- Email: [email protected]
Electronic structure properties of UO2 as a Mott insulator
Accepted Manuscript
Electronic Structure Properties of UO2 as a Mott Insulator Samira Sheykhi, Mahmoud Payami PII: DOI: Reference:
S0921-4534(17)30294-0 10.1016/j.physc.2018.02.028 PHYSC 1253285
To appear in:
Physica C: Superconductivity and its applications
Received date: Accepted date:
13 July 2017 28 February 2018
Please cite this article as: Samira Sheykhi, Mahmoud Payami, Electronic Structure Properties of UO2 as a Mott Insulator, Physica C: Superconductivity and its applications (2018), doi: 10.1016/j.physc.2018.02.028
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Highlights • -LDA+U method as well as the hybrid-functional-based HSE-ACE method predict correct insulating behaviors for UO2.
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• -In LDA+U calculations one needs to avoid metastable states, while there is no need to such tricks in HSE-ACE method.
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• -The predicted band gap usig HSE-ACE is in a better agreement with experiment than LDA+U ones.
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ACCEPTED MANUSCRIPT
Electronic Structure Properties of UO2 as a Mott Insulator
a Physics
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Samira Sheykhi, Mahmoud Payami∗ & Accelerators Research School, Nuclear Science and Technology Research Institute, P. O. Box 14395-836, Tehran, Iran
Abstract
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In this work using the density functional theory (DFT), we have studied the structural, electronic and magnetic properties of uranium dioxide with antiferromagnetic 1k-, 2k-, and 3k-order structures. Ordinary approximations in DFT, such as the local density approximation (LDA) or generalized gradient approximation (GGA), usually predict incorrect metallic behaviors for this strongly correlated electron system. Using Hubbard term correction for f-electrons, LDA+U method, as well as using the screened Heyd-Scuseria-Ernzerhof (HSE) hybrid functional for the exchange-correlation (XC), we have obtained the correct ground-state behavior as an insulator, with band gaps in good agreement with experiment.
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Keywords: Mott insulator; Antiferromagnetic; Uranium dioxide; Density functional theory; Hybrid functional
1. Introduction
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Urania (UO2) is one of the most common fuels used in nuclear power reactors, and understanding its properties, both experimentally [1] and theoretically [2, 3, 4, 5], has been one of the hot topics of research activity for several years. The crystal structure of urania has been experimentally determined to be an antiferromagnetic 3k-order Mott insulator at temperatures below 30 ◦ K, in which the uranium atoms are located in an fcc lattice with a=b=c=5.47˚ A, and the oxygen atoms are located at positions with symmetry P a¯ 3 [6]. In Fig 1(a)-(c), we have shown the antiferromagnetic 1k-, 2k-, and 3k-order structures. DFT is one of the most powerful methods for calculation of electronic structure properties of materials [7, 8]. Application of ordinary DFT, using LDA or GGA for the exchange-correlation functional, incorrectly predicts a metal behavior (see Fig 2) for urania, while it is known as a Mott insulator solid. This behavior is due to the localized “d” and “f” electrons that in ordinary DFT
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∗ Corresponding
author Email address: [email protected] (Mahmoud Payami)
Preprint submitted to Journal of Physica C: Superconductivity and its ApplicationsMarch 6, 2018
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ACCEPTED MANUSCRIPT
Figure 1: Uo2 in (a) 1k-order, (b) 2k-order, and (c) 3k-order antiferromagnetic structures.
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2. Calculation methods
All calculations are based on DFT and the solution of the Kohn-Sham equations [8] using the Quantum-ESPRESSO code package [12]. For the atoms U and O, we have used the pseudopotentials U.pz-mt-fhi.UPF and O.pz-mt-fhi.UPF which are available at http://www.quantum-espresso.org. By convergency tests, the kinetic energy cutoffs for the plane-wave bases are chosen as 40 and 160 Ry for the wave functions and charge density, respectively. In HSE calculations, the plane-wave cutoff for expansion of the Fock exchange operator is taken as 80 Ry. For the Brillouin-zone integrations, a 4 × 4 × 4 grid with a shift were used. In LDA+U calculations, we have used the values 4.5 and 0.54 eV for U and J parameters, respectively as determined by other works [13, 14]. All geometries are fully optimized for pressures on unit cells to within 1kPa, and forces on atoms to within 1mRy/a.u.
