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A DFT study of adsorption of imidazole, triazole, and tetrazole on oxidized copper surfaces: Cu₂O(111) and Cu₂O(111)-w/o-CuCUS.

Azoles and their derivatives are known for their corrosion inhibition ability for copper. For this reason the bonding of imidazole, triazole, and tetrazole-used as archetypal models of azole corrosion inhibitors-to Cu2O(111) and Cu2O(111)-w/o-Cu(CUS) was characterized using density functional theory (DFT) calculations. The former surface contains coordinatively-saturated (CSA) and coordinatively-unsaturated (CUS) Cu sites, whereas the latter lacks the CUS sites. We find that the molecules preferentially bond with a single unsaturated N atom to a surface Cu ion and concomitantly form a hydrogen bond with the surface O ion. They adsorb rather strongly at CUS sites with an adsorption energy of about -1.6 eV (as calculated with the PBE functional), whereas the bonding at CSA sites is about three times weaker thus being similar as on metallic Cu(111). The impact of van der Waals dispersion interactions on molecular adsorption bonding is also addressed. Depending on specifics of the adsorption structure, they strengthen the adsorption bonding by about 0.2-0.5 eV. Due to this specific bonding enhancement, dispersion interactions alter the relative stability of adsorption modes for tetrazole. An atomistic thermodynamics approach was used to construct two-dimensional phase diagrams for all the three molecules. In the viable range of oxygen chemical potential only three phases appear in the phase-diagrams, two of which are the high coverage (1 × 1) molecular phases (one on Cu2O(111) and the other on Cu2O(111)-w/o-Cu(CUS)) and the third is clean Cu2O(111)-w/o-Cu(CUS). The current results indicate that molecular adsorption at CUS sites is strong enough to compensate the thermodynamic deficiency of stoichiometric Cu2O(111) thus making it more stable than Cu2O(111)-w/o-Cu(CUS), unless the conditions are too oxygen rich and/or for azole lean. This finding may tentatively suggest that the corrosion inhibition capability of azoles stems from their ability to passivate reactive surface sites.


Introduction
Azole molecules and their derivatives are well known for their ability to slow down the corrosion of metals, 1,2 i.e., many of them are efficient corrosion inhibitors. Although the atomic scale mechanism of how organic corrosion inhibitors work is usually not known, it is widely accepted that the adsorption of inhibitors onto surfaces represents an important step in achieving the inhibitory effect. 3 From this point of view, it is therefore important to characterize the molecule-surface bonding, although it represents only one aspect towards the atomic-scale understanding of corrosion protection mechanisms (for a more thorough approach, which involves a deconstruction of various relevant elements and their integration into a multiscale model, see the recent paper of Taylor 4 ). Moreover, the interaction of organic molecules with surfaces has also been receiving considerable attention due to its importance in many other technological applications as well as for reasons of scientific curiosity.
In previous publications, the adsorption of imidazole, triazole, and tetrazole-used as archetypal models of azole inhibitors-has been characterized on Cu(111) by means of DFT calculations 5,6 to provide an atomic-scale insight into the chemistry of azole-copper bonding. It has been shown that neutral molecules bind weakly with Cu(111) via unsaturated N heteroatoms through the s-type bonding and the magnitude of adsorption energy decreases from imidazole to tetrazole. However, oxide-free copper surfaces are more relevant at acidic pH, but under other conditions copper surfaces are often oxidized. 7 In order to explain how the adsorption bonding of azole molecules depends on the oxidation state of copper, we extend the previous studies 5, 6 by investigating the adsorption of these molecules on oxidized copper surfaces.
