In this talk, I will explain how non-equilibrium Green’s
function (NEGF) approach combined with density functional theory (DFT)
compute transport properties of molecular junctions. In the first
part, successes and failures of local and semi-local density
functionals are discussed, and an inexpensive, GW-based correction,
known as DFT+Sigma, is reviewed. The method is applied to complicated
systems involving transition metals, where semi-local functionals fail
qualitatively. In the second part, a method to compute molecular
resonance width in the junction is developed, based on NEGF and
diagonalization of non-Hermitian matrices. The energy-dependent
broadening functions, combined with Breit-Wigner formula, accurately
reproduce transmission calculated from Landauer formula.