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
difference, which is resulted from the substitution of heavy and light isotopes
in the cluster, of vibrations 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, RPFRC 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.
Share and Cite:
Yuan, J. (2014) Reduced Partition Function Ratio in the Frequency Complex Plane: A Mathematical Approach.
Open Journal of Geology,
4, 654-664. doi:
10.4236/ojg.2014.412049.