Generalized finite polynomial approximation (WINIMAX) to the reduced partition function of isotopic molecules

Journal Article · Sat Apr 15 04:00:00 EST 1978 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.436258· OSTI ID:7286723

Lee, M W; Bigeleisen, J

The MINIMAX finite polynomial approximation to an arbitrary function has been generalized to include a weighting function (WINIMAX). It is suggested that an exponential is a reasonable weighting function for the logarithm of the reduced partition function of a harmonic oscillator. Comparison of the error function for finite orthogonal polynomial (FOP), MINIMAX, and WINIMAX expansions of the logarithm of the reduced vibrational partition function show WINIMAX to be the best of the three approximations. A condensed table of WINIMAX coefficients is presented. The FOP, MINIMAX, and WINIMAX approximations are compared with exact calculations of the logarithm of the reduced partition function ratios for isotopic substitution in H/sub 2/O, CH/sub 4/, CH/sub 2/O, C/sub 2/H/sub 4/, and C/sub 2/H/sub 6/ at 300 /sup 0/K. Both deuterium and heavy atom isotope substitution are studied. Except for a third order expansion involving deuterium substitution, the WINIMAX method is superior to FOP and MINIMAX. At the level of a second order expansion WINIMAX approximations to ln(s/s')f are good to 2.5% and 6.5% for deuterium and heavy atom substitution, respectively.

• Research Organization: Department of Chemistry, University of Rochester, Rochester, New York 14627
• OSTI ID: 7286723
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 68:8; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400000 -- Chemistry
640300* -- Atomic
Molecular & Chemical Physics
74 ATOMIC AND MOLECULAR PHYSICS
ALKANES
ALKENES
CRYOGENIC FLUIDS
DEUTERIUM
ETHANE
ETHYLENE
FLUIDS
FUNCTIONS
HYDROCARBONS
HYDROGEN COMPOUNDS
HYDROGEN ISOTOPES
ISOTOPES
ISOTOPIC EXCHANGE
LIGHT NUCLEI
MECHANICS
METHANE
MOLECULES
NUCLEI
ODD-ODD NUCLEI
ORGANIC COMPOUNDS
OXYGEN COMPOUNDS
PARTITION FUNCTIONS
STABLE ISOTOPES
STATISTICAL MECHANICS
THERMODYNAMICS
WATER