Determination of vibrational parameters of methanol from matrix-isolation infrared spectroscopy and ab initio calculations. Part 2 – Theoretical treatment including a perturbative approach of the resonances within the methyl group

Ab initio calculations of the potential energy surface of methanol have been developed for the determination of vibrational parameters and their comparison with vibrational data reported in the first part of this work. The strong resonances between the methyl bending and stretching modes, giving rise to polyads of levels P_n in the ranges 3000–2800 (P₂), 4500–4250 (P₃) and 6000–5600 cm⁻¹ (P₄), have been treated by solving for each polyad two Hamiltonian matrices containing off-diagonal terms including both Fermi and Darling-Dennison anharmonic contributions. These terms were calculated from the ab initio determination of the potential energy surface developed up to the quartic terms using the Möller–Plesset 2 method. The choice of the basis set was made to minimize the problem of divergence of the Darling-Dennison constants. Their determination requires however the omission of the terms in which the difference between the harmonic frequencies of the symmetrical methyl stretching and the sum of the two A′ bendings (ω₃–ω₄–ω₅) appears in the denominator. Then, by adjustment of the diagonal elements of the Hamiltonian matrices, it becomes possible to propose a realistic assignment of the matrix spectra.