Adiabatic Treatment of Torsional Anharmonicity and Mode Coupling in Molecular Partition Functions and Statistical Rate Coefficients: Application to Hydrogen Peroxide
A semi-classical method is proposed for accurately incorporating torsional degrees of freedom into molecular state sums and partition functions in a computationally economic way. This method applies an adiabatic separation of the ‘slow’ torsional mode from the other ‘fast’ internal degrees of freedom. The state sum is carried out quantum mechanically over the fast vibrations and the molecular rotations as a local function of the slow torsion coordinate. The torsional states are then included as a classical phase space integral over the local state sum with a zero point energy correction. The method is formulated for both bound and reactive systems. This method was applied to two test cases: (a) a simple coupled-harmonic oscillators model problem; and (b) the HOOH molecule, its isotopomer DOOH, and with the explicit calculation of the unimolecular rate coefficient for the dissociation reaction. The results are compared with those obtained from the usual separable treatments, including the harmonic oscillator–rigid rotor (HO-RR) and Pitzer–Gwinn separable hinder rotor methods. The coupled oscillator model shows the tendency of the HO-RR model to significantly miscount states at high energy. It is generally observed that the separable models tend to underestimate the state count of the HOOH molecule at lower energies relative to the more rigorous semi-classical method. The Rice–Ramsberger–Kassel–Marcus; (RRKM) rate constants predicted for the O–O bond breaking of HOOH are higher for the semi-classical model than those of the separable models. These differences highlight the necessity of accounting for the coupling between torsional motion and other degrees of freedom in any sophisticated model and we recommend the semi-classical adiabatic torsion method in future applications.