Thermodynamic Functions of Triatomic Molecules: An Analytical View

An analytical representation is presented of the thermodynamic functions of nonlinear triatomic molecules in closed form. Analytical formulas for vibrational and rotational statistical sums are derived. Coupled nonlinear oscillator and asymmetric top approximations are used to calculate these partition functions. Upper bounds on vibrational quantum numbers and the behavior of thermodynamic functions as a function of temperature are given in graphs and discussed in detail for water as a test system. The reliability of the analytical approach is verified by comparing it to experimental data and direct summation with theoretical values of energy levels. The analytical approach is much more efficient than explicit summation across states.