The Gaussian Electrostatic Model GEM

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. 

This method relies on the use of an auxiliary gaussian basis set to fit the molecular electron density obtained from an ab initio one-electron density matrix  

we use the formalism of the variational density fitting method [55, 56] where the Coulomb self-interaction energy of the error is minimized  

E2 from Eq. (6-3) can be minimized with respect to the expansion coefficients x/ and a linear system of equations can be obtained  

The GEM force field follows exactly the SIBFA energy scheme. However, once computed, the auxiliary coefficients can be directly used to compute integrals. That way, the evaluation of the electrostatic interaction can virtually be exact for an perfect fit of the density as the three terms of the coulomb energy, namely the nucleus-nucleus repulsion, electron-nucleus attraction and electron-electron repulsion, through the use of p [2, 14-16, 58], 

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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. 

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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