Search results for "Fock matrix"
showing 3 items of 3 documents
Cholesky decomposition techniques in electronic structure theory
2011
We review recently developed methods to efficiently utilize the Cholesky decomposition technique in electronic structure calculations. The review starts with a brief introduction to the basics of the Cholesky decomposition technique. Subsequently, examples of applications of the technique to ab inito procedures are presented. The technique is demonstrated to be a special type of a resolution-of-identity or density-fitting scheme. This is followed by explicit examples of the Cholesky techniques used in orbital localization, computation of the exchange contribution to the Fock matrix, in MP2, gradient calculations, and so-called method specific Cholesky decomposition. Subsequently, examples o…
Reduced scaling in electronic structure calculations using Cholesky decompositions
2003
The small numerical rank of the two-electron integral matrix for large molecular systems and large basis sets was demonstrated. Though, the current implementation still requires some improvements on the calculations done in the inner most loop of the decomposition do not exploit the parsity in the Cholesky vectors. With respect to the practical applicability of the presented method an efficient approach to geometrical derivatives was imperative. Such an approach was obtained including certain derivative product functions and decomposing an expanded integral matrix.
Method specific Cholesky decomposition : Coulomb and exchange energies
2008
We present a novel approach to the calculation of the Coulomb and exchange contributions to the total electronic energy in self consistent field and density functional theory. The numerical procedure is based on the Cholesky decomposition and involves decomposition of specific Hadamard product matrices that enter the energy expression. In this way, we determine an auxiliary basis and obtain a dramatic reduction in size as compared to the resolution of identity (RI) method. Although the auxiliary basis is determined from the energy expression, we have complete control of the errors in the gradient or Fock matrix. Another important advantage of this method specific Cholesky decomposition is t…