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Density functional theory based calculations of the transfer integral in a redox-active single molecule junction

There are various quantum chemical approaches for an ab initio description of transfer integrals within the framework of Marcus theory in the context of electron transfer reactions. In our article we aim to calculate transfer integrals in redox-active single molecule junctions, where we focus on the coherent tunneling limit with the metal leads taking the position of donor and acceptor and the molecule acting as a transport mediating bridge. This setup allows us to derive a conductance, which can be directly compared with recent results from a non-equilibrium Green's function approach. Compared with purely molecular systems we face additional challenges due to the metallic nature of the leads, which rules out some of the common techniques, and due to their periodicity, which requires {\bf k} space integration. We present three different methods, all based on density functional theory, for calculating the transfer integral under these constraints, which we benchmark on molecular test systems from the relevant literature. We also discuss manybody effects and apply all three techniques to a junction with a Ruthenium complex in different oxidation states.