## 1 Introduction  
Understanding and controlling charge transport in single molecule junctions have been important since it was first suggested that a single molecule might function as an active electronic component [1], and therefore, that metal-organic interfaces are building blocks for the next generation of electronic devices [2; 3]. Charge transport properties are mainly measured using scanning-probe methods, in particular, scanning tunneling microscopy break junctions (STM-BJ) [4; 5], and mechanically-controlled microscopy break junctions (MC-BJ) [6; 7]. Such measurements are typically carried out in solution and at room temperature, and data from thousands of measurements are compiled to generate conductance histograms [8; 9; 10]. However, in those experiments, the geometry of the interface on the atomic scale is not known, as it cannot be measured in situ, and it is also changing during the experiment, or from sample to sample. Therefore, theoretical methods to understand and guide experiments are extremely valuable [3; 11]. Density functional theory (DFT) is the fundamental approach to calculate the electronic properties and optimize the geometry of the junction [12; 13]. Similarly, electron transport calculations are normally performed within the non-equilibrium Green's function (NEGF) formalism. DFT-NEGF, even at zero bias (DFT-Landauer), has been able to correctly reproduce trends in conductance with the correct physical picture [14; 15; 16; 17; 18; 19; 20]. However, despite the significant progress that DFT simulations have offered, their limitations are well known. Among them, perhaps the most relevant for electron transport is the underestimation of the fundamental energy gap at the metal/molecule interface [21; 22; 23; 24]. To go beyond the semi-quantitative picture provided by DFT, it would be desirable to make quantitative comparisons with experimentally measured conductance. For this, corrections to the DFT electronic structure at the interface need to be made. The most widely used approach is the DFT + \(\Sigma\) method [25; 26; 27; 28; 29; 30; 31], where corrections to conducting orbital(s) are calculated externally and added onto the converged system Hamiltonian after the DFT cycle. The correction is a self-energy composed of two terms: one that corrects the molecular gas-phase and one that accounts for the nonlocal polarization due the metal electrodes [25; 32; 33]. A typical molecular junction is composed of a single molecule bonded to electrodes on either side using chemical linker groups. Electrodes are generally metallic, and Au has been the most commonly used electrode material in scanning-probe studies because of its inertness, which enables consistent and reproducible measurements over a wide range of conditions [5; 34]. Linker groups connect the molecule to the electrodes mechanically and electronically [35]. Depending on their chemical nature, linker groups bind to the electrodes either forming donor-acceptor bonds with surface asperities (for example, amine groups -NH\({}_{2}\)) [25; 36], geometry-dependent binding using pyridine groups (\(-\)NC\({}_{5}\)H\({}_{5}\)) [37; 38], covalent bonding (such as thiol groups \(-\)SH) [39; 40; 41] or through carboxylic groups (\(-\)COOH) [42; 43]. The atomistic details of the metal-molecule interface have been shown to tune the electronic and conducting properties of the junction [44; 45; 46; 47]. Experimentally, variations in conductance strongly depend on the nature of the linker group. While for thiolate-Au linkers, they are very large [9; 47; 48; 49; 50], for amine-terminated molecules, these are significantly smaller [25; 26; 33; 51]. The benzenediamine (BDA)-Au interface is a prototypical metal-molecule structure that has been extensively investigated experimentally [25; 33; 51] and theoretically [26; 27; 52; 53], and is, therefore, an excellent benchmark. STM-BJ studies of BDA between Au electrodes yield a conductance peak at \(6.4\times 10^{-3}\) G\({}_{0}\)[25; 51; 52].