Isotope chemistry and molecular structure. The WINIMAX weighting factor

Journal Article · Sat Dec 01 04:00:00 EST 1979 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.438248· OSTI ID:5757982

Lee, M W; Bigeleisen, J

The modulating coefficients for the finite polynomial expansion of the logarithm of the reduced partition function, lnb (u), of a harmonic oscillator have been obtained for the range of 0< or =u< or =u/sub max/ with a weighting function g (u) =u/sup a/ by the method of least squares. The coefficients obtained for a=o are almost identical with the MINIMAX coefficients which correspond to an unweighted expansion; the least square coefficients obtained with a=1 are almost identical with the finite orthogonal polynomial coefficients derived by Ishida, Spindel, and Bigeleisen with the assumption g (u) approx.u. Comparison of the least square modulating coefficients derived as a function of u shows that the WINIMAX coefficients for the reduced vibrational partition function derived by Lee and Bigeleisen corresponds to a weighting function u/sup 6/. It is shown that this weighting function is near optimum to insure minimum amplitudes of oscillation in the expansion of lnb (u) as a function of the order of the expansion and to include most of the important molecular structure information contained in the moments of the eigenvalues. Beyond ..sigma..u/sub i//sup 6/, there is little new structural information.

• Research Organization: Savannah River Laboratory, E. I. du Pont de Nemours Co., Aiken, South Carolina 29801
• OSTI ID: 5757982
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 71:11; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640300* -- Atomic
Molecular &amp; Chemical Physics
74 ATOMIC AND MOLECULAR PHYSICS
FUNCTIONS
HARMONIC OSCILLATOR MODELS
ISOTOPE EFFECTS
MATHEMATICAL MODELS
MOLECULAR STRUCTURE
PARTITION FUNCTIONS
POLYNOMIALS
SERIES EXPANSION