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1 2 3 4 5 6 7 8 Ab-initio Transport Calculations for Single-atom 9 10 11 12 Copper Junctions in the Presence of Hydrogen 13 14 15 Chloride 16 17 18 19 Paul Schn¨abele,†,‡ Richard Koryt´ar,∗,¶ Alexei Bagrets,† Tanglaw Roman,§ 20 21 k,†,⊥ § †,‡,⊥ 22 Thomas Schimmel, Axel Groß, and Ferdinand Evers 23 24 25 Institute of Nanotechnology, Karlsruhe Institute of Technology, Campus North, D-76344 26 27 Karlsruhe, Germany, Institut f¨urTheorie der Kondensierten Materie, Karlsruhe Institute 28 29 of Technology, Campus South, D-76128 Karlsruhe, Germany, Institute of Nanotechnology, 30 31 Karlsruhe Institute of Technology, Campus North, D-76344 Karlsruhe, Germany, Institute 32 33 of Theoretical Chemistry, Ulm University, 89069 Ulm, Germany, Institute of Applied 34 35 Physics, Karlsruhe Institute of Technology, Campus South, D-76131 Karlsruhe, Germany, 36 37 and Center of Functional Nanostructures, Karlsruhe Institute of Technology, Campus 38 39 South, D-76131 Karlsruhe, Germany 40 41 42 E-mail: [email protected] 43 44 45 46 ∗ 47 To whom correspondence should be addressed † 48 Institute of Nanotechnology, Karlsruhe Institute of Technology, Campus North, D-76344 Karlsruhe, 49 Germany ‡ 50 Institut f¨urTheorie der Kondensierten Materie, Karlsruhe Institute of Technology, Campus South, D- 51 76128 Karlsruhe, Germany 52 ¶Institute of Nanotechnology, Karlsruhe Institute of Technology, Campus North, D-76344 Karlsruhe, 53 Germany 54 §Institute of Theoretical Chemistry, Ulm University, 89069 Ulm, Germany 55 kInstitute of Applied Physics, Karlsruhe Institute of Technology, Campus South, D-76131 Karlsruhe, 56 Germany 57 ⊥Center of Functional Nanostructures, Karlsruhe Institute of Technology, Campus South, D-76131 Karl- 58 sruhe, Germany 59 60 1 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 2 of 18

1 2 3 Abstract 4 5 6 We study the transport properties of single-atom thick Cu-wires submerged in an 7 8 electrochemical solvent containing HCl. As a first step, we investigate the stability 9 10 of hydrogen co-adsorbing with chlorine on the Cu(111) surface in an implicit electro- 11 12 chemical environment. We find that adding hydrogen to a Cl-covered Cu surface is 13 14 energetically unfavorable. The result serves as an estimate for the number of Cl-atoms 15 16 that adsorbs near the single-atom wire. We use it in order to construct model junc- 17 18 tions (Cu-wire plus adsorbates) the transport properties of which we investigate with 19 density functional theory (DFT). We find that the Cl and H adsorbates tend to de- 20 21 plete the density of states of the Cu-wire near the Fermi energy. As a consequence, 22 23 the transmission is reduced. Interestingly, we observe that in the case of H-adsorption 24 25 the amount of depletion is quite sensitive to the wire geometry (relaxed vs unrelaxed), 26 27 while this is not the case with Cl. 28 29 30 31 32 Keywords 33 34 35 Helmholtz double-layer, electrochemical gating, nano-scale junction, ab-initio transport cal- 36 37 culations 38 39 40 41 42 Introduction 43 44 45 The controlled manipulation of charge transport through atomic and molecular wires contin- 46 47 ues to be a significant experimental challenge. Essentially, the difficulties and the fascination 48 49 associated with this research field emerge from the same fundamental fact: small changes 50 51 on atomistic scales can significantly alter the junction’s functionality. One of the control 52 53 strategies that is successful even on the atomistic scale operates in electrochemical environ- 54 55 ments. It embarks on the possibility to manipulate the Helmholtz-double-layer (HDL) via 56 57 the third (electrochemical) electrode potential. (The HDL forms at the interface between 58 59 60 2 ACS Paragon Plus Environment Page 3 of 18 The Journal of Physical Chemistry

