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First principles calculations of the L2,3-edge XANES spectra for V2O3
ARTICLE IN PRESS
Radiation Physics and Chemistry 75 (2006) 1564–1570 www.elsevier.com/locate/radphyschem
First principles calculations of the L2,3-edge XANES spectra for V2O3 M.G. Brika,b,, K. Ogasawarab, T. Ishiib, H. Ikenoc, I. Tanakac a
Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4, Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan b School of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda, Hyogo 669-1337, Japan c Department of Materials Science & Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan Accepted 27 July 2005
Abstract Vanadium L2,3-edge XANES spectra have been calculated for V2O3 crystal. A fully relativistic first-principles many electron method based on the numerical solution of the Dirac equation was used. The key-points of the method are: (i) use of the molecular orbitals (MO); (ii) absence of any fitting parameters; (iii) possibility to apply to any ion in any symmetry; (iv) possibility of numerical analysis of the many-electron states in terms of the MO-based Slater determinants. The calculated spectra are in good agreement with experimental ones available in the literature, including the absolute values of the transition energy and the shape of the absorption bands. Experimental trends in the polarized XANES spectra of V2O3 are reproduced. r 2006 Elsevier Ltd. All rights reserved. Keywords: L2,3-edge; Xanes spectra; Vanadium oxides
1. Introduction During last several decades, 3d transitional elements have been a subject to many thorough investigations due to their numerous applications. Among various experimental methods, X-ray absorption near edge structure (XANES) spectroscopy is a very powerful method of gaining knowledge about the electronic structure of the transitional metal ions. The transition-metal L2,3-edge Corresponding author. Fukui Institute for Fundamental
Chemistry, Kyoto University, 34-4, Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan. Tel.: +81 75 7117708; fax: +81 75 7814757. E-mail addresses: [email protected], [email protected] (M.G. Brik).
XANES spectra mainly correspond to the electric-dipole transitions between the fully occupied 2p-core levels and partially filled 3d electron shell. Coulomb and exchange interactions between the 2p and 3d electrons give rise to structured XANES bands, detailed analysis of which can give information about the occupied and unoccupied states, energy level splitting (including the splittings caused by the spin–orbit interaction and crystal field), configuration interaction, splitting of the core and outer electron shells, etc. Fast development of the materials science and search for new functional compounds for various applications imply the need for detailed knowledge of the electronic structure of chemical elements whose properties or special features are supposed to be made use of. Quantum mechanical calculations serve this purpose
0969-806X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2005.07.055
ARTICLE IN PRESS M.G. Brik et al. / Radiation Physics and Chemistry 75 (2006) 1564–1570
very well, since they allow not only for precise description of physical processes which occur in wellknown materials, but for prediction and design of new compounds whose properties have not been studied experimentally so far. In the present paper, we report on the calculations of the L2,3-edge XANES spectra in the V2O3 crystal. Experimental studies of the vanadium oxides XANES spectra have been reported previously by Zimmermann et al. (1998) and Gloter et al. (2001). In the above oxide vanadium ions occupy octahedral positions. In the octahedral crystal field the 3d orbitals split into t2g and eg orbitals with the former being the lower state and the latter being the higher with the energy separation of 10 Dq (where Dq is referred to as the crystal field strength (Sugano et al., 1970). The 2p level is split by spin–orbit interaction into 2p1/2 and 2p3/2 (or L2 and L3, respectively) with the subscripts representing the quantum number of the total angular momentum. After absorbing an X-ray quantum, an electron from the 2p level is excited into the t2g or eg states, and the schematic diagram of this excitation looks as shown in Fig. 1a, where one-electron transitions between the 2p and 3d states are shown by vertical arrows. As follows from the figure, the energy separation between the L2 and L3 bands is mainly due to the spin–orbit splitting of 2p-orbitals, whereas the splitting within each band is caused by the crystal field splitting of 3d orbitals. However, as was shown by Adachi and Ogasawara (2003) such one-electron consideration is insufficient to produce good agreement between the calculated and experimental spectra, and more elaborated approach taking into account the interaction between the multiplets arising from all the possible electron configuration (Fig. 1b) was proposed. It also was shown that the proper consideration of the multiplets interaction leads
(a)
1565
to the significant changes in the intensity ratio and improves the agreement between theory and experiment drastically.
