The Coulomb operator in a Gaussian product basis

138

Articles you may be interested inOn the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: Benchmarks approaching the complete basis set limitThe Coulomb force in density-functional theory calculations is efficiently evaluated based on a partitioning into near-field ͑NF͒ and far-field ͑FF͒ interactions. For the NF contributions, a J force engine method is developed based on our previous J matrix engine methods, and offers a significant speedup over derivative electron repulsion integral evaluation, without any approximation. In test calculations on water clusters and linear alkanes, the computer time for the NF force is reduced by a factor of 5-7 with a 3-21G basis set and 6-8 with a 6-31G** basis set. The FF force is treated by a generalization of the continuous fast multipole method, and the FF computational cost is found to be comparable to that of an energy evaluation.

Section: Methodsmentioning

confidence: 99%

Efficient evaluation of the Coulomb force in density-functional theory calculations

Shao

White²,

Head‐Gordon

2001

138

“…Fortunately, there has been much interest in the use of auxiliary basis sets in the context of traditional ab initio methods [25][26][27][28][29][30] and polarizable density-fitted force fields, [31][32][33][34] whose ideas we can draw upon. In the context of Kohn-Sham potential energy expansion methods, however, we seek to tailor the methodology to allow for the precomputation of these "mapping coefficients" on numerical splines, in a manner analogous to SCC-DFTB.…”

Section: Introductionmentioning

confidence: 99%

Density-functional expansion methods: Generalization of the auxiliary basis

Giese¹,

York²

2011

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.

“…The method begins with a previously described decomposition of the density into families of Hermite Gaussian-type functions ͑HGTFs͒. 17,16,62 In this representation, insignificant contributions to J and are eliminated, yielding an O (N) complexity for both. Then, by structuring the density, a competitive algorithm for the thresholding and evaluation of primitive ERI contributions to J is obtained.…”

Section: A Direct Methods For Computing Jmentioning

confidence: 99%

“…It is possible to obtain a compact representation of the density in terms of HGTF families by accumulation of contributions to each family q, 17,16,62 via…”

Section: B In a Hermite Gaussian Basismentioning

confidence: 99%

Linear scaling computation of the Fock matrix

Challacombe¹,

Schwegler²

1997

201

155

Computation of the Fock matrix is currently the limiting factor in the application of Hartree-Fock and hybrid Hartree-Fock/density functional theories to larger systems. Computation of the Fock matrix is dominated by calculation of the Coulomb and exchange matrices. With conventional Gaussian-based methods, computation of the Fock matrix typically scales as ϳN 2.7 , where N is the number of basis functions. A hierarchical multipole method is developed for fast computation of the Coulomb matrix. This method, together with a recently described approach to computing the Hartree-Fock exchange matrix of insulators ͓J. Chem. Phys. 105, 2726 ͑1900͔͒, leads to a linear scaling algorithm for calculation of the Fock matrix. Linear scaling computation the Fock matrix is demonstrated for a sequence of water clusters at the restricted Hartree-Fock/3-21G level of theory, and corresponding accuracies in converged total energies are shown to be comparable with those obtained from standard quantum chemistry programs. Restricted Hartree-Fock/3-21G calculations on several proteins of current interest are documented, including endothelin, charybdotoxin, and the tetramerization monomer of P53. The P53 calculation, involving 698 atoms and 3836 basis functions, may be the largest Hartree-Fock calculation to date. The electrostatic potentials of charybdotoxin and the tetramerization monomer of P53 are visualized and the results are related to molecular function.