In general, the interaction of corrosion inhibitors has been explicitly modeled by DFT methods mainly on bare metallic surfaces; the reason is likely related to the fact that metallic surfaces are structurally and electronically simpler than oxidized surfaces. Computational DFT studies concerning the adsorption of azole inhibitors on oxidized copper surfaces are very scarce, i.e., Jiang 8 and Peljhan and Kokalj 9,10 considered the adsorption of benzotriazole on Cu 2 O, and Blajiev and Hubin 11 considered two thiadiazole derivatives. But several other studies modeled adsorption of probe molecules on Cu 2 O, such as CO, NO, H 2 O and CO 2 , [12][13][14][15][16][17][18][19] and also cylic organic molecules, such as 2-chlorophenol, 20 bromobenzene, aniline 21 and cyclohexanol. 22 Soon 23 emphasized the importance of surface defects on copper oxide surfaces and showed that several non-stoichiometric surfaces are more stable than stoichiometric Cu 2 O(111). Due to this several studies of molecular adsorption were performed on non-stoichiometric surfaces. 9,10,20,21 In the current paper, we investigate the bonding of imidazole, triazole, and tetrazole (their molecular structures are shown in Scheme 1) on Cu 2 O(111) and Cu 2 O(111)-w/o-Cu CUS surfaces; the latter surface is considered, because it is thermodynamically more stable than the former in ambient oxygen atmosphere. 23 The difference between the two surfaces is that the latter lacks the coordinatively unsaturated (CUS) Cu sites; the notation Cu 2 O(111)-w/o-Cu CUS thus stands for ''Cu 2 O(111) without the Cu CUS sites''. Molecular adsorption is currently considered at a solid/vacuum interface, although in the context of corrosion inhibition it would be more appropriate to consider adsorption at a solid/water interface. This choice is due to obvious modeling reasons, and moreover because the adsorption from an aqueous phase is a rather involved phenomenon with a number of competitive effects, such as molecule-surface, molecule-water, and surface-water interactions. Hence, it is appropriate to start with a simpler system that allows a more direct chemical characterization of the molecule-Cu 2 O bonding, which is the issue that the current paper is targeted at.

Computational
The calculations were performed in the framework of DFT using the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE). 24 In addition to the plain PBE functional, adsorption calculations were also performed using a PBE-D 00 functional, which includes a reparametrized empirical dispersion correction of Grimme 25,26 that consists of a damped C 6 R À6 like energy term on top of the PBE. The double prime in the PBE-D 00 label is used to indicate the reparametrization of the original method. This reparametrization is slightly different from our previous PBE-D 0 reparametrization of ref. 27, ‡ which was also used in ref. 9, 10 and 31-34. By default, all the presented results refer to the PBE functional, unless explicitly stated otherwise.
A pseudopotential method with ultrasoft pseudopotentials was used. 35,36 All calculations were done using the PWscf code from the Quantum ESPRESSO distribution, 37 whereas visualization and molecular graphics were produced by the XCRYSDEN graphical package. 38 The Kohn-Sham orbitals were expanded in a plane-wave basis set up to a kinetic energy cutoff of 30 Ry (240 Ry for the charge density cutoff). Brillouin zone (BZ) integrations were performed employing the special-point technique 39 using a Marzari-Vanderbilt cold smearing 40 of 0.01 Ry.

Model of oxidized copper surfaces
Oxidized copper surfaces were modeled by Cu 2 O slabs without a metal support underneath. This model is appropriate for cases where the oxide layer on top of metal is not ultrathin, because the reactivity of few Å thick oxide films supported on metals can be very different from the reactivity of surfaces of bulk oxides. 41 In a recent study, 42 the average thicknesses of Cu 2 O oxide layers formed on Cu immersed in 3 wt% NaCl solution were estimated to be about 2.2 AE 0.3 nm for the noninhibited sample and 1.3 AE 0.2 nm for the sample inhibited by benzotriazole. These thicknesses seem therefore sufficient to make the current model adequate.
