Ab initio statistical thermodynamical models for the computation of third-law entropies

Abstract

Third-law gas-phase statistical entropies are computed for a variety of closed-shell singlet state species using standard formulae based upon canonical partition functions. Molecular parameters are determined ab initio, and sensitivity analyses are performed to determine expected accuracies. Several choices for the canonical partition function are examined for internal rotations. Three general utility procedures for calculating the entropies are developed and designated E1, E2, and E3 in order of increased accuracy. The E1 procedure adheres to the harmonic oscillator approximation for all vibrational degrees of freedom other than for very low barrier internal rotations, these being treated as free rotations, and yields entropies to an accuracy of better than 1 J mol−1 K−1 for molecules with no internal rotations. For molecules with internal rotations, errors of up to 1.8 J mol−1 K−1 per internal rotation are observed. Our E2 procedure, which treats each individual internal rotation explicitly with a simple cosine potential, yields total entropies to an accuracy of better than 1 J mol−1 K−1 for species with zero or one internal rotation, and better than 2 J mol−1K−1 for species with two internal rotation modes. Rotor–rotor coupling is found to contribute on the order of 1 J mol−1 K−1 for a third-law entropy. Our E3 procedure takes this into account and, with the aid of new ab initio two-dimensional torsional potential energy surfaces of state-of-the-art accuracy, improves the accuracy of the predicted entropy for species with two internal rotation modes to approximately 1 J mol−1 K−1.