First-principles based matrix Green's function approach to molecular electronic devices: General formalism

Transport in molecular electronic devices is different from that in semiconductor mesoscopic devices in two important aspects: (1) the effect of the electronic structure and (2) the effect of the interface to the external contact. A rigorous treatment of molecular electronic devices will require the inclusion of these effects in the context of an open system exchanging particle and energy with the external environment. This calls for combining the theory of quantum transport with the theory of electronic structure starting from the first-principles. We present a self-consistent yet tractable matrix Green's function (MGF) approach for studying transport in molecular electronic devices, based on the non-equilibrium Green's function formalism of quantum transport and the density functional theory (DFT) of electronic structure using local orbital basis sets. By separating the device rigorously (within an effective single-particle theory) into the molecular region and the contact region, we can take full advantage of the natural spatial locality associated with the metallic screening in the electrodes and focus on the physical processes in the finite molecular region. This not only opens up the possibility of using the existing well-established technique of molecular electronic structure theory in transport calculations with little change, but also allows us to use the language of qualitative molecular orbital theory to interpret and rationalize the results of the computation. We emphasize the importance of the self-consistent charge transfer and voltage drop on the transport characteristics and describe the self-consistent formulation for both device at equilibrium and device out of equilibrium. For the device at equilibrium, our method provides an alternative approach for solving the molecular chemisorption problem. For the device out of equilibrium, we show that the calculation of elastic current transport through molecules, both conceptually and computationally, is no more difficult than solving the chemisorption problem.