An Example for Angular Overlap Modeling of 5F Systems
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Published in "Inorganic Chemistry 55(14): 6853–6860, 2016" which should be cited to refer to this work. 4+ The Electronic States of U in U(PO4)Cl: An Example for Angular Overlap Modeling of 5fn Systems Anna Bronova,† Thomas Bredow,‡ Robert Glaum,*,† and Werner Urland§ † Institute of Inorganic Chemistry, Rheinische Friedrich-Wilhelms-Universitat,̈ Gerhard-Domagk-Straße 1, D-53121 Bonn, Germany ‡ Mulliken Center for Theoretical Chemistry, Rheinische Friedrich-Wilhelms-Universitat,̈ Beringstr. 4, D-53121 Bonn, Germany § Chemistry Department, University of Fribourg, Chemin du Museé 9, CH-1700 Fribourg, Switzerland *S Supporting Information ABSTRACT: Detailed experimental data on UPO4Cl comprising single-crystal UV/vis/NIR spectra and temperature-dependent 4+ magnetic susceptibilities form the basis for the investigation of the electronic structure of the U cation in UPO4Cl. For modeling of the observed physical properties the angular overlap model (AOM) was successfully employed. The computations were performed using the newly developed computer program BonnMag. The calculations show that all electronic transitions and the magnetic susceptibility as well as its temperature dependence are well-reproduced within the AOM framework. Using Judd−Ofelt theory BonnMag allows estimation of the relative absorption coefficients of the electronic transitions with reasonable accuracy. Ligand field splitting for states originating from f-electron configurations are determined. Slater−Condon−Shortley parameters and the spin−orbit coupling constant for U4+ were taken from literature. The good transferability of AOM parameters 4+ fi ff fi for U is con rmed by calculations of the absorption spectra of UP2O7 and (U2O)(PO4)2. The e ect of variation of the t parameters is investigated. AOM parameters for U4+ (5f) are compared to those of the rare-earth elements (4f) and transition metals (3d). ■ INTRODUCTION and estimation of their absorption coefficients, symmetry fi analysis of the underlying electronic states is required as Calculation of the energies of f-electron con gurations and of − 9,10 physical properties based thereon within the framework of the prerequisite for the application of Judd Ofelt theory. In this 1−4 study, we present examples of such calculations using the newly angular overlap model (AOM) are of interest due to the 11 various technically important properties of f n systems. These developed computer program BonnMag. As basis for our χ detailed treatment of metal−ligand interactions and of the properties include magnetic ( , g) and optical behavior. For fi fl their investigation, fast and reliable calculations with a ligand eld in uence highly resolved, polarized single-crystal computationally efficient approach are desirable for screening absorption spectra and temperature-dependent magnetic susceptibilities of UPO4Cl shown in the preceding paper of purpose and for analyses of the electronic structure of rare earth 12 metal compounds. Up to now, only f 1−f 3 and f 11−f 13 systems this issue are used. Our AOM calculations using BonnMag allow separation of could be treated within the AOM (implemented in the ff fi − programs SURGEV,5 AOMX,6 and LIGFIELD7). For 4fn the e ects of ligand eld splitting and spin orbit coupling on systems featuring large spin−orbit coupling and small ligand the energy of the observed electronic states. Because of the field effects the assignment of the split terms using the well- simple and fast procedure, a large number of calculations with known Dieke diagrams8 is straightforward, ignoring, however, variation of parameters is possible. Thus, assessment of the “ fi ” ligand field splitting. Since in 5f n systems ligand field splitting best t AOM parameters is accomplished. We want to and spin−orbit coupling effects are of similar magnitude, such a simple analysis of the optical spectra is impossible. For a reasonable assignment of the observed electronic transitions 1 emphasize here that as further advantages the AOM approach transitions, magnetic susceptibilities, crystal susceptibilities, and has no symmetry restrictions and that the parameters are well- g-tensors (for odd numbers of f-electrons) for the complete − founded in molecular orbital theory.1 4 It will be shown that range of f n systems. An additional improvement of BonnMag is the computer program BonnMag11 is well-suited for perform- the calculation of (relative) absorption coefficients9,10 for each ing these calculations. On request BonnMag may be obtained transition and a symmetry analysis of the split terms with from the authors (A.B. and R.G). assignment of their irreducible representations. Parametrization. BonnMag includes several atomic and 20 ■ THE ANGULAR OVERLAP APPROACH interatomic parameters. The SCS parameters F2, F4, and F6 − ζ 1−4 fi and the spin orbit coupling constant are needed for the In AOM the global ligand eld, which can be given by 10 calculation of the transition energies of the free ion. The AOM Dq or Δ for transition metals, is split into the contributions