Quantized vibrational densities of states and ergodic energy transfer in molecular collisions

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

“…Besides an approach based on efficient microcanonical sampling (EMS) of the classical phase space that was applied to small model systems [45], recent developments in the calculation of reliable anharmonic densities of states include the thermodynamic method [46,47], the STAIR method [48] and the use of density correlation functions [52,53]. The thermodynamic method [46,47] makes use of the molecular partition function and its first and second moments (average internal energy and constant volume heat capacity) as functionals of qðEÞ, assuming that a simple power law dependence with three unknown parameters can describe the density of states as a function of energy.…”

“…The thermodynamic method [46,47] makes use of the molecular partition function and its first and second moments (average internal energy and constant volume heat capacity) as functionals of qðEÞ, assuming that a simple power law dependence with three unknown parameters can describe the density of states as a function of energy.…”

Laguerre polynomial solutions to master equation for vibrational energy relaxation in gases

“…We believe that the model, involving a realistic vibrational density of states, can be used to remove this assumption in evaluating P(E → E ). Recently, the simple relations between the thermodynamic properties and the molecular density of states have been applied to formulate an accurate method for determining the vibrational state density, taking into account both the quantum and anharmonic effects [12][13][14]. The energy dependence of the state density is of the form…”

Numbers and densities of vibrational states for the system represented by harmonic oscillators with a cutoff

“…The analytical expression for the density of states follows directly from Eq. (20) into which we should introduce the approximate g a (s, N; n) from (15). Let us write the resulting expression in more detail…”

“…Considerable progress in numerical computations has made it possible to create efficient algorithms for exact counts of states that are of practical use for most moderate-sized molecules [10][11][12][13][14]. Despite these achievements, the attempts to develop simplified analytical approaches to solving similar problems are still in progress [15][16][17][18][19]. In many cases, analytical models provide the basis for introducing further corrections and improvements so as to make general conclusions, and correctly formulate the problems for numerical estimations.…”