Hartree-Fock instabilities and the diagonal Born-Oppenheimer correction

Abstract

The NO and NO${}_2$ radicals are used to demonstrate how instabilities in Hartree-Fock wavefunctions can result in unsatisfactory, or even unphysical, values of the diagonal Born-Oppenheimer correction (DBOC). For NO, an avoided crossing between two UHF solutions of ${}^2\mathrm{\Pi }$ symmetry results in a nearly 1 kJ/mol (80 cm${}^{-1}$) defect in the SCF-level DBOC just beyond the equilibrium bond distance. In that case, CCSD is able to recover essentially correct behaviour. For ground-state (${\tilde{X}}^2{A}_1$) NO${}_2$, a second-order CPHF pole is observed in the dependence of the DBOC on the bending angle at a geometry rather far from the true conical intersection between the ${\tilde{X}}^2{A}_1$ and ${\tilde{A}}^2{B}_2$ states, an artifact that cannot be completely ameliorated by any method short of full CI. These effects arise from well-known problems associated with (near) instabilities of Hartree-Fock solutions, though there is little in the literature about this in the current context. The goal of this paper is to raise awareness of these potential problems, as the DBOC (adiabatic correction) is now an essential part of many modern protocols for high-accuracy calculations, and to provide some comments of the causes of these phenomena.

GRAPHICAL ABSTRACT

Keywords:

• Quantum chemistry
• diagonal born-oppenheimer correction
• nonadiabatic behavior
• thermochemistry

Acknowledgements

This paper is dedicated to honouring the 60'th birthday of Jürgen Gauss, whose mastery of coupled-cluster gradient theory has benefited us all, as well as the memory of Werner Kutzelnigg.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors of this paper were funded by the National Science Foundation under Award No. CHE-1664325 and by the Air Force Office of Scientific Research under Award No. FA9550-16-1-0117.