An interesting case of symmetry breaking in the absence of symmetry: the bicarbonate radical (HCO₃)

Abstract

As part of a computational study of the thermochemical properties of systems related to carbonic acid (H${}_2$CO${}_3$), an interesting phenomenon was observed in the bicarbonate radical (HCO${}_3$). This species belongs to the class of formoxyl radicals, but lacks the $C_{2v}$ geometric symmetry of the more heavily-studied and prototypical HCO${}_2$ and FCO${}_2$ molecules. However, it is not immune from the problems that those molecules present to electronic structure calculations. Specifically, at geometries in the vicinity of the equilibrium structure, three solutions to the unrestricted Hartree-Fock equations can be found: two in which the unpaired spin is largely localized onto one of the (inequivalent) carbonyl oxygen atoms, and one in which the spin is delocalized. While all three of these reference functions comprise orbitals that transform as pure irreducible representations of the $C_s$ point group, the two localized choices qualitatively correspond to the symmetry-broken solution of the $C_{2v}$ formoxyl species and the delocalized solution qualitatively corresponds to the symmetry-preserving (but orbitally unstable) solution. The three solutions are described in this work, as well as the corresponding ambiguities that result in the thermochemical characterization of this species.

GRAPHICAL ABSTRACT

Keywords:

• Symmetry Breaking
• Coupled Cluster
• Orbital Instabilities

Acknowledgments

This work is dedicated to Prof. Péter Szalay of Eötvös University, Budapest, on the occasion of his 60th birthday. Péter has been a great friend and collaborator of the senior author (JFS) since they were postdocs together in Gainesville some thirty years ago. Péter's expertise in analytic derivative techniques led to the implementation of UHF-CCSD(T) analytic second derivatives, the availability of which greatly facilitated the calculations involved in this paper. The topic of this work belongs generally to a category of ‘unconventional’ symmetry breaking, a subject that Szalay previously explored (in a slightly different context) in collaboration with JFS during the term of his Fulbright Award at the University of Texas at Austin.

Disclosure statement

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

Additional information

Funding

This work was financially supported by the U.S. Department of Energy, Office of Basic Energy Sciences under Award DE-SC0018164, and was completed while JFS was visiting Eötvös University during the term of another Fulbright Award.