Computational protocol: Impact of Anchoring Groups on Ballistic Transport:Single Molecule vs Monolayer Junctions

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[…] In our calculations, we study molecular junctions based on “Tour-wire”-type molecules, i.e., 1,2-bis(2-phenylethynyl)benzene attached to gold electrodes via thiolate (−S), methylthiolate (−CH2S), isocyanide (−NC), and pyridine (−Pyr) anchor groups (see a). These molecules differ in the electron donating/accepting properties due to the different anchoring groups, which changes the associated local dipoles, as well as in the bonding mechanism with the gold leads.For the corresponding metal–molecule–metal junctions, we consider different molecular packing densities Θ. These span the range between the two limiting cases represented by the (periodically repeated) unit cells shown in b and c, where the latter models a single molecule and the former a densely packed monolayer: we use one molecule in a (2 × 2) Au(111) surface unit-cell to model the Θ = 1 case (i.e., a densely packed SAM), and reduce the packing density gradually by expanding the cell laterally and removing all except one molecule. With this procedure, molecular packing densities of Θ = 1/2, 1/4, 1/8, and 1/16 are realized. The latter corresponds to a single molecule per 8 × 8 surface unit-cell of gold (for more details see Supporting Information). This we consider as the single-molecule junction limit, an assessment supported by the analysis of the changes in the electrostatic energy due to the bond formation discussed below. The metallic leads are represented by three layers of Au(111) on each side of the junction (i.e., six layers of Au separating periodic replicas of the molecules/monolayers). We optimized the structure of the SAM-based junctions (at full packing density, Θ = 1) including the innermost gold layers, and also relaxed the dimensions of the junction in the transport direction to allow for a more systematic structural setup. The geometry was not reoptimized at lower molecular packing densities, as the impact on the junction properties is expected to be minor and in this way we can also isolate the role of collective electrostatic effects. A detailed description of the geometry-optimization process employed for such junctions can be found in the Supporting Information of ref ().For the thiolate anchoring group, the sulfur atom was found to be situated close to the fcc hollow site, while for the methylthiolate a docking position between fcc hollow and bridge was observed, in accordance with previous findings. The optimization for the isocyanide anchoring group also led to a docking position between fcc hollow and bridge. In the case of the pyridine anchoring group we investigated two different adsorption geometries, because the pyridine linker is characterized by a double-peak conductance signature corresponding to two distinctly different binding geometries that are present predominantly in the junction. The lower conductance feature corresponds to a vertical geometry, and the higher conductance value to a geometry where the molecule is significantly tilted and the electrode separation is smaller than the molecular length. Quek et al. further demonstrated that switching between these two conductance states can be achieved reversibly through repeated junction elongation and compression. We modeled the vertical “low-conductance” pyridine structure (tilted by 5° relative to the surface normal and denoted as (−Pyr)) by a standard planar gold geometry, where after optimization the nitrogen atom is found in an on top position. A tilting of the pyridine docked molecule is energetically very costly for a flat Au surface; to overcome gold–hydrogen steric repulsion, we studied a pyridine-docked molecule in the presence of an ad atom added to an fcc hollow site as a second structure. This results in a “high conductance” structure, tilted by 15° and denoted as (−Pyrad). Note that depending on the specific docking sites chosen for the electrodes and influenced also by the relative alignment of the electrodes in the experiment, of course other (higher) tilt angles are also conceivable, but the two geometries studied here already provide fundamental insight into the peculiarities of transport through pyridine docked systems (vide infra).Geometry optimizations and electronic structure calculations were performed applying periodic boundary conditions within the framework of density functional theory (DFT) using the VASP code. We employed the Perdew-Burke-Enzerhof PBE exchange-correlation functional and a plane-wave basis set (cutoff: ca. 20 Ry). Geometries were optimized for the full packing density, Θ = 1, by applying the conjugate gradient scheme as implemented in VASP. Charge-transport calculations were done in a three-step procedure combining DFT and nonequilibrium surface Green’s functions to calculate I-V curves from (zero-bias) transmission functions in the Landauer-Büttiker formalism., First, we used a locally modified version of the DFT based code SIESTA, where we applied a double-ζ polarized orbital basis set (DZP) in conjunction with a “PAO.EnergyShift” of 0.001 Ry, for extracting the Hamilton and overlap matrix of a region comprising the molecule and three gold layers at each side (a detailed discussion of why for the present study this choice of the “PAO.EnergyShift” is crucial in conjunction with the standard DZP basis functions of SIESTA can be found in ref ()). Successively, using recursive Green’s functions we computed the self-energies of the electrodes. Finally, we obtained the zero-bias transmission function T(E) and used it to calculate the current–voltage characteristics I(V) within the Landauer-Büttiker formalism as1Here, f(x) is the Fermi–Dirac occupation function at 300 K and μleft/right = EF ± (eV/2), with EF the Fermi energy, e the elementary charge, and V the voltage. Further details regarding the implementation of this approach can be found in the Supporting Information of ref (). The zero-bias conductance G(EF) also discussed in the following was calculated as G(EF) = T(EF)·G0, where T(EF) is the value of the zero-bias transmission function T at EF, and G0 = (2e2/h) is the quantum of conductance.Bonding-induced charge rearrangements are defined as the difference between the charge density of the full metal–molecule–metal junction, ρsys, and the sum of densities of the isolated noninteracting subsystems, Δρ = ρsys – (ρmono + ρslab). ρslab is the charge density of the electrodes and ρmono the charge density of the free-standing monolayer. In the thiolates the charge density of the H-layers also has to be included., The changes in the electrostatic energies due to metal–molecule bonding are calculated as differences of the electrostatic energies of the individual systems obtained from the VASP calculations. XCrySDen, VMD, Mayavi2, and Ovito were used for graphical visualization. […]

Pipeline specifications

Software tools PyRAD, VMD
Application Protein structure analysis