1 2 3 4 the source/drain-electrodes, i.e. the wire and the solvent. It consists of physisorbed solvent 5 6 particles together with the genuine wire surface.) 7 8 The technique has been employed previously in order to realize single atom switches 9 1 2–4 10 (single-atom transistors ), but also molecular switches have been operated in this way. 11 12 Due to this success it is at least conceivable that electrochemical control might be a 13 14 successful strategy for operating nanosystems also in a broader scope, such as transport con- 15 5 16 trol in nanoporous media (through opening and closing of current bottlenecks). Moreover, 17 18 transport of charge close to nanostructured electrochemical interfaces is also an issue for 19 20 battery materials.6 21 22 Despite the fundamental role of charge transport near electrochemical interfaces, the re- 23 24 search area is still in its infancy. In part this is due to the fact that the inner structure of the 25 26 HDL is difficult to investigate and by and large not very well understood. It is considerably 27 28 challenging to investigate experimentally, but first steps in this direction have been made.7 29 30 At present, the main understanding relies on macroscopic ideas, such as incorporated in the 31 32 Gouy-Chapman theory.8,9 Due to recent developments in computational high-performance 33 34 ab-initio codes, some of the most pressing questions have become amenable to computer 35 36 simulations. But clearly, in the absence of specific experimental data to validate the compu- 37 38 tational assumptions, the building of effective microscopic models still is a very challenging 39 40 task. 41 42 In this work, we investigate the charge transport through single-atom copper wires in 43 44 an electrochemical environment that contains HCl. Our goal is to qualitatively understand 45 46 47 the physical mechanism that is most important for the electro-chemical control of the wire’s 48 49 conductance. To this end we employ the density functional theory (DFT) in order to estimate 50 51 the typical coverage of the junction with Cl and H atoms in and near the thermodynamic 52 53 equilibrium. We find that on flat surfaces ( Cu(111) ) under ambient conditions there is a 54 55 wide window of electrode potentials in which the Cl-coverage is 1/3, i.e. there is a single 56 57 Cl-atom per three surface Cu-atoms. Our calculations suggest that there is no hydrogen in 58 59 60 3 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 4 of 18

1 2 3 4 the immediate vicinity of the Cu-surface under the aforementioned conditions. 5 6 Based on this information about the relevant structural elements of the Helmholtz layer, 7 8 reasonable configurations of Cl-adatoms can be chosen that serve as input for Kohn-Sham 9 10 (KS) based transport studies. The transport calculations indicate that there is a strong 11 12 impact of the Cl-atoms reducing the conductance of the Cu-wire. The effect can be inter- 13 14 preted as a depletion of the wire’s local density of states (LDoS) near the Fermi energy due 15 16 to the binding of the Cl adsorbates. In the absence of Cl, we find a similar transmission 17 18 reduction induced by adsorbing H atoms. Interestingly, we observe that the strength of the 19 20 suppression is very sensitive to the deformation of the wire’s geometry after the adatoms 21 22 have been adsorbed. 23 24 25 26 27 Methods and results 28 29 30 Surface morphology of Cu(111) in Cl-containing environment 31 32 33 A crucial quantity for the simulations is the number of chlorine atoms adsorbed on the 34 35 copper junction under electrochemical conditions. In order to estimate this number, density 36 37 functional theory (DFT) calculations were performed for flat Cu(111) electrodes. The (111) 38 39 surface was modeled by a slab with five atomic layers in a periodic supercell implementation 40 41 of DFT. The slab surfaces were separated by 25 A˚ wide vacuum regions. For the adsorption 42 43 energetics, the two bottom atomic layers were fixed at bulk atomic separation, allowing the 44 45 rest of the metal atoms to relax together with the adatoms. 46 47 All calculations were carried out using the DFT code VASP.10 Electron-electron exchange 48 49 and correlation interactions within the generalized gradient approximation were included in 50 51 the calculations using the PBE functional.11 The interaction between electrons and ions was 52 53 described by the projector-augmented wave (PAW) method12 as implemented by Kresse and 54 55 Joubert.13 Electronic wave functions were expanded in terms of a discrete plane-wave basis 56 √ √ 57 set with kinetic energies of up to 400 eV. Calculations were performed using a 2 3 × 2 3 58 59 60 4 ACS Paragon Plus Environment Page 5 of 18 The Journal of Physical Chemistry

