Understanding the Restoring Force From a Local Bonding Perspective: A First-Principles Picture of Phonons and Elasticity

Though the calculation of bulk elastic quantities and phonon frequencies using modern ab-initio techniques is now routine, understanding the crystal chemical origins of these properties is still an open question. How do we relate the value of a specific bulk elastic constant or vibrational mode to chemically intuitive ideas about local structure and bonding, especially when our calculations are often done in a delocalized Bloch basis? Using a basis of maximally localized Wannier functions, we partition the total electronic energy onto real space representations of occupied states, as well of the curvature of that energy with respect to distortions such as mechanical strain or phonon excitation. By understanding how the energy of each individual bond changes with these distortions, we can obtain orbitally decomposed, chemically specific understanding of bulk properties. We use this approach to explore various perovskite oxides, exploring the chemical origins of elasticity, structural phase transitions, Grüneisen parameters, and thermal expansion properties, and discuss the possibility of enhancing or controlling these properties.