2. Method of calculations We apply the fully relativistic discrete-variational multi-electron (DV-ME) method, which is a configuration-interaction (CI) calculation program using the fourcomponent fully relativistic molecular spinors obtained by the discrete-variational Dirac–Slater (DV–DS) cluster calculations, developed by Ogasawara et al. (2001). The method is based on the numerical solution of the Dirac equation, and its main advantages are as follows: (1) the first-principles method without any fitting parameters (this is especially important for the development of new materials and prediction of their expected properties); (2) very wide area of applications: to any atom or ion in any symmetry from spherical to C1 for any energy interval from IR to X-ray; (3) possibility to take into account all effects of chemical bond formation, exchange and configuration interaction by numerical integration; (4) potential to calculate a wide variety of physical properties (such as transition probabilities, for example) using the obtained wave functions. All relativistic effects are taken into account automatically. The key idea of the method is that the molecular orbitals (MO) are used throughout the calculations rather than atomic wave functions. This makes the effects of covalency taken into account explicitly. The many-electron wave functions are expressed as linear combination of the MO-based Slater determinants and the absorption peaks assignment can be done in terms of these Slater determinants. The relativistic many-electron Hamiltonian is expressed as
(b)
Fig. 1. Schematic representation of one-electron transitions corresponding to the L2 and L3 absorption bands in the XANES spectra: (a) one-elecron picture; (b) many-electron picture; n and m correspond to the number of 3d-electrons distributed through t2g and eg orbitals.
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M.G. Brik et al. / Radiation Physics and Chemistry 75 (2006) 1564–1570
(in atomic units) " n X X capi þ bc2 H¼
Zn jr Rn j i n i¼1 # n X n X X Zeff 1 m þ . þV 0 ðri Þ þ jr R j rj j jr i m i m i¼1 j4i
ð1Þ
where a, b are the Dirac matrices, c the velocity of light, ri, pi the position and the momentum operator of the ith electron, Zn and Rn the charge and position of the vth nucleus, Zeff m and Rm the effective charge and position of the mth ion outside the model cluster, n the number of explicitly treated electrons. V0(ri) is the potential from the remaining electrons (Watanabe and Kamimura, 1989): Z G 0 r0 ðr Þ 0 dr V0 ¼ jr r0 j G G 3 r ðrÞV xc frG ðrÞg rG 0 ðrÞV xc fr0 ðrÞg þ G 4 r 1 ð rÞ ð2Þ V xc frG 1 ðrÞg , G where rG, rG 1 , r0 represent the charge density of all electrons, that of the explicitly treated electrons and that of the remaining electrons, respectively, and Vxc is the Slater’s Xa potential. The superscript G indicates the values for the ground state. Diagonalization of the Hamiltonian (1) provides a complete electron energy level scheme. Since the eigenfunctions are also obtained, the absorption spectra (for electric dipole, electric quadrupole, and magnetic dipole transitions) can be obtained in a straightforward manner after calculating appropriate matrix elements. For example, in the case of electric dipole transitions the oscillator strength (averaged over all possible polarizations) is calculated as follows: * + 2 X n 2 I if ¼ ðE f E i Þ Cf rk Ci , (3) k¼1 3
Ci and Cf are the initial and final states with energies of Ei and Ef, respectively. In the case of the XANES spectra only those electrons occupying the MO mainly composed of 2p and 3d states in the ground state are treated explicitly, since they are involved into the absorption transitions.
