Bond lengths of vibrationally hot AXn molecules. A simple treatment

Given the form of an anharmonic, modified Urey–Bradley molecular force field for AXn molecules, it is shown how to express the mean vibrational displacements of bond lengths from equilibrium lengths re simply in terms of elementary quantities. The dominant terms isolated are due to Morse stretching anharmonicity, nonbonded interactions, and the centrifugal stretching of bonds encountered as the atoms swing over arced trajectories in bending vibrations. Illustrative calculations are presented for CH4 and CD4.