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

• 作者: Jie Yuan
• 来源期刊: 地质学期刊(英文)
• 学科: 数学
• 关键词: ISOTOPE FRACTIONATION Cluster REDUCED PARTITION Function RATIO FREQUENCY Complex Plane
• 年，卷（期）: 2014,（12）
• 页码范围: 654-664
• 页数: 11页
• 分类号: O1

摘要

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.