Isotope Partition Function ("The Urey Equation")

The partition function for determining equilibrium isotope fractionation factors as formulated by Urey (1947) for diatomic molecules (sometimes called the "Urey Equation"):

Where,

σ = symmetry number for molecule
I = moment of inertia for molecule
M = molecular mass
h = Planck's Constant
c = Speed of Light
ω = vibrational frequency
k = Boltzmann's Constant
T = Temperature

The subscripts 1 and 2 refer to two isotopologues that are undergoing an isotope exchange reaction.   

Isotopologue definition: Molecules that differ from one another only in isotopic composition, e.g., C¹⁶O and C¹⁸O.