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RAtom overview

Zbigniew Romanowski

RAtom solves nonlinear Kohn-Sham equation for an neutral atom.
The adaptive algorithm based on finite element method (FEM) is implemented.

The implemented algorithm is described in the following papers:

Z. Romanowski, Adaptive solver of a Kohn-Sham equation for an atom
Modelling Simul. Mater. Sci. Eng. vol. 17, 045001 (2009)
http://iopscience.iop.org/article/10.1088/0965-0393/17/4/045001/meta (abstract)

Z. Romanowski, Application of h-adaptive, high order finite
element method to solve radial Schrödinger equation,
Molecular Physics, vol. 107, pp. 1339-1348 (2009).
http://www.tandfonline.com/doi/abs/10.1080/00268970902873554 (abstract)

Z. Romanowski, A B-spline finite element solution of Kohn Sham equation for an atom
Modelling and Simulation in Materials Science and Engineering, vol. 16, p. 015003 (2008)
http://iopscience.iop.org/article/10.1088/0965-0393/16/1/015003/meta (abstract)

Z. Romanowski, Numerical Solution of Kohn–Sham Equation for Atom,
Acta Physica Polonica B, vol. 38, p. 3263 (2007)
http://www.actaphys.uj.edu.pl/fulltext?series=Reg&vol=38&page=3263 (full paper)

Discretization of the differential eigenvalue problem is done
by Finite Element method with Lobatto polynomials as a basis functions.

Disctretization leads to generalized eigenvalue problem,
which is solved by procedures from LAPACK libraries.

The program RAtom is implemented in C++, it runs as a single thread.

High order Gauss quadratures are applied in order to obtain
the total energy of atom with absolut accuracy of 1E-6 hartree.

For given atom, RAtom calculates:

  • electron eigenvalues,
  • electron eiegenfunctions,
  • electron density,
  • total energy,
  • contributions of total energy.

Author: Zbigniew Romanowski
e-mai: romz@wp.pl

Project Members:

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