The grasp2K relativistic atomic structure package

This paper describes grasp2K, a general-purpose relativistic atomic structure package. It is a modification and extension of the GRASP92 package by [F.A. Parpia, C. Froese Fischer, I.P. Grant, Comput. Phys. Comm. 94 (1996) 249]. For the sake of continuity, two versions are included. Version 1 retains the GRASP92 formats for wave functions and expansion coefficients, but no longer requires preprocessing and more default options have been introduced. Modifications have eliminated some errors, improved the stability, and simplified interactive use. The transition code has been extended to cases where the initial and final states have different orbital sets. Several utility programs have been added. Whereas Version 1 constructs a single interaction matrix for all the J's and parities, Version 2 treats each J and parity as a separate matrix. This block structure results in a reduction of memory use and considerably shorter eigenvectors. Additional tools have been developed for this format. The CPU intensive parts of Version 2 have been parallelized using MPI. The package includes a “make” facility that relies on environment variables. These make it easier to port the application to different platforms. The present version supports the 32-bit Linux and ibmSP environments where the former is compatible with many Unix systems. Descriptions of the features and the program/data flow of the package will be given in some detail in this report.Program summaryProgram title: grasp2KCatalogue identifier: ADZL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZL_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 213 524No. of bytes in distributed program, including test data, etc.: 1 328 588Distribution format: tar.gzProgramming language: Fortran and CComputer: Intel Xeon, 3.06 GHzOperating system: Suse LINUXRAM: 500 MB or moreClassification: 2.1Nature 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+sj=l+s, and the parity operator Π=βπΠ=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.Restrictions:   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 [F.A. Parpia, C. Froese Fischer, I.P. Grant, Comput. Phys. Comm. 94 (1996) 249] 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⩽7/2j⩽7/2; occupied subshells with j=9/2j=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 [C. Froese Fischer, G. Gaigalas, Y. Ralchenko, Comput. Phys. Comm. 175 (2006) 739] 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=4n=4 calculation with 2190 CSFs) and 52.7 minutes (n=5n=5 calculation with 6752 CSFs)