Electrostatic interactions multipole representations

More realistic treatment of the electrostatic interactions of the solvent can be made. The dipolar hard-sphere model is a simple representation of the polar nature of the solvent and has been adopted in studies of bulk electrolyte and electrolyte interfaces [35-39], Recently, it was found that this model gives rise to phase behavior that does not exist in experiments [40,41] and that the Stockmeyer potential [41,42] with soft cores should be better to avoid artifacts. Representation of higher-order multipoles are given in several popular models of water, namely, the simple point charge (SPC) model [43] and its extension (SPC/E) [44], the transferable interaction potential (T1PS)[45], and other central force models [46-48], Models have also been proposed to treat the polarizability of water [49],... 

The electrostatic interaction, which is defined as the classical Coulombic interaction between the undistorted charge distributions of the isolated molecules, is the easiest to derive from wavefunctions. When there is no overlap of the charge distributions of the molecules, all that is required is a representation of the molecular charge density. The traditional, and simplest, representation of the molecular charge distribution is in terms of the total multipole moments. The first nonvanishing multipole moment could often be derived from experi-... 

The accuracy of a distributed multipole representation can always be tested by evaluating the effect on the calculated electrostatic energies in the region of interest of increasing the number of interaction sites (e.g., by adding sites at the midpoints of bonds) or the order of multipoles. Similarly, simplifications of the model, such as removing small multipole components, can be evaluated. However, the accuracy of the calculated electrostatic energies is inevitably limited by the quality of the wavefunction and the absence of penetration effects. 

Volkov, A., Koritsanszky, T, and Coppens, P. [2004]. Combination of the exact potential and multipole methods [EP/MM] for evaluation of intermolecular electrostatic interaction enei ies with pseudoatom representation of molecular electron densities, Chem. Phys. Lett 391, pp. 170-175, dol 10.1016/j.cplett.2004.04.097. von Lilienfeld, 0. A., Tavernelli, 1., Rothlisberger, U., and Sebastian , D. [2004]. Optimization of effective atom centered potentials for London dispersion forces in density functional theory, Phys. Rev. Lett 93,15, p. 153004. 

Electrostatic interactions can also be represented by a distribution of point charges, an approach used in numerous force fields. Both representations (point charges and atomic multipoles) are strictly valid only at long range. The electrostatic interaction which acts between a pair of point charges qt and qj is described by Coulomb s law ... 

An alternative approach was to include explicit, higher order electrostatic moments in the pairwise interactions. This approach has not been extensively developed for use in molecular simulations because of the complex set of moments needed to obtain sensible results, particularly to mimic hydrogen bonding. A notable exception is the polarizable electropole model, which relies on a central polarizability as well as higher order moments to capture the electrostatic part of the interactions." The computational effort required for a multipole-based representation of the electrostatics is much greater than is involved in the use of distributed charges to represent the electrostatic interactions. If, on the other hand, the number of partial charge sites is substantially increased, a local expansion of multipole moments can become computationally economical. ... 

The development of the new techniques for the computation of charge, the efficient calculation of long range electrostatic interactions by fast multipole and Particle Mesh Ewald techniques, and for the increased efficiency of integration by the multiple time step methods (RESPA) lead to a spirit of optimism in the computational chemistry community, Improvements in force fields, such as the incorporation of polarizability and a more accurate representation of the electron density in molecules should lead to even better agreement with experiment,... 

Over the years various approximate formulas for interactions between large molecules have been derived from perturbation theory (91) The better of such perturbation theory expansions customarily include a short-range first order "exchange" term and long range terms (electrostatic, polarization and dispersion). Various approximations (such as the multi-centered multipole expansion, representation of transition densities by bond dipole and the decomposition of molecular polarizability into bond polarizabilities, the use of atomic polarizabilities, bond-bond interaction terms, etc.) have been introduced for the calculation of certain of the terms. 

A Gaussian-based electrostatic model (GEM) has been explored as an alternative to distributed point multipole electrostatic representation. GEM computes the molecular interaction energies using an approach similar to SIBFA... 

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