Premium
Rapid and accurate calculation of small‐angle scattering profiles using the golden ratio
Author(s) -
Watson Max C.,
Curtis Joseph E.
Publication year - 2013
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s002188981301666x
Subject(s) - multipole expansion , scattering , physics , fast multipole method , computational physics , lattice (music) , intensity (physics) , small angle scattering , atomic physics , optics , molecular physics , chemistry , quantum mechanics , acoustics
Calculating the scattering intensity of an N ‐atom system is a numerically exhausting O ( N 2 ) task. A simple approximation technique that scales linearly with the number of atoms is presented. Using an exact expression for the scattering intensity I ( q ) at a given wavevector q , the rotationally averaged intensity I ( q ) is computed by evaluating I ( q ) in several scattering directions. The orientations of the q vectors are taken from a quasi‐uniform spherical grid generated by the golden ratio. Using various biomolecules as examples, this technique is compared with an established multipole expansion method. For a given level of speed, the technique is more accurate than the multipole expansion for anisotropically shaped molecules, while comparable in accuracy for globular shapes. The processing time scales sub‐linearly in N when the atoms are identical and lie on a lattice. The procedure is easily implemented and should accelerate the analysis of small‐angle scattering data.