A simple approach to hopping matrix elements between nearby molecules

Abstract

The hopping matrix element $t$ quantifies the quantum-mechanical coupling between frontier orbitals on a pair of nearby molecules. Convenient and generally applicable methods to determine $t$ from DFT calculations are lacking; $t$ can be obtained from coupling-induced energy splittings only if the interacting molecules are identical and symmetrically placed. We present a simple approach to determine $t$ from DFT results that relies on measuring hybridization, projecting hybridized pair orbitals onto constituent frontier orbitals of the interacting molecules, using spatially discretized wavefunctions (``cube files'') rather than analytical representations. We demonstrate the method by exploring how $t$ depends on the identity and relative placement of typical moieties found in semiconducting polymers.