The Application of the Non-Equilibrium Green's Function Formalism for Electronic Transport Calculations

The thesis focuses on coherent electron transport in molecular junctions facilitated by a quantum tunneling mechanism. Theoretical description of the quantum transport can be formulated at various levels of sophistication, differing in accuracy, computational demand, scaling, and applicability. Here, the non-equilibrium Green's function (NEGF) formalism, which enables a proper description of open systems affected by applied bias potentials, is discussed. The Keldysh formalism and the key Meir-Wingreen relation for transmission for elastic transport are reviewed. In a computational part, practical applicability of NEGF within density functional theory (DFT) or tight-binding (TB) potentials is demonstrated on different model systems, ranging from small molecular junctions to redox-active porphyrin junctions or even large protein junctions. Aspects of the popular TranSiesta and CP2K implementations are discussed and compared on transmission calculations. Further, the influence of structural features, such as contact shapes and molecular anchoring groups, on the transport properties is demonstrated. Finally, we discuss more approximate approaches allowing large-scale system transport calculations and discuss their accuracy together with ad-hoc approaches such as DFT+Sigma to reach agreement with experimental current-voltage data.