First-Principles Analysis for the Optical Absorption Spectra of Metal Ions in Solids TAKUGO ISHII, 1 KAZUYOSHI OGASAWARA, 2 HIROHIKO ADACHI, 3 PHILIPP BURMESTER, 1 GU ¨ NTER HUBER 1 1 Institut fu ¨ r Laser-Physik, Universita ¨t Hamburg, Jungiusstrasse 9a, 20355 Hamburg, Germany 2 School of Science, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337, Japan 3 Department of Materials Science and Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan Received 11 December 2002; accepted 10 October 2003 Published online 5 February 2004 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/qua.10854 ABSTRACT: The authors developed a general first-principles method for the direct calculation of multiplet structures. The method is a configuration interaction (CI) method combined with a general cluster method based on density functional theory. The present version of the method is based on a fully relativistic framework in which four-component wave functions are handled. The calculations run independently of the semiempirical crystal field and ligand field theories, which have been the only the methods to analyze the absorption spectra involving the multiplet structures of transition metal and rare-earth ion centers. One application of the present method is the analyses of the absorption spectra of solid-state laser crystals. In this article, the authors focus on the multiplet structures originating from the f–f transition of Eu 3+ ion in solids. In Eu 3+ -doped Y 2 O 3 , the overall electronic structure is shown in agreement with the experimentally known absorption spectrum. A comparison of the multiplet structures between Eu 3+ and Sm 2+ ions is also shown. Although they have the same 4f 6 electron configuration, the electronic structures showed different energy positions, and the tendency well agreed with that observed in experimentally known absorption spectra. In the one-electron molecular orbital energies, the energies of Sm 4f levels were higher than those of Eu 4f levels. The difference is considered to originate from the difference in electron–nucleus attractive potential. The molecular orbitals of Eu 4f levels showed obvious mixing with O 2p orbitals, but those of Sm 4f levels did not. The calculated multiplet energies of Sm 2+ were systematically smaller than those of Eu 3+ . The smaller multiplet energies originated from the smaller values of two-electron integrals, indicating the relatively larger distribution of Sm 4f orbitals than those of Eu. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem 99: 488 – 494, 2004 Correspondence to: T. Ishii; e-mail: tishii@physnet.uni- hamburg.de International Journal of Quantum Chemistry, Vol 99, 488 – 494 (2004) © 2004 Wiley Periodicals, Inc.