Efficient algorithm for expanding theoretical electron densities in canterakis–zernike functions

Abstract

An algorithm for the efficient computation of Canterakis–Zernike moments of theoretically computed molecular electron densities and rotationally invariant Fingerprint indices derived from them is reported. The algorithm is suitable for any density expressed in terms of Gaussian‐ or Slater‐type functions within the Linear Combination of Atomic Orbitals framework at any level of computation. Electron density is expressed as a one‐center expansion of real regular spherical harmonics times radial factors by means of translation techniques, which facilitates the efficient computation of the moments in terms of a single one‐dimension numerical integration. The performance of the algorithm is analyzed showing that the computation of radial factors in the quadrature points is responsible for almost all computational time. The procedure is applicable to any density obtained with standard packages for molecular structure calculations. © 2018 Wiley Periodicals, Inc.