Scheme 1 Skeletal formulae of imidazole, triazole, and tetrazole with the numbering of N atoms (top) and ball-and-stick models of optimized molecular structures (bottom). The arrows indicate the N atoms that preferentially bond with the considered Cu 2 O surfaces (see Section 3). ‡ The reason for the reparametrization is that the original PBE-D overestimates a molecular bonding to copper surfaces, [27][28][29][30] which can be attributed to a too large C 6 value of a Cu atom. 29 Both the PBE-D 0 and the current PBE-D 00 are re-parametrized so as to match the experimental adsorption energy of a flat lying benzene on Cu(111). For PBE-D 0 this was achieved in a dirty way by adjusting the s 6 scaling parameter to the value of 0.47 (the original value is 0.75), because the Quantum ESPRESSO code did not allow to set the C 6 values in the input. Consequently, PBE-D 0 cannot handle well the lateral molecule-molecule dispersion interactions and is therefore mainly applicable for the molecule copper bonding at low coverage. In contrast, for PBE-D 00 the Quantum ESPRESSO code was modified to allow the specification of C 6 parameters in the input and the C 6 parameter of Cu was set to the value of 140 Ry Bohr À6 (the original value is 375 Ry Bohr À6 ), while the s 6 was kept at its original value of 0.75.  44 ), several test calculations revealed that the effect of magnetism on the total energy is marginal, 9 hence all the presented results refer to spin unpolarized slab calculations.

Surface free energy calculations
Surface free energies were calculated using symmetric (1 Â 1)slabs in which both surfaces are equivalent. The slabs consisting of 6, 7, and 9 O-Cu-O trilayers were used. The in-plane lattice spacing was fixed to the calculated equilibrium bulk lattice parameter, while other degrees of freedom were relaxed. The BZ integrations were performed using a 3 Â 3 Â 1 uniformly shifted k-mesh.
It has been shown that to a first approximation total energies can be used to represent Gibbs free energies of solids, 23,45 hence the surface free energies (g surf ) were calculated by fitting the equation: 9 for several values of N tl , where N tl is the number of O-Cu-O trilayers in a (111) slab, E slab is the total energy of the slab, A is the area spanned by a supercell (factor 2 comes from the fact that a slab has two equivalent surfaces), E tl is the total energy of a single trilayer in the bulk, m O is the chemical potential of oxygen, and DN stoich O is the number of excess O atoms, i.e.,

Adsorption calculations
The adsorption calculations were performed using slabs consisting of four O-Cu-O trilayers. The molecules were adsorbed on the top side of the slab and a dipole correction of Bengtsson 46 was applied to cancel an artificial electric field that develops along the direction normal to the slab due to periodic boundary conditions imposed on the electrostatic potential. The thickness of the vacuum region-the distance between the top of ad-molecules and the adjacent slab-was set to about 20 Å. Adsorption properties were calculated with (1 Â 1), (2 Â 2), and (3 Â 3) supercells, using the 3 Â 3 Â 1, 2 Â 2 Â 1, and 1 Â 1 Â 1 uniformly shifted k-meshes for the BZ integrations, respectively. The adsorption energy was calculated as: where E mol , E slab , and E mol/slab are the total energies of the isolated molecule, slab, and molecule/slab systems, respectively; ''mol'' will be used as a generic label to indicate a molecule. Thermodynamic stability of adsorption structures that differ in surface coverage is evaluated by means of the adsorption surface free energy, g ads , as a function of the molecular chemical potential, m mol . To a first approximation g ads can be related to adsorption energy and m mol via the relation: where n is the number of adsorbed molecules per supercell and Dm mol = m mol À E mol . The important point of eqn (5) is that g ads is a linear function of m mol with the slope being proportional to the negative of the (absolute) surface coverage, Àn/A. This implies that the larger the coverage the steeper is the slope of the corresponding g ads line. Thermodynamically the most stable structure at a given m mol is the one that displays the lowest adsorption surface free energy. The stabilization of surface free energy due to a molecular adsorption can be estimated as: where e ads is the molecular adsorption energy per unit area: Hence the more exothermic the e ads , the more the surface stabilized.
