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

Conference · Sun Jan 01 04:00:00 EST 1978

OSTI ID:6812239

Bigeleisen, J; Lee, M W; Ishida, T

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.

• Research Organization: Rochester Univ., NY (USA). Dept. of Chemistry; Brooklyn Coll., NY (USA). Dept. of Chemistry
• OSTI ID: 6812239
• Report Number(s): CONF-780864-1
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400302* -- Organic Chemistry-- Isotope Effects-- (-1987)
CHEMICAL SHIFT
CORRELATIONS
FUNCTIONS
ISOMERS
ISOTOPE EFFECTS
MATRIX ELEMENTS
MOLECULAR STRUCTURE
ORGANIC COMPOUNDS
PARTITION FUNCTIONS
PERTURBATION THEORY
POLYNOMIALS