[en] Expansion of the isotopic reduced partition function ratio in terms of a number of arguments has led to greater insight into the relationship between isotopic fractionation factors and molecular structure than can be obtained even from a critical analysis of each of the terms that contribute to the isotopic reduced partition function ratio. The most significant of these expansion methods are: (1) expansion of ln(s/s')f, logarithm of the isotopic reduced partition function ratio, in terms of the even moments of the vibrational frequencies, and (2) expansion of either (s/s')f or ln(s/s')f around a reference molecule which has no off-diagonal elements in the G (kinetic energy) and F (force constant) matrices whose solution yield the molecular vibrations. The diagonal element approximation, ln(s/s')f₀(ln(s/s')f₀ is the logarithm of the isotopic reduced partition function for the reference molecules which has eigenvalues defined by lambda/sub i0/ = f/sub ii/g/sub ii/.), gives very good results for hydrogen isotope substitution. The latter is a consequence of the fact that the off-diagonal G matrix elements involving the mass of hydrogen are either zero, or negligible, and the relatively light mass of hydrogen compared with other elements. The off-diagonal element corrections to ln(s/s')f₀ are of the order of 10 to 20% of the latter for carbon and oxygen isotope substitutions. These are easily evaluated by the WINIMAX polynomials. The correction terms, through second order (h/kT)⁴, added to ln(s/s')f₀ provide an analytical formulation for the direct evaluation of ln(s/s')f for any molecule in terms of the F and G matrix elements. Through this method it is now possible to analyze ln(s/s')f in terms of the stretching, bending, and interaction force constants in a molecule