3. Results of calculations and discussion V2O3 has a trigonal structure with the space group R-3cH and lattice constants a ¼ 4.9537 A˚, b ¼ 4.9537 A˚, and c ¼ 14.0111 A˚ (Rozier et al., 2002). There are six formula units per unit cell. Eight electrons involved into the L2,3-edge transitions are distributed through the 2p
states (six electrons) and 3d orbital (two electrons). All possible electron configurations are listed below in Table 1. 780 Slater determinants from the above table were used to construct the MOs in the [VO6]9 cluster with two different types of the V3+–O2 bond lengths: 1.9026 A˚ (three bonds) and 2.1685 A˚ (three bonds). The Madelung potential was taken into account using the point charges to effectively represent the influence of crystal lattice ions. Mulliken population analysis (Mulliken, 1955) shows that the contributions of the oxygen 2p orbitals to the t2g states are about 4–5%, whereas the same contributions to the eg states are more significant—about 12%. The results of the XANES spectra calculations are shown in Fig. 2. The shape of the spectrum is reproduced well, though there is a relatively small (1–2 eV) blue shift of the calculated spectrum with respect to the experimental. Such overestimation of the energy level positions in the DV-ME calculations was reported earlier (Ogasawara et al., 2004; Brik et al., 2006) and is an intrinsic feature of configuration interaction calculations with insufficient number of Slater determinants. (In other words, we need to increase the number of Slater determinants for quantitatively more accurate calculations.) If the relative positions of the energy levels are more important (as is in the case of the absorption spectrum calculations, when the differences between the pairs of the energy levels are of main interest), this overestimation can be left out of consideration. Analysis of the partial contributions of the excited electron configurations to the calculated spectrum (Fig. 3) shows that the small peak ‘‘a’’ is due to the
Table 1 Distribution of electrons through the V3+ 2p and 3d orbitals in V2O3 (3d2 open shell) 2p1/2
2p3/2
t2g
eg
Number of Slater determinants
Ground state configurations 2 4 2 2 4 1 2 4 0
0 1 2
30 24 6
Excited configurations 2 3 3 2 3 2 2 3 1 2 3 0 1 4 3 1 4 2 1 4 1 1 4 0
0 1 2 3 0 1 2 3
80 240 144 16 40 120 72 8
ARTICLE IN PRESS M.G. Brik et al. / Radiation Physics and Chemistry 75 (2006) 1564–1570
c
Intensity (arb. units)
e
b
f
d
a
510
515
520 Energy, eV
(a)
525
530
14 c
Intensity (arb. units)
12 10
6
d L3
0 510 (b)
(2p3/2)4(t2g)1(eg)2 being mixed together produce two peaks ‘‘d’’ and ‘‘e’’. The highest excited configuration (2p1/2)1(2p3/2)4(t2g)0(eg)3 practically does not contribute to the calculated spectrum, since this configuration corresponds to triple-electron excitation. Polarized vanadium L2,3 spectra in (V0.988Cr0.012)2O3 were recorded by Park et al. (2000) (Fig. 4a). Fig. 4b shows the calculated vanadium L2,3 spectra for s and p polarizations. All the trends within each polarization in the experimental spectrum are confirmed by the theoretical calculations: the peak ‘‘d’’ at around 520 eV is more intensive in p polarization then in s; the peak ‘‘e’’ is more intensive than the ‘‘f’’ peak in p polarization, and less intensive then the ‘‘f’’ peak in s polarization. Also in both experimental and calculated spectra the maxima of the L3 band are slightly shifted with respect to each other in different polarizations. However, the calculated peak ‘‘f’’ in s polarization is more intensive than the same peak in p polarization, what is in contradiction with experimental polarized spectrum. From the calculated spectra, it is possible to estimate the spin–orbit splitting of the vanadium 2p state as the energy separation between the L2 and L3 bands (which is about 8 eV) and the crystal field strength 10 Dq as the splitting of the L2 and L3 bands (which is about 2 eV).
b
4 2
f
e
8
1567
4. Conclusion
L2
a
515
520 Energy, eV
525
530
Fig. 2. V2O3 XANES spectra: (a) experimental results (Zimmermann et al., 1998) and (b) calculated spectrum (this work).
