On the accuracy of the algebraic approximation in molecular electronic structure calculations. II. Comparison of diatomic molecule self-consistent field calculations using basis sets of elliptical functions with fully numerical Hartree-Fock studies

Abstract

It is shown that, by using basis sets of elliptical functions in electronic structure calculations for the diatomic molecules LiH, Li,, LiHe+, BeH+ and Be,, excellent agreement with fully numerical calculations is obtained within the self-consistent field model. Total energies can be reproduced to within a few pHartree.

Systematic construction of basis subsets of higher angular momentum functions in electron correlation energy calculations

“…The present paper complements a series devoted to the accurate implementation of the algebraic approximation in molecular electronic structure studies [4][5][6][7][8][9][10]. Comparisons of finite-difference and finite basis set Hartree-Fock calculations for diatomic molecules have demonstrated that energies approaching the sub-µHartree level of accuracy can be obtained by exploiting standard quantum chemical procedures in a systematic fashion [11][12][13][14][15][16].…”

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

“…Previous papers in this series [1][2][3][4] (hereinafter referred to as parts I-IV) have examined the accuracy with which Hartree-Fock ground-state energies of molecules, both diatomic and polyatomic, can be calculated by employing the algebraic approximation, that is by 0953-4075/96/122425+27$19.50 c 1996 IOP Publishing Ltd means of finite basis set expansions in terms of global basis functions. In part I [1], it was demonstrated that sub-µHartree accuracy can be achieved for one-electron diatomic systems and two-electron systems within the Hartree-Fock model by using atom-centred basis sets of Gaussian-type functions.…”

“…In part I [1], it was demonstrated that sub-µHartree accuracy can be achieved for one-electron diatomic systems and two-electron systems within the Hartree-Fock model by using atom-centred basis sets of Gaussian-type functions. In part II [2], the use of elliptical basis functions for diatomic molecules in the Hartree-Fock model was investigated. It was shown in part III [3] that an accuracy approaching the sub-µHartree level could be achieved for the total Hartree-Fock energy of the ground state of the nitrogen molecule using basis sets of Gaussian-type functions by including both atom-centred and bond-centred functions.…”

On the accuracy of the algebraic approximation in molecular electronic structure calculations: VI. Matrix Hartree - Fock and many-body perturbation theory calculations for the ground state of the water molecule

“…Previous papers [1][2][3][4][5] in this series have examined the accuracy of the algebraic approximation for diatomic and linear polyatomic molecules within the Hartree-Fock model and have demonstrated that an accuracy of ∼ 1 µHartree in the total energy can be achieved. In the fifth of this set of papers [5], the calculation of the second-order correlation energy components for a diatomic molecule was considered and it was shown that ∼ 99.1% of an estimate of the exact second-order correlation energy for the ground state of the nitrogen molecule could be supported by a suitably constructed basis set.…”