On the accuracy of the algebraic approximation in molecular electronic structure calculations. I. Calculations for H₂⁺, HeH²⁺, H₂and HeH⁺using basis sets of atom-centred Gaussian-type functions

Abstract

The accuracy of electronic structure calculations made within the algebraic approximation (that is by making finite basis set expansions) is compared with the results of previously reported fully numerical calculations for diatomic molecules. Sequences of even tempered basis sets of atom-centred Gaussian-type functions are employed to explore the accuracy that can be achieved in matrix calculations for the H i , HeH+ and HeH2+ molecular ions and the H2 molecule. It is demonstrated that sub-pHartree accuracy can be achieved in energy calculations. The relevance of these results to the accuracy that can be achieved in studies of polyatomic studies is emphasised.

Application of an optimization technique to the discretized version of the Griffin–Hill–Wheeler–Hartree–Fock equations

“…Table IV compares the results obtained by that procedure with the OID technique of this work. The OID approach produces better total energies than do the results reported in [20]. In fact, the total energy using the OID scheme with 14 primitives only was attained by the even-tempered method [20] with 18 functions.…”

“…The OID approach produces better total energies than do the results reported in [20]. In fact, the total energy using the OID scheme with 14 primitives only was attained by the even-tempered method [20] with 18 functions. These results suggest that somewhat smaller and better (in energetic terms) basis sets can be obtained for Hz using OID.…”

“…Wells and Wilson [20] have presented a systematic approach to construct accurate basis sets for some one-and two-electron molecules based on the eventempered method [16,19]. Table IV compares the results obtained by that procedure with the OID technique of this work.…”

A Program for Single-center Expansion in Laguerre-type Orbitals for the Hydrogen Molecular Ion

“…This contrasts with the rapid convergence of the multi-center expansion method (linear combination of atomic orbitals, LCAO) using GTOs. Wells and Wilson [18] quote an energy accuracy of 2 × 10 −7 a.u. with a reasonably compact basis set of [23s 9p 4d 4f 2g] (232 primitive GTOs in total).…”

Improved generator coordinate Hartree-Fock method for molecular systems: application to H 2 , Li 2 and LiH

“…The purpose of this work is to demonstrate the power of this new method when basis sets of atom-centred GTFs are employed. This is achieved by comparing our HF total energies of the diatomic molecules to those obtained with the original MGCHF method [10], with eventempered basis sets [12], and numerical HF (NHF) calculations [13±15]. We also compare our results of some molecular properties with the corresponding ones obtained with other approaches.…”