Analysis and classification of symmetry breaking in linear ABA-type triatomics

The symmetry of the nuclear framework of polyatomic molecules is qualitatively lowered by small changes in their geometry. This may lead to a dramatic change in the nature of their Hartree-Fock (HF) solutions and to a singular behavior of the corresponding potential energy surfaces (PESs), which may persist even at the correlated level if based on these HF references. We examine a general shape of the restricted HF (RHF) and open-shell RHF PESs for the linear triatomic molecules of the ABA type in the vicinity of the symmetric D(2h) geometries and the role played by the spin-restricted (singlet or doublet) stability of the corresponding HF solutions. This enabled us to classify the character of these surfaces into three basic types depending on the nature of the cut of the PES along the asymmetric stretching mode coordinate. We also examine the implications of the type of these nodes on the PES obtained at the post-HF correlated CCSD(T) level as well as on the determination of the vibrational frequencies for both the symmetric and asymmetric stretching modes. When using either the numerical differentiation of the PES or the solution of the Schrodinger equation for the nuclear motion for this purpose, it is shown that either method yields very good results for the symmetric mode frequencies, while the former approach may yield highly erroneous values for the asymmetric mode frequencies depending on the type of the HF PES at the equilibrium geometry in which case the latter approach still provides us with reasonably good results.