A universal Gaussian basis set for atoms Li through Ne based on a generator coordinate version of the Hartree–Fock equations

Abstract

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Universal Gaussian basis functions in relativistic quantum chemistry: atomic Dirac–Fock–Coulomb and Dirac–Fock–Breit calculations

“…The exponents of this basis set are derived from the non-relativistic generator coordinate version of the Hartree-Fock equations (22) and are collected in Table 1. The exponents were used in our DFC and DFB SCF calculations without further optimization.…”

“…The concept of a universal basis set arose from these considerations and basis set exponent non-optimization has been so far almost the rule in relativistic quantum chemistry. We chose to adopt the UGTF (18s, 12p, 116) basis set recently reported by Da Silva et al (lo), which is based on the earlier work of Mohallem et al (22). The significance of the UGTF basis set (10,22) lies in the fact that no a priori information is forced on an atom, which is characterized in the SCF algorithm only by the atomic number in the Fock operator, i.e., an atom is characterized only by its Harniltonian.…”

“…We chose to adopt the UGTF (18s, 12p, 116) basis set recently reported by Da Silva et al (lo), which is based on the earlier work of Mohallem et al (22). The significance of the UGTF basis set (10,22) lies in the fact that no a priori information is forced on an atom, which is characterized in the SCF algorithm only by the atomic number in the Fock operator, i.e., an atom is characterized only by its Harniltonian. This method of designing a UGTF basis introduces a new algorithm for basis set exponent selection.…”

QMC Calculations of Total Energy and Bond Length of Some Polyatomic Organic Molecules

“…Quantum-Monte-Carlo (QMC) methods have proven most suitable for obtaining precise results [1,2] for the ground-state or low-lying states of molecules or atoms and are superior to perturbative methods [3]. Mohallem et al [4] in 1986 developed a Generator Coordinate HartreeFock (GCHF) method and it was used by [4] and in 2001 by [5] to generate atomic and molecular wave-functions. In 1999 Jorge and Castro [6], developed an improved GCHF (IGCHF) which generated accurate Gaussian basis sets (GBSs) and was in 2004 used by Barreto et al [7] to generate atomic and some diatomic molecular systems.…”

Aplicação de uma nova proposta de discretização das equações Griffin-Wheeler-Hartree-Fock na geração de bases Gaussianas para cálculos de átomos e moléculas

“…A versão integral das equações de Hartree-Fock foi denominada de Método da Coordenada Geradora Hartree-Fock (MCG-HF), e uma de suas primeiras aplicações foi na geração de bases atômicas universais [7,8]. De fato, uma integração numérica cuidadosa das equações de GW-HF permite a geração de bases universais bem mais generalizadas do que as já publicadas na literatura [9].…”