This paper presents a number of new additions to the charge transfer multiplet calculations as used in the calculation of L edge X-ray absorption spectra of 3d and 4d transition metal systems, both oxides and coordination compounds. The focus of the paper is on the consequences of the optimized spectral simulations for the ground state, where we make use of a recently developed projection technique. This method is also used to develop the concept of a mixed-spin ground state, i.e. a state that is a mixture of a high-spin and low-spin state due to spin-orbit coupling combined with strong covalency. The charge transfer mechanism to describe {pi}-bonding uses the mixing of the metal-to-ligand charge transfer (MLCT) channel in addition to the normal CT channel and allows for the accurate simulation of {pi}-bonding systems, for example cyanides

/LBL, Berkeley

/Stanford U., Chem. Dept.

de Groot, F.M.F.

Hedman, B.

Hocking, R.K.

Hodgson, K.O.

Piamonteze, C.

Solomon, E.I.

U., /Utrecht

UNT Digital Library

Work supported in part by the US Department of Energy contract DE-AC02-76SF00515New Developments in Charge Transfer Multiplet Calculations: Projection Operators, Mixed-Spin States and π-Bonding  F.M.F. de Groot1, R. K. Hocking2, C. Piamonteze3, B. Hedman2,  K.O. Hodgson2 and E.I. Solomon2 1Department of Chemistry, Utrecht University, Sorbonnelaan 16, 3584 CA Utrecht, Netherlands,  2Department of Chemistry, Stanford University, Stanford, California 94305, USA,  3Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Abstract.  This paper presents a number of new additions to the charge transfer multiplet calculations as used in the calculation of L edge X-ray absorption spectra of 3d and 4d transition metal systems, both oxides and coordination compounds. The focus of the paper is on the consequences of the optimized spectral simulations for the ground state, where we make use of a recently developed projection technique. This method is also used to develop the concept of a mixed-spin ground state, i.e. a state that is a mixture of a high-spin and low-spin state due to spin-orbit coupling combined with strong covalency. The charge transfer mechanism to describe π-bonding uses the mixing of the metal-to-ligand charge transfer (MLCT) channel in addition to the normal CT channel and allows for the accurate simulation of π-bonding systems, for example cyanides. Keywords: X-ray absorption, π-bonding, charge transfer multiplet theory PACS: 78.70.Dm INTRODUCTION The present understanding of the shapes of X-ray absorption spectra of transition metal systems is based on two distinctive models, (1) the single-particle excitation model for the metal and ligand K edges and (2) the charge transfer multiplet model for the metal L and M edges. In the X-ray absorption process an electron is excited from a core state to an empty state. In the single-particle excitation model it is, implicitly, assumed that all other electrons do not participate in the X-ray induced transition. This makes it possible to rewrite the Fermi Golden rule into a simple equation that identifies the X-ray absorption cross section with the empty density of states, modified by the transition matrix element. The most popular codes to calculate the density of states of both molecules and solids are based on Density Functional Theory.  The main approximation made in this approach is that many body effects are not important. This includes both valence band many body effects and many body effects that involve the core electron, or better the core hole in the final state. The wave function of the core hole interacts with the valence electrons (holes), which is a standard result from the quantum description of atomic structure. These atomic interactions turned out to be essentially unscreened in the solid state and need to be treated explicitly for all core states except K edges. In case of 1s core holes, their overlap with valence electrons has energy effects in the meV range, whereas the 2p, 3s and 3p core holes in 3d metals have energy effects in the order of 10 eV, where in case of the 3s core hole this interaction is simplified to an exchange interaction. In addition to these multiplet effects, core spectra are subject to screening effects that involve localized electron states. These charge transfer effects can be treated with the charge transfer model and the combination of both effects has lead to the development of the charge transfer multiplet (CTM) model. The advantage of the CTM model is that the calculations are fast and apply to all core level spectroscopies using the same ground state. In this paper, three recent additions of the CTM model will be discussed: (1) a projection