Correlation of the isotope chemistry of hydrogen, carbon, and oxygen with molecular forces by the WIMPER (2) method

Journal Article · Sun Feb 01 04:00:00 EST 1981 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.441268· OSTI ID:6651567

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

The WIMPER (2) approximation to the logarithm of the reduced partition function ratio is used to develop analytical expressions for the contribution of individual molecular vibrational force constants to the logarithm of the reduced partition function ratio of isotopic molecules. The method inherently accounts properly for contributions from quadratic terms of the form ..beta../sub p/qx/sub p/x/sub q/, which are counted twice in any numerical method. The zero order (diagonal F--diagonal G) approximation leads to values of ln(s/s')f/sub 0/ which are always larger than the exact value when the site of isotopic substitution is a central atom. In the latter case the first order correction (j=1 term) is always negative because of the sign of the off- diagonal G matrix element. As a result of the convergence properties of the WINIMAX polynomials the sign of the j=1 correction to ln(s/s')f/sub 0/ usually determines the final sign of the correction to ln(s/s')f/sub 0/ associated with any off-diagonal F matrix element. Calculations are given for the contribution of each force constant to ln(s/s')f, ln(s/s')f/sub 0/, and the j=1 and j=2 correction terms for D/H, /sup 13/C//sup 12/C, and /sup 18/O//sup 16/O isotopic substitutions. Molecules studied include H/sub 2/O, CO/sub 2/, H/sub 2/CO, CH/sub 4/, C/sub 2/H/sub 4/, C/sub 2/H/sub 6/, and C/sub 6/H/sub 6/. The contributions for off-diagonal F matrix elements for D/H substitution are found to be small in agreement with previous work. The largest effects associated with off-diagonal F matrix elements arise in the torsion of ring structures. These are illustrated in detail by numerical evaluation of each of the terms contributing to ln(s/s')f for /sup 13/C//sup 12/C for the out-of-plane vibrations in benzene. Even in the latter case the WIMPER (2) method leads to approximate values of ln(s/s')f within 3.6% of the exact value.

• Research Organization: Department of Chemistry, State University of New York, Stony Brook, Stony Brook, New York 11794
• OSTI ID: 6651567
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 74:3; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400302* -- Organic Chemistry-- Isotope Effects-- (-1987)
ALDEHYDES
ALKANES
ALKENES
AROMATICS
BENZENE
CARBON 13
CARBON COMPOUNDS
CARBON DIOXIDE
CARBON ISOTOPES
CARBON OXIDES
CHALCOGENIDES
CHEMICAL REACTIONS
CORRELATIONS
DEUTERIUM
ELEMENTS
ENERGY LEVELS
ETHANE
ETHYLENE
EVEN-EVEN NUCLEI
EVEN-ODD NUCLEI
EXCITED STATES
FLUIDS
FORMALDEHYDE
GASES
HYDROCARBONS
HYDROGEN
HYDROGEN ISOTOPES
ISOTOPE EFFECTS
ISOTOPES
LIGHT NUCLEI
METHANE
MOLECULAR STRUCTURE
NONMETALS
NUCLEI
ODD-ODD NUCLEI
ORGANIC COMPOUNDS
OXIDES
OXYGEN 18
OXYGEN COMPOUNDS
OXYGEN ISOTOPES
STABLE ISOTOPES
VAPORS
VIBRATIONAL STATES
WATER VAPOR