THEORY OF U CENTERS IN ALKALINE EARTH PLUORIDES USING THE SCF-MSXα METHOD

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THEORY OF U CENTERS IN ALKALINE EARTH

PLUORIDES USING THE SCF-MSXα METHOD

L. Oliveira, B. Maffeo, H. Brandi, M. de Siqueira

To cite this version:

JOURNAL DE PHYSIQUE Colloque C7, suppldment au

no

12, Tome 37, Ddcembre 1976, page C7-225

THEORY OF U CENTERS IN ALKALINE EARTH

FLUORIDES USING THE SCF-MSXa METHOD

L. E. OLIVEIRA, B. MAFFEO and

H.

S. BRAND1 Departamento de Fisica da Pontificia Universidade Catblica

20.000, Rio de Janeiro, Brasil and

M. L. D E SIQUEIRA

Departamento de Fisica da Universidade Federal de Minas Gerais, 30.000, Belo Horizonte, Brasil

Rhsumh. - La structure Clectronique et les transitions optiques du centre U dans CaF2, SrF2 et BaFz sont calculkes en employant la mkthode SCF-MSXa. Le complexe utilisk pour representer le dkfaut a la symetrie Ta et consiste en un ion H- entour6 de six F- et quatre cations.

Nos calculs reproduisent trks bien la bande d'absorption optique experimentale (position du maximum et largeur) [I] et indiquent que cette bande n'est pas associk a une transition unique dans H- mais a un ensemble de transitions permises par symktrie pour lesquelles les Btats initiaux sont essentiellement F- 2p. Ce resultat vient du fait que le niveau hydrogenofde se situe en dessous de la bande F- 2p, ce qui est contraire B ce qui a kt6 obtenu par Yu [2], pour la structure klectronique du centre U dans les halogknures alcalins, en utilisant le m2me schkma de calcul. Nos calculs montrent que les mod&les d'ions ponctuels utilisks prkckdemment [3, 41 pour traiter ce problkme dans les fluorures d'alcalins terreux ne sont pas convenables.

Abstract. - The electronic structure and the optical transitions of the U center in CaF2, SrF2 and BaF2 are calculated using the SCF multiple-scattering Xa method. The complex used to repre- sent the defect has T d symmetry and consisted of an H- ion surrounded by six F- and four cations. Our calculations reproduce very well the experimental optical absorption band (peak position and width) [I] and indicate that this band is not associated to a single transition in H- but to a group of symmetry allowed transitions where the initial states are basically F- 2p. This result comes essentially from the fact that the hjdrogenic level lies below the F- 2p band, in contrary to the level structure of the U center, obtained using this same scheme by Yu [2] in alkali halides. The present calculations show that point-ion models previously used 13, 41 to treat this problem in alkaline- earth fluorides are particularly inadequate.

References

[I] BEAUMONT, J. H., GEE, J. V. and HAYES, W., J. Phys. C 3 [3] SINGH, R. S., GALIPEAU, D. W. and MITRA, S. S., J. Chem.

(1970) 152L. Phys. 52 (1970) 2341.

121 Yu, H.-L., PhD Thesis, University of Florida (1975). [4] BENNETT, H. S., Phys. Rev. B 6 (1972) 3936.

DISCUSSION

0. SCHIRMER.

-

Did YOU make any assumption on T. M. WILSON. - In order to support your conclu- the dependence of the energies on the configuration sion that the U-band is primarily due to charge trans- coordinates in order to derive the theoretical optical fer transitions from the F - 2p-like states, you need to

lineshape ? calculate their relative oscillator strengths.

H. S. BRANDI.

-

NO, we have not done this so H. S. BRANDI. - I basically agree with you but we far, but calculations are in progress. can make a rough estimation of the oscillator's

C7-226 L. E. OLIVEIRA, B. MAFFEO, H. S. BRAND1 AND M. L. DE SIQUEIRA strengths since the levels between 4 a, and 3 a, are

basically 2 p, thus r:+',f can be approximated to be the same for all levels, and only the final density of states will be important. This indicates that all tran- sitions are approximately equally important.

R. MONNIER.

-

HOW many values of a did you need to treat a cluster, and how were they determined ?

1 would also suggest that you repeat your calculation

with a theoretically more sound local exchange- correlation potential due to Hedin and Lundquist, which has been successfully tested on a wide variety of systems like Na metal, H atom, H, molecule ; this potential is the result of a fit to electron gas data (including correlation effects) ; and is trivial to imple- ment on an existing X, program.

H. S. BRANDI. - We have basically used the Schwarz's ci values. We have also checked the depen-

dence of the results on the variation of a, taking Slater's and Gaspar-Kohn and Sham values. The results do not strongly depend on a.

About your suggestion, there are calculations using different local potential, but the main problem is that you can lose the concept of transition state, naturally coming from X,. Unfortunately

I

do not know the Hedin and Lundquist calculations.

R. BAUER. - Can you comment on the choice of the constant potential in the intersphere space ? How many adjustable parameters are contained in the treatment ?