method to determine the nature of the ground state that is used in the CTM model, also in order to compare it to the ground states used in DFT calculations, (2) the description of mixed spin ground states in orbital-SLAC-PUB-12220November 2006Contributed to 13th International Conference On X-Ray Absorption Fine Structure (XAFS13), July 9-14, 2006, Stanford, Californiaordered transition metal oxides, and (3) the special role of π-bonding. GROUND STATE PROJECTION  In transition metal systems with only σ-bonding, including all bulk oxides, only ligand to metal charge transfer plays a role. This implies that it is sufficient to describe the initial state as 3dn + 3dn+1L. For example, FeIII has a 3d5 ground state and only mixing with 3d6L turned out to be crucial for the description of the 2p XAS and 2p XPS spectral shapes, where in case of 2p XPS additional improvements are seen with the inclusion of the double ligand to metal charge transfer to 3d7L2.  A high-spin 3d5 ground state in octahedral symmetry has a 6A1 ground state with the electrons essentially in a t2g3eg2 configuration, where all electrons are spin-up. There are two important 3d6L configurations, one with t2g-mxing to t2g4eg2 and one with eg-mixing to t2g3eg3. The difference is that the added 3d electron is spin-down t2g respectively eg. In octahedral symmetry there is the approximate rule that eg mixing is twice as important as t2g mixing and this rule is confirmed for the actual results for FeIII(acac)2, where one finds 90% metal character (10% transfer) to t2g and 75% (24% transfer) to eg [1]. Another interesting case is a 3d5 low-spin ground state that has five t2g states filled (one empty) and all eg states empty. T2g-mixing leads to a t2g6L-configuration, which has one multiplet state, whereas eg-mixing leads to t2g5eg1L, which can have a large range of multiplet states. It turns out that in case of FeIII(tacn)2 the contribution of t2g-mixing is only a few percent, versus 37% for eg-mixing. This means that in a good first approximation, there is only eg-mixing in these systems. An interesting feature of low-spin 3d5 systems is that in octahedral symmetry the leading edge is only visible in the L3 edge. The leading edge is due to a 2p5t2g6 final state and this state has pure 2p3/2 respectively 2p1/2 character because the 3d-manifold has no moments. The ground state is 2T2 and the dipole selection rule dictates that only the L3 peak is visible, as confirmed by data on RuIII(NH3)6 [2]. In contrast a diverse range of systems shows a small leading peak at the L2 edge, which can be explained from the combined action of 3d(4d) spin-orbit coupling and a trigonal distortion. Systems that show this effect include FeIII(tacn)2, FeIII(CN)6 [3], RuIII(bpy)2 [4], but also oxides including the low spin CoIV system NaxCoO2 [5]. MIXED-SPIN GROUND STATES  In general transition metal (oxide) systems are divided into high-spin and low-spin. In some cases, there is the possibility of intermediate spin, for example for 3d5 systems, that can be high-spin S=5/2, intermediate spin S=3/2 and low-spin S=1/2.  We discuss the NiIII ground state in more detail. NiIII is a 3d7 system and its octahedral high-spin ground state is 4T1. This ground state has a t2g5eg2 configuration, where it is noticed that this one-electron configuration is only approximate due to the effects of the 3d3d interactions. Calculations show that the ground state has a ~90% t2g5eg2 configuration, with the remaining ~10% other configurations. If 3d spin-orbit coupling is included, the spin state deviates slightly from S=3/2 due to admixture of, mainly, S=1/2 low-spin configurations.  FIGURE 1.  The contributions of the various 3-hole orbital states are given for a NiIII ion in D4H symmetry. A1 identifies with a z2 orbital; B1 is x2-y2; B2 is xy and E is xz and yz. The ground state changes from high-spin 4E at low crystal field values to low-spin 2A1.  Next we introduce charge transfer with 3d8L states, and in addition lower the symmetry to tetragonal. Because NiIII is rather covalent, the high-spin ground state is only 60% pure in t2g5eg2, as indicated in Figure 1 with its three holes in x2-y2, z2 and xz/yz orbitals. Figure 1 gives the six largest contributions to the ground state, with ~15% a 3d8L configuration with holes in x2-y2, xz/yz and a ligand hole of z2 character, [6]. At large crystal fields, the ground state is 2E low-spin with a ~50% contribution from two coupled holes in x2-y2 and a hole in z2. The experimental spectrum of EuNiO3 at room temperature can best be simulated with 10Dqeff=2.0 eV, which indicates a ground state that is a mixture of ~45% high-spin A1B1E, ~15% low-spin B1B1A1 and ~40% charge transfer states. This state is neither high-spin nor low-spin and can best be named a mixed spin ground state. Mixed spin ground states need a number of ingredients (1) the possibility of high-spin and low-spin states, (2) a non-zero effect of the 3d spin-orbit coupling, (3) large charge transfer effects, and (4) most importantly, a crystal field that is makes HS and LS states near degenerate. Systems where these conditions could be fulfilled include the oxides containing NiIII, CoIII and MnIII ions.  