Calculation of the vibrational partition function of diatomic molecules from a scaled Wigner-Kirkwood expansion

Abstract

New approximations to the partition function of diatomic molecules are given. The semiclassical Wigner-Kirkwood expansion truncated at the second or fourth order diverges as T. Various methods of scaling the Wigner-Kirkwood expansion are given which avoid this disadvantage and give sufficient accuracy in the low-temperature region. In addition, two modifications of the Pitzer-Gwinn method are discussed. Most molecular potentials can be considered almost harmonic near the minimum. For the scaling of the Wigner-Kirkwood expansion, therefore, a functional form is chosen, which would be exact for every temperature in the case of a purely harmonic potential. In the high-temperature limit the scaled and the conventional Wigner-Kirkwood expansion become identical.

Exact and Poisson summation thermodynamic properties for diatomic molecules with shifted Tietz potential

“…Different techniques have been developed by many researchers in finding partition function of some systems. These methods include exact method [3], semi-classical expansion method [4], Pade method [5], Poisson summation method [6] and Wigner-Kirkwood formulation [7]. Analytical expression for the partition function of Morse oscillators had been obtained by Strekalov [8].…”

Vibrational Partition Function for the Multitemperature Theories of High-Temperature Flows of Gases and Plasmas

“…The research of ref is one of the rare examples of the partition function calculation with the Wigner–Kirkwood expansion. In the case of the CO molecule, the vibrational partition functions at 5000 K reasonably agree (higher temperatures were not investigated), but at 1000 K, they do not, probably because that study uses only one term of the expansion.…”

Numbers and densities of states and partition functions from an efficient approach to phase space integration

“…path integral methods,16h19 the thermal Hartree method,20 the thermal cluster cumulant method21,22 and the thermodynamic variation perturbation method.23h25 Other approaches are based on approximants26,27 and a Pade modiÐcation of the WignerÈKirkwood expansion. 28 In this work, we will calculate the partition function from the density of states using exact quantum mechanical eigenvalues in the low energy region and the classical number of states for higher energies.…”