Geodesic
On the precision increasing in calculation of potential for the systems of interactive atoms
Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 101-110

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We propose a high precision method of finding of potential for multi-atomic quantum-mechanical tasks in real space. The method is based on dividing of electron density and potential of a multi-atomic system into two parts. The first part of density is found as a sum of spherical atomic densities; the second part is a variation of density generated by interatomic interaction. The first part of potential is formed by the first part of density and may be calculated correctly using simple integrals. The second part of potential is found through a Poisson equation from the second part of density. To provide a high precision we divided a work space into Voronoy's polyhedrons and found the boundary conditions by means of a multi-pole distribution of potentials formed by local densities concentrated in these polyhedrons. Then we used double-grid approach, and fast Fourier transformations as initial functions for iterative solution of the Poisson's equation. We estimated accuracy of the offered method and carried out test calculations which showed that this method gives the accuracy several times better than accuracy of the fast Fourier transformation.
Keywords: Poisson equation, electrostatic potential, Voronoy polihedra, multipole expansion, double-grid method. 
@article{CHEB_2018_19_2_a7,
     author = {V. G. Zavodinsk{\cyru} and O. A. Gorkusha},
     title = {On the precision increasing in calculation of potential for the systems of interactive atoms},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {101--110},
     publisher = {mathdoc},
     volume = {19},
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     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a7/}
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V. G. Zavodinskу; O. A. Gorkusha. On the precision increasing in calculation of potential for the systems of interactive atoms. Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 101-110. http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a7/