1 2 3 4 surface unit cell. For the integration over the first Brillouin zone, we used a mesh of 4×4×1 5 14 15 6 special k-points with a Methfessel-Paxton smearing of 0.1 eV. Geometry optimizations 7 8 were terminated once the forces on relaxed chlorine and copper atoms became less than 9 ˚ 10 0.01 eV/A. 11 12 Since we are modeling the adsorption in an electrochemical environment, the reference for 13 14 the adsorption energy is the corresponding hydrated species in the electrolyte. This requires 15 16 in principle the determination of solvation energies which can be quite cumbersome. Some 17 − + 18 estimate to derive the adsorption energies of solvated Cl and H ions can be made via a 19 20 thermodynamics cycle.16,17 21 22 However, there is a more elegant way to calculate the energies of solvated species using 23 24 the concept of what is now coined the computational hydrogen electrode.18,19 Within this 25 26 approach, the electrolyte is viewed as a thermodynamical reservoir for the adsorbates and 27 28 the fact is used that at the redox potential and standard conditions the solvated species is 29 30 in equilibrium with the corresponding species in gas phase. 31 32 This approach has recently be used to determine the equilibrium coverage of halides on 33 34 Cu(111) and Pt(111) as a function of the electrode potential.20 We illustrate this method 35 36 for the chloride adsorption. At the redox potential of the chlorine, the chloride anion is 37 38 in equilbrium with the chlorine molecule Cl in gas phase. Furthermore, it is known how 39 2 40 the electrochemical potential of the chloride changes with the electrode potential and the 41 42 43 Table 1: Adsorption energies Eads in eV for H, Cl adsorption on Cu(111) at 44 different coverages (in ML) and positions 45 46 47 top fcc hcp 48 ΘH = 1/12 +0.35 −0.23 −0.23 49 ΘH = 1/3 +0.40 −0.22 −0.23 50 Θ = 1 +0.71 −0.17 −0.17 51 H 52 ΘCl = 1/12 −1.51 −1.89 −1.88 53 ΘCl = 1/3 −1.40 −1.84 −1.84 54 55 56 57 58 59 60 5 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 6 of 18