The one-dimensional treatment of eqn (5) can be extended by treating the adsorption surface free energy as a twodimensional function of m mol and m O . We utilize the following approximate relation: and s 0 is the surface energy at the oxygen rich limit (Dm O = 0), i.e., 2.4.1 Other definitions. Electron charge density difference was calculated as: where the subscripts have the same meaning as in eqn (4). The geometries of the standalone ''mol'' and ''slab'' structures were kept the same as in the ''mol/slab'' system. The local geometry of adsorption structures are specified as N list + H bond , where N list specifies with which N atoms a molecule bonds to the surface. If the adsorbed molecule also forms a hydrogen bond with the surface then the H bond specifier characterizes it. Here are two examples: (1) the label N2 + N1HÁ Á ÁO up indicates that a molecule bonds with its N2 atom to the surface and also forms the N1-HÁ Á ÁO up hydrogen bond; (2) the label N2 + N3 indicates that a molecule bonds to the surface via its N2 and N3 atoms without any hydrogen bond.
The global geometry of adsorption phases are designated either as ''(N Â N)-mol@site'' or as ''(N Â N)-mol@surface'', where (N Â N) represents a periodic pattern that molecules form with respect to the surface unit-cell, site designates a specific site the molecules bond to (CSA or CUS), and surface specifies the surface

Results and discussion
The calculated surface free energies of Cu 2 O(111) and Cu 2 O(111)w/o-Cu CUS as a function of the oxygen chemical potential are shown in Fig. S1 in the ESI; † they are in good agreement with those reported previously by Soon. 23 Given that Cu 2 O(111)w/o-Cu CUS is considerably more stable than stoichiometric Cu 2 O(111), it is taken as a reference and a starting point for the current investigation of the adsorption of azoles on oxidized copper surfaces. This model is used to ascertain the molecular bonding at CSA sites. In addition, the adsorption is also modeled at individual CUS sites, which can be regarded as extraneous or defect sites on Cu 2 O(111)-w/o-Cu CUS ; the corresponding model therefore contains only as many CUS ions as adsorbed molecules. This model is used to ascertain the molecular bonding at CUS sites.

Adsorption structures and energies
Several adsorption geometries were investigated for each molecule adsorbed at CSA and CUS sites and the corresponding results are presented in Fig. 1 and 2, respectively. These figures plot the dependence of adsorption energies on the nearest neighbor intermolecular distance, R nn . ¶ Beneath these plots the structures of pertinent adsorption modes-optimized at the lowest considered coverage using the (3 Â 3) supercell-are shown; dipole-moment vectors of isolated molecules, oriented as in the respective adsorption state, are drawn superimposed with the adsorbed molecules and the N-Cu and HÁ Á ÁO bond distances are also stated. It is worth noting that currently only the adsorption of intact molecules is considered, because the dissociation of the molecular N1-H bond, to form OH with the nearby surface O ion (note that on the Cu 2 O surface an H binds more strongly to an O than a Cu ion), was found to be endothermic by more than 1 eV for imidazole and over 0.1 eV for triazole and tetrazole; this issue will be considered in more detail in the forthcoming publication.
Imidazole binds with the N3 atom to the CSA and CUS sites and forms a weak C-HÁ Á ÁO hydrogen bond with either O up near , O up far , or O sub ion when bonded at the CSA sites ( Fig. 1, left) and with the O up ion when adsorbed at the CUS sites (Fig. 2, left). Triazole and tetrazole bind preferably with the N2 atom to the CSA and CUS sites and form a N-HÁ Á ÁO hydrogen bond ( Fig. 1 and 2, middle and right) which is shorter and stronger than the C-HÁ Á ÁO bond of imidazole (for the strength of these hydrogen bonds see Fig. S2 in the ESI †). That the N-HÁ Á ÁO hydrogen bond is stronger than the C-HÁ Á ÁO bond can be also inferred by comparing the adsorption energies of triazole N2 + N1HÁ Á ÁO up vs. N3 + C4HÁ Á ÁO up as well as tetrazole N2 + N1HÁ Á ÁO up vs. N4 + C5HÁ Á ÁO up structures at the CUS sites (Fig. 2, middle and right). Triazole can also bind with the N2 and N3 atoms to two neighboring CSA sites (N2 + N3 adsorption mode), but this mode is stable only at low coverage8 and even then it is inferior  to the N2 bonding modes, presumably due to the lack of N-HÁ Á ÁO bonding.
