  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.
