Using benzene-diamine and benzene-dithiol molecular junctions as benchmarks, we investigate the widespread analysis of the quantum transport conductance $mathcal{G}(epsilon)$ in terms of the projected density of states (PDOS) onto molecular orbitals
(MOs). We first consider two different methods for identifying the relevant MOs: 1) diagonalization of the Hamiltonian of the isolated molecule, and 2) diagonalization of a submatrix of the junction Hamiltonian constructed by considering only basis elements localized on the molecule. We find that these two methods can lead to substantially different MOs and hence PDOS. Furthermore, within Method 1, the PDOS can differ depending on the isolated molecule chosen to represent the molecular junction (e.g. benzene-dithiol or -dithiolate); and, within Method 2, the PDOS depends on the chosen basis set. We show that these differences can be critical when the PDOS is used to provide a physical interpretation of the conductance (especially, when it has small values as it happens typically at zero bias). In this work, we propose a new approach trying to reconcile the two traditional methods. Though some improvements are achieved, the main problems are still unsolved. Our results raise more general questions and doubts on a PDOS-based analysis of the conductance.
Measurable spectra are theoretically very often derived from complicated many-body Greens functions. In this way, one calculates much more information than actually needed. Here we present an in principle exact approach to construct effective potenti
als and kernels for the direct calculation of electronic spectra. In particular, the potential that yields the spectral function needed to describe photoemission turns out to be dynamical but {it local} and {it real}. As example we illustrate this ``photoemission potential for sodium and aluminium, modelled as homogeneous electron gas, and discuss in particular its frequency dependence stemming from the nonlocality of the corresponding self-energy. We also show that our approach leads to a very short derivation of a kernel that is known to well describe absorption and energy-loss spectra of a wide range of materials.
