Non-Adiabatic Effect in Perovskites: Model and Ab Initio Hamiltonian for Spectral/Ferroelectric Properties

This review presents a comprehensive analysis of Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) effects in perovskite systems, emphasizing their roles on phase transitions through vibronic coupling. A combined theoretical and computational approach has been applied to focus on roto-vibrational features in dielectric spectra of ${\text{LaMnO}}_3$ as well as the origin of ferroelectric behavior in ${\text{BaTiO}}_3$. The centrifugal stabilization of JT-active excited states in ${\text{LaMnO}}_3$ and strong PJT coupling in ${\text{TiO}}_6^{8-}$ clusters of ${\text{BaTiO}}_3$ are crucial for exploring observed spectral and structural phenomena. The construction of diabatic Hamiltonians from ab initio adiabatic potential energy surfaces (PESs) and non-adiabatic coupling terms (NACTs) enables accurate quantum dynamics on both systems. We highlight the effectiveness of model and ab initio Hamiltonians in capturing spectral features and spontaneous polarization, and thereby, establish a framework for understanding vibronic interactions in complex oxides.