of − σ π δ parameters eσ and eπ describe the various metal ligand individual bonding interactions ( , , ) between the ligand and interactions. To account for different metal−ligand distances metal orbitals (d or f). Chromophores with different (low- −n eσ and eπ are assumed to depend on d(M−L) . symmetry) geometric structure can be described without As prerequisite for the calculations a global coordinate symmetry restriction by this model using transferable and system must be defined that allows the geometric description of chemically meaningful bonding parameters. Note: In a strict the ML chromophore (see Figure 1). For the calculation of sense, these parameters describe for most ligands the m antibonding effect between metal and ligand orbitals. The ligand field is described by the sum of all σ and π interactions between the ligands and the central metal atom. The δ interaction is included in AOM theory but is neglected in most studies due to its small contribution.13 The interaction −1 parameters are denoted as eσ and eπ (cm ). For these parameters transferability from already parametrized com- pounds is assumed (and confirmed for many cases) when considering new systems. Thus, the AOM has some predictive power. Interpretation of ligand behavior is possible due to the correlation of the bonding parameters with the metal−ligand interaction. It is important to note that AOM contains a number of approximations. Those are the use of Slater− Condon−Shortley (SCS) theory for the description of the electronic states of the free ion and restriction of the individual Figure 1. ORTEP representation of the [UIVO Cl ] chromophore in − σ π 6 2 ligand metal interaction to one - and two perpendicular - UPO4Cl given with the second coordination sphere and coordinate bonds. A fundamental aspect of this model is the para- systems for the central atom (global coordinate system) and one metrization of the metal−ligand interactions by fitting of the ligand as example (index L).12 calculated properties to experimental data. Thus, AOM accounts in a simple way for the ligand field influence. Already, during the 1960s and 1970s the AOM was used for calculations orientation dependent properties, a careful choice of this global of properties of rare earth metal compounds that are based on coordinate system is required. For details on this topic, we refer the energies of their f electronic states.4,14,15 These inves- to ref 16. The calculated transition energies are, however, 1− 3 11− 13 independent of the chosen coordinate system. The global tigations were limited to systems f f ,f f , and, in most fi cases, to high-symmetry coordination polyhedra. The main coordinate system must be de ned according to the point- reason for these limitations was the lack of computing power. group symmetry to get the irreducible representations of the For dn systems several computer programs are widely spread eigenstates. In addition, the local ligand coordinate systems 16 must be set for each ligand in the chromophore. Here the in the scientific community, CAMMAG by GERLOCH (PC 17 atoms of the first and, if necessary, the second coordination Version by RILEY ), AOMX by SCHMIDTKE, ATANASOV, and 6 7 sphere are used. “Dummy” atoms can be introduced too, to ADAMSKY, and LIGFIELD by BENDIX. With these programs the fi energies of all electronic states and, depending on these allow facile de nition of directions. The second coordination n sphere can be used for definition of the ligand coordinate energies, magnetic susceptibilities (as well as g values) for d π systems can be calculated. systems if an anisotropic -interaction must be accounted for in the calculations. As already mentioned Judd−Ofelt Theory9,10 is applied for ■ ANGULAR OVERLAP MODEL WITH BONNMAG estimating the absorption coefficients for electronic transitions For the calculation of absorption spectra and magnetic in f n systems. It contains several approximations. In general 2 Δ Δ ± susceptibilities of UPO4Cl (f ) the computer program electric dipole transitions are allowed, if S =0, L =0or 1, BonnMag11 was used. This program is based on SURGEV, and ΔJ =0or±1(J =0↔ J = 0 forbidden) and Laporte’s rule which was developed by W. Urland during the 1970s.5 Its code is obeyed.21 Judd−Ofelt theory is based on the assumption that bears also some resemblance to CAMMAG.16,17 As its configuration interaction between 4f n and high-energy predecessor, BonnMag uses the angular overlap approach to 4f n−15d 1 states lends intensity to the otherwise Laporte approximate the ligand field effect. All possible configuration forbidden transitions between pure 4f n states. Configuration interactions are considered by the coefficients of fractional interaction depends on the symmetry of the interacting states; parentage (CFP) and reduced matrix elements (RME).18,19 These thus, symmetry analysis is required. Judd−Ofelt theory further have been implemented in the program. In contrast to its assumes an average energy for excited 4f n−15d 1 21 config- predecessors, BonnMag allows calculation of energies of f−f uration above the states derived from the 4f n configuration.