1 2 3 4 concentration, namely according to 5 6 7 − − 1 0 µ˜(Cl (aq)) − µ(e ) = µ(Cl2(g)) + e(USHE − U ) + kBT ln a − , (1) 8 2 Cl 9 10 0 11 where U is the reduction potential of the chloride and aCl− its activity coefficient. The free 12 13 energy of adsorption as a function of the electrode potential at standard conditions can then 14 15 be calculated acoording to 16 17 18 Nads 0
19 ∆γ(USHE) = Eads − e(USHE − U ) − kBT ln aCl− , (2) 20 As 21 22 23 where the adsorption energy Eads in Eq. 2 is taken with respect to the chlorine molecule 24 25 in the gas phase. Thus this approach avoids to derive solvation energies as a reference for 26 18 + 27 adsorption energies . The same formalism applies to the adsorption of the H where also 28 29 the energy of the free H2 molecule can be used as a reference. Thus we will in the following 30 31 discuss the adsorption energy Eads with respect to the free molecular species. 32 33 First, separate calculations for H-covered and Cl-covered copper surfaces have been per- 34 35 formed at different coverages. The adsorption energies that are listed in Table 1 were calcu- 36 37 lated with regard to the respective free molecules, 38 39 40 E − (E + N E ) E = X/Cu Cu 2 X2 , (3) 41 ads N 42 43 44 where X =H,Cl, and N is the number of adatoms in the supercell. The calculated energies 45 46 agree well with previous studies.21–23 For both adsorbates, the most stable adsorption sites 47 48 49 are the threefold hollow sites with the fcc and hcp threefold hollow sites being energetically 50 24 51 almost degenerate. Calculations for 1/9 coverage on seven-layer symmetric slabs confirm 52 53 that the hollow sites are energetically equivalent for Cl adsorption on Cu(111). Adsorption 54 55 becomes weaker with increasing coverage, suggesting that the interaction of adatoms among 56 57 themselves is repulsive on the metal surface. 58 59 60 6 ACS Paragon Plus Environment Page 7 of 18 The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Figure 1: Co-adsorbed H with 1/3 ML Cl on Cu(111): (a) 1/12 ML H, (b) 1 ML H. 19 20 21 22 From Table 1, it is clear that the adsorption of chlorine is much stronger than hydrogen 23 24 (∆Eads ∼ 1.7eV). Hence we assume that the presence of hydrogen hardly affects the ad- 25 26 sorption of chlorine. Therefore we focus on the equilibrium coverage of chlorine on Cu(111), 27 28 wherein the electrochemical environment is considered as a reservoir from which the adsor- 29 30 bates come. Using the concept of the computational hydrogen electrode,18,19 it was already 31 32 shown that over a wide range of electrode potentials a ratio of one adsorbed chlorine atom 33 34 20 25 35 per three copper atoms is thermodynamically stable, in agreement with the experiment. 36 37 We considered two co-adsorption systems of hydrogen and chlorine on the flat copper 38 39 surface shown in Fig. 1: co-adsorbed H with 1/3 ML Cl on Cu(111), for hydrogen surface 40 41 coverages of 1/12 ML and 1 ML H (representing low and high amounts of additional hy- 42 43 drogen). These models are consistent with cyclic voltammetry measurements complemented 44 25,26 45 with in situ STM of Cu(111) electrodes in dilute HCl solutions. Guided by Table 1, we 46 47 have chosen adsorption only on threefold hollow sites for the co-adsorption configurations 48 49 considered. 50 51 Assuming chlorine is already present at the Cu surface, the energy associated with adding 52 53 hydrogen to the surface is 54 55 56 E − (E + NH E ) E = (H+Cl)/Cu Cl/Cu 2 H2 . (4) 57 H N 58 H 59 60 7 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 8 of 18

1 2 3 4 DFT calculations yield EH = 0.15 eV and 0.59 eV for the addition of hydrogen at coverages 5 6 of 1/12 and 1 ML, respectively.These adsorption energies are significantly more positive than 7 8 the corresponding hydrogen adsorption on clean Cu(111) of EH = −0.23 eV and −0.17 eV at 9 10 coverages of 1/12 and 1 ML, respectively (see Tab. 1). This indicates that there is a repulsive 11 27 12 interaction between adsorbed hydrogen and chlorine and that adsorbed hydrogen atoms 13 14 are unstable with respect to the desorption if the Cu surface is already covered with chlo- 15 16 rine.The positive adsorption energies indicate that there is a repulsive interaction between 17 27 18 adsorbed hydrogen and chlorine – adsorbed hydrogen atoms are unstable with respect to 19 20 the desorption if the Cu surface is already covered with chlorine. This is consistent with the 21 22 observation that in the hydrogen evolution reaction on Cu the Volmer step H + e → Had is 23 24 the rate-limiting step.28 25 26 Knowing that (1) chlorine adsorbs much more strongly on the surface compared to H, 27 28 (2) its equilibrium coverage is 1/3 ML, and (3) that adding hydrogen to this Cl-covered 29 30 Cu surface is energetically unfavorable, we conclude that single-atom Cu wires in an elec- 31 32 trochemical solvent containing HCl will have only adsorbed chlorine. Thus, this section’s 33 34 results provide an estimate for the number of Cl-atoms that adsorb near the single-atom 35 36 wire. 37 38 39 40 Transport of Cu-wires in H- and Cl-containing environments 41 42 43 We now study the effect that H and Cl adatoms have on the transmission properties of a 44 45 single-atom copper wire. Although we just have shown that under electrochemical conditions 46 47 hydrogen adsorption on copper is rather unlikely, we consider the influence of adsorbed 48 49 hydrogen on the transport properties of the junction as hydrogen is a common adsorbate 50 51 under electrochemical conditions on other electrode metals such as platinum.29 As a very 52 53 rough estimate of the number of adatoms that adsorb near the junction, we will assume 54 55 that also the Cu wire exhibits a coverage close to 1/3, i.e. about every third Cu atom 56 57 binds to a Cl atom. Like in the previous section, we treat exchange and correlation in the 58 59 60 8 ACS Paragon Plus Environment Page 9 of 18 The Journal of Physical Chemistry

