Published: February 22, 2011 r2011 American Chemical Society 1922 dx.doi.org/10.1021/jp111620e | J. Phys. Chem. A 2011, 115, 1922–1932 ARTICLE pubs.acs.org/JPCA Theoretical Study of the Crystal-Field Energy Levels and Two-Photon Absorption Intensities of Tb 3þ in Cubic Host Lattices Chang-Kui Duan †,‡,§ and Peter A. Tanner* ,‡ † College of Physics and Mathematics, Chongqing University of Post and Telecommunications, Chongqing, P.R. China ‡ Department of Biology and Chemistry, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong S.A.R., P.R. China ABSTRACT: Published two photon excitation (TPE) intensities for the cubic elpasolite sys- tems Cs 2 NaTbX 6 (X = Cl, F) have been simulated by a calculation of two photon absorption (TPA) intensities which takes into account electric dipole transitions involving the detailed crystal-field structure of 4f 7 5d intermediate states, as well as the interactions of the 4f 7 core with the d-electron. The intensity calculation employed parameters from an energy level calculation which not only presented an accurate fit, but also yielded parameters consistent with those from other lanthanide ions. The calculated intensities were used to confirm or adjust the previous assignments of energy levels, resulting in some minor revisions. Generally, the TPA intensity simulations were in better agreement with experimental data for the fluoride, rather than the chloride, system and possible reasons for this are given. ’ INTRODUCTION This work presents calculations of the 4f 8 crystal-field (CF) energy levels of Tb 3þ in Cs 2 NaTbX 6 (X = Cl, F) and utilizes the wave functions thereby obtained for the further calculations of intensities in the two-photon absorption (TPA) spectra of these crystals. Experimental two photon excitation (TPE) data have been recorded by Denning and co-workers in several detailed studies at temperatures down to 6 K from oriented crystals using polarized radiation and the use of a magnetic field. 1-6 Other studies of Cs 2 NaTbCl 6 have utilized conventional one photon luminescence and absorption spectroscopy, as well as magnetic circular dichroism. 7-10 We recognize that the results of CF calculations which indicate systematic trends of CF parameters (CFPs) throughout the lanthanide series not only serve to validate the correctness of the calculations, but also to throw light upon the physical meaning of the parameters. 11 Such calculations require representative, securely assigned energy level data sets so that the derived CFPs have less uncertainties. Some previous calculations have employed incorrect matrix elements, and we also find in the present study that a few assignments can be changed in order to provide a more accurate data set fitting. 12 Although semiempirical CF theory has been successful in the simulation of the energy levels of lanthanide ions (Ln 3þ ), it can be more useful if it can be used to predict, rather than explain, the positions and properties of the Stark levels. Whereas ab initio/first principle calculations have gained tremendous successes in various fields of materials science, and there are also some notable attempts for lanthanide materials, 13-16 it is not yet possible to perform calculations using these methods alone which can give a good comparison with experimental results down to the level of Stark splittings. Recently, Reid and co-workers 17 have proposed to combine ab initio/first principle calculations with the semiempirical CF effective Hamiltonian for energy level and intensity calculations and have demonstrated the method with an example for CF energy levels. Along these lines, it is important to obtain accurate CFPs from model systems to test the theoretical methods, and to elucidate the mechanisms of the contributions to those parameters. The elpasolite host, Cs 2 NaLnX 6 , has the attractive property of providing sites of high symmetry (O h molecular symmetry point group) for Ln 3þ . The absorption spectrum for the transition from an initial state (usually the ground state or a low-lying excited state) to an excited state by the simultaneous absorption of two photons (two-photon absorption, TPA) can give com- plementary information to the one-photon absorption spectrum. The mechanism of TPA for Tb 3þ is depicted in Figure 1 (refer also to the Theory section). TPA is usually extremely weak so the subsequent emission due to absorption is detected instead in the two-photon excitation (TPE) spectrum. The TPE studies using polarized radiation have been particularly powerful in the assign- ment of symmetry representations to crystal-field levels since stricter point group selection rules determine the intensities of electronic transitions between CF levels, 1 by comparison with the one photon electronic spectra of these cubic crystals. The one-color TPE studies also possess the advantage that high-lying Stark levels are accessible by using visible laser radiation, since the laser photon energy involved is only half of that for the terminal level. The spectra comprise pure electronic transitions and are mostly un- cluttered by vibronic structure. By contrast, the one photon ultraviolet spectra tend to be very congested so that spectral assignments are frequently ambiguous. Transition intensity calculations can be useful in checking the assignments of Stark levels, and also they serve to check the Received: December 7, 2010 Revised: January 18, 2011