Validation of convolution approximation to the thermal-average electron density

摘要

Analytic evaluation of the dynamic (thermally smeared) molecular electron density (ED) is described within the LCAO-MO and harmonic-convolution approximations. The key step is to assign vibration probability density functions (PDFs) to the two-center products of Gaussian basis functions used in quantum chemical models, if the PDFs of the nuclear centers are known. Based on internal modes of vibrations of small molecules it is demonstrated how the convoluted ED relates to the stationary (static) ED, as well as to that of the average over an ensemble of static EDs calculated for near-equilibrium nuclear geometries using clamped Hamiltonians. The overall effect of neglecting correlated nuclear motions on the convoluted ED is also illuminated.