Calculation of radial distribution functions for molecules in excited vibrational states

It is shown how to reduce N-dimensional probability densities calculated from vibrational wave functions of polyatomic molecules to one-dimensional radial distribution functions. Such distributions are, in principle, derivable from diffraction experiments. In this initial treatment, anharmonicity and nonlinearities in transformations between normal coordinates and internuclear distances are neglected. Illustrative calculations are given for H2O, CF3Cl, and SF6 in various vibrational states or thermal distributions among vibrational states. Possible applications are briefly discussed.