A rotation-torsion-vibration treatment with three-dimensional internal coordinate approach and additional FTIR spectral assignments for the CH3-bending fundamentals of methanol

A theoretical model has been developed to account for certain features of both newly observed and previously reported CH₃-bending subbands between 1450 and 1570 cm⁻¹ in the high-resolution Fourier transform infrared spectrum of CH₃OH [Can. J. Phys. 79 (2001) 435]. The features include (i) an apparent inversion of the rotationless E-A torsional splitting with respect to the ground state, i.e., the A state located above the E state, (ii) a pronounced upward slope in the K-reduced torsion-vibration energy pattern for the subband origins, and (iii) unexpected A₁/A₂ inversion of the K=2A and K=3AJ-rotational levels that led to ambiguity in identifying the vibrational mode as or . The model is an effective internal coordinate Hamiltonian constructed in G₆ molecular symmetry with the CH₃-bends coupled to each other and to torsion and including a- and γ-type Coriolis coupling. With this model, 33 out of 36 experimental upper-state K-term values for newly assigned , and ν₁₀ subbands plus previous ν₄ subbands have together been fitted successfully, employing 9 adjustable parameters and 17 fixed parameters to give a standard deviation of 0.14 cm⁻¹. The P_γ Coriolis term appears to be the leading cause of the upward shift in the K-reduced energies. When J-dependence is introduced via a rotational Hamiltonian including b- and c-type Coriolis terms in addition to molecular asymmetry, the observed A₁/A₂ inversion of the K=2A and 3A rotational levels can also be reproduced. Predictions using the fitted K-rotation-torsion-vibration Hamiltonian show an interesting Coriolis-induced crossover and mixing of the ν₅ and ν₁₀ torsion-vibration energy patterns. These predictions played a role in identifying two of the new ν₅ subbands in the crossing region, thereby helping to validate the model.