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calculations are accounted as nearly delocalized ones which is appropriate for s-p bonded solid materials. One of the methods to rectify this deficiency is the use of DFT+U method [9] in which a Hubbard term for the localized “f” electrons is added to the Hamiltonian, and this correction leads to an opening of a gap, leading to an insulating properties. The method is somewhat tricky and to obtain the true ground state, one has to avoid metastable states [2]. Another method, which is rather new and more appropriate, is using the screened HSE hybrid functional [10] which partially uses the exact exchange operator. Using this orbital-dependent functional is computationally very expensive and the newly formulated Adaptively Compressed Exchange (ACE) Operator [11] significantly reduces the computational efforts while keeping its accuracy. In this work, we have used LDA and LDA+U methods for 1k, 2k, and 3k antiferromagnetic configurations. The HSE-ACE method is applied only to the 1k-order. All LDA+U results as well as the HSE-ACE, correctly predict insulating behaviors for UO2 .
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(a) LDA+U, 1k
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(ε-εF) (eV)
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Figure 2: Density of states: (a)-(c) for LDA+U, (d) for HSE, (e)-(g) for LDA. The zero of energy is identified as the Fermi level.
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The LDA calculations for all UO2 antiferromagnetic structures lead to metallic states, as are shown by density-of-states (DOS) plots in Figs. 2(e)-(g). The LDA+U calculations for the 1k-order configuration, led to a small deformation in c-axis corresponding to a tetragonal structure with a=b=5.49, and c=5.44˚ A, with a gap of 1.5 eV. As to 2k-order configuration, locating the ground-state in LDA+U was somewhat tricky in that one should avoid metastable states, and the true ground state was achieved by some modifications in the occupation matrix. The results show a similar deformation as in 1k-order but with a=b=5.50, and c=5.49˚ A, with 1.9 eV gap. For 3k-order, the optimization of the structure maintained the cubic structure with a=b=c=5.50˚ A, but with a small Jahn-Teller distortion for the oxygen atoms (0.0153˚ Ain < 111 > direction) in good agreement with experiment. The energy gap was found to be 1.7 eV, in good agreement with the experiment (2.1 eV). Here, locating the true ground state was also tricky as in 2k case. Finally, the HSE-ACE calculations for the 1k-order led to a similar tetragonal structure with a=b=5.53, and c=5.54˚ A. In this calculation, the c-axis is slightly elongated in contrast to our LDA+U results. It has been shown that the c < a or c > a behavior depends on the choice of Hubbard U and J values [15]. This calculation relulted in a gap of 2.02 eV which is quite in good agreement with experiment as compared with the LDA+U results. The DOS plots for LDA+U and HSE-ACE are shown in Figs. 2(a)-(d), respectively. It should be mentioned that the lower band-gap shown in Fig 2(d) compared to those of
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3. Results and Discussions
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LDA+U (whereas it should be higher) is due to low-density k-mesh for producing the DOS-plot. We have presented the HSE-ACE plot only to show that HSE correctly reproduce the insulating behavior; the band gap is simply read off from the calculated Kohn-Sham eigenvalues. 4. Conclusions
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LDA or GGA calculations for UO2 lead to an incorrect metallic behavior. This is corrected using the LDA+U method and using HSE hybrid functional. The 1k- and 2k-order antiferromagnetic structures lead to a small deformation in the c-axis, while the 3k-order LDA+U preserves the cubic symmetry for U atoms even though the O atoms are slightly distorted along the < 111 > direction. All LDA+U and HSE calculations led to correct insulating behaviors. More interestingly, the gap reproduced by HSE calculation is in a very good agreement with experimental value. Acknowledgements
This work is part of research program in Theoretical and Computational Physics Group, NSTRI, AEOI.
[1] S. Wilkins, R. Caciuffo, C. Detlefs, J. Rebizant, E. Colineau, F. Wastin, G. Lander, Direct observation of electric-quadrupolar order in u o 2, Physical Review B 73 (6) (2006) 060406.
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References
[2] M. Freyss, B. Dorado, M. Bertolus, G. Jomard, E. Vathonne, P. Garcia, B. Amadon, 4 scientific highlight of the month. [3] R. Laskowski, G. K. Madsen, P. Blaha, K. Schwarz, Magnetic structure and electric-field gradients of uranium dioxide: An ab initio study, Physical Review B 69 (14) (2004) 140408.
