A general local algebraic approach for molecules with normal mode behavior: Application to FCN

Abstract

A general local algebraic model is proposed to describe the vibrational spectroscopy of molecules, including systems with normal mode behavior. The approach is based on the anharmonization of the algebraic representation of the normal modes at the local level without analogue in configuration space, albeit keeping the connection with it. An algebraic representation is obtained by introducing the bosonic realization associated with the normal modes. Latter on, a canonical transformation to pseudo local operators is proposed, which in turn are mapped to $su\left(2\right)$-operators associated with Morse ladder operators. The principal isotopologue of FCN is taken as an example. The vibrational description was carried out including 159 experimental energies with $\mathrm{rm}s=0.25$ cm${}^{\text{-1}}$. A description of the isotopologues is described with similar quality. It is shown that the estimation of the force constants allows the correct wave functions to be obtained.