transition to the (2p1/2)2(2p3/2)3(t2g)3(eg)0 configuration; peak ‘‘b’’ arises from the superposition of the (2p1/2)2 (2p3/2)3(t2g)3(eg)0 and (2p1/2)2(2p3/2)3(t2g)2(eg)1 configurations. The most intensive peak ‘‘c’’ and a small peak ‘‘d’’ are mainly a superposition of two configurations: (2p1/2)2 (2p3/2)3(t2g)2(eg)1 and (2p1/2)2(2p3/2)3(t2g)1(eg)2. Finally, four configurations (2p1/2)2(2p3/2)3(t2g)0(eg)3, (2p1/2)1 (2p3/2)4(t2g)3(eg)0, (2p1/2)1(2p3/2)4(t2g)2(eg)1, and (2p1/2)1
In the present paper, the first principles calculations of the vanadium L2,3 XANES spectra in V2O3 have been performed using the first principles multi-electron method developed recently. The method allows to account for the covalency effects by means of introducing the MO concept. The contribution of the oxygen 2p orbitals to the vanadium 3d orbitals was calculated numerically to show the importance of the covalency effects in the considered case. The calculations not only reproduce the shape and relative intensities in the experimental spectra but give an unambiguous assignment of the absorption peaks in terms of the electronic configurations involved into the X-ray absorption. The partial contributions of all excited electron configurations to the calculated XANES spectra were determined and represented in a graphical way. From the calculations, the crystal field splitting of 3d orbitals was found to be about 2 eV, and the spin–orbit splitting of 2p orbitals was estimated as about 8 eV.
ARTICLE IN PRESS M.G. Brik et al. / Radiation Physics and Chemistry 75 (2006) 1564–1570
1568
1
1
(2p1/2)2(2p3/2)3(t2g)3(eg)0
(2p1/2)2(2p3/2)3(t2g)2(eg)1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0 510
515
520
525
530
0 510
515
Energy, eV 1
530
525
530
525
530
(2p1/2)2(2p3/2)3(t2g)0(eg)3
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
515
520
525
530
0 510
515
Energy, eV
520
Energy, eV
1
1
(2p1/2)1(2p3/2)4(t2g)3(eg)0
(2p1/2)1(2p3/2)4(t2g)2(eg)1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0 510
525
1
(2p1/2)2(2p3/2)3(t2g)1(eg)2
0 510
520
Energy, eV
515
520
Energy, eV
525
530
0 510
515
520
Energy, eV
Fig. 3. Partial contributions of all excited configurations (Table 1) to the calculated V2O3 XANES spectrum.
ARTICLE IN PRESS M.G. Brik et al. / Radiation Physics and Chemistry 75 (2006) 1564–1570
1569
1
1
(2p1/2)1(2p3/2)4(t2g)1(eg)2
(2p1/2)1(2p3/2)4(t2g)0(eg)3
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0 510
515
520
525
530
0 510
515
Energy, eV
520
525
530
Energy, eV Fig. 3. (Continued)
4
E || CH
Intensity (arb. units)
E ⊥ CH 3
2
References
515
(a)
520 Energy, eV
525
14 12 Intensity (arb. units)
M.G. Brik appreciates financial support from the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) in a project on computational materials science unit at Kyoto University.
1
0
E||c E||xy
10 8 6 4 2 0 510
(b)
Acknowledgement
515
520 Energy, eV
525
530
Fig. 4. Polarization-dependent V L2,3 XANES spectra: (a) experimental results (Park et al., 2000) and (b) calculated spectrum (this work).
Adachi, H., Ogasawara, K., 2003. Many-electron theory for electronic transition process—its importance inmaterials science. Adv. Quantum Chem. 42, 1–22. Brik, M.G., Tanaka, I., Ishii, T., Ogasawara, K., Nakamura, A., Watanabe, S., 2006. Crystal field analysis of energy level structure of LaF3:Eu3+. J. Alloys Compd. 408–412, 753–756. Gloter, A., Serin, V., Turquat, Ch., Cesari, C., Leroux, Ch., Nihoul, G., 2001. Vanadium valency and hybridization in V-doped hafnia investigated by electron loss spectroscopy. Eur. Phys. J. B 22, 179–186. Mulliken, R.S., 1955. Electronic population analysis on LCAOMO molecular wave functions. J. Chem. Phys. 23, 1833–1840. Ogasawara, K., Iwata, T., Koyama, Y., Ishii, T., Tanaka, I., Adachi, H., 2001. Relativistic cluster calculation of ligandfield multiplet effects on cation L-2, L-3 X-ray absorption edges of SrTiO3, NiO, and CaF2. Phys. Rev. B 64, 1154131–115413-5. Ogasawara, K., Watanabe, S., Sakai, Y., Toyoshima, H., Ishii, T., Brik, M.G., Tanaka, I., 2004. Calculations of complete 4fn and 4fn15d1 energy level schemes of free trivalent rareearth ions. Jpn. J. Appl. Phys. 43, L611–L613. Park, J.H., Tjeng, L.H., Tanaka, A., Allen, J.W., Chen, C.T., Metcalf, P., Honig, J.M., de Croot, F.M.F., Sawatzky,
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G.A., 2000. Spin and orbital occupation and phase transitions in V2O3. Phys. Rev. B 61, 11506–11509. Rozier, P., Ratuszna, A., Galy, J., 2002. Comparative structural and electrical studies of V2O3 and V2xNixO3 (0oxo0.75) solid solution. Z. Anorg. Allg. Chem. 628, 1236–1242. Sugano, S., Tanabe, Y., Kamimura, H., 1970. Multiplets of Transition-Metal Ions in Crystals. Academic Press, New York, London.