While on plain metallic Cu surfaces the dependence of adsorption energy on the R nn or on the coverage (Y, note that Y p R À2 nn ) can be straightforwardly understood in terms of the orientation of molecular dipoles-i.e., dipoles oriented normally (parallelly) to the surface result in lateral repulsive (attractive) interactions 5,32,47 -the situation is bit more complicated on the Cu 2 O(111)-w/o-Cu CUS surface, because each Cu CUS vacancy displays an inward pointing dipole of about 0.5 D and it is the cumulative (molecule + vacancies) dipole that matters. Nevertheless, the orientation of molecular dipoles seems still useful to roughly understand the lateral dependence. For example, imidazole displays the most repulsive and tetrazole the most attractive lateral interactions and, indeed, the dipoles of the former point largely upright and that of the latter almost parallel to the surface, e.g., see the left and right panels of Fig. 2 and also the dipole orientation of imidazole N3 + C2HÁ Á ÁO up near and tetrazole N2 + N1HÁ Á ÁO up near adsorption modes in Fig. 1. The current results reveal that molecular bonding to the CSA sites is considerably weaker than that to the CUS sites. The strongest adsorption energy for the three molecules at the CSA sites is about À0.5 eV (Fig. 1), whereas at the CUS sites it is more than three times stronger, being about À1.6 eV for imidazole, À1.7 eV for triazole, and À1.75 eV for tetrazole (Fig. 2). This stronger bonding at CUS sites is also reflected in the N-Cu bond distances, which are about 1.9 Å at the CUS site and in the range between about 2.0 and 2.3 Å at the CSA sites. A similar strong bonding at the CUS sites was reported for benzotriazole. [8][9][10] Several other molecules were also found to bind significantly stronger at CUS sites than at coordinatively saturated sites. 16,18,21 A comparison with the previous results, obtained on metallic Cu(111), 5 reveals that the bonding of imidazole, triazole, and tetrazole to CSA sites is similar in strength as their bonding to Cu(111). To facilitate the comprehension of trends, Fig. 3 compares adsorption energy magnitudes obtained on currently considered CSA and CUS sites to that on metallic Cu(111); the shown magnitudes refer to the most exothermic adsorption energies, regardless of the coverage. This figure clearly reveals that the bonding at CUS sites is considerably stronger than to Cu(111) and to CSA sites of Cu 2 O(111)-w/o-Cu CUS . Indeed, the bonding at the CUS sites is even stronger than, for example, the bonding of benzotriazole at very low coordinated surface defects on metallic Cu surfaces, which was calculated to be about À1.3 eV. 32 A few more comments should be made with respect to the adsorption energy trends (cf. Fig. 1-3). On Cu(111) the magnitude of adsorption energy, |E ads |, decreases from imidazole to tetrazole at any coverage (for more details see ref. 5), whereas on Cu 2 O(111)-w/o-Cu CUS the trends are bit more intricate due to the coverage dependence. At the lowest considered coverage, where the lateral dipolar intermolecular interactions are the smallest, the adsorption bonding strength follows the imidazole E triazole 4 tetrazole trend on both the CSA and CUS sites,** whereas at a larger coverage the trend is affected by lateral dipolar interactions. Considering the largest adsorption energy magnitudes (cf. Fig. 3), irrespective of the coverage, the |E ads | trend at the CSA sites is imidazole E triazole E tetrazole, whereas at the CUS sites it is imidazole o triazole t tetrazole.

Phase diagrams
The coverage dependence of molecular adsorption energies, presented in Fig. 1 and 2, allows us to construct phase diagrams to ascertain which adsorbate structures are thermodynamically the most stable at a given molecular chemical potential, m mol . It should be noted that only three discrete coverages are considered using one molecule per (N Â N) supercell, where N A [1,3]. To provide better comprehension of how densely the molecules cover the surface at these coverages, Fig. 4 plots the top view snapshots of adsorbed triazole.
