Isotope chemistry and molecular structure. The WINIMAX weighting factor

Abstract

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⩽u⩽umax with a weighting function g (u) =ua 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) ∼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 u6. 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 Σui6, there is little new structural information.