The Coulson–Fischer wave functions for the ground and excited states of H₂ and HeH⁺: parametrisation using distributed Gaussian basis sets

Abstract

Coulson–Fischer wave functions are used to determine complete potential energy curves for the X¹Σ⁺_g ground state of the H₂ molecule and for the first excited state (EF¹Σ⁺_g) having the same symmetry. The Coulson–Fischer orbitals are parametrised by expansion in distributed Gaussian basis sets of s-type functions. The exponents of the Gaussian functions are generated by using an even-tempered prescription. An anharmonic model is used to locate the basis functions along the internuclear axis. Sequences of basis sets are used to reduce the basis set truncation error to the sub-μhartree level. Equations are derived to determine the generalised Coulson–Fischer orbitals for the excited state which ensure that orthogonality conditions with respect to the ground state are satisfied. Potential energy curves are also calculated using smaller basis sets for which both exponents and basis function positions are determined by invoking the variation principle. The results of calculations for the isoelectronic heteronuclear HeH⁺ ion are also reported. The potential energy curves obtained in the present study are compared with literature values for both H₂ and HeH⁺.

Keywords:

• Coulson–Fischer theory
• distributed Gaussian basis sets
• ground state and excited state
• potential energy curve
• H₂
• HeH⁺

Acknowledgements

This paper is dedicated to Professor R. McWeeny on the occasion of his 90 birthday.

Notes

1. For a recent discussion of the Coulson–Fischer note, see [18].

2. See, for example, chapter 5 of [5] and references therein for a discussion of the group theoretical aspects of the many-electron problem.