Improved Formulas for the Calculation of the Electrostatic Contribution to the Intermolecular Interaction Energy from Multipolar Expansion of the Electronic Distribution

The formulation of density-functional expansion methods is extended to treat the second and higherorder terms involving the response density and spin densities with an arbitrary single-center auxiliary basis. The two-center atomic orbital products are represented by the auxiliary functions centered about those two atoms, and the mapping coefficients are determined from a local constrained variational procedure. This two-center variational procedure allows the mapping coefficients to be pretabulated and splined as a function of internuclear separation for efficient look up. The splines of mapping coefficients have a range no longer than that of the overlap integrals, and the auxiliary density appears as a single point-multipole expansion to all nonoverlapping atoms, thus allowing for the trivial implementation of a linear-scaling algorithm. The method is tested using Gaussian multipole expansions, and the effect of angular and radial completeness is explored. Several auxiliary basis sets are parametrized and compared to an auxiliary basis analogous to that used in the selfconsistent-charge density-functional tight-binding model, and the method is demonstrated to greatly improve the representation of the density response with respect to a reference expansion model that does not use an auxiliary basis.

Section: Introductionmentioning

confidence: 99%

Density-functional expansion methods: Generalization of the auxiliary basis

Giese¹,

York²

2011

“…This disadvantage has been addressed to an extent by the use of damping functions that correct the interaction energies at close intermolecular distances. [14][15][16] It has been shown that another possibility for the accurate determination of the intermolecular Coulomb contribution is by interacting the unperturbed frozen densities of the two molecules either numerically 17 or analytically. 18 The latter method is based on the density fitting (DF) formalism (Coulomb fitting), [19][20][21] where the electron density is expanded using Gaussian auxiliary basis sets (ABSs) centered on specific sites on the molecule.…”

Section: Introductionmentioning

confidence: 99%

“…All results are compared to reference values calculated with CSOV. 15,23 In addition, the Coulomb interaction energy for a set of water boxes of increasing size is calculated to predetermined accuracy using reciprocal space methods and timing results are discussed.…”

Section: Introductionmentioning

confidence: 99%

Generalization of the Gaussian electrostatic model: Extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods

Cisneros

Piquemal

Darden

2006

Self Cite

112

192

The simulation of biological systems by means of current empirical force fields presents shortcomings due to their lack of accuracy, especially in the description of the nonbonded terms. We have previously introduced a force field based on density fitting termed the Gaussian electrostatic model-0 (GEM-0) J.-P. Piquemal et al. [J. Chem. Phys. 124, 104101 (2006)] that improves the description of the nonbonded interactions. GEM-0 relies on density fitting methodology to reproduce each contribution of the constrained space orbital variation (CSOV) energy decomposition scheme, by expanding the electronic density of the molecule in s-type Gaussian functions centered at specific sites. In the present contribution we extend the Coulomb and exchange components of the force field to auxiliary basis sets of arbitrary angular momentum. Since the basis functions with higher angular momentum have directionality, a reference molecular frame (local frame) formalism is employed for the rotation of the fitted expansion coefficients. In all cases the intermolecular interaction energies are calculated by means of Hermite Gaussian functions using the McMurchie-Davidson [J. Comput. Phys. 26, 218 (1978)] recursion to calculate all the required integrals. Furthermore, the use of Hermite Gaussian functions allows a point multipole decomposition determination at each expansion site. Additionally, the issue of computational speed is investigated by reciprocal space based formalisms which include the particle mesh Ewald (PME) and fast Fourier-Poisson (FFP) methods. Frozen-core (Coulomb and exchange-repulsion) intermolecular interaction results for ten stationary points on the water dimer potential-energy surface, as well as a one-dimensional surface scan for the canonical water dimer, formamide, stacked benzene, and benzene water dimers, are presented. All results show reasonable agreement with the corresponding CSOV calculated reference contributions, around 0.1 and 0.15 kcal/mol error for Coulomb and exchange, respectively. Timing results for single Coulomb energy-force calculations for (H 2 O) n , n=64, 128, 256, 512, and 1024, in periodic boundary conditions with PME and FFP at two different rms force tolerances are also presented. For the small and intermediate auxiliaries, PME shows faster times than FFP at both accuracies and the advantage of PME widens at higher accuracy, while for the largest auxiliary, the opposite occurs.

“…This shortcoming may be overcome to an extent by using damping functions that correct the intermolecular interaction energy. 18,19 Equation (1) can also be solved without approximations with either numerical or analytical procedures. Gavezzotti has proposed a method that relies on the direct numerical integration over molecular electron density.…”

Section: Introductionmentioning

confidence: 99%

Intermolecular electrostatic energies using density fitting

Cisneros¹,

Piquemal²,

Darden³

2005

Self Cite

A method is presented to calculate the electron-electron and nuclear-electron intermolecular Coulomb interaction energy between two molecules by separately fitting the unperturbed molecular electron density of each monomer. This method is based on the variational Coulomb fitting method which relies on the expansion of the ab initio molecular electron density in site-centered auxiliary basis sets. By expanding the electron density of each monomer in this way the integral expressions for the intermolecular electrostatic calculations are simplified, lowering the operation count as well as the memory usage. Furthermore, this method allows the calculation of intermolecular Coulomb interactions with any level of theory from which a one-electron density matrix can be obtained. Our implementation is initially tested by calculating molecular properties with the density fitting method using three different auxiliary basis sets and comparing them to results obtained from ab initio calculations. These properties include dipoles for a series of molecules, as well as the molecular electrostatic potential and electric field for water. Subsequently, the intermolecular electrostatic energy is tested by calculating ten stationary points on the water dimer potential-energy surface. Results are presented for electron densities obtained at four different levels of theory using two different basis sets, fitted with three auxiliary basis sets. Additionally, a one-dimensional electrostatic energy surface scan is performed for four different systems (H 2 O dimer, Mg 2+ -H 2 O, Cu + -H 2 O, and n-methyl-formamide dimer). Our results show a very good agreement with ab initio calculations for all properties as well as interaction energies.