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Destructive quantum interference (DQI) in single molecule electronics is apurely quantum mechanical effect and entirely defined by inherent properties ofthe molecule in the junction such as its structure and symmetry. Thisdefinition of DQI by molecular properties alone suggests its relation to othermore general concepts in chemistry as well as the possibility of derivingsimple models for its understanding and molecular device design. Recently, twosuch models have gained wide spread attention, where one was a graphical schemebased on visually inspecting the connectivity of carbon sites in conjugated pisystems in an atomic orbital (AO) basis and the other one put the emphasis onthe amplitudes and signs of the frontier molecular orbitals (MOs). There havebeen discussions on the range of applicability for these schemes, butultimately conclusions from topological molecular Hamiltonians should notdepend on whether they are drawn from an AO or a MO representation, as long asall the orbitals are taken into account. In this article we clarify therelation between both models in terms of the zeroth order Green's function andcompare their predictions for a variety of systems. From this comparison weconclude that for a correct description of DQI from a MO perspective it isnecessary to include the contributions from all MOs rather than just those fromthe frontier orbitals. The cases where DQI effects can be successfullypredicted within a frontier orbital approximation we show to be limited toalternant even-membered hydrocarbons, as a a direct consequence of theCoulson-Rushbrooke pairing theorem in quantum chemistry.

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