Knowledge Bank

A theoretical model has been developed to account for certain features of $CH3$-bending subbands of methanol observed between 1450 and $1570cm-1$. The observed features in $v4$ include (i) an apparent inversion of the rotationless E-A torsional splitting with respect to the ground state, (ii) a pronounced upward slope in the K-reduced torsion-vibration energy pattern for the subband origins, and (iii) $A1-A2$ inversion of the K = 2A and 3A J-rotational levels leading initially to ambiguity in identifying the vibrational mode as $\nu 4(A1)$ or $\nu 10(A2)$. 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 $\gamma$-type Coriolis coupling terms. Experimental upper state energies for $\nu 4,\nu 10$, and $\nu 5$ have together been fitted successfully employing 12 adjustable parameters to give a standard deviation of $\pm 0.13cm-1$. J-dependence is introduced via a rotational Hamiltonian including molecular asymmetry, plus b- and c-type Coriolis terms which account for the observed $A1-A2$ inversion of the rotational levels at low K. The computer program for our model was set up in a CH-stretch/$CH3$-bend local mode polyad scheme, with polyad number $p=2(v1+v2+v3)+(v4+v5+v6)$, for ready extension to the $3\mu$m CH-stretching region in future.