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Multiplet Effects in X-Ray Spectroscopy

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Multiplet Effects in X-Ray Spectroscopy Coordination Chemistry Reviews xxx (2004) xxx–xxx Review Multiplet effects in X-ray spectroscopy Frank de Groot∗ Department of Inorganic Chemistry and Catalysis, Utrecht University, Sorbonnelaan 16, 3584 CA Utrecht, The Netherlands Received 29 May 2003; accepted 9 March 2004 Contents Abstract ................................................................................................................................. 00 1. Basic aspects of multiplet effects....................................................................................................... 00 1.1. The interaction of X-rays with matter ............................................................................................. 00 1.2. The origin of multiplet effects ................................................................................................... 00 1.3. Atomic multiplets .............................................................................................................. 00 1.3.1. Term symbols .......................................................................................................... 00 1.3.2. Matrix elements ........................................................................................................ 00 1.3.3. X-ray absorption spectra described with atomic multiplets................................................................... 00 1.4. The crystal field multiplet model ................................................................................................. 00 1.4.1. Cubic crystal fields...................................................................................................... 00 1.4.2. The definitions of the crystal field parameters .............................................................................. 00 1.4.3. The energies of the 3dN configurations .................................................................................... 00 1.4.4. Symmetry effects in D4h symmetry ....................................................................................... 00 1.4.5. The effect of the 3d spin–orbit coupling ................................................................................... 00 1.4.6. The effects on the X-ray absorption calculations............................................................................ 00 1.4.7. 3d Systems in lower symmetries .......................................................................................... 00 1.4.8. X-ray absorption spectra of 3dN systems .................................................................................. 00 1.5. The charge transfer multiplet model .............................................................................................. 00 1.5.1. Initial state effects ...................................................................................................... 00 1.5.2. Final state effects ....................................................................................................... 00 1.5.3. The X-ray absorption spectrum with charge transfer effects.................................................................. 00 2. An overview of X-ray spectroscopies ................................................................................................... 00 2.1. X-ray absorption (XAS)......................................................................................................... 00 2.2. X-ray photoemission (XPS) ..................................................................................................... 00 2.3. Resonant photoemission and Auger .............................................................................................. 00 2.3.1. Resonant photoemission ................................................................................................. 00 2.3.2. Resonant Auger ........................................................................................................ 00 2.3.3. Auger photoemission coincidence spectroscopy ............................................................................ 00 2.4. X-ray emission ................................................................................................................. 00 2.4.1. 1s X-ray emission....................................................................................................... 00 2.4.2. 2p X-ray emission ...................................................................................................... 00 3. Examples for 3d coordination compounds............................................................................................... 00 3.1. The 1s XAS pre-edge shapes of coordination complexes............................................................................ 00 3.2. The 1s XAS pre-edge intensity and energy of minerals ............................................................................. 00 3.3. The 2p XAS and EELS of coordination compounds and proteins .................................................................... 00 3.4. The differential orbital covalence derived from 2p XAS ............................................................................ 00 3.5. The 2p XPS spectrum of Cu(acac)2 ............................................................................................... 00 3.6. Valence, site, spin and symmetry selective XAS ................................................................................... 00 4. Outlook ............................................................................................................................. 00 References............................................................................................................................... 00 ∗ Tel.: +31-30-25-36-763; fax: +31-30-25-31-027. E-mail address: [email protected] (F. de Groot). URL: http://www.anorg.chem.uu.nl/people/staff/FrankdeGroot. 0010-8545/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ccr.2004.03.018 2 F. de Groot / Coordination Chemistry Reviews xxx (2004) xxx–xxx Abstract This review gives an overview of the presence of multiplet effects in X-ray spectroscopy, with an emphasis on X-ray absorption studies on 3d transition metal ions in inorganic oxides and coordination compounds. The first part of the review discusses the basics of multiplet theory and respectively, atomic multiplets, crystal field effects and charge transfer effects are explained. The consequences of 3d-spin–orbit coupling and of 3d systems in symmetries lower than cubic are discussed. The second part of the paper gives a short overview of all X-ray spectroscopies, where the focus is on the multiplet aspects of those spectroscopies and on the various configurations that play a role in combined spectroscopies such as resonant photoemission, resonant X-ray emission and coincidence spectroscopy. The review is concluded with a section that gives an overview of the use of multiplet theory for 3d coordination compounds. Some new developments are sketched, such as the determination of differential orbital covalence and the inclusion of ␲-(back)bonding. © 2004 Elsevier B.V. All rights reserved. Keywords: X-ray absorption; X-ray emission; Multiplet theory; Crystal field splitting; Charge transfer 1. Basic aspects of multiplet effects The delta function takes care of the energy conservation and a transition takes place if the energy of the final state Multiplet effects play an important role in a large fraction equals the energy of the initial state plus the X-ray energy. of X-ray and electron spectroscopies. In all cases where a The squared matrix element gives the transition rate. The core hole other than a 1 s hole is present in the initial of final transition operator T1 describes one-photon transitions such state, multiplet effects are important. They determine the as X-ray absorption. It contains the exponential eikr describ- spectral shapes and influence the L3 to L2 branching ratio. ing the electric field. Using a Taylor expansion, this expo- X-ray absorption spectroscopy (XAS) has become an im- nential can be approximated as 1 + ikr + (higher terms). In portant tool for the characterization of materials as well as case of the K edges from carbon (Z = 6, edge = 284 eV) to for fundamental studies of atoms, molecules, adsorbates, zinc (Z = 30, edge = 9659 eV), the value of k·r is ∼0.04. surfaces, liquids and solids. The particular assets of XAS The transition probability is equal to the matrix element spectroscopy are its element specificity and the possibility squared, hence the electric quadrupole transition is smaller to obtain detailed information without the presence of any by ∼2 × 10−3 and can be neglected compared to dipole long-range order. Below it will be shown that the X-ray ab- transitions. Rewriting the Fermi golden rule with the dipole sorption spectrum in some cases is closely related to the approximation gives: empty density of states of a system. As such XAS is able to 2 W ∝ |Φ |ˆe · r|Φ | δE −E −hω provide a detailed picture of the local electronic structure of fi f q i f i ¯ the element studied. q The Fermi golden rule is a very general expression and 1.1. The interaction of X-rays with matter uses the initial state (Φi) and final state (Φf ) wave functions. These wave functions are not exactly known and in practi- If an assembly of atoms is exposed to X-rays it will absorb cal calculations one must make approximations to actually part of the incoming photons. At a certain energy a sharp calculate the X-ray absorption cross-section. An often-used rise in the absorption
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