Alternative Title線形応答理論による有効オンサイトクーロン相互作用の第一原理計算と金属錯体への応用
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In investigations on electronic structures of correlated materials such as transition-metal oxides, are-earth compounds, and organometallic molecules, first-principles calculations based on density functional theory (DFT) play a central role. However, there is a problem remaining to deal with correlation effects in the DFT for correlated materials. On a practical level, DFT+U method that introduces Hubbard-model parameters to represent screened on-site Coulomb (U) and exchange (J) interaction is one of the powerful and conventional tools suitable or calculations of large systems without expensive costs. The values of U and J are commonly chosen to match experimental observations, but optimal values depend on which exchange- correlation functional is used and the calculated material properties are very sensitive to values of on-site U and J even in the ground state. More recently the parameters have been calculated directly from first-principles calculations, but they vary over wide ranges of values even for the same ionic state in a given material. Unfortunately, this implies that choosing """"good"""" values is problematic. In order to address this issue, here, non-empirical method for deriving scaled +U parameters is developed and applied to the prototypical materials of correlated transition-metal monoxides and organometallic molecules. This dissertation consists of five chapters. After an introduction to electronic structures of correlated materials and general failures of the DFT-based first-principles calculations in chapter one, methodologies of the DFT and linear response approach to estimate an effective on-site Coulomb interaction, Ueff , of correlated elements are described in chapter two, where the Ueff values determined from the second derivative of the total energy with respect to the occupation numbers of localized d-electrons within the linear response theory. All calculations were carried out by means of the all-electron full-potential linearized augmented plane wave (FLAPW) method. Chapter three devotes to an application of this approach to the transition-metal monoxides, TMO (TM ＝ Mn, Fe, Co, and Ni), where the variation of Ueff values by changing the muffin-tin (MT) sphere radius was examined. It is found that the Ueff value depends strongly on MT sphere size by more than 2 3 eV in all systems, for example, in MnO when the MT radius is 2.0 bohr, the Ueff value results in 10.1 eV but it decreases to 7.2 eV as the MT radius increases to 2.7 bohr. The same trend in the Ueff values was confirmed in other considered oxide systems. However, despite this large variation, essentially identical valence band structures are obtained, and I found an approximate scaling of Ueff with regard to size of MT sphere. Thus, although simple transferability of the Ueff value among different calculation methods is not allowed, guidelines for estimating Ueff are proposed. In chapter four, this approach was applied to ground-state electronic structure calculations of correlated organometallic metallocens, TMCp2 (TM ＝ V, Cr, Mn, Fe, Co, and Ni). In these complexes, however, an additional difficulty intrinsically related to various electronic configurations of d electrons that nearly degenerate is raised, which may numerically trap in one of multiple local energy minima corresponding to meta-stable electronic configurations, instead of a global minimum of the ground state. The changes due to the presence of the ligand field of molecules further complicate theoretical analysis so that the DFT+U calculations may fail to search a ground-state electronic configuration truly. To overcome this problem, I implemented the constraint DFT+U approach that controls electronic configurations by introducing Lagrange multipliers to the d electron density matrix. Thus, the total energies of all electronic configurations allowed by a symmetric group were calculated self-consistently with the Lagrange multipliers and then the ground electronic configuration was energetically determined. The predicted results demonstrate precisely the experimentally observed grand-states, i.e., 4A2g, 3E2g, 6A1g, 1A1g, 2E1g, and 3A2g for VCp2, CrCp2, MnCp2, FeCp2, CoCp2, and NiCp2, respectively, while the stability between different electronic configurations is found to be very sensitive de-pending on the Ueff values. Thus, an utility of constraint DFT+U method combined with non-empirical Ueff values for analyzing properties of correlated systems was demonstrated. Chapter five concludes the thesis that by using the proposed methodology opens a new avenue toward reliable predictions of structures and physical properties in strongly correlated metal complexes and gives suggestions for future calculations.
本文 / MIE UNIVERSITY, Graduate School of Engineering, Division of Materials Science
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Collection (particular)国立国会図書館デジタルコレクション > デジタル化資料 > 博士論文
Date Accepted (W3CDTF)2018-01-02T17:18:43+09:00
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