Hi,

First you should tell us more about the kind of plasma you are interested in. Do you mean the vibrational degrees of freedom of the electron-nucleus interaction associated with the fact that ionization is only partial ? In that case, I don't think it is of great significance to add the complex dynamics of these degrees of freedom in a kinetic model as I assume they would not significantly modify the overall behaviour of the plasma. What matters is, is this electron free or bond to an atom ? I may be wrong, but I assume the polarizability of the medium due to there being incompletely stripped atoms must be negligible compared to the polarizability due to there being free electrons in the medium. Thus, as soon as you know the distribution function of the free electrons, I don't think it is necessary to go further. At least, this is what my physical intuition tells me. Maybe I misunderstood your question.

To model thermal nonequilibrium in the discharges the most used is the state-to-state approach. You can look at some of my papers for this or the book Fundamental Aspects of Plasma Chemical Physics: Kinetics by

Mario Capitelli, Roberto Celiberto, Gianpiero Colonna, Fabrizio Esposito, Claudine Gorse, Khaled Hassouni, Annarita Laricchiuta, Savino Longo.

This is not multi-temperature, but it describes all the internal states as independent species. Multi temperature model assumes that each degree of freedom is described by a Bolzmann distribution with its own temperature. However, each state has a different relaxation time, different excitation cross section by electron impact and therefore non-Boltzmann distributions are obtained.

Multi-temperature model is often used in modeling high enthalpy flows, even if in the last years, the state-to-state model is studied by many researchers. It is possible to build a multi temperature model starting from a state to state one summing the state to state rates considering a Boltzmann vibrational distribution with Tv. You can look at the work of Anne Bourdon for some papers.  

The most used multi temperature model was developed by Chul Park, before at NASA and now in Corea. 

When comparing with experimental vibrational temperature, great care must be taken. If you consider homonuclear molecules such as N2, H2, O2, the vibrational temperature measured by spectroscopic refers to electronically excited state the is not related to what is usually described by state to state, which consider vibrational ground state. A model to include vibrational kinetics of electronically excited states was describe by Christophe Laux. 

Hope it helps