Gaussian electrostatic model

As the SIBFA approach relies on the use of distributed multipoles and on approximation derived form localized MOs, it is possible to generalize the philosophy to a direct use of electron density. That way, the Gaussian electrostatic model (GEM) [2, 14-16] relies on ab initio-derived fragment electron densities to compute the components of the total interaction energy. It offers the possibility of a continuous electrostatic model going from distributed multipoles to densities and allows a direct inclusion of short-range quantum effects such as overlap and penetration effects in the molecular mechanics energies. 

Cisneros GA, Piquemal J-P, Darden TA (2006) Generalization of the Gaussian electrostatic model extension to arbitrary angular momentum, distributed multipoles and speedup with reciprocal space methods. J Chem Phys 125 184101... 

Cisneros, G. A. [2012], Application of gaussian electrostatic model [GEM] distributed multipoles in the AMOEBA force field, J. Chem. Theory Comput. 8, pp. 5072-5080, doi 10.1021/ct300630u. 

Status of the Gaussian Electrostatic Model, a Density-Based Polarizable Force Field... 

G. A. Cisneros, J. P. Piquemal, and T. A. Darden,/. Chem. Phys., 125(18), 184101 (2006). Generalization of the Gaussian Electrostatic Model Extension to Arbitrary Angular Momentum, Distributed Multipoles, and Speedup with Reciprocal Space Methods. 

The static dipole polarizabilities of alkali dimers have been calculated as a function of the internuclear distance and of the vibrational index for both their electronic ground state and lowest triplet state. The method is based on /-dependent pseudopotentials for atomic core representation, Gaussian basis sets, effective core potentials to account for core polarization, the evaluation of molecular orbitals by the restricted HF method, and then a full valence Cl treatment. For all alkali pairs, the parallel and perpendicular components of the ground state a at equilibrium distance Rg scale as the cube of Re, which can be related to a simple electrostatic model of an ellipsoidal charge distribution. So, for the ground state, the longitudinal polarizability exhibits a maximum at a distance corresponding to 1.3-1.5 times the equilibrium distance. 

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... 

Fig. 2.2. Average electrostatic potential mc at the position of the methane-like Lennard-Jones particle Me as a function of its charge q. mc contains corrections for the finite system size. Results are shown from Monte Carlo simulations using Ewald summation with N = 256 (plus) and N = 128 (cross) as well as GRF calculations with N = 256 water molecules (square). Statistical errors are smaller than the size of the symbols. Also included are linear tits to the data with q < 0 and q > 0 (solid lines). The fit to the tanh-weighted model of two Gaussian distributions is shown with a dashed line. Reproduced with permission of the American Chemical Society...

Hummer, G. Pratt, L. Garcia, A. E., Multistate Gaussian model for electrostatic solvation free energies, J. Am. Chem. Soc. 1997,119, 8523-8527... 

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