1 2 3 11 4 generalized gradient approximation (PBE functional ). For cluster-type transport studies, it 5 6 is advantageous to switch from a plane-wave to a strictly localized basis on solving the Kohn- 7 30 8 Sham equations. For this reason, we made use of the Fhi-Aims package. We employed 9 30 10 an optimized atom-centered basis set from the reference of the size equivalent to standard 11 12 double-ζ sets of quantum chemistry [the “light” settings]. Structure relaxations have been 13 −1 14 performed until all force components per atom fell below the threshold 0.01 eVA˚ . 15 16 17 Model structures and electron transport method 18 19 20 Structure optimization. To define representative structures for the transport calcula- 21 22 tions, we first choose a vacuum geometry for “clean” wire composed of few atoms and suit- 23 24 able model electrodes (pyramids). A catalogue of the possible choices for the latter has been 25 26 proposed and tested in conjunction with the AITRANSS module for DFT-based transport 27 28 calculations.31–33 29 30 When attaching the adatoms, the structure optimization proceeds in two steps. First, 31 32 we start with an initial (guess) structure and perform a “constrained relaxation”: all Cu 33 34 atoms are constrained to their vacuum positions; only the adsorbate atoms are allowed to 35 36 move. Second, the constraint on the central part of the Cu junction – both apices, the 37 38 atom in the middle and the three-atoms-top layers of the pyramids – is released, while 39 40 remaining electrode atoms were fixed. In Fig. 2 we show two examples of initial and final 41 42 (unconstrained) geometries. Clearly, the final structure for an unconstrained optimization 43 44 45 may depend on the initial position of the Cl atoms. Fig. 2(d) shows a metastable state. Its 46 47 energy is about 1eV higher than the one of the structure shown in Fig. 2 (b). 48 49 50 Electron transport calculations. Transport calculations have been performed with the 51 52 module AITRANSS.31–33 It relies on the Landauer-theory with Kohn-Sham scattering states 53 54 obtained from the underlying ground-state DFT calculation. For a basic discussion of KS- 55 56 based scattering theory see, e.g.,34 and references therein. We note that the cluster-type 57 58 59 60 9 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 10 of 18

