Reduced Partition Function Ratio in the Frequency Complex Plane: A Mathematical Approach

Abstract

This paper gives a mathematical approach to calculate the fractionation factor of isotopes in a general cluster (also known as super-molecule), which composes of necessary chemical effect within three bonds outside the interested atom(s). The cluster might have imaginary frequencies after being optimized in quantum softwares. The approach includes the contribution of the dif-ference, which is resulted from the substitution of heavy and light isotopes in the cluster, of vibra-tions of imaginary frequencies to give precise prediction of isotope fractionation factor. We call the new mathematical approximation " reduced partition function ratio in the frequency complex plane (RPFRC) " . If there is no imaginary frequency for a cluster, RPFR C is simplified to be Urey (1947) or Bigeleisen and Mayer (1947) formula. Final results of this new algorithm are in good agreement with those in earlier studies.