We first consider the adsorption surface free energy as a function of the molecular chemical potential (cf. eqn (5)). The corresponding plots of g ads for the current molecules are shown in the top row panels of Fig. 5, where the upper plots correspond to the adsorption at CSA and lower plots at CUS sites. Thermodynamically the most stable structure at a given m mol is the one that displays the lowest adsorption surface free energy. In these plots the black horizontal line at g ads = 0.0 meV Å À2 corresponds to a clean surface, which is the most stable at a low m mol , before any of the molecular line intersects it. It should be noted that for a given molecule at a given coverage only the structure with the most exothermic adsorption energy is considered here. It can be seen that for tetrazole and in part triazole, which display attractive lateral interactions, the high-coverage phases are always the most stable, unless the m mol is so low that the bare surfaces become the most stable. In addition, for triazole at the CSA sites, the lower coverage phases are competitive with the high-coverage phase around Dm mol E À0.5 eV, where their g ads lines intersect the clean surface line. In contrast, the situation is different for imidazole, because it displays repulsive lateral interactions. At the CSA sites, the highcoverage (1 Â 1) phase is the most stable at Dm mol 4 À0.27 eV. Below this value the lower coverage phases are the most stable, first the (2 Â 2) and then the (3 Â 3), but only down to Dm mol = À0.51 eV, where the clean surface becomes the most stable. Note that only a few discrete coverages are considered in Fig. 5, hence there can be intermediate situations, but the point is that one passes from low-to high-coverage imidazole structures as the m mol increases from À0.51 eV to À0.27 eV. A similar relationship Middle row: Surface free energies, g surf , of Cu 2 O(111) and Cu 2 O(111)-w/o-Cu CUS and their stabilization due to high coverage molecular adsorption (for a given surface the upper g surf line corresponds to a bare surface and the lower line to molecularly covered surface, while the vertical arrow indicates the stabilization due to high-coverage molecular adsorption). Bottom row: Two-dimensional phase diagrams as a function of molecular and oxygen chemical potentials. ImiH, TriH, and TetH stand for imidazole, triazole, and tetrazole, respectively, whereas ''(1 Â 1)-mol@CSA'' is a shorthand label for (1 Â 1)-mol@Cu 2 O(111)-w/o-Cu CUS , where mol is either ImiH, TriH, or TetH. between high and lower coverage phases of imidazole also exists at the CUS sites with the exception that the stability intercepts are shifted to the left by about 1 eV due to much stronger molecular bonding at CUS compared to CSA sites. † † It should be noted that for the high-coverage (1 Â 1) adsorption phases the number of adsorbed molecules equals to the number of CUS sites on stoichiometric Cu 2 O(111), which implies that (1 Â 1) molecular phases at CUS sites correspond to molecular adsorption on stoichiometric Cu 2 O(111). Given that the high-coverage (1 Â 1) molecular phases dominate in the g ads (m mol ) phase diagrams and the molecules bind much strongly to CUS than to CSA sites, opens a question whether this bonding enhancement is sufficient to stabilize the stoichio-

Electronic structure analysis
To gain more insight into the chemistry of the molecule-surface bonding, Fig. 6 displays the charge density difference, Dr(r), for imidazole, triazole, and tetrazole bound to the CSA (top row) and CUS (bottom row) sites. Only the most stable adsorption structures at a low coverage are considered, i.e., N3 + C2HÁ Á ÁO up for imidazole and N2 + N1HÁ Á ÁO up for triazole § § and tetrazole. In the Dr(r) plots, the red color represents electron charge accumulation and the blue color represents electron deficit regions. The formation of direct N-Cu bonds is clearly seen by the red colored charge accumulation lobes in the midst of these bonds. These electron charge accumulation lobes are weak at the CSA sites and much stronger at the CUS sites, which readily explains the much stronger molecular