Multiplicity of symmetry-broken Hartree-Fock solutions in multiple bonds and atomic clusters: An asymptotic view

Abstract

In molecular Hartree-Fock instability problems (here restricted to the types of instabilities known as axial-spin-density waves and charge-density waves in Fukutome’s classification), attention is usually concentrated on the lowest solution of each type, and the one appearing at shortest interatomic distances. As shown, for instance, on the cyclic ${\mathrm{Li}}_6$ cluster problem, an asymptotic look at the symmetry-breaking problem enables one to generate a multiplicity of solutions which have generally been ignored. For ${\mathrm{N}}_2$ we find ten different types of triplet instabilities, dissociating into three different asymptotes and five different types of singlet instabilities, all having components in the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ ground state. At long interatomic distances all these solutions are true minima of the energy, some of them becoming saddle points at short interatomic distances. It is shown for the ${\mathrm{C}}_2$ problem that multiple symmetry-broken solutions may exist at short interatomic distances; these various solutions might be used in nonorthogonal valence configuration-interaction calculation for strongly correlated multiple bonds such as in ${\mathrm{C}}_2$ or ${\mathrm{Cr}}_2$.