orbital of Ti had to be occupied by one electron.
R.A. Evarestov, A.V. Leko, and V.A. Veryazov
St.-Petersburg State University, Chemistry Department,
University st.2, St.-Petersburg 198904, Russia
Phone: (07)-(812)-2182455,
E-mail: robert@hq.pu.ru
(Received September 22, 1998; accepted October 5, 1998)
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, Ti2O3).
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 d1 configuration (as in Ti2O3 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 Ti2O3 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 Ti2O3 crystal obtained in HF
self-consistent calculations with different initial density
matrices are listed in the table. Three groups of results
correspond to density matrix with equal occupancies for
different spins (so that this solution is the same as in
restricted HF (RHF) hamiltonian), antiferromagnetic (AFM)
and ferromagnetic (FM) ordering of spins. For all these
cases we have obtained pairs of solutions, corresponding to the
insulating and metallic state. We found that the insulating state
of Ti2O3 can be obtained with the standard
initial density matrix, but to obtain the metallic state only
the
orbital of Ti had to be occupied by one electron.
Although for insulating states the total energies appear to be lower than for the metallic ones, it is necessary to emphasize that the insulating and the metallic solutions were obtained independent of magnetic ordering of titanium atoms. Our results show that in contradiction with widely spread point of view the metal-insulator transition occurrence in the Ti2O3 crystal may be explained without consideration of any magnetic effects.
Given in the table, atomic charges QA, covalencies CA, total atomic valencies VA, and bond orders BA–B show that local properties of the electronic structure depend on initial atomic orbital occupancies. However, atomic charges and orders of Ti–O bonds are not sensitive to the different type of chemical bonding and spin ordering in Ti2O3 crystal. In contrary, the bond order between nearest titanium atoms changes significantly and depends on the details of calculation. Calculated atomic valencies for titanium atom in insulating unrestricted HF solutions correlate well with the expected stoichiometrical values.
The results obtained demonstrate the necessity of considering HF solutions for different electronic configurations to make the complete analysis of the electronic structure for a crystal with a strongly correlated d-electron subsystem. Using of standard procedure for HF calculation may lead to incomplete or wrong results.
Table 1: Local properties of chemical bonding in Ti2O3 crystal
Acknowledgement. We thank Prof. C. Pisani and Prof. R. Dovesi for CRYSTAL 95 code. This work was supporded by Russian Foundation of Basic Research (grant 96-03-33796-a).
