Unrestricted HF Calculations of Crystals with Strongly Correlated d‐Electron Subsystem: Chemical Bonding in Ti ₂ O ₃ Crystal

Abstract

Theoretical description of crystalline transition metal oxides is complicated by the coexistence of strongly localized atomic-like 3d-states and delocalized band states. As a result either insulating or metallic properties and the metal±insulator transition are observed in such crystals (for example, Ti 2 O 3 ).It is well known that the Hartree-Fock solutions corresponding to different electronic configurations may be found. In particular, it may be the result of different choice of the initial density matrix. In crystalline transition metal oxides d-electron states remain highly localized, and one can expect the dependence of the calculated electronic structure of a crystal on the electronic configuration of the constituent atoms. Moreover, one has to have in mind that the atomic states in a crystal are splitted up in accordance with the symmetry of the surrounding crystalline field.In the self-consistent HF-LCAO calculations the initial density matrix is taken by fixing the initial occupancies of basis atomic orbitals. Usually these occupancies are taken to be the same for different components of degenerated atomic orbitals. For example, when a minimal basis set is used, an atom with d 1 configuration (as in Ti 2 O 3 crystal), the initial occupancy for degenerated d-orbitals is usually taken to be 0.2e. However, for different choices of the initial density matrix the HF self-consistent procedure may lead to different solutions because the occupied and vacant states are considered in HF approximation with different potentials.In this work we have studied the electronic structure of Ti 2 O 3 crystal within unrestricted HF approximation using different initial occupancies for d-atomic orbitals of titanium atoms. Calculations of the electronic structure were performed by CRYSTAL95 code [1]. The pseudopotential atomic basis for Ti and O atoms was taken from [2]. The analysis of chemical bonding was made according to [3], extended to the case of periodic systems.Main electronic properties of Ti 2 O 3 crystal obtained in HF self-consistent calculations with different initial density matrices are listed in the table. Three groups of results correspond to density Rapid Research Notes R3

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“…Table 1 demonstrates the effect of a cyclic cluster increase for the HF method. The main calculated properties are: the total energy (per primitive unit cell), one-electron band edge energies of the valence band top and conduction band bottom, and c, and Mulliken effective atomic charges, q, and atomic valencies, V [18]. Based on results of Table 1, the conclusion can be drawn that in the HF calculations of a perfect crystal the electronic structure is reasonably well reproduced by the cyclic cluster of 80 atoms (L=16).…”

“…The impurity iron atoms were treated as all electron atoms. The basis for Ti and 0 was taken from previous Ti02 calculations [18], whereas that for Fe and Sr from [15,19].…”