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Manuscript Title: Program to calculate pure angular momentum coefficients in jj- coupling.
Authors: G. Gaigalas, S. Fritzsche, I.P. Grant
Program title: ANCO
Catalogue identifier: ADOO_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 139(2001)263
Programming language: Fortran.
Computer: IBM RS 6000, PC Pentium II.
Operating system: IBM AIX 4.1.2+, Linux 6.1+.
RAM: 100K words
Keywords: Atomic many-body perturbation theory, Complex atom, Configuration interaction, Effective Hamiltonian, Energy level, Racah algebra, Reduced coefficients of fractional parentage, Reduced matrix element, Relativistic, Second quantization, Standard unit tensors, Tensor operators, 9/2-subshell, Atomic physics, Structure.
Classification: 2.1.

Nature of problem:
The matrix elements of a one-electron tensor operator A^k of rank k with respect to a set of configuration state functions |gammai Ji> can be written Sigma ab tij^k(ab)(a|A^k|b) where the angular coefficients tij^k(ab) are independent of the operator A^k, i, j are CSF labels and a, b run over the relevant interacting orbital labels. Similarly, the matrix elements of the Dirac-Coulomb Hamiltonian can be written in the form Sigma ab tij^0(ab)(a|H^D|b) + Sigma k Sigma abcd Vij^k(abcd)X^k(abcd), where H^D is the one-electron Dirac Hamiltonian operator, with tensor rank zero, vij^k(abcd) are pure angular momentum coefficients for two-electron interactions, and X^k(abcd) denotes an effective interaction strength for the two electron interaction. The effective interaction strengths for Coulomb and Breit interaction have different selection rules and make use of subsets of the full set of coefficients vij^k(abcd).
Such matrix elements are required for the theoretical determination of atomic energy levels, orbitals and radiative transition data in relativistic atomic structure theory. The code is intended for use in configuration interaction or multiconfiguration Dirac-Fock calculations [2], or for calculation of matrix elements of the effective Hamiltonian in many-body perturbation theory [3].

Solution method:
A combination of second quantization and quasispin methods with the theory of angular momentum and irreducible tensor operators leads to a more efficient evaluation of (many-particle) matrix elements and to faster execution of the code [4].

Tables of reduced matrix elements of the tensor operators a^(q j) and W^(kq kj) are provided for (nj) with j = 1/2, 3/2, 5/2, 7/2, and 9/2. Users wishing to extend the tables must provide the necessary data.

Unusual features:
The program is designed for large-scale atomic structure calculations and its computational cost is less than that of the corresponding angular modules of GRASP92. The present version of the program generates pure angular momentum coefficients tij^0(ab) and vij^k(abcd), but coefficients tij^k(ab) with k > 0 have not been enabled. An option is provided for generating coefficients compatible with existing GRASP92.
Configurational states with any distribution of electrons in shells with j <= 9/2 are allowed. This permits a user to take into account the single, double, triple excitations form open d- and f- shells for the systematic MCDF studies of heavy and superheavy elements (Z > 95).
Number of bits in a word: All real variables are parametrized by a selected kind parameter. Currently this is set to double precision for consistency with other components of the RATIP package [1].

Running time:
3.5 seconds for both examples on a 450 MHz Pentum III processor.

[1] S. Fritzsche, C.F. Fischer, and C.Z. Dong, Comput. Phys. Commun. 124 (1999) 240.
[2] I.P. Grant, Methods of Computational Chemistry, Vol 2. (ed. S. Wilson) pp. 1-71 (New York, Plenum Press, 1988); K.G. Dyall, I.P. Grant, C.T. Johnson, F.A. Parpia and E.P. Plummer, Comput. Phys. Commun. 55 (1989) 425; F.A. Parpia, C. Froese Fischer and I.P. Grant, Comput. Phys. Commun. 92 (1996) 249.
[3] G. Merkelis, G. Gaigalas, J. Kaniauskas, and Z. Rudzikas, Izvest. Acad. Nauk SSSR, Phys. Series 50 (1986) 1403.
[4] G. Gaigalas, Lithuanian Journal of Physics 39 (1999) 80.