Calculation of Atomic Force Constants from Electron Densities

An expression is derived which relates molecular electron densities to the atomic force constants obtained from an analysis of the frequency sum rule for polyatomic molecules. Using approximate electron densities computed by Pople and Segal by the CNDO method [J. A. Pople and G. A. Segal, J. Chem. Phys. 43, S136 (1965)], it was found that not only the magnitudes of the atomic force constants for H, C, N, O, and F atoms were accounted for, but also their observed independence of bond multiplicity.