π-BONDING   In systems that contain significant π-bonding an additional charge transfer channel becomes dominant. In addition to ligand metal charge transfer (CT) that mixes 3dn + 3dn+1L, metal ligand charge transfer (MLCT) is important. This can be described as 3dn + 3dn-1L. Figure 2 shows the mixing of 3d5+3d6L+ 3d4L. The creation of a 2p core hole transfers the extra electron to the 3d-band, which is essentially a charge conserving optical transition. This implies that the ordering of states remains similar to the ground state, where it is noticed that each 3dn configuration consist of the full crystal field multiplet manifold. In addition, the final state 2p53dn configurations contain the effects of the 2p spin-orbit coupling and the 2p3d multiplet effects.  FIGURE 2.  The mixing of a 3d5 ground state with 3d6L at energy Δ and with 3d4L at energy Δπ. The final state energies shift down for CT and up for MLCT by a small energy, given as the difference between the core hole potential Q and the Hubbard U.  This methodology to describe π-bonding has been used to describe the L edge spectra of FeIII(CN)6 and FeII(CN)6 [3]. The tacn-complex only allows σ-bonding and the cyanide complex both σ- and π-bonding. The FeIII(tacn)2 spectrum shows essentially the structure of the 2p53d6 final state multiplet, where the fine details can be simulated after inclusion of charge transfer effects, using the different orbital covelency (DOC) effect with much larger eg mixing [1]. Figure 3 shows the FeIII(CN)6 spectrum that shows a similar structure as the FeIII(tacn)2 spectrum, with one major difference, which is the extra large peak at 712 eV. CTM calculations using the configurations  3d5+3d6L+ 3d4L do exactly reproduce the FeIII(CN)6 spectrum as can be seen in Figure 3. The fact that the peak induced by mixing with 3d4L is this large, implies that the (lowest energy) 3d5 and the 3d4L configurations are near degenerate, i.e. Δπ~0 eV. In the final state the 2p53d6 and 2p53d5L configurations forms bonding and anti-bonding states that are visible at ~710 eV and at ~712 eV, where in Figure 2 we have seen that this energy difference increases by ~2.0 eV in the final state. In addition to the energy difference, also the hopping is modified in the final state, and all evidence to date suggests that all hopping terms are a bit reduced in the final state [7], which will help in the creation of a large satellite for MLCT, where it always makes normal CT satellites smaller [8].               FIGURE 3.  The experimental L edge spectra of FeIII(CN)6 (thick line) compared with CTM calculations (sticks and broadened to thin line).  These results show that the improvements in CTM simulations allow for a detailed simulation of systems with both σ- and π-bonding. With regard to the mixed-spin ground states, it remains to be seen how often they occur in actual systems. The analysis shows the could be present in covalent Mn, Co and Ni (oxide) systems and the ordering properties of many of these oxides suggest a complex local spin- and orbital moment situation.  REFERENCES 1. E.C. Wasinger, F.M.F. de Groot, B. Hedman, K.O. Hodgson and E.I. Solomon E. I. J. Am. Chem. Soc. 125, 12894 (2003). 2. T.K. Sham, J. Am. Chem. Soc. 105, 2269-2273 (1983). 3 R.K. Hocking, E.C. Wasinger, F.M.F. de Groot, K.O. Hodgson, B. Hedman, and E.I. Solomon E. I. J. Am. Chem. Soc. 128, 10442 (2006). 4 W. Gawelda, M. Johnson, F. M. F. de Groot,  R. Abela, C. Bressler, and M. Chergui, J. Am. Chem. Soc. 128, 5001 (2006).  5 T. Kroll et al. Cond-Mat. 0606518 (2006) 6 C. Piamonteze, F.M.F. de Groot, H.C.N. Tolentino, A.Y. Ramos, N.E. Massa, J.A. Alonso, and M.J. Martínez-Lope, Phys. Rev. B. 71, 020406 (2005) 7 S.M. Butorin, J. Elec. Spec. 110, 213 (2000). 8 F.M.F. de Groot, Coord. Chem. Rev. 249, 31 (2005). 012345678700 705 710 715 720 725 730 735Energy (eV)Normalized Absorption

New Developments in Charge Transfer Multiplet Calculations: Projection Operations, Mixed-Spin States and pi-Bonding

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New Developments in Charge Transfer Multiplet Calculations: Projection Operations, Mixed-Spin States and pi-Bonding

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