Computational analysis of thermal-motion effects on the topological properties of the electron density

The distributions of bond topological properties (BTPs) of the electron density upon thermal vibrations of the nuclei are computationally examined to estimate different statistical figures, especially uncertainties, of these properties. The statistical analysis is based on a large ensemble of BTPs of the electron densities for thermally perturbed nuclear geometries of the formamide molecule. Each bond critical point (BCP) is found to follow a normal distribution whose covariance correlates with the displacement amplitudes of the nuclei involved in the bond. The BTPs are found to be markedly affected not only by normal modes of the significant bond-stretching component but also by modes that involve mainly hydrogen-atom displacements. Their probability distribution function can be decently described by Gumbel-type functions of positive (negative) skewness for the bonds formed by non-hydrogen (hydrogen) atoms.