1 2 3 4 transport calculations often require bigger electrode volumes than structural (relaxation) 5 6 studies. Transmission resonances can be quite sensitive to the level spacing. To check for 7 8 possible issues with level spacing, we have added new layers of Cu on the outer planes of 9 10 both pyramids in successive steps and compared respective transmission functions. Figure 3 11 12 shows transmission for electrodes differing by the number of Cu atoms, NCu. We find that 13 14 the salient features of the transmission curve turn out to be captured already with NCu = 18. 15 16 All transport data shown in the Results section have been obtained for this electrode size. 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Figure 2: (a) Initial geometry, first structure. (b) Structure after relaxation of the cen- 36 tral part of the junction, “unconstrained geometry”, see text. (c) Initial geometry, second 37 38 structure and (d) a corresponding relaxed structure. 39 40 41 42 Local density of states and electron transport 43 44 45 LDoS: copper junction The valence electronic structure of a copper atom is [Ar]4s13d10. 46 47 In Fig. 4, top-left, we plot the local (central atom) density of states for a clean Cu junc- 48 49 tion. As it is quite common with transition metals, the (quasi) d-band is clearly recognized 50 51 in the LDoS as a pronounced ridge; for the Cu junction the ridge develops in the range 52 53 [−7., −1.] eV. We note that all the eigenstates in the energy window of several eV around 54 55 E should be considered as spd hybrids. The eigenstates of the three Cu atoms – apices 56 F 57 and central atom – can be classified according to the C group of the two-dimensional 58 ∞v 59 60 10 ACS Paragon Plus Environment Page 11 of 18 The Journal of Physical Chemistry

1 2 3 4 10 5 N = 18 6 Cu 7 NCu = 33 8 NCu = 37 9 10 1 11 12 13 14 T(E) 15 0.1 16 17 18 19 20 0.01 21 22 -3 -2 -1 0 1 2 3 23 E − EF [eV] 24 25 Figure 3: Convergence of the transmission function with respect to the cluster size. The 26 27 number NCu refers to the amount of Cu atoms of the clusters. The structure contained Cl 28 adsorbates with optimized positions (constrained relaxation). 29 30 31 103 10 32 2 pure Cu junction pure Cu junction 10 (a) Cu (b) Cu+Cl 33 10 Cl 34 1 1 35 10−1 10−2 36 10−3 T(E) −1 −4 10

37 LDOS [1/eV] 10 38 10−5 −6 39 10 10−7 10−2 40 -8 -6 -4 -2 0 2 4 -3 -2 -1 0 1 2 3 41 E − EF [eV] E − EF [eV] 42 103 10 2 pure Cu junction pure Cu junction 43 10 (c) Cu (d) Cu+H 10 H 44 1 45 10−1 46 10−2 1 10−3 T(E) 47 −4

LDOS [1/eV] 10 48 10−5 49 10−6 10−7 10−1 50 -8 -6 -4 -2 0 2 4 -3 -2 -1 0 1 2 3

51 E − EF [eV] E − EF [eV] 52 53 Figure 4: Local density of states (a,c) taken on the central part of the junction (red arrows 54 in inset) and transmission (b,d) for constrained geometries with Cl-adsorbates (a,b) and H- 55 adsorbates, (c,d). Blue traces correspond to reference data obtained for the junction without 56 57 adsorbates. Additionally, LDoS on the adsorbates is shown by green traces. 58 59 60 11 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 12 of 18

