Calculation of dynamic electron density distributions from static molecular wave functions

A procedure is described for calculating dynamic molecular densities, within the convolution approximation, from rigid-body translational and librational thermal motions and static wave functions calculated with Gaussian basis orbitals. Fourier transformation of the librationally smeared wave function is shown to be equivalent to convolution of the molecular scattering factor with a distribution of orientations of the scattering vector. The proper thermal parameters to be applied to two-center products are well defined in this procedure. Static and dynamic molecular deformation densities are plotted for an extended-basis-set wave function of the azide ion, N^-₃, with rigid-body thermal parameters as determined in the crystal structures of NaN₃ and KN₃.