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By Maurits W Haverkort

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Extra info for Spin and orbital degrees of freedom in transition metal oxides and oxide thin films studied by soft X-ray absorption spectroscopy

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2 we see that for the t2g orbital the IIpx − IV px combination is bonding while the IIpx + IV px (not shown) combination is non-bonding. The IIpx + IV px has a positive overlap for oxygen II, but exactly the same amount of negative overlap for oxygen IV. Each d orbital has exactly one linear combination of p orbitals with which an overlap exists. The other orbitals are non-bonding. 2. Using a basis set of only bonding orbitals greatly reduces the size of the basis set. For a cluster consisting of one transition metal and 6 oxygens there are 10 + 6 × 6 = 46 orbitals.

8: Multiplets of the 2p5 3dn+1 final states of 2p-XAS. 8 we show the atomic multiplet calculations for n = 9 to n = 6. Each configuration has its own amount of final states and its own multiplet. Naturally if one changes from one element to an other some parameters change. 3 Multiplets and selection rules 27 The Slater integrals, determining the size of the electron electron repulsion differ from element to element and the crystal fields present are different from material to material, but the general structure of a multiplet is strongly dependent on the configuration one has.

Later they have been re-derived within a one-electron approximation [112]. It has been shown that the sum-rules are a result of symmetries already present in the 3J symbols [113]. In other words, the sum-rules are an intrinsic property of the dipole operator. They do not depend on the assumptions made on the local symmetry and they are independent of the framework in which one 56 Sum-rules is working, namely, many-electron theory or one-electron theory. In this chapter we will show the derivation of the sum-rules in second quantization, along the lines of M.

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