An accurate closed-form expression for the partition function of Morse oscillators

On the basis of the Poisson summation formula, an explicit expression is proposed to evaluate the vibrational partition function for a mode with either negative or positive anharmonicity. This formula gives numerical values almost identical to exact values over the entire temperature range from zero to infinity. The developed approximation will also be available in numerical calculations of the whole vibrational partition function for polyatomic molecules.

Even in the case where only the first two terms are retained in the partition function of Morse oscillators our approximate analytical formula gives the maximum error not exceeding 4% for all values of the parameter θ = ω/kBT.