# The Role of Metal Ions in the Electron Transport through Azurin-Based Junctions
## 2 Methods
### Density Functional Theory Calculations on Metal-Protein-Metal Junctions  
We carried out density functional theory (DFT) calculations on metal-protein-metal junctions obtained by replacing, in the geometries obtained for the work in [34], the Cu ion with Zn, Co or Ni without re-optimizing the structure. This strategy makes it possible to identify effects in the electrical conductance due to changes in the electronic structure only, ruling out factors which may rather be related with geometrical differences. As mentioned in the Introduction, we focused on the structures that describe a gold tip approaching the protein sideways since, among the possible scenarios analyzed in [34], this was found to yield one of the highest conductance values. Further details about the protocol followed for obtaining these metal-protein-metal geometries can be found in the Supplementary Materials.  
In all cases, the substrate and tip employed in these calculations consist of 969 and 252 atoms, respectively. Note that the corresponding number of gold atoms employed in the MD simulations was instead much larger (2538 and 835, respectively): this is because, when importing the MD output structures for the Cu-based junctions as an input for the DFT calculations, the outermost layers in both the surface and the tip as well as the surrounding water molecules were removed in order to comply with the computational limitations. The OpenMX code was used, which is based on highly optimized numerical pseudoatomic orbitals (PAOs) [58; 59] and which we already used for our previous work on proteins [8; 34; 60; 61]. We used the Perdew-Burke-Ernzerhof (PBE) exchange and correlation functional [62] and norm-conserving pseudopotentials [63]. Single-\(\zeta\) basis sets were used for all species involved in the calculations (including the gold tip and substrate) except for the metallic ion for which a double-\(\zeta\) basis set was employed instead. The cutoff radii used for the PAOs were 8 Bohr for the metal ion, 7 Bohr for S and 5 Bohr for C, N, O and H. As for the gold electrodes, the Au atoms belonging to the tip and the substrate were described by the cutoff radii of 9 Bohr in those regions closer to the protein, whereas a 7-Bohr cutoff radius was chosen for the rest of the atoms. Due to computational reasons, these calculations were performed without spin polarization. The electronic self-consistency is achieved by a Pulay mixing scheme based on the residual minimization method in the direct inversion iterative subspace (RMM-DIIS) [64] with a Kerker metric [65], using an energy cutoff of \(10^{-8}\) Ha as convergence criterion. Further details about the strategies used to reach the self-consistent-cycle convergence can be found in [60; 61]. The overlap and Hamiltonian matrices obtained by the DFT calculations were subsequently used to compute the zero-bias transmission as a function of energy in the spirit of the [PERSON] formalism and making use of [PERSON]'s function techniques. Within this method, the structure is divided in three regions (left (L), center (C) and right (R)) and the energy dependent transmission is given by  
\[\tau(E)\ =\ \mathrm{Tr}[\mathbf{\Gamma}_{\mathrm{L}}\mathbf{G}_{\mathrm{CC}}^{ \mathrm{r}}\mathbf{\Gamma}_{\mathrm{R}}\mathbf{G}_{\mathrm{CC}}^{\mathrm{a}}], \tag{1}\]  
where \(\mathbf{\Gamma}_{\mathrm{L/R}}\) are the scattering rate matrices and \(\mathbf{G}_{\mathrm{CC}}^{\mathrm{r(a)}}\) is the retarded (advanced) [PERSON]'s function (see [34] for further details).