Statistical–mechanical calculations of thermal properties of diatomic gases

Abstract

The impact of rotational-vibrational dynamics of molecules on the molecular partition functions, law of mass action and thermodynamic functions of partially dissociated diatomic gases is discussed. A group of 11 gases, expected to have their partition functions the most sensitive to the molecular rotational-vibrational properties, is selected for rigorous and detailed studies, and the partition functions, dissociation degrees and free energies of the gases are calculated ͑using various models of molecular rotational-vibrational dynamics͒ and compared in a broad range of temperature and particle density.

Molecular energies of the improved Rosen−Morse potential energy model

“…In 2012, Jia et al 33 presented a more convenient form of the original Rosen−Morse potential energy function: (2) U RM (r) ϭ D eͩ 1 Ϫ e ␣r e ϩ 1 e ␣r ϩ 1 ͪ 2 where ␣ = 2/d, D e is the dissociation energy, and r e is the equilibrium bond length. Here, one term, 1 2 D e ͑e 4r e /d ϩ 1͒, has been added to the original Rosen−Morse potential (eq.…”

“…1 The expression for the rotation-vibrational energy spectra for diatomic molecules also plays an important role in calculations of thermal properties of diatomic gases. 2 In terms of the wave functions for diatomic molecules, one can calculate the transition dipole matrix elements. [3][4][5] Some authors have investigated analytical solutions of the Schrödinger equation with typical diatomic molecule potential models, such as the Morse potential, 6 Deng−Fan potential, 7-10 Rosen−Morse potential, 11,12 Manning−Rosen potential, [13][14][15][16][17] Wei potential, 18 and Schiöberg potential.…”

Spectroscopic study of some diatomic molecules via the proper quantization rule

“…[27], [29] and [31] and the conversion factors used are taken from NIST database [32]: 1cm −1 = 1.239841930eV,hc = 1973.29eVÅ and 1amu = 931.494061Mev/c 2 . In Table 2, we test the accuracy of the method utilized in this study by finding the energy spectra of H 2 and CO diatomic molecules.…”

Molecular energies of the improved Tietz potential energy model

“…The expressions for the rotation-vibrational energy spectra and the wave functions for diatomic molecules play an important role in many issues, such as calculations of rotational constants and centrifugal distortion constants, 1 computations of transition dipole matrix elements, 2 and calculations of thermal properties, [3][4][5] etc. There has been considerable interest in investigating the analytical solutions of the Schrödinger equation with diatomic molecular potential models, such as the Morse potential, 6 Deng−Fan potential, [7][8][9] Rosen−Morse potential, [10][11][12] Manning−Rosen potential, [13][14][15][16] and Schiöberg potential.…”