Anharmonic Vibrational Properties from Intrinsic n-Mode State Densities

Abstract

A method for calculating fully anharmonic vibrational state counts, state densities, and partition functions for molecules is presented. The method makes use of a new quantity, the intrinsic density of states, which is associated with the states that uniquely arise from a given mode, mode pairing, or higher-order mode coupling. By using only low-order intrinsic densities, the fully coupled anharmonic vibrational result can be constructed, as shown by our application of the method to methane, CH 4 , and cyclopropene, C 3 H 4 . Truncation of the intrinsic expansion at the coupling of pairs of modes yields greatly improved scaling over direct evaluation of the full-dimensional result and recovers a large fraction of the total anharmonicity. We also discuss the relation of the new quantities to the structure of the potential energy surface.

Harnessing the Combined Power of Theoretical and Experimental Data through Multiscale Informatics

“…More accurate kinetics calculations and more representative descriptions of the uncertainties in the calculations can be expected through use of more rigorous theoretical models (e.g., for anharmonicity , tunneling , E , J ‐resolved energy transfer ). As concluded elsewhere and demonstrated in Figs.…”

“…In addition to the uncertainties in the calculation of molecular properties discussed above, there are additional uncertainties that can arise in some situations from inadequacy of the employed elementary kinetics model, e.g., the breakdown of standard assumptions in cases where non‐Boltzmann reactant distributions , non‐RRKM , nonadiabatic , coupled torsions , multidimensional tunneling , weak‐collision‐in‐ J energy transfer , or nonlinear mixture rules are important. For example, in previous implementations of the multiscale informatics approach for Cl‐initiated C 3 H 8 oxidation , the structural uncertainty parameter describing uncertainty due to non‐Boltzmann reactant distributions was identified to play a key role in the interpretation of some of the experimental data (γ n‐B in Fig.…”

“…First of all, the uncertainty in the calculated rate constant is no longer exclusively dominated by uncertainties in the calculation of the relevant energetics, i.e., the barrier height. As a result, refinements to the calculation of other aspects of the theoretical treatment (including anharmonicity , rates of tunneling , and collisional energy transfer among others) are rapidly becoming the subject of increased attention. Second of all, uncertainty in calculated rate constants is no longer negligible compared to experimental uncertainty.…”

Analytic energy-level densities of separable harmonic oscillators including approximate hindered rotor corrections

“…[7][8][9][10][11][12] McClurg et al 7 developed an approximate description for the hindered rotor energy-level density based on a partition function expansion. Wadi and Pollak approximated the energy-level density of large polyatomic molecules with a rather narrow energy-level spacing based on a short-time expansion of the thermal energy-level density.…”

“…9 Recently, Kamarchik and Jasper formulated an approximation for the energy-level density of fully coupled anharmonic vibrational modes. 12 Bozzelli et al 13 proposed a three-frequency model to extract energy-level density information from heat capacities, which has been used by Allen et al 14 to compute energy-level densities in an automated manner. The most general approach to obtain energy-level densities is presumably the use of steepest descents of an arbitrary partition function, as described by Baer and Hase.…”