Abstract
In this chapter, the working equations for the vibrational, rotational and electronic partition functions of the diatomic species and their contribution to the thermodynamic properties will be discussed. First, we present closed forms for the vibrational and rotational partition functions based on the harmonic oscillator and rigid rotor models. These approximations can be used for both diatomic and polyatomic molecules. This model considers the molecular partition function as the product of the contributions of four independent degrees of freedom, nuclear (n), vibration (vib), rotation (rot) and electronic (el):
The energy is the sum of the three corresponding contributions
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Notes
- 1.
Commonly θ r ≈ 10 K, except for H 2 having θ r ≈ 90 K.
- 2.
It must be noted that J even is coupled with the antisymmetric nuclear state if s is semi-integer and with the symmetric nuclear state if s is integer.
- 3.
Note that ortho- and para-hydrogen have the same translational partition function, because it depends only on the mass of the species.
- 4.
When considering ortho–para effects (5.34), must be extended considering the whole internal partition function, including the contribution of electronically excited states, of ortho-and para-configurations calculated separately.
- 5.
The centrifugal potential introduces a barrier in the energy curve, resulting in the existence of quasi-bound states above the dissociation limit. The inclusion of these states in the internal partition function is argument of a debate.
- 6.
The spectroscopic constants are usually expressed as wave numbers (the reverse of a length), therefore, to be converted in energy unit, the energy equations must be multiplied by the factor hc.
- 7.
This result can be obtained easily by considering that a system with n a atoms has 3n a degrees of freedom, three directions of motion (x, y, z) for each atom. However, three degrees of freedom, corresponding to the translational motion of the centre of mass, must be eliminated, together with the rotational motion of the molecule. In general a polyatomic molecule has three independent rotational axes, but for linear molecules, having only two axes, because the molecular axis is not a rotational one.
- 8.
The vibrational modes are calculated finding the eigenvalues and eigenvectors of the Hessian matrix of the potential. As a consequence, the hypothesis of independent modes is valid only for weakly excited molecules.
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Capitelli, M., Colonna, G., D’Angola, A. (2012). Molecular Partition Function: Vibrational, Rotational and Electronic Contributions. In: Fundamental Aspects of Plasma Chemical Physics. Springer Series on Atomic, Optical, and Plasma Physics, vol 66. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8182-0_5
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