Programs in Physics & Physical Chemistry
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|Manuscript Title: GRASP: a general-purpose relativistic atomic structure program. See erratum Comp. Phys. Commun. 58(1990)345.|
|Authors: K.G. Dyall, I.P. Grant, C.T. Johnson, F.A. Parpia, E.P. Plummer|
|Program title: GRASP|
|Catalogue identifier: ABJN_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 55(1989)425|
|Programming language: Fortran.|
|Computer: VAX 8700, VAX 8700/8800.|
|Operating system: VAX/VMS VERSION 4.|
|RAM: 1024K words|
|Keywords: Atomic physics, Breit interaction, Complex atoms, Dirac equation, Dirac-Fock, Energy levels, Finite nucleus, Fractional parentage, jj-coupling, jl-coupling, ls-coupling, Multiconfiguration, Numerical integration, Oscillator strength, QED, Racah algebra, Radiative transition, Radiative corrections, Recoupling coefficients, Relativistic, Rydberg, Self-consistent field, Self-energy, Slater exchange, Slater integrals, Structure, Transverse photon interaction, Vacuum-polarization.|
Nature of problem:
Calculation of atomic energy levels, orbitals, and radiative transition data within the relativistic formalism.
Relativistic atomic orbitals are one-electron spinor eigenfunctions of parity, p^, and angular momentum j^2,j^z. Configuration state functions (CSFs) are built from antisymmetrized products of such orbitals, and have prescribed coupling scheme, and parity, P, and angular momentum, J, M, quantum numbers. Multiconfiguration atomic state functions (ASFs) are linear combinations of CSFs having common values of P, J, and M. Matrix elements between CSFs are calulated using the Racah algebra. Finite-difference methods are used in all operations on radial functions.
When the orbital radial functions are specified, the program operates in a configuration-interaction (CI) mode to determine the ASFs and the corresponding energy levels by diagonalizing the Hamiltonian matrix. Radial wavefunctions of a great variety can be generated by the program itself. Most important among these are the extended-average-level (EAL) and the extended-optimal-level (EOL) self-consistent-field (SCF) functions. In the EAL procedure, an average-of-configurations approximation is used to define the radial equations, whereas variational optimization on the average energy of a selected subset of ASFs yields the equations in the EOL mode.
Only the Coulomb repulsion of the electrons is included in the SCF process. Corrections to the energy levels due to the retarded Coulomb interaction and the polarization of the vaccum by the nuclear charge distribution are included in a perturbation approximation. A rough estimate of the electron self-energy is also made.
The size of the problem is limited primarily by its numerical stability and the computing power available; array dimensions may be assigned by the user. A single pair (large and small components) of radial functions describes all <_ 2j + 1 electrons in an nlj subshell. Radial functions for orbitals with different n but the same lj quantum numbers are constrained to be orthogonal. Input of configurational data in nonrelativistic notation is limited to a maximum of four open nl subshells. Tables of one-electron coefficients of fractional parentage are provided for nlj subshells with j = 1/2, 3/2, 5/2, and 7/2. These tables must be extended by the user to define open subshells with occupation numbers greater than 2 for j >_ 9/2. Transformation from jj- to LS-coupling is also limited by tables of coefficients of fractional parentage for occupation numbers greater than 2 to l <_ 2. The EOL procedure does not generate fully optimized wavefunctions for the case where CSF's differ by the excitation of a single electron from one orbital to another with the same lj quantum numbers.
The program interface, based on keywords, unformatted numerical data, and descriptive error messages, presents a simple aspect to the user. CSF data may be input using either relativistic (nlj) or nonrelativistic (nl) orbital notation. Besides the standard jj-coupled basis, results may be expressed in nonstandard jj-LS-, or jl-coupled bases. A wide range of other program and input/output control options is available. The accompanying preprocessor program automates the setting of array dimensions and selection of installation-dependent features before compilation. A comprehensive User's Manual is supplied as part of the package.
This varies widely and is strongly dependent on the problem to be solved. Test case 1a: 29s on VAX 8700.
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