Implications of the complete basis set limit in valence bond theory: a case study of molecular hydrogen

Brian J Duke,Remco W A Havenith

doi:10.1007/s00214-016-1831-y

Brian J Duke, Remco W A Havenith

Open Access

https://doi.org/10.1007/s00214-016-1831-y

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Abstract

The use of larger basis sets to approach the complete basis limit, now common in quantum chemistry, is applied for the first time to a range of valence bond functions for the simplest case of molecular hydrogen. Good convergence of the energy is slow due to difficulty in getting a correct cusp near the nuclei, but it is significant. The form of the orbitals converges much faster, leading to a slight distortion of the valence bond orbitals and an enhanced overlap, irrespective whether the basis set is restricted to basis functions centred on one atom for each valence bond orbital or the full use of the basis set is allowed. This blurs the distinction between these two approaches and shows that basis set restrictions are not tenable in the complete basis set limit. Furthermore, it supports the general use of the full basis as advocated in the spin-coupled and generalised valence bond methods.

Highlights

Valence bond (VB) theory is an old theory, going back to the first quantum mechanics study of the hydrogen molecule by Heitler and London [1], which was followed by many other studies listed by McLean et al [2]
G-Wang and generalised valence bond (GVB) differ only in that G-Wang uses a VBlocal basis set and GVB uses a VB-delocal basis set. Since the latter is more flexible, the energy of GVB is lower than the energy of G-Wang
The G-Weinbaum function is only equivalent to the GVB function for minimal basis sets; for larger basis sets, the GVB wavefunction is more flexible as the use of the VB-delocal basis sets leads to a different use of the basis functions in the GVB orbitals on the two atoms

Summary

Introduction

Valence bond (VB) theory is an old theory, going back to the first quantum mechanics study of the hydrogen molecule by Heitler and London [1], which was followed by many other studies listed by McLean et al [2] It continues to have relevance in the way we think about molecules and the covalent bond, and, in the guise of various methods that are often called “modern valence bond” theory, it is proving a useful computational method. The CBS limit can be reached by many different choices of basis set. While the extrapolation method is valuable, the idea of the CBS limit is much more valuable. While we rarely aim to obtain that limit, or need to, its presence gives

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Computational details

Results and discussion

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Conclusion