Transformation from internal coordinates to cartesian displacements in the Eckart frame for a triatomic molecule

摘要

Analytic expressions are obtained for the cartesian displacements in the Eckart frame that relate distorted and undistorted configurations for any triatomic molecule. The displacements are given in the terms of the instantaneous values of the internal coordinates (r_1,r_2,θ). Besides their application in spectroscopy, these formulas could be useful in semiclassical simulations of molecular liquids. The present derivation recovers previous results for the angle of rotation between the instantaneous and Eckart bisector axis.