Construction of First Principle Based Adiabatic and Diabatic Hamiltonian for TiO${}_6^{8-}$ unit of BaTiO${}_3$ Crystal: Photoemission Spectra and Ferroelectricity

The ferroelectric property of BaTiO${}_3$ crystal arises from the strong Pseudo Jahn-Teller (PJT) interactions between the non-degenerate ground electronic state, ${}^1{A}_{1g}$ and the degenerate ${}^1{T}_{1u}$ symmetry states through the nuclear distortions of $t_{1u}$ modes in TiO${}_6^{8-}$ unit. In a $d^0$ electronic configuration of $T{i}^{4+}$ ion, the PJT interaction leads to a stabilization effect, which has been explored using Beyond Born-Oppenheimer (BBO) theory. The ${}^1{T}_{1u}$ excited states form a three-state degeneracy, exhibiting feeble Jahn-Teller (JT) distortions over the $t_{2g}$ planes. For the first time, we compute $\mathit{\text{ab}}\mathit{\text{initio}}$ adiabatic potential energy surfaces (PESs) and non-adiabatic coupling terms (NACTs), and thereafter, diabatic PESs and couplings for the perovskite unit, TiO${}_6^{8-}$. Using a Time-Dependent Discrete Variable Representation (TDDVR) approach, the theoretical photoemission spectra exhibit good agreement with the experimental ones. Moreover, the experimental observation on order parameter associated with ferroelectric properties of BaTiO${}_3$ crystal show close resemblance with present and other theoretical predictions.