Watanabe, S., Kamimura, H., 1989. First-principles calculations of multiplet structures of transition-metal deep impurities in II–VI and III–V semiconductors. Mater. Sci. Eng. B 3, 313–324. Zimmermann, R., Claessen, R., Reinsert, F., Steiner, P., Hu¨fner, S., 1998. Strong hybridization in vanadium oxides: evidence from photoemission and absorption spectroscopy. J. Phys.: Condens. Matter 10, 5697–5716.
Radiation Physics and Chemistry 75 (2006) 1564–1570 www.elsevier.com/locate/radphyschem
First principles calculations of the L2,3-edge XANES spectra for V2O3 M.G. Brika,b,, K. Ogasawarab, T. Ishiib, H. Ikenoc, I. Tanakac a
Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4, Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan b School of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda, Hyogo 669-1337, Japan c Department of Materials Science & Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan Accepted 27 July 2005
Abstract Vanadium L2,3-edge XANES spectra have been calculated for V2O3 crystal. A fully relativistic first-principles many electron method based on the numerical solution of the Dirac equation was used. The key-points of the method are: (i) use of the molecular orbitals (MO); (ii) absence of any fitting parameters; (iii) possibility to apply to any ion in any symmetry; (iv) possibility of numerical analysis of the many-electron states in terms of the MO-based Slater determinants. The calculated spectra are in good agreement with experimental ones available in the literature, including the absolute values of the transition energy and the shape of the absorption bands. Experimental trends in the polarized XANES spectra of V2O3 are reproduced. r 2006 Elsevier Ltd. All rights reserved. Keywords: L2,3-edge; Xanes spectra; Vanadium oxides
1. Introduction During last several decades, 3d transitional elements have been a subject to many thorough investigations due to their numerous applications. Among various experimental methods, X-ray absorption near edge structure (XANES) spectroscopy is a very powerful method of gaining knowledge about the electronic structure of the transitional metal ions. The transition-metal L2,3-edge Corresponding author. Fukui Institute for Fundamental
Chemistry, Kyoto University, 34-4, Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan. Tel.: +81 75 7117708; fax: +81 75 7814757. E-mail addresses: [email protected], [email protected] (M.G. Brik).
