Full dimensional theoretical study of the torsion-vibration eigenstates and torsional splittings of CH3OH

Abstract

The vibrations of methanol are studied theoretically via a fully coupled treatment of the small amplitude motions and the large amplitude torsional mode. Van Vleck perturbation theory is used to find a representation in which the coupling between the vibrational states is reduced. The full vibration-torsion eigenstates are obtained subsequently via matrix diagonalization. The convergence of the perturbation theory and variational calculations are discussed. The torsion-vibration energies and the torsional tunneling splittings are compared with available spectroscopic data for all the fundamentals. The unusual inverted E-A torsional tunneling splitting pattern observed spectroscopically for rotationless torsion-vibrational states is predicted by our calculation.

Fourier transform spectroscopy of CH3OH: rotation–torsion–vibration structure for the CH3-rocking and OH-bending modes

“…While the energy patterns for the ðt 7 ; t t Þ ¼ ð1; 0Þ in-plane and ðt 11 ; t t Þ ¼ ð1; 0Þ out-of-plane CH 3 -rocking modes follow well-defined oscillatory curves as a function of K, this is not the case for the excited torsional levels. We find that the t t ¼ 1 states are coupled to the OH bend by significant resonances, as also has been predicted from ab initio calculations [27]. The ðt 7 ; t t Þ ¼ ð1; 1Þ in-plane CH 3 -rocking, ðt 8 ; t t Þ ¼ ð1; 1Þ CO-stretching, ðt 6 ; t t Þ ¼ ð1; 0Þ OH-bending, and possibly ðt 11 ; t t Þ ¼ ð1; 1Þ out-of-plane CH 3 -rocking states interact and mix together in a complex energy region in which the patterns are quite unlike the traditional picture.…”

“…In recent years, analyses of optically pumped FIR laser emission [18][19][20] as well as continuing FTIR studies have also provided high-resolution information for the other low-frequency modes, highlighted by the discovery of inverted torsional structure in the m 11 out-of-plane CH 3 -rocking band [9] and the m 4 in-plane asymmetric CH 3 -deformation band [21,22]. These latter results paralleled the original finding of inverted splitting for the m 2 CHstretching mode of CH 3 OH [23], and have helped to stimulate a variety of recent approaches to the torsionvibration Hamiltonian that have had some striking successes in modeling the observed structures [22,[24][25][26][27].…”

“…However, they predict that all such modes should display inversion, unlike our above observations for m 7 . Another recent full-dimensional ab initio treatment [27], on the other hand, calculates the splittings to be normal for m 7 and inverted for m 11 as we observe experimentally, so that there are still interesting differences between theoretical models and the need for additional precise spectroscopic data.…”

“…Furthermore, the dramatic departures from the traditional model, notably torsional inversion, that have been observed for the t t ¼ 0 ground torsional levels of certain of the CH 3 -rocking, CH 3 -deformation, and CH-stretching modes [9,10,21,23] imply that similar changes may be expected for their excited torsional states. Such states have not yet been explored for these modes within the framework of the new torsion-vibration formalisms [22,[24][25][26][27]; we hope that the present results may serve as a stimulus to do so.…”

“…In general, it appears that there is new perturbation physics at work in this energy region that is creating new energy patterns. The interesting thing will be to see whether these can be explained by treating the ðt 6 ; t t Þ ¼ ð1; 0Þ, ðt 7 ; t t Þ ¼ ð1; 1Þ, ðt 8 ; t t Þ ¼ ð1; 1Þ, and ðt 11 ; t t Þ ¼ ð1; 1Þ states together as a coupled system with appropriate interaction terms in a unified torsion-vibration Hamiltonian [22,[24][25][26][27].…”