42]. Only a limited number of applications of P(r) for analysis of intermolecular interactions have appeared in the literature. The most common approach of analysis has been to calculate a total interaction index, a "polarization-corrected electrostatic potential", defined by... 

The belief that electrostatic (Coulomb) interactions exhibit little directionality (i.e., that their energy hardly depends on the bond angle) is widespread. This is because the concept of net atomic charges (atom-centered monopoles) has become ingrained in chemists thinking, so that Coulomb interactions with a polar atom are believed to be necessarily isotropic and directionahty of Coulomb interactions only to be the result of secondary interactions with more distant atoms. Neither of these assumptions is correct and the reasons have been known for decades. Nonetheless, directionality in noncovalent interactions is still often attributed to covalent contributions or donor-acceptor interactions because the Coulomb interaction is believed not to be able to give rise to significant directionality. The purpose of this chapter is to discuss Coulomb interactions with special emphasis on directionality and anisotropy of the molecular electrostatic potential (MEP) [1] around atoms. 

In a QM calculation the wavefunction and, hence, the electron density of the system is determined. Thus, in a QM/MM hybrid potential calculation, in which there are electrostatic interactions between e QM and MM atoms, the electron density of the QM region will be influenced by the charges on the MM atoms. In contrast, in most MM force fields, the charges on the MM atoms are fixed parameters and so the MM charge distribution will not respond to changes in its environment. These MM polarization corrections can be significant in many systems and so some work has been done to try to include them. 

Fig. 3.7. Spatial variations of the electric field (full lines) and of the electrostatic potential V (dashed line) in a thin sample cut along a polar direction, (a) When the planes bear charge densities equal to + a, the electrostatic potential increases monotonically through the sample, (b) The charge density on the outer planes is corrected by a = a/2 the electrostatic potential no longer increases proportionally to the sample thickness, but oscillates around a non-zero value, (c) A dipole moment a"R is added on the outer faces the electrostatic potential oscillates around a zero value if a" = <7/4.

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