Construction of first-principles-based adiabatic and diabatic Hamiltonians for the TiO ₆ ⁸⁻ unit of the BaTiO ₃ crystal: photoemission spectra and ferroelectricity

The ferroelectric properties of the BaTiO₃ crystal arise from the strong pseudo Jahn-Teller (PJT) interactions between the non-degenerate ground electronic state, ¹A_1g, and the degenerate ¹T_1u symmetry states through the nuclear distortions of t_1u modes in the TiO₆^8- unit. In the d⁰ electronic configuration of the Ti⁴⁺ ion, the PJT interaction leads to a stabilization effect, which has been explored using Beyond Born-Oppenheimer (BBO) theory. The ¹T_1u excited states form a three-state degeneracy, exhibiting feeble Jahn-Teller (JT) distortions over the t_2g planes. For the first time, we compute <i>ab initio</i> adiabatic potential energy surfaces (PESs) and non-adiabatic coupling terms (NACTs), and, thereafter, diabatic PESs and couplings for the perovskite unit, TiO₆^8-. Using a time-dependent discrete variable representation (TDDVR) approach, the theoretical photoemission spectra exhibit good agreement with the experimental results. Moreover, the experimental observation on the order parameter associated with the ferroelectric properties of the BaTiO₃ crystal shows a close resemblance to the present work and other theoretical predictions.