The Determination of Relative Symmetry Numbers for Isotopomers

One can rewrite Equation 4.115 to yield a formula for the symmetry number 

Equation 4.117 makes complete sense. One of the first things one learns in dealing with phase space integrals is to be careful and not over-count the phase space volume as has already been repeatedly pointed out. In quantum mechanics equivalent particles are indistinguishable. The factor n ni is exactly the number of indistinguishable permutations, while A accounts for multiple minima in the BO surface. It is proper that this factor be included in the symmetry number. Since the BO potential energy surface is independent of isotopic substitution it follows that A is also independent of isotope substitution and cannot affect the isotopic partition function ratio. From Equation 4.116 it follows 

No detailed symmetry analysis is needed. Let us take a quick look at an example and calculate the symmetry number ratio for CH3D/CH4. For CH3Dni = 3, n2 = 1 and nni- = (3 )(1 ) = 6 while for CH4ni = 4 = 24, there is no n2. Thus 

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