XANES spectra mainly correspond to the electric-dipole transitions between the fully occupied 2p-core levels and partially filled 3d electron shell. Coulomb and exchange interactions between the 2p and 3d electrons give rise to structured XANES bands, detailed analysis of which can give information about the occupied and unoccupied states, energy level splitting (including the splittings caused by the spin–orbit interaction and crystal field), configuration interaction, splitting of the core and outer electron shells, etc. Fast development of the materials science and search for new functional compounds for various applications imply the need for detailed knowledge of the electronic structure of chemical elements whose properties or special features are supposed to be made use of. Quantum mechanical calculations serve this purpose
0969-806X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2005.07.055
ARTICLE IN PRESS M.G. Brik et al. / Radiation Physics and Chemistry 75 (2006) 1564–1570
very well, since they allow not only for precise description of physical processes which occur in wellknown materials, but for prediction and design of new compounds whose properties have not been studied experimentally so far. In the present paper, we report on the calculations of the L2,3-edge XANES spectra in the V2O3 crystal. Experimental studies of the vanadium oxides XANES spectra have been reported previously by Zimmermann et al. (1998) and Gloter et al. (2001). In the above oxide vanadium ions occupy octahedral positions. In the octahedral crystal field the 3d orbitals split into t2g and eg orbitals with the former being the lower state and the latter being the higher with the energy separation of 10 Dq (where Dq is referred to as the crystal field strength (Sugano et al., 1970). The 2p level is split by spin–orbit interaction into 2p1/2 and 2p3/2 (or L2 and L3, respectively) with the subscripts representing the quantum number of the total angular momentum. After absorbing an X-ray quantum, an electron from the 2p level is excited into the t2g or eg states, and the schematic diagram of this excitation looks as shown in Fig. 1a, where one-electron transitions between the 2p and 3d states are shown by vertical arrows. As follows from the figure, the energy separation between the L2 and L3 bands is mainly due to the spin–orbit splitting of 2p-orbitals, whereas the splitting within each band is caused by the crystal field splitting of 3d orbitals. However, as was shown by Adachi and Ogasawara (2003) such one-electron consideration is insufficient to produce good agreement between the calculated and experimental spectra, and more elaborated approach taking into account the interaction between the multiplets arising from all the possible electron configuration (Fig. 1b) was proposed. It also was shown that the proper consideration of the multiplets interaction leads
(a)
1565
to the significant changes in the intensity ratio and improves the agreement between theory and experiment drastically.
2. Method of calculations We apply the fully relativistic discrete-variational multi-electron (DV-ME) method, which is a configuration-interaction (CI) calculation program using the fourcomponent fully relativistic molecular spinors obtained by the discrete-variational Dirac–Slater (DV–DS) cluster calculations, developed by Ogasawara et al. (2001). The method is based on the numerical solution of the Dirac equation, and its main advantages are as follows: (1) the first-principles method without any fitting parameters (this is especially important for the development of new materials and prediction of their expected properties); (2) very wide area of applications: to any atom or ion in any symmetry from spherical to C1 for any energy interval from IR to X-ray; (3) possibility to take into account all effects of chemical bond formation, exchange and configuration interaction by numerical integration; (4) potential to calculate a wide variety of physical properties (such as transition probabilities, for example) using the obtained wave functions. All relativistic effects are taken into account automatically. The key idea of the method is that the molecular orbitals (MO) are used throughout the calculations rather than atomic wave functions. This makes the effects of covalency taken into account explicitly. The many-electron wave functions are expressed as linear combination of the MO-based Slater determinants and the absorption peaks assignment can be done in terms of these Slater determinants. The relativistic many-electron Hamiltonian is expressed as
(b)
Fig. 1. Schematic representation of one-electron transitions corresponding to the L2 and L3 absorption bands in the XANES spectra: (a) one-elecron picture; (b) many-electron picture; n and m correspond to the number of 3d-electrons distributed through t2g and eg orbitals.
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M.G. Brik et al. / Radiation Physics and Chemistry 75 (2006) 1564–1570
(in atomic units) " n X X capi þ bc2 H¼
Zn jr Rn j i n i¼1 # n X n X X Zeff 1 m þ . þV 0 ðri Þ þ jr R j rj j jr i m i m i¼1 j4i
ð1Þ
where a, b are the Dirac matrices, c the velocity of light, ri, pi the position and the momentum operator of the ith electron, Zn and Rn the charge and position of the vth nucleus, Zeff m and Rm the effective charge and position of the mth ion outside the model cluster, n the number of explicitly treated electrons. V0(ri) is the potential from the remaining electrons (Watanabe and Kamimura, 1989): Z G 0 r0 ðr Þ 0 dr V0 ¼ jr r0 j G G 3 r ðrÞV xc frG ðrÞg rG 0 ðrÞV xc fr0 ðrÞg þ G 4 r 1 ð rÞ ð2Þ V xc frG 1 ðrÞg , G where rG, rG 1 , r0 represent the charge density of all electrons, that of the explicitly treated electrons and that of the remaining electrons, respectively, and Vxc is the Slater’s Xa potential. The superscript G indicates the values for the ground state. Diagonalization of the Hamiltonian (1) provides a complete electron energy level scheme. Since the eigenfunctions are also obtained, the absorption spectra (for electric dipole, electric quadrupole, and magnetic dipole transitions) can be obtained in a straightforward manner after calculating appropriate matrix elements. For example, in the case of electric dipole transitions the oscillator strength (averaged over all possible polarizations) is calculated as follows: * + 2 X n 2 I if ¼ ðE f E i Þ Cf rk Ci , (3) k¼1 3
Ci and Cf are the initial and final states with energies of Ei and Ef, respectively. In the case of the XANES spectra only those electrons occupying the MO mainly composed of 2p and 3d states in the ground state are treated explicitly, since they are involved into the absorption transitions.
