Statistical description of multimodal atomic probability densities

A general method for describing multimodal atomic densities is presented. It is based on series expansions of a harmonic Gaussian probability density function. The most suitable expansion is of the Gram-Charlier type; its Fourier transform can be easily inserted in a structure factor equation. This statistical method yields a satisfactory fit to the data and allows for a better interpretation of the fit parameters than sophisticated split-atom models. The method is especially useful for weakly resolved modes and allows a better distinction between disorder and anharmonic motion than in conventional Fourier syntheses. Calculations on CsPbCl₃, ice Ih and RbAg₄I₅ are presented to show the strengths and the limitations of this method.