The total "partition function" or "state sum" of the molecule is what I meant. According to the book "Spectrophysics" by A. Thorne, U. Litzen, S. Johnsson (and other books in molecular and atomic spectroscopy) the partition function only depends on temperature (i.e. is a function of T). At least they write Q(T) in the book?? There are expressions for the vibrational, rotational and electronic partition functions which can be approximated to something that requires some other parameters like vibrational constant, rotational constant and such. But again, this is not the total internal state sum. My understanding is that the partition function is the same for each species (there are same amounts of energy levels in the atom or molecule) and that only changes is the population of these levels with the temperature and thus it only varies on the temperature?? But I could be wrong...
Today I actually found a file (TIPS) which produces the partition function values for different species and isotopes in the hitran database (which they have obtained and is fitted with Lagrange 4 points fitting) with the input of the temperature.
Thank you all for trying to help me.