Conical Intersections Between Vibrationally Adiabatic Surfaces In Methanol

The discovery of a set of seven conical intersections (CI’s) between vibrationally adiabatic surfaces in methanol is reported. The intersecting surfaces represent the energies of the two asymmetric CH stretch vibrations, \nub{2} and \nub{9}, regarded as adiabatic functions of the torsional angle, $\gamma$, and COH bend angle, $\rho$. One conical intersection, required by symmetry, is located at the C$_{3v}$ geometry where the COH group is linear ($\rho$ = $0^{\circ}$); the other six are in eclipsed conformations with $\rho$ = $62^{\circ}$ and $94^{\circ}$. The three CI’s at $\rho$ = $62^{\circ}$ are close to the equilibrium geometry ($\rho$ = $71.4^{\circ}$), within the zero-point amplitude of the COH bending vibration. CI’s between electronic surfaces have long been recognized as crucial conduits for ultrafast relaxation, and recently Hamm, and Stock\footnote{P.~Hamm and G.~Stock, \textit{Phys.~Rev.~Lett.} \underline{\textbf{109}},~173201, (2012).} \footnote{P.~Hamm, and G.~Stock, \textit{Mol.~Phys.} \underline{\textbf{111}},~2046, (2013).} have shown that vibrational CI’s may also provide a mechanism for ultrafast vibrational relaxation. The ab initio data reported here are well described by an extended Zwanziger and Grant model\footnote{J.~W.~ Zwanziger, and E.~R.~Grant, \textit{J.~Chem.~Phys.} \underline{\textbf{87}},~2954, (1987).} for E $\otimes$ e Jahn-Teller systems in which Renner-Teller coupling is also active. However, in the present case, the distortion $\rho$ from C$_{3v}$ symmetry is much larger than is typical in the Jahn-Teller coupling of electronic surfaces and accordingly higher-order terms in $\rho$ are required. The present results are also consistent with the two-state model of Xu et al\footnote{L.-H.~Xu, J.~T. ~Hougen, and R.~M. ~Lees, \textit{J.~Mol.~Spectrosc.} \underline{\textbf{293-294}},~38, (2013).}. The cusp-like features, which they found along the internal-rotation path, are explained in the context of the present work in terms of proximity to the CI’s. The presence of multiple CI’s near the torsional minimum energy path impacts the role of geometric phase in this three-fold internal-rotor system. When the dimensionality of the low-frequency space is extended to include the CO bond length as well as $\gamma$ and $\rho$, the individual CI’s become seams of CI’s. It is shown that the CI’s at $\rho$ = $62^{\circ}$ and $94^{\circ}$ lie along the same seam of CI’s in this higher dimensional space