A Theoretical Study of CoCN in the $^3 \, \Phi $ Electronic Ground State
Résumé
We report here {\it ab initio} calculations of three-dimensional potential energy surfaces for CoCN in its electronic ground state $\tilde{X}\,^{3}\Phi_{i}$ at the MR-SDCI+Q+$E_{\rm rel}$/[Roos ANO (Co), aug-cc-pVQZ (C,N)] level of theory. Molecular constants for Co$^{12}$CN and Co$^{13}$CN have been derived by second-% order perturbation theory, and rotation-vibration energies have been obtained by the variational MORBID method. At equilibrium, $^{3}\Phi_{i}$ CoCN is linear with $r_{\rm e}$(Co-C) = 1.8540 {Å} and $r_{\rm e}$(C-N) = 1.1677 {Å}. The zero-point averaged structure, however, is bent; the average bond angle is $\langle \angle\mbox{(Co-C-N)} \rangle_0$ $=$ 172$^\circ$ and the average bond lengths are $\langle r\mbox{(Co-C)}\rangle_0$ = 1.8733 {Å} and $\langle r\mbox{(C-N)}\rangle_0$ = 1.1718 {Å}. Sheridan \textit{et al.} [P.~M.~Sheridan, M.~A.~Flory, and L.~M.~Ziurys. {\it J.~Chem.~Phys.,} {\bf 121}, 8360 (2004)] have determined from the pure rotational spectrum that $r_{0}$(C-N) = 1.1313(10) {Å} for $^{3}\Phi_{i}$ CoCN; this value is significantly shorter (by about 3.5{\%}) than the {\it ab initio} value of $\langle r\mbox{(C-N)}\rangle_0$. In contrast, our theoretical value for the rotational constant $B_{0,\Omega = 4}$ differs only 0.7{\%} from the experimental value. As discussed previously for $^{6}\Delta_{i}$ FeNC [T.~Hirano, R.~Okuda, U.~Nagashima, V.~\v{S}pirko, and P.~Jensen. {\it J.~Mol.~Spectrosc.,} {\bf 236}, 234 (2006)], the poor agreement between theory and experiment for the C-N bond length is caused by an inadequate treatment of the large-amplitude bending motion of $\tilde{X}\,^{3}\Phi_{i}$ CoCN in the experimental $r_{0}$ determination.
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