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.

Comparison of the polarizabilities and hyperpolarizabilities obtained from finite basis set and finite difference Hartree–Fock calculations for diatomic molecules: III. The ground states of N2, CO and BF

“…The results of the present finite basis set Hartree-Fock calculations for the N 2 ground state are displayed in table 1. The distributed universal even-tempered basis sets developed in our previous work [79] on the Hartree-Fock energy of this molecule provided the starting point for our present experiments. Calculations were carried out for 19 different basis sets, which are labelled a-s in table 1.…”

“…The results are compared with finite basis set calculations of the corresponding quantities which are carried out analytically using coupled perturbed Hartree-Fock theory. The basis sets developed in our previous studies [66,67] have also been used in the construction of basis set suitable for electron correlation studies [79][80][81]. It is anticipated that the basis sets developed in the present work will provide a starting point for studies of molecular polarizabilities and hyperpolarizabilities which take account of electron correlation effects.…”

On the use of Brillouin-Wigner perturbation theory for many-body systems

“…It facilitates the use of the large and flexible basis sets, such as universal basis sets, that are required to achieve high accuracy particularly when implemented via a 'direct' algorithm [15][16][17][18] in which the need to store large numbers of two-electron integrals is avoided. For the ground state of the nitrogen molecule [19], second-order many-body perturbation theory can account for over 99% of the empirical correlation energy estimate whilst for the water molecule [20] ground state the second-order energy represents some 97.7% of the estimate. Attempts to extend this systematic order-by-order approach to situations which demand the use of a multireference perturbation theory have met with limited success.…”

On the accuracy of the algebraic approximation in molecular electronic structure calculations: VIII. Matrix Hartree-Fock and many-body perturbation theory applied to a negative molecular ion

“…In our previous work [23] on the N 2 molecule ground state, we have considered basis sets corresponding to n = 5, 10 and 15. Whilst n = 15, i.e.…”