Interplay of electron correlations and lattice distortions in transition metal coordination compounds

of Dissertation In transition metal compounds with octahedral geometry, symmetry breaking effects play a key role in many spectroscopic phenomena in the physics and chemistry of these materials. An understanding of the links between octahedral coordination and how it impacts the electronic and magnetic structures of these materials is of key importance in this connection. With this motivation, I invoke first-principles methods to analyze electronic structures and spectroscopies of novel functional materials that show unique interplay of octahedral distortion, magnetism, electron correlation and spin orbit coupling effects. Specifically, this thesis deploys theoretical and computational methodologies to interpret spectral response of various experimental probes such as Compton scattering, x-ray absorption (XAS), x-ray emission (XES) and angle-resolved photoemission spectroscopy (ARPES), where electronic structure, electron correlation, spin-orbit coupling, and matrix element effects are considered in material-specific detail. The thesis first presents the electronic structure and ARPES spectroscopy of 5d transition metal iridates. When doped with carriers, these Mott insulators show a rich variety of phases and provide a playground to investigate the universalities of many exotic phenomena observed in 3d and 4dMott insulators. The thesis discusses the unconventional Fermi surface topology of iridates where Fermi arcs and Fermi pockets can be observed due to the competition between lattice distortion, electron correlations and spin-orbit coupling. Iridates also harbor a unique electronic anomaly called negative electronic compressibility (NEC). The first-principles study and the corresponding ARPES spectroscopy presented in this thesis demonstrate the signature of NEC for the first time in a quasi-three dimensional strongly correlated metal. The second part of the thesis focuses on the study of Li-ion battery (LIB) cathodes. High energy x-ray Compton scattering spectra along with parallel first-principles computations have been used to develop advanced spectroscopic tools for characterizing LIB cathodes such as lithium iron phosphate (LFP) and lithium manganese oxides (LMO). Our electronic