3. Results of calculations and discussion V2O3 has a trigonal structure with the space group R-3cH and lattice constants a ¼ 4.9537 A˚, b ¼ 4.9537 A˚, and c ¼ 14.0111 A˚ (Rozier et al., 2002). There are six formula units per unit cell. Eight electrons involved into the L2,3-edge transitions are distributed through the 2p
states (six electrons) and 3d orbital (two electrons). All possible electron configurations are listed below in Table 1. 780 Slater determinants from the above table were used to construct the MOs in the [VO6]9 cluster with two different types of the V3+–O2 bond lengths: 1.9026 A˚ (three bonds) and 2.1685 A˚ (three bonds). The Madelung potential was taken into account using the point charges to effectively represent the influence of crystal lattice ions. Mulliken population analysis (Mulliken, 1955) shows that the contributions of the oxygen 2p orbitals to the t2g states are about 4–5%, whereas the same contributions to the eg states are more significant—about 12%. The results of the XANES spectra calculations are shown in Fig. 2. The shape of the spectrum is reproduced well, though there is a relatively small (1–2 eV) blue shift of the calculated spectrum with respect to the experimental. Such overestimation of the energy level positions in the DV-ME calculations was reported earlier (Ogasawara et al., 2004; Brik et al., 2006) and is an intrinsic feature of configuration interaction calculations with insufficient number of Slater determinants. (In other words, we need to increase the number of Slater determinants for quantitatively more accurate calculations.) If the relative positions of the energy levels are more important (as is in the case of the absorption spectrum calculations, when the differences between the pairs of the energy levels are of main interest), this overestimation can be left out of consideration. Analysis of the partial contributions of the excited electron configurations to the calculated spectrum (Fig. 3) shows that the small peak ‘‘a’’ is due to the
Table 1 Distribution of electrons through the V3+ 2p and 3d orbitals in V2O3 (3d2 open shell) 2p1/2
2p3/2
t2g
eg
Number of Slater determinants
Ground state configurations 2 4 2 2 4 1 2 4 0
0 1 2
30 24 6
Excited configurations 2 3 3 2 3 2 2 3 1 2 3 0 1 4 3 1 4 2 1 4 1 1 4 0
0 1 2 3 0 1 2 3
80 240 144 16 40 120 72 8
ARTICLE IN PRESS M.G. Brik et al. / Radiation Physics and Chemistry 75 (2006) 1564–1570
c
Intensity (arb. units)
e
b
f
d
a
510
515
520 Energy, eV
(a)
525
530
14 c
Intensity (arb. units)
12 10
6
d L3
0 510 (b)
(2p3/2)4(t2g)1(eg)2 being mixed together produce two peaks ‘‘d’’ and ‘‘e’’. The highest excited configuration (2p1/2)1(2p3/2)4(t2g)0(eg)3 practically does not contribute to the calculated spectrum, since this configuration corresponds to triple-electron excitation. Polarized vanadium L2,3 spectra in (V0.988Cr0.012)2O3 were recorded by Park et al. (2000) (Fig. 4a). Fig. 4b shows the calculated vanadium L2,3 spectra for s and p polarizations. All the trends within each polarization in the experimental spectrum are confirmed by the theoretical calculations: the peak ‘‘d’’ at around 520 eV is more intensive in p polarization then in s; the peak ‘‘e’’ is more intensive than the ‘‘f’’ peak in p polarization, and less intensive then the ‘‘f’’ peak in s polarization. Also in both experimental and calculated spectra the maxima of the L3 band are slightly shifted with respect to each other in different polarizations. However, the calculated peak ‘‘f’’ in s polarization is more intensive than the same peak in p polarization, what is in contradiction with experimental polarized spectrum. From the calculated spectra, it is possible to estimate the spin–orbit splitting of the vanadium 2p state as the energy separation between the L2 and L3 bands (which is about 8 eV) and the crystal field strength 10 Dq as the splitting of the L2 and L3 bands (which is about 2 eV).
