RO-VIBRATIONALLY AVERAGED STRUCTURE OF 2Π NCS: RE-INTERPRETATION OF THE B0 VALUES

We have constructed \textit{ab initio} 3D potential energy surfaces (PESs) for $\tilde{X}\;^{2}\Pi$ NCS in core-valence SDCI+$Q$/[aCVQZ(N,C,S)] calculations. The $B_{0}$ value predicted from these PESs deviates only 0.05\%\ from the corresponding experimental values for NC$^{32}$S and NC$^{34}$S. Since we have quite accurate 3D PESs, we can determine both the equilibrium structure and the $r_0$ structure accurately: $r_{\rm e}$(N--C) = 1.1778~\AA, $r_{\rm e}$(C--S) = 1.6335~\AA, and $\angle_{\rm e}$(N--C--S) = 180$^\circ$. The ro-vibrationally averaged structure, determined as expectation values over DVR3D wavefunctions, has $\langle r$(N--C)$\rangle_0$ = 1.1836~\AA, $\langle r$(C--S)$\rangle_0$ = 1.6356~\AA, and $\langle \angle$(N--C--S)$ \rangle_0$ = 172.5$^\circ$. The 3D PESs show that the $\tilde{X}\, ^2\Pi$ NCS has its potential energy minimum at a linear configuration, and hence it is a ``linear molecule.'' Experimentally, $B_{0}$ values are reported for two isotopologues only.\footnote{A.~Maeda, H.~Habara, T.~Amano, {\it Mol. Phys.}, {\bf 105}, 477--495 (2007).} Using the expectation values given above as the initial guess, a bent $r_{0}$ structure having an $\langle \angle$(N--C--S)$ \rangle_0$ of 172.2$^\circ$ is deduced from the experimentally reported $B_{0}$ values for NC$^{32}$S and NC$^{34}$S. It shows that the linear molecule NCS has a ``bent'' ro-vibrationally averaged structure, confirming our previous predictions:\footnote{T.~Hirano, U.~Nagashima, {\it J. Mol. Spectrosc.}, {\bf 314}, 35--47 (2015); % T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} {\bf 343}, 54--61 (2018).} any linear molecule is observed as being bent on ro-vibrational average. See Ref.~$c$ \footnote{T.~Hirano, U.~Nagashima, P.~Jensen, {\it J. Mol. Spectrosc.} (2018), https://doi.org/10.1016/j.jms.2017.12.011.} for further discussion of this molecule. $^{2}\Pi$ NCS is a typical Renner molecule. The Renner spectroscopy of this molecule will be presented in a separate talk.\footnote{J.~Freund et al, ``Computational spectroscopy of NCS in the Renner-degenerate Electronic state $\tilde{X}\, ^2\Pi$.''