Internal coordinate formulation for the vibration–rotation energies of polyatomic molecules

Abstract

The vibration–rotation energies of polyatomic molecules are obtained under the assumption of small oscillations using curvilinear internal coordinates for the vibrational degrees of freedom. The use of curvilinear coordinates introduces anharmonic terms into the vibrational kinetic energy and gives second derivative terms for the moments of inertia that include the motion of an atom along its natural curved path during vibration. Coordinate transformation of the intramolecular potential energy is unnecessary. Perturbation expansion is used to obtain all of the vibration–rotation coefficients, αik, χkk, χkk′, χlsls, χlsls, for linear, symmetric top, and asymmetric top molecules. Vibration–rotation constants are given for the linear X2Y and XYZ and nonlinear X2Y molecules in terms of the molecular structure. Analysis is made of the vibration–rotation and anharmonic vibrational coefficients using previously determined anharmonic force constants for CO2 and H2O. Partial analysis of vibration–rotation coefficients is made for additional molecules.