b
4 2
f
e
8
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4. Conclusion
L2
a
515
520 Energy, eV
525
530
Fig. 2. V2O3 XANES spectra: (a) experimental results (Zimmermann et al., 1998) and (b) calculated spectrum (this work).
transition to the (2p1/2)2(2p3/2)3(t2g)3(eg)0 configuration; peak ‘‘b’’ arises from the superposition of the (2p1/2)2 (2p3/2)3(t2g)3(eg)0 and (2p1/2)2(2p3/2)3(t2g)2(eg)1 configurations. The most intensive peak ‘‘c’’ and a small peak ‘‘d’’ are mainly a superposition of two configurations: (2p1/2)2 (2p3/2)3(t2g)2(eg)1 and (2p1/2)2(2p3/2)3(t2g)1(eg)2. Finally, four configurations (2p1/2)2(2p3/2)3(t2g)0(eg)3, (2p1/2)1 (2p3/2)4(t2g)3(eg)0, (2p1/2)1(2p3/2)4(t2g)2(eg)1, and (2p1/2)1
In the present paper, the first principles calculations of the vanadium L2,3 XANES spectra in V2O3 have been performed using the first principles multi-electron method developed recently. The method allows to account for the covalency effects by means of introducing the MO concept. The contribution of the oxygen 2p orbitals to the vanadium 3d orbitals was calculated numerically to show the importance of the covalency effects in the considered case. The calculations not only reproduce the shape and relative intensities in the experimental spectra but give an unambiguous assignment of the absorption peaks in terms of the electronic configurations involved into the X-ray absorption. The partial contributions of all excited electron configurations to the calculated XANES spectra were determined and represented in a graphical way. From the calculations, the crystal field splitting of 3d orbitals was found to be about 2 eV, and the spin–orbit splitting of 2p orbitals was estimated as about 8 eV.
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1
1
(2p1/2)2(2p3/2)3(t2g)3(eg)0
(2p1/2)2(2p3/2)3(t2g)2(eg)1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0 510
515
520
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530
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(2p1/2)2(2p3/2)3(t2g)0(eg)3
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520
Energy, eV
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1
(2p1/2)1(2p3/2)4(t2g)3(eg)0
(2p1/2)1(2p3/2)4(t2g)2(eg)1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0 510
525
1
(2p1/2)2(2p3/2)3(t2g)1(eg)2
0 510
520
Energy, eV
515
520
Energy, eV
525
530
0 510
515
520
Energy, eV
Fig. 3. Partial contributions of all excited configurations (Table 1) to the calculated V2O3 XANES spectrum.
ARTICLE IN PRESS M.G. Brik et al. / Radiation Physics and Chemistry 75 (2006) 1564–1570
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(2p1/2)1(2p3/2)4(t2g)1(eg)2
(2p1/2)1(2p3/2)4(t2g)0(eg)3
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Energy, eV Fig. 3. (Continued)
4
E || CH
Intensity (arb. units)
E ⊥ CH 3
2
References
515
(a)
520 Energy, eV
525
14 12 Intensity (arb. units)
M.G. Brik appreciates financial support from the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) in a project on computational materials science unit at Kyoto University.
1
0
E||c E||xy
10 8 6 4 2 0 510
(b)
Acknowledgement
515
520 Energy, eV
525
530
Fig. 4. Polarization-dependent V L2,3 XANES spectra: (a) experimental results (Park et al., 2000) and (b) calculated spectrum (this work).
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