Corresponding Orbitals Derived from Periodic Bloch States for Electron Transfer Calculations of Transition Metal...

An approach for modeling electron transfer in solids and at surfaces of iron-(oxyhydr)oxides and other redox active solids has been developed for electronic structure methods (i.e., plane-wave density functional theory) capable of performing calculations with periodic cells and large system sizes efficiently while at the same time being accurate enough to be used in the estimation of the electron-transfer coupling matrix element, V _AB, and the electron transfer transmission factor, κ_el. This method is an extension of the valence bond theory electron transfer method for molecules and clusters implemented by Dupuis and others and used extensively by Rosso and co-workers in which scaled corresponding orbitals derived from the Bloch states are used to calculate the off-diagonal matrix elements H _AB and S _AB. A key development of the present work is the formulation of algorithms to improve the accuracy of the integration of the exact exchange integral in periodic boundary conditions. This method is demonstrated on model systems for electron small polaron transfer in iron-(oxyhydr)oxides, including bare Fe²⁺-Fe³⁺ ions, and in [Fe³⁺(OH₂)₂ (OH^-)₂)] _nⁿ⁺ chains representing the common edge-sharing Fe octahedral motif in these materials.