The total canonical partition function Z of a system of N identical, indistinguishable, noninteracting atoms or molecules can be divided into the atomic or molecular partition functions ζ ζ : Z = ζ ζ N N ! with: ζ ζ = ∑ ∑ j g j e − − E j / k B T , where g j is the degeneracy of the j -th quantum level of an individual particle, k B is the Boltzmann constant, and T is the absolute temperature of system. For molecules, under the assumption that total energy levels E j can be partitioned into its contributions from different degrees of freedom (weakly coupled degrees of freedom) E j = ∑ ∑ i E j i = E j trans + E j ns + E j rot + E j vib + E j e and the number of degenerate states are given as products of the single contributions g j = ∏ ∏ i g j i = g j trans g j ns g j rot g j vib g j e , where "trans", "ns", "rot", "vib" and "e" denotes translational, nuclear spin, rotational and vibrational contributions as well as electron excitation, the molecular partition functions ζ ζ = ∑ ∑ j g j e − − E j / k B T can be written as a product itself ζ ζ = ∏ ∏ i ζ ζ i = ζ ζ trans ζ ζ ns ζ ζ rot ζ ζ vib ζ ζ e .