Chapter 6
Molecular Systems
This chapter determines the contributions of molecular internal states associated
with molecular rotations, vibrations, and electronic excitations to thermodynamic
functions. Diatomic molecules are treated using rigid-rotor and simple harmonic
oscillator approximations, then corrected for small effects, including rotational
quantum effects. Special attention is paid to homonuclear diatomic molecules, as
nuclear interchange symmetry plays an important role in determining the nature
of rotational contributions to thermodynamic properties and affects intensity ratios
in molecular spectra. Summary expressions are given for the canonical partition
function and for the translational, rotational, vibrational, and electronic contributions to the thermodynamic properties of diatomic and of both linear and nonlinear
polyatomic molecules. Third-law and residual entropies are explained in terms
of ‘frozen in’ states. Finally, an examination of the effect of hindered rotational
motions is given, using ethane as a typical example.
6.1 Introduction
When we deal with polyatomic molecules we have to deal with translational motion
of the polyatomic molecule, and in addition to that, also with the internal rotational,
vibrational, and electronic motions associated with the molecule. This makes
the derivation of expressions for the thermodynamic functions considerably more
difficult than it is for monatomic species. It is nonetheless straightforward, provided
that we make use of one or two simple, but remarkably accurate, approximations.
As a first step, we write the energy for a polyatomic molecule in the form
= tr + int ,
(6.1.1)
© Springer Nature Switzerland AG 2021
F. R. W. McCourt, Statistical Thermodynamics for Pure and Applied Sciences,
https://doi.org/10.1007/978-3-030-52006-9_6
257
Molecular Systems
This chapter determines the contributions of molecular internal states associated
with molecular rotations, vibrations, and electronic excitations to thermodynamic
functions. Diatomic molecules are treated using rigid-rotor and simple harmonic
oscillator approximations, then corrected for small effects, including rotational
quantum effects. Special attention is paid to homonuclear diatomic molecules, as
nuclear interchange symmetry plays an important role in determining the nature
of rotational contributions to thermodynamic properties and affects intensity ratios
in molecular spectra. Summary expressions are given for the canonical partition
function and for the translational, rotational, vibrational, and electronic contributions to the thermodynamic properties of diatomic and of both linear and nonlinear
polyatomic molecules. Third-law and residual entropies are explained in terms
of ‘frozen in’ states. Finally, an examination of the effect of hindered rotational
motions is given, using ethane as a typical example.
6.1 Introduction
When we deal with polyatomic molecules we have to deal with translational motion
of the polyatomic molecule, and in addition to that, also with the internal rotational,
vibrational, and electronic motions associated with the molecule. This makes
the derivation of expressions for the thermodynamic functions considerably more
difficult than it is for monatomic species. It is nonetheless straightforward, provided
that we make use of one or two simple, but remarkably accurate, approximations.
As a first step, we write the energy for a polyatomic molecule in the form
= tr + int ,
(6.1.1)
© Springer Nature Switzerland AG 2021
F. R. W. McCourt, Statistical Thermodynamics for Pure and Applied Sciences,
https://doi.org/10.1007/978-3-030-52006-9_6
257