Anharmonic Rovibrational Partition Functions at High Temperatures: Tests of Reduced-Dimensional Models for Systems with up to Three Fluxional Modes

Abstract

Curvilinear coordinate Monte Carlo phase space integration and a series of full-dimensional fitted potential energy surfaces are used to study the effectiveness of reduced-dimensional models for predicting rovibrational anharmonicity at high temperatures. Fully coupled and fully anharmonic, but classical, rovibrational partition functions Q are computed for 14 species with two or three fluxional modes (inversions or torsions) and as many as 30 degrees of freedom. These results are converted to semiclassical anharmonicity correction factors f and are analyzed alongside results obtained previously for 22 species with up to two fluxional modes. As expected, fluxional species show considerable variation in f at high temperatures; f is as small as 0.2 for acetone and is as large as 9 for methylene glycol at 2500 K. This set of full-dimensional results is used to test the accuracy of reduced-dimensional models where fluxional modes are treated as coupled to one another but as separable from the remaining nonfluxional modes. For most systems, we find that such an approximation is accurate at high temperatures, with average errors in Q of just ∼25%. For some systems, however, larger errors are found, and these are attributed to strong coupling of the fluxional modes to one or more nonfluxional modes. In particular, we identify strong coupling to low-frequency bends for some systems, and we show that by comparing curvilinear and rectilinear harmonic frequencies for the fluxional modes, we can estimate the effect of this coupling on rovibrational anharmonicity. We also quantify the accuracy of the more severe but common assumption of treating fluxional modes as separable from one another, that is, as sets of uncoupled one-dimensional inversions and torsions. This approach can work well for methyl and alkyl rotors, but it is shown to have errors as large as a factor of 7 at high temperatures for more complex systems. Finally, we note that while the present analysis focuses on the treatment of fluxional modes, the collective anharmonicity correction associated with the more numerous nonfluxional modes, although simpler to describe, comprises a significant fraction of the overall anharmonicity.

Extreme Low-Temperature Combustion Chemistry: Ozone-Initiated Oxidation of Methyl Hexanoate

“…In our own recent studies comparing fully coupled and fully anharmonic Monte Carlo phase space integral partition functions with RRHO, separable 1DHR, and multidimensional HR models, we found that the error in the partition function using a 1DHR model increased from just 20%, on average, for systems with one fluxional mode (such as a torsion) to factors of 2 and 7 for systems with two and three fluxional modes, respectively. , These errors are in fact comparable in magnitude to those quantified in the same study for a single conformer RRHO model. (Note that E1 and E2 improve on the single conformer RRHO model by including the effects of multiple conformers, but such a multiconformer RRHO method was not tested in ref .) It is unknown how well conclusions drawn for stable species can be applied to the description of transition states, but we can say that it is generally more difficult to define and separate torsions for transition states (which necessarily have a variety of low-frequency motions, many of which cannot be straightforwardly described as torsions) than for stable species.…”

“…1DHR results are generally assumed to be more accurate, but we caution against this assumption for large systems, where the scaling of the accuracy of 1DHR approaches is not well-understood. In our own recent studies comparing fully coupled and fully anharmonic Monte Carlo phase space integral partition functions with RRHO, separable 1DHR, and multidimensional HR models, we found that the error in the partition function using a 1DHR model increased from just 20%, on average, for systems with one fluxional mode (such as a torsion) to factors of 2 and 7 for systems with two and three fluxional modes, respectively. , These errors are in fact comparable in magnitude to those quantified in the same study for a single conformer RRHO model. (Note that E1 and E2 improve on the single conformer RRHO model by including the effects of multiple conformers, but such a multiconformer RRHO method was not tested in ref .)…”

Microcanonical Rate Constants for Unimolecular Reactions in the Low-Pressure Limit

“…The small error for our best a priori semiclassical model is notable, as errors of this magnitude (<30%) are characteristic of the best a priori semiclassical methods for kinetics, such as those for tunneling, 110 high-temperature anharmonicity, 111 and nonadiabatic treatments of intersystem crossing. 107,112 Errors of this magnitude in kinetics are likewise comparable to those of many kinetics measurements, thus positioning a priori semiclassical theories as competitive with experiment as practical sources of quantitative chemical kinetics data.…”

The High Temperature Vibrational Partition Function of Stretching of Triatomic Systems

“…In principle is seems theoretically to be the most effective model for thermal decomposition. Note also usefulness of reduced-dimensionality models in the research of larger molecules [27].…”