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Manuscript Title: The grasp2K relativistic atomic structure package
Authors: P. Jönsson, X. He, C. Froese Fischer, I.P. Grant
Program title: grasp2K
Catalogue identifier: ADZL_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 177(2007)597
Programming language: Fortran.
Computer: Intel Xeon, 3.06 Ghz.
Operating system: Suse LINUX.
RAM: 500 MB or more
Keywords: atomic structure calculations, Breit interaction, configuration interaction, correlation, Dirac theory, energy levels, hyperfine structure, isotope shift parameter, jj-coupling, multiconfiguration Dirac-Hartree-Fock, nuclear volume effects, QED, relativistic effects in atoms, specific mass shift, transverse photon interaction, transition probabilities, Zeeman effects.
PACS: 2.70, 32.10.-f, 31.15Ne, 31.25.-v, 32.30.-r.
Classification: 2.1.

Nature of problem:
Prediction of atomic spectra - atomic energy levels, oscillator strengths, and radiative decay rates - using a 'fully relativistic' approach.

Solution method:
Atomic orbitals are assumed to be four-component spinor eigenstates of the angular momentum operator, j = l + s, and the parity operator Π = βπ. Configuration state functions (CSFs) are linear combinations of Slater determinants of atomic orbitals, and are simultaneous eigenfunctions of the atomic electronic angular momentum operator, J, and the atomic parity operator, P. Approximate atomic state functions (ASFs) are linear combinations of CSFs. A variational functional may be constructed by combining expressions for the energies of one or more ASFs. Average energy level (EAL) functionals are weighted sums of energies of all possible ASFs that may be constructed from a set of CSFs; the number of ASFs is then the same as the number of CSFs. Extended optimal level (EOL) functionals are weighted sums of energies of some subset of ASFs. Radial functions may be determined by numerically solving the multiconfiguration Dirac-Hartree-Fock (MCDHF) equations that define an extremum of the variational functional by the self-consistent-field (SCF) method. Lists of CSFs are generated from a set of reference CSFs and rules for deriving other CSFs from these. Expansion coefficients are obtained using sparse-matrix methods for solving the relativistic configuration interaction (CI) problem. Transition properties for pairs of ASFs are computed from matrix elements of multipole operators of the electromagnetic field. Biorthogonal transformation methods are employed so that all matrix elements between CSFs can be evaluated using Racah algebra.

The maximum number of radial orbitals is limited to 120 by the packing algorithm used for 32-bit integers. The maximum size of a multiconfiguration (MC) calculation, as measured by the length of the configuration state function (CSF) list, is limited by numerical stability, processing time, or storage which may be either in memory or on disk. Numerical stability is the same as GRASP92 [1] with a slight improvement in memory management for Version 2 codes. Sufficient disk space is needed to store angular data. In configuration interaction calculations the matrix may be either in memory or on disk. The tables of coefficients of fractional parentage, as in GRASP92, are limited to subshells with j ≤ 7/2; occupied subshells with j = 9/2 are, therefore, restricted to a maximum of two electrons.

Unusual features:
The installation process has been simplified so that pre-processing of the raw code needed with GRASP92 can be eliminated. Dynamic memory allocation reduces the number of parameters needed to define fixed array dimensions to nine. The corrections discussed in [2] have also been implemented. Environment variables are used to facilitate the compilation of the libraries, applications, and tools with different compilers on different platforms. Computationally intensive applications have been parallelized using the message passing interface (MPI). When standard output is redirected, prompts and critical information about the progress of a calculation or convergence are still directed to the screen through the standard error output unit.

Running time:
CPU time required to execute test cases: 5 min (n=4 calculation with 2190 CSFs) and 52.7 minutes (n=5 calculation with 6752 CSFs).

[1] F. A. Parpia, C. Froese Fischer, and I. P. Grant, Comput. Phys. Commun. { 94, 249 (1996).
[2] C. Froese Fischer, G. Gaigalas, and Y. Ralchenko, Comput. Phys. Commun. 175, 739 (2006).