TITLE:
Reduced Partition Function Ratio in the Frequency Complex Plane: A Mathematical Approach
AUTHORS:
Jie Yuan
KEYWORDS:
Isotope Fractionation, Cluster, Reduced Partition Function Ratio, Frequency Complex Plane
JOURNAL NAME:
Open Journal of Geology,
Vol.4 No.12,
December
31,
2014
ABSTRACT: This paper gives a
mathematical approach to calculate the fractionation factor of isotopes in a
general cluster (also known assuper-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, RPFRCis 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.