Distributed Gaussian basis sets in correlation energy studies: the second order correlation energy for the ground state of the hydrogen molecule

Abstract

The use of distributed basis sets of s-type Gaussian functions in electron correlation energy studies is investigated for the ground state of the hydrogen molecule at its equilibrium nuclear geometry. Empirical schemes are developed both to generate the exponents defining the basis functions and to define their distribution in space. The matrix Hartree-Fock reference energy obtained with the largest distributed basis set developed in this work is in error by less than ˜ 0.1 Hartree. The second-order many-body perturbation theory correlation energy component is determined and, for the largest of the distributed basis sets studied in the present work, is in error by ˜ 0.6 m Hartree. Our previous study of the hydrogen molecule ground state has demonstrated that the error in the matrix Hartree-Fock and second-order correlation energies can be reduced to ˜ 3 μHartree and ˜ 0.15 m Hartree, respectively, by using a systematically generated sequence of atom-centred, even-tempered basis sets containing functions of s, p, d and f symmetry.