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[4] S. Peng-Fei, D. Zhen-Hong, Z. Xiao-Ling, Z. Yin-Chang, Electronic structure and optical properties in uranium dioxide: the first principle calculations, Chinese Physics Letters 32 (7) (2015) 077101. [5] J. P. Allen, G. W. Watson, Occupation matrix control of d-and f-electron localisations using dft+ u, Physical Chemistry Chemical Physics 16 (39) (2014) 21016–21031.
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[6] M. Idiri, T. Le Bihan, S. Heathman, J. Rebizant, Behavior of actinide dioxides under pressure: Uo2 and tho2, Physical Review B 70 (1) (2004) 014113. [7] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Physical review 136 (3B) (1964) B864. 5
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[8] W. Kohn, L. J. Sham, Self-consistent equations including exchange and correlation effects, Physical review 140 (4A) (1965) A1133.
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[9] A. Liechtenstein, V. Anisimov, J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in mott-hubbard insulators, Physical Review B 52 (8) (1995) R5467.
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[10] J. Heyd, G. E. Scuseria, M. Ernzerhof, Hybrid functionals based on a screened coulomb potential, The Journal of Chemical Physics 118 (18) (2003) 8207–8215. [11] L. Lin, Adaptively compressed exchange operator, Journal of chemical theory and computation 12 (5) (2016) 2242–2249.
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[12] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, et al., Quantum espresso: a modular and open-source software project for quantum simulations of materials, Journal of physics: Condensed matter 21 (39) (2009) 395502. [13] T. Yamazaki, A. Kotani, Systematic analysis of 4 f core photoemission spectra in actinide oxides, Journal of the Physical Society of Japan 60 (1) (1991) 49–52.
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[14] A. Kotani, T. Yamazaki, Systematic analysis of core photoemission spectra for actinide di-oxides and rare-earth sesqui-oxides, Progress of Theoretical Physics Supplement 108 (1992) 117–131.
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[15] J. Yu, R. Devanathan, W. J. Weber, First-principles study of defects and phase transition in uo2, Journal of Physics: Condensed Matter 21 (43) (2009) 435401.
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Electronic Structure Properties of UO2 as a Mott Insulator Samira Sheykhi, Mahmoud Payami PII: DOI: Reference:
S0921-4534(17)30294-0 10.1016/j.physc.2018.02.028 PHYSC 1253285
To appear in:
Physica C: Superconductivity and its applications
Received date: Accepted date:
13 July 2017 28 February 2018
Please cite this article as: Samira Sheykhi, Mahmoud Payami, Electronic Structure Properties of UO2 as a Mott Insulator, Physica C: Superconductivity and its applications (2018), doi: 10.1016/j.physc.2018.02.028
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Highlights • -LDA+U method as well as the hybrid-functional-based HSE-ACE method predict correct insulating behaviors for UO2.
CR IP T
• -In LDA+U calculations one needs to avoid metastable states, while there is no need to such tricks in HSE-ACE method.
AC
CE
PT
ED
M
AN US
• -The predicted band gap usig HSE-ACE is in a better agreement with experiment than LDA+U ones.
1
ACCEPTED MANUSCRIPT
Electronic Structure Properties of UO2 as a Mott Insulator
a Physics
CR IP T
Samira Sheykhi, Mahmoud Payami∗ & Accelerators Research School, Nuclear Science and Technology Research Institute, P. O. Box 14395-836, Tehran, Iran
Abstract
M
AN US
In this work using the density functional theory (DFT), we have studied the structural, electronic and magnetic properties of uranium dioxide with antiferromagnetic 1k-, 2k-, and 3k-order structures. Ordinary approximations in DFT, such as the local density approximation (LDA) or generalized gradient approximation (GGA), usually predict incorrect metallic behaviors for this strongly correlated electron system. Using Hubbard term correction for f-electrons, LDA+U method, as well as using the screened Heyd-Scuseria-Ernzerhof (HSE) hybrid functional for the exchange-correlation (XC), we have obtained the correct ground-state behavior as an insulator, with band gaps in good agreement with experiment.