1 2 3 4 rotor. The first three irreducible representations are Σ (atomic angular-momentum states 5 6 s, pz, dz2 ), Π (px, py, dxz, dyz) and ∆ (dxy, dx2−y2 ) with ascending angular momentum w.r.t. 7 8 the z axis that goes through the three atoms. The inter-atomic hoppings decrease as the 9 10 angular momentum increases. It is thus not surprising that the ridge consists of sharp spikes, 11 12 as well as a relatively broad background. At E = EF the Σ character is prominent, where it 13 14 gives rise to a flat LDoS. 15 16 17 10 10 pure Cu junction pure Cu junction 18 Cu+Cl Cu+H 1 19 1 20 21 0.1 0.1 T(E) 22 T(E) 0.01 23 0.01 24 0.001 25 26 0.0001 0.001 27 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 E − E [eV] E − E [eV] 28 F F 29 Figure 5: Comparison of transmission functions for a junction with adsorbates (red curves) 30 and without adsorbates (blue curves). The central junction atoms were relaxed without 31 32 constraints. Adsorption of Cl is addressed in the left panel, H in the right panel. 33 34 35 LDoS: wire with adsorbates After placing the adsorbates, the LDoS changes signifi- 36 37 cantly, because the coordination number of the central Cu atom changes from two to four. 38 39 In general, the copper orbitals may lower their energy as the bonds to adsorbates are formed. 40 41 In turn, the LDoS at the Fermi level is depleted. If the geometry of the Cu backbone is held 42 43 fixed, i.e., does not react to the adsorbates, then the effect turns out to be much stronger for 44 45 the Cl atom as compared to H. Presumably, this is because Cl binds with 3p orbitals that 46 47 rehybridize and thereby can optimize the overlap with the orbitals of Cu more efficiently than 48 49 the single 1s-orbital of a proton. Interestingly, this qualitative difference between Cl and H 50 51 52 adsorbates is largely erased once one allows the geometry of the Cu backbone to respond to 53 54 the presence of adsorbates, see Fig. 5. When the Cu backbone reconstructs, then it does so 55 56 by shifting Cu atoms in a way so as to optimize overlaps with all neighboring atoms. In this 57 58 process, re-hybridization of the Cu orbitals can take better advantage of the protons, too, 59 60 12 ACS Paragon Plus Environment Page 13 of 18 The Journal of Physical Chemistry

1 2 3 4 and so the spectral gap near the Fermi energy is enhanced also with H adsorbates. 5 6 7 Transmission The clean wire has unity transmission at the Fermi level (Fig. 4, blue 8 9 curve) indicating the presence of a single almost perfectly transmitting transport channel. 10 11 This channel arises due to the Σ states discussed previously. The impact of adsorbates on 12 13 the transmission is very strongly dependent on the adsorbate, if the geometry of the Cu 14 15 backbone is held fixed, i.e., does not reconstruct. As we show in Fig. 4, in this situation the 16 17 Cl atoms suppress the transmission by an order of magnitude, while the H adsorbates leave 18 19 it almost invariant. Again, after relaxation of the Cu backbone this difference is erased and 20 21 in both cases the transmission is strongly suppressed, see Fig. 5. 22 23 It is expected that the Cl-Cu bonds have a stronger polar character than H-Cu, implying 24 25 stronger adsorption-induced electrostatic fields that act as potential barriers for electrons. 26 27 This can be verified by a direct comparison of transmissions and LDoS in Fig. 4. On the 28 29 30 H adsorption, the LDoS at EF and T (EF) undergo very small changes. Due to the Cl 31 32 adsorption, the LDoS at EF is reduced by a factor ≈ 3, but T (EF) drops by a factor ≈ 12, 33 34 indicating reflection of scattering electrons at the Cl barrier. 35 36 37 38 Conclusions and Outlook 39 40 41 We have investigated the transport through single-atom thick metal wires in an electro- 42 43 chemical environment. The model system that we have considered was a Cu wire in an 44 45 environment with Cl and/or H ions. The amount of adatom coverage has been calculated 46 47 for planar Cu(111) surface with DFT-based methods. The result served as an input for the 48 49 50 construction of model geometries which have been underlying the electron transport calcu- 51 52 lation. We observe that adatoms have a drastic effect on the transmission of the atomic 53 54 junction, because they tend to form a chemical bond with the central (bottleneck) metal 55 56 atom. The bond formation, depletes the density of states locally within the junction, and 57 58 as a consequence the transmission probability is decreased as well – in our example by more 59 60 13 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 14 of 18

