Revisiting the extraction of coupling strengths for polaron hopping from an <i>ab initio</i> approach

Accurately determining the coupling strength between polaron states is essential to describe charge-hopping transport in materials. In this paper, we revisit methodologies to extract coupling strengths using $ab\phantom{\rule{3.33333pt}{0ex}}initio$ approaches. Our findings underscore the critical role of incorporating anharmonic effects in the model Hamiltonian when analyzing total energy variations along reaction coordinates. Furthermore, we demonstrate that coupling strength extraction based on total energy calculated from $ab\phantom{\rule{3.33333pt}{0ex}}initio$ approaches is fundamentally limited owing to the stabilization of diabatic states, which do not involve coupling strength. We demonstrate that such limitation exists in both $\mathrm{DFT}+\mathrm{U}$ and HSE hybrid functional, which are widely used in the study of polaron transport. Instead, we suggest extracting coupling strength directly from the electronic structure of a system in neutral conditions. The neutral condition avoids overestimating coupling strength because of additional energy splitting between bonding and antibonding states from the charging energy. This study highlights the limitations of existing methods and introduces a robust framework for accurately extracting coupling parameters, paving the way for improved modeling of charge transport in complex materials.