Anharmonicity in Vibrational State Sums

Abstract

Articles you may be interested in Molecular vibrational energy flow and dilution factors in an anharmonic state space Sum and density of states for anharmonic polyatomic molecules. Effect of bend-stretch couplingRefinements have been made in the treatment of vibrational state sums. These modifications are particularly important at energies greater than the dissociation energies. It was not possible to extend the available analytical treatments of harmonic oscillators, and numerical sums were computed for several anharmonic examples and compared with previous work. Values of the empirical correction factor a were given and the previously derived approximate equations involving a extended to the anharmonic case.

Approximate calculation of anharmonic densities of vibrational states for very large molecules

“…But at least the behavior of local stretching vibrations can be reproduced when D i is identified with the dissociation energy of the pertinent bond. Early attempts for the calculation of anharmonic densities of states assumed Morse potentials for all degrees of freedom [32]. This is certainly incorrect because bending modes cannot ''dissociate" and the level spacings in these degrees of freedom increase for higher energies (see next section).…”

“…In the past, several attempts have been made to include the deviations from the harmonic oscillator model in density of states calculations, mainly employing spectroscopically derived expressions up to quadratic terms in the vibrational quantum numbers (e.g., the Dunham expansion [29]) to determine rovibrational energy levels [30][31][32][33][34][35]. As was pointed out by some authors, this is a physically dangerous procedure because these expressions have been derived in the framework of perturbation theory and are valid only for the low energy regime, so that an extrapolation towards higher energies, in particular up to the dissociation limit, may not only yield quantitatively incorrect results for the energy levels, but even energies below the zero-point level.…”

Efficient and reliable calculation of rice-ramsperger—kassel-marcus unimolecular reaction rate constants for biopolymers: Modification of beyer-swinehart algorithm for degenerate vibrations

“…It is obvious that reduction in computation time may occur if a method to treat degenerate vibrations all at the same time can be devised. In the grouped-frequency direct counting mode [17][18][19] of RRKM calculation used before the advent of the BS algorithm, this was achieved by taking advantage of the fact that the number of ways to distribute j vibrational quanta into g degenerate vibrations is given by g H j ϭ gϩjϪ1 C j . To see how the same relation plays in the original BS algorithm, let us inspect the energy density, or the number of state at the internal energy 9 in T 3 , or T 3 (10) ϭ 6, in the preceding example.…”

“…In the grouped-frequency direct counting method used previously [17][18][19], a complete frequency set, either of the reactant or of TS, was split into several subsets, each consisting of frequencies with similar magnitudes. The representative frequency for each subset was calculated as the geometrical mean of the constituents.…”

“…Direct counting of states [17][18][19] was attempted from the early days of study together with the computationally less demanding version of using grouped frequencies [20] and approximate methods such as the Whitten-Rabinovitch (WR) semiclassical method [21] and the steepest-descent method [22]. It was observed that all the approximate methods provided erroneous results at low internal energy [4,20,23].…”