PROGRAM SUMMARY
Title of program:
ANCO
Catalogue identifier:
ADOO
Ref. in CPC:
139(2001)263
Distribution format: tar gzip file
Operating system: IBM AIX 4.1.2+, Linux 6.1+
High speed store required:
100K words
Number of lines in distributed program, including test data, etc:
14800
Keywords:
Atomic many-body perturbation theory, Complex atom, Configuration
interaction, Effective Hamiltonian, Energy level, Racah algebra,
Coefficients (reduced) of fractional parentage,
Matrix element reduced, Relativistic, Second quantization,
Standard unit tensors, Tensor operators, 9/2-subshell,
Atomic physics, Structure.
Programming language used: Fortran
Computer:
IBM RS 6000 ,
PC Pentium II .
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].
Method of solution:
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].
Restrictions:
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.
Typical running time:
3.5 seconds for both examples on a 450 MHz Pentum III processor.
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].
References:
[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.