First-Principles Calculation of Laser Crystal Multiplet Levels via Hybridized Density Functional Theory and Configuration Interaction within the OLCAO Method

Benjamin Walker


Computation of highly-localized multiplet energy levels of transition metal dopants is essential to the design of materials such as laser host crystals. A purely first-principles density functional theory-configuration interaction (DFT-CI) hybrid computational method has been developed to accurately compute multiplet energy levels for single atoms of carbon, nitrogen, oxygen, sodium, aluminum, silicon, titanium, and chromium. The multiplet energy levels have been computed with close experimental agreement in terms of magnitude and degeneracy, and the method does not depend on empirical information (i.e. Racah parameters). The computed multiplet energy level results are distributed according to term symbols, which are then compared to experimentally-observed multiplet energy levels. The hybrid method consists of analytic computation of two-electron integrals via the DFT-based orthogonalized linear combination of atomic orbitals (OLCAO) method, which are subsequently used as input for the CI-based discrete variational multi-electron (DVME) method to obtain the multiplet energy values.

Keywords: exchange-correlation; elecron repulsion integral; multiplet; DVME; OLCAO; density functional theory; configuration interaction

Full Text:



Zunger, A., Wagner, S. & Petroff, P. M. New Materials and Structures for Photovoltaics. J. Electron. Mater. 22, 3–16 (1993).

Atherton, L. J., Payne, S. A. & Brandle, C. D. Oxide and Fluoride Laser Crystals. Annu. Rev. Mater. Sci. 23, 453–502 (1993).

Antoni, R. Heterostructure Infrared Photovoltaic Detectors. Infrared Phys. Technol. 41, 213–238 (2000).

Lin, C. C. & Liu, R.-S. Advances in Phosphors for Light-emitting Diodes. J. Phys. Chem. Lett. 2, 1268–1277 (2011).

Ramsay, A. J. A Review of the Coherent Optical Control of the Exciton and Spin States of Semiconductor Quantum Dots. Semicond. Sci. Technol. 25, 103001 (2010).

Cocoletzi, G. H. & Mochán, W. L. Excitons: From Excitations at Surfaces to Confinement in Nanostructures. Surf. Sci. Rep. 57, 1–58 (2005).

Buse. Light-Induced Charge Transport Processes in Photorefractive Crystals I: Models and Experimental Methods. Appl. Phys. B Lasers Opt. 64, 273–291 (1997).

Shen, Z.-X. & Dessau, D. S. Electronic Structure and Photoemission Studies of Late Transition-Metal Oxides — Mott Insulators and High-Temperature Superconductors. Phys. Rep. 253, 1–162 (1995).

Huang, P. & Carter, E. A. Advances in Correlated Electronic Structure Methods for Solids, Surfaces, and Nanostructures. Annu. Rev. Phys. Chem. 59, 261–290 (2008).

Klepeis, J. E. Introduction to First-Principles Electronic Structure Methods: Application to Actinide Materials. J. Mater. Res. 21, 2979–2985 (2006).

Ohnishi, S. & Sugano, S. Theoretical Studies of High-Pressure Effects on Optical Properties of Ruby. Jpn. J. Appl. Phys. 21, L309–L311 (1982).

Ogasawara, K. et al. Analysis of Covalent Effects on the Multiplet Structure of Ruby Based on First-Principles Cluster Calculations. Jpn. J. Appl. Phys. 37, 4590–4594 (1998).

Tomohiko Ishii, Hisanobu Wakita, Kazuyoshi Ogasawara, & Yang-Soo Kim. The DV-Xα Molecular-Orbital Calculation Method. (Springer International Publishing, 2015).

Fairbank, W. M., Klauminzer, G. K. & Schawlow, A. L. Excited-State Absorption in Ruby, Emerald, and MgO:Cr3+. Phys. Rev. B 11, 60–76 (1975).

Tanabe, Y. & Sugano, S. On the Absorption Spectra of Complex Ions. I. J. Phys. Soc. Jpn. 9, 753–766 (1954).

Tanabe, Y. & Sugano, S. On the Absorption Spectra of Complex Ions II. J. Phys. Soc. Jpn. 9, 766–779 (1954).

Multiplets of Transition-Metal Ions in Crystals - 1st Edition. Available at: (Accessed: 14th December 2017)

Ogasawara, K., Ishii, T., Tanaka, I. & Adachi, H. Calculation of Multiplet Structures of Cr3+ and V3+ in α-Al2O3 Based on a Hybrid Method of Density-Functional Theory and the Configuration Interaction. Phys. Rev. B 61, 143 (2000).

Ching, W. Y. Theoretical Studies of the Electronic Properties of Ceramic Materials. J. Am. Ceram. Soc. 73, 3135–3160 (1990).

Ogasawara, K. & Watanabe, S. Chapter 22 Current Situation and Future Development of Discrete Variational Multielectron Method. in Advances in Quantum Chemistry Volume 54, 297–314 (Academic Press, 2008).

Ching, W.-Y. & Rulis, P. Electronic Structure Methods for Complex Materials: The Orthogonalized Linear Combination of Atomic Orbitals. (Oxford University Press, USA, 2012).

Griffiths, D. J. Introduction to Quantum Mechanics. (Pearson Prentice Hall, 2004).

Sansonetti, J. E. Wavelengths, Transition Probabilities, and Energy Levels for the Spectra of Sodium (NaI–NaXI). J. Phys. Chem. Ref. Data 37, 1659–1763 (2008).

Tables of Spectra of Hydrogen, Carbon, Nitrogen, and Oxygen Atoms and Ions. CRC Press (1993). Available at: (Accessed: 9th August 2017)

Martin, W. C. & Zalubas, R. Energy levels of aluminum, Al I through Al XIII. J. Phys. Chem. Ref. Data 8, 817–864 (1979).

Kaufman, V. & Martin, W. C. Wavelengths and Energy Level Classifications for the Spectra of Aluminum (Al I through Al XIII). J. Phys. Chem. Ref. Data 20, 775–858 (1991).

Martin, W. C. & Zalubas, R. Energy Levels of Silicon, Si I through Si XIV. J. Phys. Chem. Ref. Data 12, 323–380 (1983).

Saloman, E. B. Energy Levels and Observed Spectral Lines of Neutral and Singly Ionized Titanium, Ti I and Ti II. J. Phys. Chem. Ref. Data 41, 013101-013101-116 (2012).

Saloman, E. B. Energy Levels and Observed Spectral Lines of Neutral and Singly Ionized Chromium, Cr I and Cr II. J. Phys. Chem. Ref. Data 41, 043103 (2012).

Hyde, K. E. Methods for Obtaining Russell-Saunders Term Symbols from Electronic Configurations. J. Chem. Educ. 52, 87 (1975).

Jönsson, P., He, X., Froese Fischer, C. & Grant, I. P. The grasp2K Relativistic Atomic Structure Package. Comput. Phys. Commun. 177, 597–622 (2007).

Jönsson, P., Li, J., Gaigalas, G. & Dong, C. Hyperfine Structures, Isotope Shifts, and Transition Rates of C II, N III, and O IV from Relativistic Configuration Interaction Calculations. At. Data Nucl. Data Tables 96, 271–298 (2010).



  • There are currently no refbacks.