Information theory and electron density

The intriguing concept of inherent uncertainty of probability schemes in information theory and statistical inference is applied to the molecular electron density. The electron density function is treated as a multimodal, three-dimensional probability density function describing the distribution of the electrons of a molecule in real space. A simple theory is proposed to introduce the amount of information associated with perturbations of the nuclear geometry such as molecular vibrations and reaction paths, in particular. It is shown by computations that the amount of information associated with the normal modes of vibration is related to the reduced mass. The proposed theory also suggests a novel Riemannian nuclear configuration space which is completely defined by the observable electron density of a molecular system.