Numerical Fitting of Molecular Properties to Hermite Gaussians

Abstract

A procedure is presented to fit gridded molecular properties to auxiliary basis sets (ABSs) of Hermite Gaussians, analogous to the density fitting (DF) method (Dunlap; et al. J. Chem. Phys. 1979, 71, 4993). In this procedure, the ab initio calculated properties (density, electrostatic potential, and/or electric field) are fitted via a linearor nonlinear-least-squares procedure to auxiliary basis sets (ABS). The calculated fitting coefficients from the numerical grids are shown to be more robust than analytic density fitting due to the neglect of the core contributions. The fitting coefficients are tested by calculating intermolecular Coulomb and exchange interactions for a set of dimers. It is shown that the numerical instabilities observed in DF are caused by the attempt of the ABS to fit the core contributions. In addition, this new approach allows us to reduce the number of functions required to obtain an accurate fit. This results in decreased computational cost, which is shown by calculating the Coulomb energy of a 4096 water box in periodic boundary conditions. Using atom centered Hermite Gaussians, this calculation is only 1 order of magnitude slower than conventional atomcentered point charges.

Classical Electrostatics for Biomolecular Simulations

“…This has enabled the reduction of numerical instabilities in the fitting procedure and the number of fitting sites. 334 Overall, the use of numerical fits produces results similar to the analytical fits with errors around 0.84 kJ/mol. The reduction of fitting sites allowed the energy/force calculation of a 4096 water box with a three-site model with 46 Hermite primitive functions using PME was performed in 2.29 s. By contrast, the same system using TIP3P charges was done in 0.2 s using SANDER on the same computer.…”

Modeling Charge Penetration Effects in Water-Water Interactions

“…Cisneros et al had tested a similar three-site model, where the GTFs were located at the oxygen and two hydrogen sites. 16 This resulted in a water monomer dipole moment of about 1.9-2.0 Debye, which is much higher than the experimental result (1.855 Debye). Thus, GEM-3S suggested in this study can be applicable as a better descriptor of the dipole moment.…”

“…This method has been developed and studied in depth by Cisneros and co-workers. [13][14][15][16][17] As a recent work, they introduced distributed multipoles based on the GEM (GEMDM) applied in the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) force field to improve the treatment of electrostatics. 17 The ab initio calculated electron density can be fit with a number of basis functions of differing angular momentum, but ABSs are usually restricted to s-type Gaussian functions for the computational efficiency.…”

LICHEM: A QM/MM program for simulations with multipolar and polarizable force fields

“…A more advanced approach for modeling the electrostatic field and polarization involves polarizable electron density on atomic centers [5, 27–30, 37, 52, 53]. These electron density models, such as the Gaussian Electrostatic Model (GEM), reduce errors even further [30, 32, 37, 52, 54]. …”