Accurate ab initio density fitting for multiconfigurational self-consistent field methods

Abstract

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field ͑CASSCF͒ method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra--acetato-dicopper͑II͒, and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals.

Gaussian basis sets for molecular applications

“…In addition to removing the need for preoptimization of ABSs, general applicability to a number of quantum chemical methods is a major strength of the CD approach, with recent applications to CASSCF and CASPT2 methods. [200,201] The number of functions in an acCD ABS is still considerably larger than in preoptimized ABSs, with a study on a test set of noncovalent interactions using TZ OBSs indicating that acCD-4 is around four times larger than the equivalent MP2-fit ABS, although, perhaps reassuring given the significantly larger number of functions, smaller errors relative to conventional methods were produced. [202] As mentioned above, fitting of the exchange integrals proves problematic when the number of occupied orbitals or size of the OBS becomes large, limiting the size of problem that may be tackled with DF-HF or DF of hybrid DFT methods.…”

Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

“…The aCD basis sets analyzed in the present work have previously 56,63 been associated with the acronym aCD-n ‫ء‬ , where n is related to the atomic CD threshold as =10 −n . In the present work, however, we will use the unstarred notation, which in previous papers 56,63 signified removal of the highest angular momentum auxiliary functions ͑i.e., we keep the highest angular momentum functions in this work͒.…”

“…In the present work, however, we will use the unstarred notation, which in previous papers 56,63 signified removal of the highest angular momentum auxiliary functions ͑i.e., we keep the highest angular momentum functions in this work͒. In Refs.…”

“…͑3͒, the unbiased nature of the resulting DF approximation is guaranteed. 56,63 The raw aCD auxiliary basis set does not have the structure of complete shells and the final auxiliary basis set is generated by adding auxiliary functions to get a complete shell structure. This gives rise to a somewhat larger auxiliary basis set as compared to, e.g., the so-called 1C-CD approximation using the same decomposition threshold.…”

“…62 Various one-center forms of the standard CD approximation have therefore been introduced, 62,63 which retain essentially all of the error control property of the standard CD but considerably reduce the associated computational cost. 56 In the present work, we will focus on the one-center CD approximation known as atomic Cholesky decomposition ͑aCD͒ for generating auxiliary basis sets from the AO basis set. 63 We will define a new family of aCD auxiliary basis sets expressed in terms of a much smaller number of primitive Gaussian basis functions.…”