Molecular density of states from estimated vapor phase heat capacities

Abstract

Heat capacity data between 298 and 1500K are used to derive a reduced set of apparent vibrational frequencies that can be used for estimation of molecular density of states, (E). Estimates for a number of molecule and radical species, using a reduced set of three frequencies with noninteger degeneracies, are shown to compare favorably to direct count methods, which require specification of the complete frequency set. Use of the reduced set of three frequencies leads to significant improvement in calculations of (E)/Q as compared to similar calculations which use only a single geometric-or arithmetic-mean frequency approximation. Since vapor phase heat capacity data of molecules and radicals can be estimated accurately by a group additivity formalism, this approach provides a method to estimate (E) for use in calculations of pressure effects in unimolecular and chemical activation reaction systems. The accuracy of the (E)/Q distributions obtained from heat capacity data makes this a viable method for those cases where the complete frequency distribution is not known. It is especially valuable for those cases where contributions to (E) from internal rotors or low frequency vibrations such as inversions are not well known. This approach is useful for quantum RRK or inverse Laplace transform calculations of k(E) since no assignment of transition state properties is necessary. The reduced frequency set can also be combined with ⌬H f (298) and S(298) to provide a compact data set to describe thermodynamic properties at any temperature.

Reaction of H + ketene to formyl methyl and acetyl radicals and reverse dissociations

“…The QRRK code utilizes a reduced set of three vibration frequencies, which accurately reproduce the molecules'(adduct) heat capacity; the code includes contribution from one external rotation in calculation of the ratio of the density of states to the partition coefficient ρ( E )/ Q . Comparisons of ratios of these ρ( E )/ Q with direct count ρ( E )/ Q 's are shown to be in good agreement 42. Rate constant results from the quantum RRK‐Master equation analysis are shown to accurately reproduce (model) experimental data on several complex systems.…”

“… a Geometric mean frequency [from CPFIT, Ref. 42, 50; CH 3 C·O: 574.8 cm −1 (3.408); 1419.3 cm −1 (4.867); 2820.3 cm −1 (3.225); C·H 2 CHO: 584.5 cm −1 (3.878); 1236.4 cm −1 (5.112); 2938.8 cm −1 (3.010)], Lennard–Jones parameters: [σ = 4.34 Å, ε/ k = 422.61 K, Ref. 51, 52], (ΔE)° down of 1000 cal/mol 39, 40 is used, N 2 for bath gas. …”

“…Reduced sets of three vibration frequencies and their associated degeneracies are computed from fits to heat capacity data, as described by Ritter and Bozzelli et al 42, 50. [CH 3 C·O: 574.8 cm −1 (3.408), 1419.3 cm −1 (4.867), 2820.3 cm −1 (3.225); C·H 2 CHO: 584.5 cm −1 (3.878), 1236.4 cm −1 (5.112), 2938.8 cm −1 (3.010)] Lennard–Jones parameters, σ(Å) and ε/ k (K) are obtained from tabulations 51 and from a calculation method based on molar volumes and compressibility 52.…”

The pyrolysis of 2-methylfuran: a quantum chemical, statistical rate theory and kinetic modelling study

“…34 Microscopic rate constants, k(E), are in turn computed from the density of states of the reactant molecule together with an estimate of the high-pressure limiting rate constant for the reaction via the Inverse Laplace Transform (ILT) method. The first is that the former derives vibrational frequencies for reactants, and subsequent sums and densities of states, from a three-frequency fit to molecular heat capacities.…”

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

“…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.…”