The electronic structure of organic-inorganic interfaces often feature resonances originating from discrete molecular orbitals coupled to continuum lead states. An example are molecular junctions, individual molecules bridging electrodes, where the s
hape and peak energy of such resonances dictate junction conductance, thermopower, I-V characteristics and related transport properties. In molecular junctions where off-resonance coherent tunneling dominates transport, resonance peaks in the transmission function are often assumed to be Lorentzian functions with an energy-independent broadening parameter $Gamma$. Here we define a new energy-dependent resonance broadening function, $Gamma(E)$, based on diagonalization of non-Hermitian matrices, which can describe resonances of a more complex, non-Lorentzian nature and can be decomposed into components associated with the left and right lead, respectively. We compute this quantity via an emph{ab initio} non-equilibrium Greens function approach based on density functional theory for both symmetric and asymmetric molecular junctions, and show that our definition of $Gamma(E)$, when combined with Breit-Wigner formula, reproduces the transmission calculated from DFT-NEGF. Through a series of examples, we illustrate how this approach can shed new light on experiments and understanding of junction transport properties in terms of molecular orbitals.
