PROGRAM SUMMARY
Title of program:
Lanthanide
Catalogue identifier:
ADMZ
Ref. in CPC:
133(2001)396
Distribution format: tar gzip file
Operating system: SUN Solaris 2.6 & 2.7, IBM AIX 4, Linux
High speed store required:
8MK words
Number of bits in a word:
32
Number of lines in distributed program, including test data, etc:
19644
Keywords:
Rare-earth ions, Crystal field energy levels, Configuration
interaction, Electron correlation, Effective operators,
Field magnetic, Three-particle operators, Determinantal product
states, Solid state physics.
Programming language used: C
Computer:
SUN SPARC Ultra 10 ,
IBM SP ,
PCs running Solaris .
Nature of problem:
Diagonalizations of various one-, two- and three-particle operators that
result in energy eigenvalues and their eigenfunctions. The various
operator parameters have to be calculated ab initio or taken from
experiment; these are used as input to the program. The approach is
non-relativistic (it is empirically known that the main relativistic and
correlation effects can be absorbed in the input parameters) making the
program mainly useful for systems such as studies of energy structure of
open valence shells of rare-earth or actinide atoms.
Method of solution:
First a basis set of determinantal product states are generated for a
pure electronic configuration according to the exclusion principle of
Pauli. Using this basis, the matrix elements of the upper triangle of
the Hermitean matrix are calculated. The matrix elements of all
operators are added. The complete matrix is subsequently diagonalized
to give the various eigenvalues and eigenvectors. Configuration
interaction effects are accounted for by using various standard two- and
three-particle operators [1-3].
Restrictions:
The hamiltonians are all classical so this program is inappropriate
(without appropriate modifications) for relativistic systems with energy
levels that have angular dependencies that cannot be absorbed into the
used classical operators. Other practical restrictions are mainly
three: computing time, matrix size and disk storage. Other than that
there are no remaining limitations built into the software. An example
of these three practical limitations are the electron configuration f7.
In this case the size of the energy matrix is 3432x3432 which places a
great demand on primary memory (approx. 200 Mb in total) and takes
several hours to diagonalize on a fast workstation. However the main
problem is not the diagonalization, in fact the calculation of the
three-particle matrix elements is even more demanding. After several
optimizations (application of several symmetries, code and compiler
optimizations), this part of the calculation still takes approximately a
day on a SUN Ultra 10. Fortunately, the calculations of the
three-particle matrix elements only need to be made once and are then
saved to the local disk. Other files are storage of the hermitean
matrix and subsequently its eigenvectors; these can become quite large.
This problem is solved within the program since these files are written
in a compressed format (zlib) causing a size reduction of approximately
a factor of ten.
Typical running time:
The running times range from a few minutes (f2) up to ~ a day (f7),
i.e., depending on the problem and whether reading of previously stored
matrix elements is used or not.
Unusual features:
The linear-algebra operations (zhpeev: complex packed format
diagonalization routine) are performed by the standard numerical
libraries CLAPACK and CBLAS [4]. Several files that otherwise could be
huge are saved in gz-format using the library zlib [5]. Rules for fast
calculations of three-particle matrix elements are derived (described
below) and implemented in the program. The program does not need or use
any tables of Racah coefficients of fractional parentage.
References:
[1] K. Rajnak and B.G. Wybourne, Phys. Rev. 132 (1963) 280. [2] K. Rajnak, J. Opt. Soc. Amer. 55 (1965) 126. [3] B.R. Judd, Phys. Rev. 141 (1966) 4. [4] http://www.netlib.org/clapack/ [5] http://sunsite.doc.ic.ac.uk/packages/zip/zlib/zlib.html