An extended hindered-rotor model with incorporation of Coriolis and vibrational-rotational coupling for calculating partition functions and derived quantities

Abstract

Large-amplitude motions, particularly internal rotations, are known to affect substantially thermodynamic functions and rate constants of reactions in which flexible molecules are involved. Up to now all methods for computing the partition functions of these motions rely on the Pitzer approximation of more than 50 years ago, in which the large-amplitude motion is treated in complete independence of the other (vibrational) degrees of freedom. In this paper an extended hindered-rotor model (EHR) is developed in which the vibrational modes, treated harmonically, are correctly separated from the large-amplitude motion and in which relaxation effects (the changes in the kinetic-energy matrix and potential curvature) are taken into account as one moves along the large-amplitude path. The model also relies on a specific coordinate system in which the Coriolis terms vanish at all times in the Hamiltonian. In this way an increased level of consistency between the various internal modes is achieved, as compared with the more usual hindered-rotor (HR) description. The method is illustrated by calculating the entropies and heat capacities on 1,3-butadiene and 1-butene (with, respectively, one and two internal rotors) and the rate constant for the addition reaction of a vinyl radical to ethene. We also discuss various variants of the one-dimensional hindered-rotor scheme existing in the literature and its relation with the EHR model. It is argued why in most cases the HR approach is already quite successful.

First‐principles based group additivity values for thermochemical properties of substituted aromatic compounds

“…To take thermochemical effects due to rotation of single bonds into consideration, the one-dimensional hindered rotor (1-D-HR) approach of Van Speybroeck and coworkers [38][39][40] is applied. It is well known that such a treatment significantly improves the calculated thermochemical properties, 39 in particular the entropy results.…”

Theoretical Determination of the Rate Coefficient for the HO2 + HO2→ H2O2+O2Reaction: Adiabatic Treatment of Anharmonic Torsional Effects

“…While there are two other modes that might also be regarded as torsional, we did not find additional saddle points for those degrees of freedom (aside from the mirror image configurations). Multifaceted transition states have received some attention in the recent literature 55,56 and are expected to be generic for systems with energetically accessible torsional conformers. Truhlar and coworkers 57 have suggested the MS-AS method in which the contributions for the various transition state structures are summed using several possible weighting factors.…”

An Efficient and Accurate Formalism for the Treatment of Large Amplitude Intramolecular Motion

“…However, it has been shown that these approximations fail when large amplitude motions are involved, 4,5 and a rigorous treatment is often required if an accurate prediction of statistical properties is required. 6−8 This is particularly the case when a torsional motion is present 7,9−11 or when a loose TS is involved in a dissociation/recombination reaction. 12−14 Numerous studies have been dedicated to the development of statistical methods in the context of one or the other application, while, to our knowledge, none has been presented for the general case.…”

“…12−14 Numerous studies have been dedicated to the development of statistical methods in the context of one or the other application, while, to our knowledge, none has been presented for the general case. In cases of torsional motions, the proposed treatments are usually derived from the one-dimensional hindered rotor (1DHR) model, originally proposed by Pitzer et al 4 Recent studies 7,9,11 show the importance of a rigorous treatment, where quantum effects, multidimensionality, as well as coupling with other internal or external motions can have a non-negligible influence. In the context of dissociation reactions involving a loose complex, two- to five-dimensional large amplitude motions need to be described.…”