Correlation of isotope effects with molecular forces, I. The diatomic molecule

The convergence properties of the individual terms in the finite orthogonal polynomial expansion of the partition function of a harmonic oscillator are examined as a function of the energy of the oscillator and the temperature of the system (u = epsilon/kT). The convergence of each term depends on the number of terms in the polynomial and the variable u. The jth term approaches within 1% of its asymptotic value when the order of the polynomial, n, equals (u/pi) + j + 1.These favorable convergence properties of the finite polynomials are used to relate the partition function of an oscillator and the difference in chemical properties of isotopes directly to molecular and intermolecular forces. A detailed discussion is given for the diatomic molecule. In this case it is possible to treat the quantum corrections of any order in terms of a single particle function multiplied by kinetic energy-coupling factors. The latter are formulated as simple mass ratios of the order of unity.