Ab-initio calculations of Judd–Ofelt intensity parameters for transitions between crystal-field levels Jun Wen a,b,n , Michael F. Reid c , Lixin Ning d , Jie Zhang a , Yongfan Zhang e , Chang-Kui Duan b , Min Yin b a School of Physics and Electric Engineering, Anqing Normal University, Anqing 246011, China b Department of Physics, University of Science and Technology of China, Hefei 230026, China c Department of Physics and Astronomy and MacDiarmid Institute for Advanced Materials and Nanotechnology, University of Canterbury, PB4800 Christchurch, New Zealand d Department of Physics, Anhui Normal University, Wuhu 241000, China e Department of Chemistry, Fuzhou University, Fuzhou, Fujian 350002, China article info Available online 31 October 2013 Keywords: Ab-initio Lanthanide ion Electric dipole moment Transition intensity parameters Superposition model abstract Wavefunction-based ab-initio calculations of the electric-dipole moments of 4f N –4f N transitions of lanthanide ions are performed to extract the A λ tp intensity parameters. The extraction method is an extension of our earlier calculations of crystal-field (CF) parameters for lanthanide ions in crystals. The CASSCF/RASSI-SO (Complete-Active-Space Self-Consistent-Field/Restricted-Active-Space State-Interaction Spin-Orbit) calcula- tions have been carried out on the chosen model system of CaF 2 : Ce 3 þ with an interstitial fluoride ion (F À i ) on z-axis (Ce 3 þ ion occupying the C 4v symmetry site). In consideration of the site symmetry and the coordination situation of Ce 3 þ ion at C 4v site in CaF 2 as well as the superposition model (SM), the calculated intensity parameters for Ce 3 þ ion can be classified into three categories, and detailed discussions are then given. & 2013 Elsevier B.V. All rights reserved. 1. Introduction The 1962 papers by Judd [1] and Ofelt [2] provided important tools for the analysis of electric-dipole transition intensities within the f N configurations of lanthanide and actinide ions in solids, solutions, and molecules [3–6]. The original work considered only the mixing of the f N configuration with excited configurations on the lanthanide or actinide ion. Subsequently it was realized that excitations involving ligand states (“ligand polarization” or “dynamic coupling”) also gave significant contributions [7,8]. The vast majority of applications use parametrizations for total transition intensities between J multiplets (T λ or Ω λ parameters [7]). However, the parametrization of transitions between individual crystal-field (CF) levels (using parameters A tp Ξ(t,λ) [1] or A λ tp [9]) gives significantly more information about the electric-dipole inten- sity mechanisms. Reid and co-workers [9] pointed out that the signs of the A λ tp parameters give information about the relative importance of the CF mixing and ligand-polarization contributions to the intensities. They also extended the work by Newman and Balasu- bramanian [10], who had shown that some of the intensity parameters violated the superposition model (SM), and demon- strated that SM violating parameters were essential in systems with complex ligands [11]. Most calculations of f N transition intensities have been carried out based on empirical models by considering point charges and electric polarizations of ligands. Reid and Ng [12] carried out a perturbation-theory calculation of intensity parameters for Pr 3 þ ions with oxygen ligands. The calculation results are in reasonable agreement with the fitted parameters. However, such a calculation is not a complete self-consistent ab-initio calculation. Some mole- cular-orbital calculations for the transition intensities between f N states have been performed [13], but these calculations do not produce the intensity parameters. Hu et al. [14] have extracted 4f and 5d CF parameters from ab-initio quantum chemistry programs (DV-Xα programs) by constructing an effective Hamiltonian from the information contained in the eigenvectors and eigenvalues produced by the ab-initio calculations on Ce 3 þ -doped crystals. In our subsequent work [15], the CF parameters were extracted from the information of wavefunctions and energies obtained from the geometry opti- mization calculations and subsequently the wavefunction-based complete-active-space self-consistent field (CASSCF) embedded cluster calculations for a series of Ce 3 þ -doped fluoride com- pounds. Excellent agreement between our calculated and the fitted CF parameters is obtained. In this work, we show how to Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jlumin Journal of Luminescence 0022-2313/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jlumin.2013.10.055 n Corresponding author at: School of Physics and Electric Engineering, Anqing Normal University, Anqing 246011, China. Tel.: þ86 15855154475. E-mail address: wenjunkd@mail.ustc.edu.cn (J. Wen). Journal of Luminescence 152 (2014) 54–57