ED
Keywords: Mott insulator; Antiferromagnetic; Uranium dioxide; Density functional theory; Hybrid functional
1. Introduction
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Urania (UO2) is one of the most common fuels used in nuclear power reactors, and understanding its properties, both experimentally [1] and theoretically [2, 3, 4, 5], has been one of the hot topics of research activity for several years. The crystal structure of urania has been experimentally determined to be an antiferromagnetic 3k-order Mott insulator at temperatures below 30 ◦ K, in which the uranium atoms are located in an fcc lattice with a=b=c=5.47˚ A, and the oxygen atoms are located at positions with symmetry P a¯ 3 [6]. In Fig 1(a)-(c), we have shown the antiferromagnetic 1k-, 2k-, and 3k-order structures. DFT is one of the most powerful methods for calculation of electronic structure properties of materials [7, 8]. Application of ordinary DFT, using LDA or GGA for the exchange-correlation functional, incorrectly predicts a metal behavior (see Fig 2) for urania, while it is known as a Mott insulator solid. This behavior is due to the localized “d” and “f” electrons that in ordinary DFT
AC
10
∗ Corresponding
author Email address: [email protected] (Mahmoud Payami)
Preprint submitted to Journal of Physica C: Superconductivity and its ApplicationsMarch 6, 2018
CR IP T
ACCEPTED MANUSCRIPT
Figure 1: Uo2 in (a) 1k-order, (b) 2k-order, and (c) 3k-order antiferromagnetic structures.
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2. Calculation methods
All calculations are based on DFT and the solution of the Kohn-Sham equations [8] using the Quantum-ESPRESSO code package [12]. For the atoms U and O, we have used the pseudopotentials U.pz-mt-fhi.UPF and O.pz-mt-fhi.UPF which are available at http://www.quantum-espresso.org. By convergency tests, the kinetic energy cutoffs for the plane-wave bases are chosen as 40 and 160 Ry for the wave functions and charge density, respectively. In HSE calculations, the plane-wave cutoff for expansion of the Fock exchange operator is taken as 80 Ry. For the Brillouin-zone integrations, a 4 × 4 × 4 grid with a shift were used. In LDA+U calculations, we have used the values 4.5 and 0.54 eV for U and J parameters, respectively as determined by other works [13, 14]. All geometries are fully optimized for pressures on unit cells to within 1kPa, and forces on atoms to within 1mRy/a.u.
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30
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calculations are accounted as nearly delocalized ones which is appropriate for s-p bonded solid materials. One of the methods to rectify this deficiency is the use of DFT+U method [9] in which a Hubbard term for the localized “f” electrons is added to the Hamiltonian, and this correction leads to an opening of a gap, leading to an insulating properties. The method is somewhat tricky and to obtain the true ground state, one has to avoid metastable states [2]. Another method, which is rather new and more appropriate, is using the screened HSE hybrid functional [10] which partially uses the exact exchange operator. Using this orbital-dependent functional is computationally very expensive and the newly formulated Adaptively Compressed Exchange (ACE) Operator [11] significantly reduces the computational efforts while keeping its accuracy. In this work, we have used LDA and LDA+U methods for 1k, 2k, and 3k antiferromagnetic configurations. The HSE-ACE method is applied only to the 1k-order. All LDA+U results as well as the HSE-ACE, correctly predict insulating behaviors for UO2 .
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(a) LDA+U, 1k
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Figure 2: Density of states: (a)-(c) for LDA+U, (d) for HSE, (e)-(g) for LDA. The zero of energy is identified as the Fermi level.
