The correlation functions of the regular tetrahedron and octahedron

TL;DR

This paper provides explicit algebraic formulas for the autocorrelation functions of regular tetrahedra and octahedra, enabling efficient and precise calculation of scattering intensities even with size variations.

Contribution

It introduces new algebraic expressions for the autocorrelation functions of these polyhedra, facilitating faster and more accurate scattering intensity computations.

Findings

Explicit algebraic formulas involving arctangent and rational functions

Formulas enable rapid and accurate scattering intensity calculations

Applicable to size dispersion scenarios

Abstract

The expressions of the autocorrelation functions (CF) of the regular tetrahedron and the regular octahedron are reported. They have an algebraic form that involves the arctangent function and rational functions of r and (a + b r2)1/2, a and b being appropriate integers and r the distance. The CF expressions make the numerical determination of the corresponding scattering intensities fast and accurate also in presence of a size dispersion.