Multiplet calculation

Fig. 11 Lines+symbols experimental x-ray absorption data at the L2j3 edge of Sc in Sc2 C84 recorded at the temperatures indicated. The energy resolution was 100 meV. The grey solid lines represent broadened atomic multiplet calculations for a purely ionic trivalent Sc (d° initial state—>2pd final state) and divalent Sc (d1 initial state— 2pd2 final state) ion...

In these charge-transfer atomic multiplet calculations, the effective formal valency of the encaged Sc ions is given by the ratio of the d° and d1 initial-state contributions, which represent trivalent and divalent Sc, respectively. Figure 12 shows how the spectrum would evolve from the pure d° initial state... 

With this example of data from the dimetallofullerene Sc2 C84, the efficacy of combining x-ray absorption and charge-transfer atomic multiplet calculations in investigating the valency, charge transfer and cage-metal interaction of more complex, hybridised systems such as Sc2 C84 has been demonstrated. Based on the valence sensitivity of the measurement, we are confident in overruling... 

Simulation of the data within the framework of charge-transfer atomic multiplet calculations shows that this hybridisation yields an effective Sc 3d electron count of about 0.4 electrons, or a valency of 2.6. 

In our previous report, however, the calculated multiplet energies tend to be overestimated especially for the doublets. This is due to the underestimation of the effect of electron correlations. Recently, we have developed a simple method to take into account the remaining effect of electron correlations. In this method, the electron-electron repulsion integrals are multiplied by a certain reduction factor (correlation correction factor), c, and the value of c is determined by the consistency between the spin-unrestricted one-electron calculations and the multiplet calculations. The details of this method will be described in another paper (5). In the present paper, the effect of electron correlations on the multiplet structure of ruby is investigated by the comparison between the results with and without the correlation corrections. 

A pair of molecular orbitals involved in the shakeup process produces two states and all the sharp peaks in the experimental spectrum can be assigned to the calculated states. The present and previously reported assignments agree with each other for the first two shakeup excitations due to the Ijt — 2n transition, however the other assignments depend on the theoretical model. The present multiplet calculations are basically performed in the same way as the SW-Xcx method but are in better agreement with the experimental results. One of the improvements was analyzed by considering the exchange Interaction and the atomic constituents of the molecular orbitals concerned. 

Figure 2 shows XPS data for dioxides of neptunium, plutonium, and americum compared to the appropriate fn multiplet calculations (8). These multiplet spectra do not represent the multiplet structure of either the fn or the fn l configurations. They are, instead, the final state multiplet structure of the fn l configuration modulated by the transition probability from the fn ground state to the fn l multiplets. 

The multiplet calculations discussed above (see Fig. 2) determine relative intensities within excited multiplets. However, the f electron intensities are not related to s, p, or d intensities. 

The distribution of intensity between the different multiplet levels is given directly if Dirac functions are used to evaluate the transition probabilities, since the electron spin is incorporated in the equations. The total intensity of all the transitions within a multiplet, calculated from Dirac functions, is inappreciably different from that obtained with Schrddinger... 

Ikeno El, de Groot EM, Stavitski E and Tanaka I 2009 Multiplet calculations of 12, 3 x-ray absorption near-edge structures for 3d transition-metal compounds. Jounud of Physics Condensed Matter 21(10), 104208. 

---