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The LDA calculations for all UO2 antiferromagnetic structures lead to metallic states, as are shown by density-of-states (DOS) plots in Figs. 2(e)-(g). The LDA+U calculations for the 1k-order configuration, led to a small deformation in c-axis corresponding to a tetragonal structure with a=b=5.49, and c=5.44˚ A, with a gap of 1.5 eV. As to 2k-order configuration, locating the ground-state in LDA+U was somewhat tricky in that one should avoid metastable states, and the true ground state was achieved by some modifications in the occupation matrix. The results show a similar deformation as in 1k-order but with a=b=5.50, and c=5.49˚ A, with 1.9 eV gap. For 3k-order, the optimization of the structure maintained the cubic structure with a=b=c=5.50˚ A, but with a small Jahn-Teller distortion for the oxygen atoms (0.0153˚ Ain < 111 > direction) in good agreement with experiment. The energy gap was found to be 1.7 eV, in good agreement with the experiment (2.1 eV). Here, locating the true ground state was also tricky as in 2k case. Finally, the HSE-ACE calculations for the 1k-order led to a similar tetragonal structure with a=b=5.53, and c=5.54˚ A. In this calculation, the c-axis is slightly elongated in contrast to our LDA+U results. It has been shown that the c < a or c > a behavior depends on the choice of Hubbard U and J values [15]. This calculation relulted in a gap of 2.02 eV which is quite in good agreement with experiment as compared with the LDA+U results. The DOS plots for LDA+U and HSE-ACE are shown in Figs. 2(a)-(d), respectively. It should be mentioned that the lower band-gap shown in Fig 2(d) compared to those of
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3. Results and Discussions
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LDA+U (whereas it should be higher) is due to low-density k-mesh for producing the DOS-plot. We have presented the HSE-ACE plot only to show that HSE correctly reproduce the insulating behavior; the band gap is simply read off from the calculated Kohn-Sham eigenvalues. 4. Conclusions
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LDA or GGA calculations for UO2 lead to an incorrect metallic behavior. This is corrected using the LDA+U method and using HSE hybrid functional. The 1k- and 2k-order antiferromagnetic structures lead to a small deformation in the c-axis, while the 3k-order LDA+U preserves the cubic symmetry for U atoms even though the O atoms are slightly distorted along the < 111 > direction. All LDA+U and HSE calculations led to correct insulating behaviors. More interestingly, the gap reproduced by HSE calculation is in a very good agreement with experimental value. Acknowledgements
This work is part of research program in Theoretical and Computational Physics Group, NSTRI, AEOI.
[1] S. Wilkins, R. Caciuffo, C. Detlefs, J. Rebizant, E. Colineau, F. Wastin, G. Lander, Direct observation of electric-quadrupolar order in u o 2, Physical Review B 73 (6) (2006) 060406.
ED
85
M
References
[2] M. Freyss, B. Dorado, M. Bertolus, G. Jomard, E. Vathonne, P. Garcia, B. Amadon, 4 scientific highlight of the month. [3] R. Laskowski, G. K. Madsen, P. Blaha, K. Schwarz, Magnetic structure and electric-field gradients of uranium dioxide: An ab initio study, Physical Review B 69 (14) (2004) 140408.
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[4] S. Peng-Fei, D. Zhen-Hong, Z. Xiao-Ling, Z. Yin-Chang, Electronic structure and optical properties in uranium dioxide: the first principle calculations, Chinese Physics Letters 32 (7) (2015) 077101. [5] J. P. Allen, G. W. Watson, Occupation matrix control of d-and f-electron localisations using dft+ u, Physical Chemistry Chemical Physics 16 (39) (2014) 21016–21031.
AC
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[6] M. Idiri, T. Le Bihan, S. Heathman, J. Rebizant, Behavior of actinide dioxides under pressure: Uo2 and tho2, Physical Review B 70 (1) (2004) 014113. [7] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Physical review 136 (3B) (1964) B864. 5
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[8] W. Kohn, L. J. Sham, Self-consistent equations including exchange and correlation effects, Physical review 140 (4A) (1965) A1133.
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[9] A. Liechtenstein, V. Anisimov, J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in mott-hubbard insulators, Physical Review B 52 (8) (1995) R5467.
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[10] J. Heyd, G. E. Scuseria, M. Ernzerhof, Hybrid functionals based on a screened coulomb potential, The Journal of Chemical Physics 118 (18) (2003) 8207–8215. [11] L. Lin, Adaptively compressed exchange operator, Journal of chemical theory and computation 12 (5) (2016) 2242–2249.
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AN US
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[12] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, et al., Quantum espresso: a modular and open-source software project for quantum simulations of materials, Journal of physics: Condensed matter 21 (39) (2009) 395502. [13] T. Yamazaki, A. Kotani, Systematic analysis of 4 f core photoemission spectra in actinide oxides, Journal of the Physical Society of Japan 60 (1) (1991) 49–52.
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[14] A. Kotani, T. Yamazaki, Systematic analysis of core photoemission spectra for actinide di-oxides and rare-earth sesqui-oxides, Progress of Theoretical Physics Supplement 108 (1992) 117–131.
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[15] J. Yu, R. Devanathan, W. J. Weber, First-principles study of defects and phase transition in uo2, Journal of Physics: Condensed Matter 21 (43) (2009) 435401.
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