  Exploring the use of individual molecules as active components in electronic
devices has been at the forefront of nanoelectronics research in recent years.
Compared to semiconductor microelectronics, modeling transport in
single-molecule devices is much more difficult due to the necessity of
including the effects of the device electronic structure and the interface to
the external contacts at the microscopic level. Theoretical formulation of the
problem therefore requires integrating the knowledge base in surface science,
electronic structure theory, quantum transport and device modeling into a
single unified framework starting from the first-principles. In this paper, we
introduce the theoretical framework for modeling single-molecule electronics
and present a simple conceptual picture for interpreting the results of
numerical computation. We model the device using a self-consistent matrix
Green's function method that combines Non-Equilibrium Green's function theory
of quantum transport with atomic-scale description of the device electronic
structure. We view the single-molecule device as "heterostructures" composed of
chemically well-defined atomic groups, and analyze the device characteristics
in terms of the charge and potential response of these atomic groups to
perturbation induced by the metal-molecule coupling and the applied bias
voltage. We demonstrate the power of this approach using as examples devices
formed by attaching benzene-based molecules of different size and internal
structure to the gold electrodes through sulfur end atoms.
