Tuning the through-bond interaction in a two-centre problem

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Abstract
Two centres A and B connected by one or more sets of bridging states (pathways) define a graph in the space of states. The Hamiltonian is decimated in this space and the problem is reduced to that of two sites with corrected energies EA and EB and an effective interaction VAB. The goal of the method is to make evident how the pathways should be modified in order to tune the resulting coupling. The condition for maximum coupling is EA=EB (resonance) and is related to a generalised reflection-inversion symmetry while the coupling minimises if VAB=0 (anti-resonance). This is a non-trivial situation allowed by the topology of the system which occurs when two or more pathways interfere destructively. The effects of resonances and anti-resonances in electron transfer and other applications are discussed.