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Destructive quantum interference in electron transport: A reconciliation of the molecular orbital and the atomic orbital perspective

Destructive quantum interference (DQI) in single molecule electronics is a purely quantum mechanical effect and entirely defined by inherent properties of the molecule in the junction such as its structure and symmetry. This definition of DQI by molecular properties alone suggests its relation to other more general concepts in chemistry as well as the possibility of deriving simple models for its understanding and molecular device design. Recently, two such models have gained wide spread attention, where one was a graphical scheme based on visually inspecting the connectivity of carbon sites in conjugated pi systems in an atomic orbital (AO) basis and the other one put the emphasis on the amplitudes and signs of the frontier molecular orbitals (MOs). There have been discussions on the range of applicability for these schemes, but ultimately conclusions from topological molecular Hamiltonians should not depend on whether they are drawn from an AO or a MO representation, as long as all the orbitals are taken into account. In this article we clarify the relation between both models in terms of the zeroth order Green's function and compare their predictions for a variety of systems. From this comparison we conclude that for a correct description of DQI from a MO perspective it is necessary to include the contributions from all MOs rather than just those from the frontier orbitals. The cases where DQI effects can be successfully predicted within a frontier orbital approximation we show to be limited to alternant even-membered hydrocarbons, as a a direct consequence of the Coulson-Rushbrooke pairing theorem in quantum chemistry.