1 2 3 4 than an order of magnitude. 5 6 It is expected that in nanowires with thickness of several atoms adsorption induced 7 8 structural changes will be weak. In our opinion, in this case H adsorption will not change 9 10 the conductance, while Cl will induce an observable decrease, as suggested by our analysis 11 12 of the constrained structures. The obvious fact that the adsorbed ions influence especially 13 14 the very thin single-atom junctions, may easily explain our experimental observation that in 15 16 many cases it seems to be much easier to observe conductance in integer multiples of G0 in 17 1,35–38 18 larger junctions than in single-atom junctions. 19 20 Our results have two relevant implications concerning the potential of electrochemical 21 22 means to control the conductance of single-atom junctions made of under-coordinated noble 23 24 metals (Cu, Ag, Au). (i) One suspects that the junction’s reactivity is relatively high, 25 26 so that electrochemical control with coverages exceeding significantly 10% and more might 27 28 have to imply binding and unbinding of adsorbates right on the junction-forming metal 29 30 atoms. (ii) Moreover, one may think about a mechanical control of the junction mediated 31 32 by electrochemical means. For instance, a proposal based on electrochemical control of the 33 34 surface tension has been made before.1,35–38 Strain can significantly influence the adsorption 35 36 properties of metal electrodes.39,40 Controlling surface tension can result in conditions under 37 38 which the contamination of the junction with solvent atoms might be sufficiently improbable 39 40 so that the mechanism of transport suppression due to adatoms could be less relevant. This 41 42 may explain the fact that according to our experimental findings, in the case of atomic 43 44 transistors operated in this way, the influence of defect scattering in most cases is remarkably 45 46 47 low. 48 49 For sure, the research field of quantum transport controlled by electrochemical means 50 51 is still in its infancy. Many more studies, theoretical and experimental, on different com- 52 53 binations of materials and transport mechanisms will have to be performed, before its full 54 55 potential could really reveal itself. 56 57 58 59 60 14 ACS Paragon Plus Environment Page 15 of 18 The Journal of Physical Chemistry

1 2 3 4 Acknowledgement 5 6 We acknowledge support by the Baden-W¨urttemberg Stiftung within the Research Network 7 8 “Functional Nanostructures”. AB acknowledges support of DFG through the research grant 9 10 AB 4265/2-1. PS, RK and FE gratefully acknowledge the Steinbuch Centre for Comput- 11 12 ing (SCC) for providing computing time on the computer HC3 at Karlsruhe Institute of 13 14 Technology (KIT). 15 16 17 18 References 19 20 21 (1) Xie, F.-Q.; Nittler, L.; Obermair, C.; Schimmel, T. Phys. Rev. Lett. 2004, 93, 128303. 22 23 24 (2) Li, C.; Mishchenko, A.; Li, Z.; Pobelov, I.; Wandlowski, T.; Li, X. Q.; W¨urthner,F.; 25 26 Bagrets, A.; Evers, F. J. Phys. Condens. Matter 2008, 20, 374122. 27 28 29 (3) Bagrets, A.; Arnold, A.; Evers, F. J. Am. Chem. Soc. 2008, 130, 9013–9018. 30 31 32 (4) Scullion, L.; Doneux, T.; Bouffier, L.; Fernig, D. G.; Higgins, S. J.; Bethell, D.; 33 34 Nichols, R. J. The Journal of Physical Chemistry C 2011, 115, 8361–8368. 35 36 37 (5) Weissm¨uller,J.; Viswanath, R. N.; Kramer, D.; Zimmer, P.; W¨urschum, R.; Gleiter, H. 38 39 Science 2003, 300, 312–315. 40 41 42 (6) Mancini, M.; Kubiak, P.; Wohlfahrt-Mehrens, M.; Marassi, R. J. Electrochem. Soc. 43 44 2010, 157, A164. 45 46 47 (7) Simeone, F. C.; Kolb, D. M.; Venkatachalam, S.; Jacob, T. Angew. Chem. Int. Ed. 48 49 Engl. 2007, 46, 8903–8906. 50 51 52 (8) Chapman, D. L. Philos. Mag. 1913, 25, 475–481. 53 54 55 (9) Gouy, G. J. Phys. 1910, 9, 457–467. 56 57 (10) Kresse, G.; Furthm¨uller,J. Phys. Rev. B. Condens. Matter 1996, 54, 11169–11186. 58 59 60 15 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 16 of 18

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