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Manuscript Title: A program for accurate solutions of two-electron atoms
Authors: Sverker Edvardsson, Daniel Aberg, Per Uddholm
Program title: corr2el
Catalogue identifier: ADUX_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 165(2005)260
Programming language: ANSI C.
Computer: Sun Fire 15K StarCat, Sun Ultra SPARC III, PC.
Operating system: Sun Solaris 9, Linux.
RAM: 3 Mwords or more
Word size: 32
Keywords: two-electron Schrodinger equation, iterative methods, MPI, shared memory.
PACS: 31.15.Fx, 31.25.-v, 31.25.Eb, 31.25.Jf.
Classification: 2.1.

Nature of problem:
The Schrödinger equation for two-electron atoms is solved using finite differences.

Solution method:
An iterative eigenvalue-solver that requires only the action of the hamiltonian on a trial function is applied. The two-electron wave function is expanded in a sum of partial waves. The finite difference method is then applied to approximate the derivatives of the pair functions. The total action of the hamiltonian on the partial waves, including correlation effects, is computed using highly optimized routines.

The hamiltonian employed here does not take relativistic or finite nuclear mass effects into account. The amount of computing time may become unreasonable for excited states far above the ground state. The use of double precision puts a limit on the accuracy obtainable.

Unusual features:
The implicitly restarted Arnoldi method used to obtain the eigenvalues is implemented by using the ARPACK/PARPACK program library [1]. This package also depends on the standard numerical libraries BLAS and LAPACK [2]. Good performance is obtained by using Sun's optimized performance libraries [3]. By using a 64-bit environment (Ultra SPARC III and Solaris9), memory limitations are non-problematic. Shared memory is used in the parallel version. Fast communication between the nodes is made over shared memory using Sun's implementation of MPI.

Additional comments:
A parallel version of the program is included in the package.

Running time:
This ranges from half a minute (to obtain 10 significant figures for the S-limit of the Helium ground state) to perhaps a day for advanced examples depending on the level of parallelization.

[1] http://www.netlib.org/arpack
[2] http://www.netlib.org/lapack
[3] http://www.sun.com