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Manuscript Title: Lanthanide crystal field fitting routine.
Authors: G.E. Stedman
Catalogue identifier: ACAB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)191
Programming language: Fortran.
Computer: ICL 1905E.
Operating system: GEORGE 2E.
RAM: 32K words
Word size: 24
Keywords: Solid state physics, Crystal field parameter, Energy level fitting, G-values, Least squares Nonlinear parameter Estimation, Paramagnetic ions.
Classification: 7.3.

Nature of problem:
The electronic states of paramagnetic ions in crystals are split by the electric field from other ions. These splittings may be fitted by a suitable choice of crystal field parameters. The routine performs this fit and outputs a comparison of experimental and theoretical energies, and also (as required) g-values and wavefunctions for the crystal field states.

Solution method:
The calculation of energies from cyrstal field parameters requires matrix diagonalisations. The parameters are adjusted under the control of an efficient fitting procedure to give a least squares fit to the experimental energies. The derivatives required are computed from the eigenvectors obtained in the diagonalisation.

The routine is useful for lanthanides only. J-mixing is neglected (cf. unusual features). As wriiten, each crystal field parameter is varied independently. However, one subroutine is easily modified so that Amn/Aon is held constant provided m>0. The assignments of states within a manifold may not be taken into account during a fitting, though they may be checked afterwards.

Unusual features:
The neglect of "J-mixing" the (coupling of the atomic manifolds by the crystal field) has many advantages, such as the possibility of using operator equivalents. The program takes full advantage of block diagonalisations consequent on the particular site symmetry, with other similar economies.

Running time:
For the test case (14 parameters, 2 manifolds, J-values 7.5 and 6.5, and non-zero imaginary parts to the matrix elements) the storage used is 24.8 K and the running time is approximately 80 s per iteration, or 30 s per function evaluation.