Correlation of isotope chemistry with molecular structure by second moment perturbation theory

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Expansion of the isotopic reduced partition function ratio in terms of a number of arguments has led to greater insight into the relationship between isotopic fractionation factors and molecular structure than can be obtained even from a critical analysis of each of the terms that contribute to the isotopic reduced partition function ratio. The most significant of these expansion methods are: (1) expansion of ln(s/s')f, logarithm of the isotopic reduced partition function ratio, in terms of the even moments of the vibrational frequencies, and (2) expansion of either (s/s')f or ln(s/s')f around a reference molecule which has no off-diagonal elements ... continued below

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Pages: 9

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Bigeleisen, J.; Lee, M.W. & Ishida, T. January 1, 1978.

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Expansion of the isotopic reduced partition function ratio in terms of a number of arguments has led to greater insight into the relationship between isotopic fractionation factors and molecular structure than can be obtained even from a critical analysis of each of the terms that contribute to the isotopic reduced partition function ratio. The most significant of these expansion methods are: (1) expansion of ln(s/s')f, logarithm of the isotopic reduced partition function ratio, in terms of the even moments of the vibrational frequencies, and (2) expansion of either (s/s')f or ln(s/s')f around a reference molecule which has no off-diagonal elements in the G (kinetic energy) and F (force constant) matrices whose solution yield the molecular vibrations. The diagonal element approximation, ln(s/s')f/sub 0/(ln(s/s')f/sub 0/ is the logarithm of the isotopic reduced partition function for the reference molecules which has eigenvalues defined by lambda/sub i0/ = f/sub ii/g/sub ii/.), gives very good results for hydrogen isotope substitution. The latter is a consequence of the fact that the off-diagonal G matrix elements involving the mass of hydrogen are either zero, or negligible, and the relatively light mass of hydrogen compared with other elements. The off-diagonal element corrections to ln(s/s')f/sub 0/ are of the order of 10 to 20% of the latter for carbon and oxygen isotope substitutions. These are easily evaluated by the WINIMAX polynomials. The correction terms, through second order (h/kT)/sup 4/, added to ln(s/s')f/sub 0/ provide an analytical formulation for the direct evaluation of ln(s/s')f for any molecule in terms of the F and G matrix elements. Through this method it is now possible to analyze ln(s/s')f in terms of the stretching, bending, and interaction force constants in a molecule.

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Pages: 9

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Dep. NTIS, PC A02/MF A01.

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  • 4. congress on isotope geology, Snowmass, CO, USA, Aug 1978

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  • Report No.: CONF-780864-1
  • Grant Number: EY-76-S-02-3498
  • Office of Scientific & Technical Information Report Number: 6812239
  • Archival Resource Key: ark:/67531/metadc1194543

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  • January 1, 1978

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  • July 2, 2018, 10:52 p.m.

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  • Aug. 8, 2018, 1:09 p.m.

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Bigeleisen, J.; Lee, M.W. & Ishida, T. Correlation of isotope chemistry with molecular structure by second moment perturbation theory, article, January 1, 1978; United States. (https://digital.library.unt.edu/ark:/67531/metadc1194543/: accessed March 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.