Vibrational energies and partition functions

Abstract Chemical reaction dynamics, as well as many fundamental molecular properties such as heat capacity, involve energy transfer in and out of vibrational states. The quantum mechanics of the harmonic oscillator is reviewed, followed by analyses of different approaches to analyze and interpret anharmonic contributions to the vibrational energy. A brief review of the nature and calculation of vibrational potential energy surfaces is provided, and available options for analyzing these with computational tools to obtain the energies of the vibrational quantum states. Finally, this chapter presents several applications to thermodynamics and kinetics of the vibrational partition function, which may be calculated from the quantized energies.