On the accuracy of the algebraic approximation in molecular electronic structure calculations: V. Electron correlation in the ground state of the nitrogen molecule

Abstract

Many-body perturbation theory, formulated within the algebraic approximation, is used to determine the correlation energy of the ground state of the nitrogen molecule. Systematically constructed even-tempered basis sets of Gaussian-type functions, which have been shown to achieve an accuracy approaching Hartree in matrix Hartree - Fock calculations, have been developed to afford basis sets suitable for electron correlation studies using the second-order many-body perturbation expansion. Over 98% of an empirical estimate of the ground-state correlation energy of the molecule at its equilibrium geometry is recovered by using a basis set constructed from even-tempered sets centred on the atoms and on the bond midpoint and containing functions of s, p, d, f, g and h symmetry. The importance of functions with i symmetry is also assessed. It is estimated that the calculated correlation energy corresponds to 99.1% of the exact second-order energy. The correlation energy obtained in the present study is compared with second-order energies obtained by using previously reported basis sets, which are shown to recover, at best, about 10% less of the empirical correlation energy estimate.