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 Ϫ1 K Ϫ1 for molecules with no internal rotations. For molecules with internal rotations, errors of up to 1.8 J mol Ϫ1 K Ϫ1 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 Ϫ1 K Ϫ1 for species with zero or one internal rotation, and better than 2 J mol Ϫ1 K Ϫ1 for species with two internal rotation modes. Rotor-rotor coupling is found to contribute on the order of 1 J mol Ϫ1 K Ϫ1 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 Ϫ1 K Ϫ1 .

Understanding the reactivity of unsaturated alcohols: Experimental and kinetic modeling study of the pyrolysis and oxidation of 3-methyl-2-butenol and 3-methyl-3-butenol

“…The obtained hindrance potential was then expressed as a Fourier series. Together with the reduced moment of inertia calculated at the I(2,3) level as defined by East and Radom [37], the hindrance potential was used to construct the Schrödinger equation for 1-D rotation. The eigenvalues of the solution to this Schrödinger equation represent the energy levels of this mode.…”

Theoretical Study of the Reaction Mechanism and Role of Water Clusters in the Gas-Phase Hydrolysis of SiCl4

“…21 Special attention was paid to hindered rotation within the molecules under consideration. The effect of hindered rotation on the entropy and the Gibbs free energy was taken into account using the E2 procedure of East 22 and the Pitzer-Gwinn independent rotor approximation. 23 In some cases, special consideration of large-amplitude motions was also undertaken using the ADANIMEHS program 24 originally developed for PES scanning of nonrigid systems.…”

Computed Rate Coefficients and Product Yields for c-C5H5 + CH3 → Products

“…The reduced moment of inertia based on the equilibrium geometry was calculated using the formulas described by Pitzer. [24][25][26] In this paper we have used the reduced moment of inertia I (2,3) , 27 and the one dimensional Schroedinger equation was solved numerically. For cyclopentadienyl an additional moment of inertia for pseudo rotation was used as described in Section 3.1.…”