bonding at the latter. In addition to the N-Cu bonds, the molecules also interact at the surface with the X-HÁ Á ÁO up hydrogen bonds (X = C2 for imidazole or N1 for triazole and tetrazole). These H-bonds are characterized by the substantial charge accumulation located above the pertinent O up ion and the charge deficit region of the nearby H atom. The intensities of these charge redistributions clearly reveal that the N-HÁ Á ÁO bonds of triazole and tetrazole are considerably stronger than the C-HÁ Á ÁO bonds of imidazole. For further characterization of the strength of N-HÁ Á ÁO and C-HÁ Á ÁO bonds see Fig. S2 in the ESI. † The Dr(r) plots reveal that the strength of N-Cu bonds increases from tetrazole to imidazole (at the CSA sites), but the strength of the X-HÁ Á ÁO hydrogen bonds follows the opposite direction, i.e., imidazole o triazole t tetrazole (at both the CSA and CUS sites). ¶ ¶ The latter is the reason that at a low coverage, where the lateral dipolar interactions are sufficiently small, the bonding † † For imidazole at the CUS site the high coverage (1 Â 1) phase is the most stable at Dm mol 4 À1.33 eV. Below this value the (2 Â 2) phase is the most stable and near its intercept with the clean surface line at Dm mol E À1.6 eV also the low coverage (3 Â 3) phase becomes competitive. ‡ ‡ These values were calculated with the thermochemistry utility of the Gaussian 09 program package. 48 § § It should be noted that for triazole at the CSA site, N2 + N1HÁ Á ÁO up far is marginally more stable at a low coverage than the considered N2 + N1HÁ Á ÁO up near (see Fig. 1), but the difference is insignificant.
¶ ¶ The Dr(r) plots clearly reveal that at the CSA site the strength of the N-Cu bond decreases from imidazole to tetrazole, which is consistent with the increasing N-Cu bond length in the same direction. In contrast, at the CUS site the N-Cu electron charge accumulation lobes as well as the N-Cu bond lengths appear to be very similar for all the three molecules. This suggests that at a low coverage the molecule-surface interaction should be the weakest for imidazole, because it lacks the strong N-HÁ Á ÁO hydrogen bond. But this is not the case. The reason can be attributed to molecular chemical hardness, which increases from imidazole to tetrazole. 5,6 Namely, at the CUS site the molecular electronic structure is sufficiently perturbed due to a strong molecule-surface interaction and the hybridization between molecular and copper states is the easiest for imidazole, which is chemically the softest among the three molecules.
strengths of imidazole and triazole are almost degenerate, but the bonding strength of tetrazole is about 0.1 eV less. The stronger N-HÁ Á ÁO bond compared to the C-HÁ Á ÁO bond is therefore able to compensate for the weaker N-Cu bond of triazole compared to that of imidazole, but falls somewhat short for compensating the even weaker N-Cu bond of tetrazole. A further analysis of the three-dimensional shape of Dr(r) (not shown) reveals that the molecules interact with the surface through s-type bonding, which is expected on the basis of the local symmetry of the N-Cu bonds. Even finer details of the molecule-surface interaction are provided for triazole in Fig. 7, where the same adsorption structure as in the Dr(r) plot is considered, i.e., the N2 + N1HÁ Á ÁO up at the CSA and CUS sites. This figure displays the density of states projected (PDOS) to the molecule and the Cu atom beneath it, before and after the molecule-surface interaction sets in. These two cases will be termed before-interaction and after-interaction; for the former case, the molecule is up-shifted such that the N-Cu distance is 6 Å. In addition, the figure also shows the integrated local density of states (ILDOS) analysis as well as the density of states projected to individual molecular orbitals (MO-PDOS) 49 of triazole, because these two techniques allow for unambiguous assignment of molecular PDOS peaks to individual molecular orbitals (MOs).
The before-interaction PDOS plots reveal that four molecular orbitals (from HOMOÀ3 to HOMO (highest-occupied MO)) lie at the position of the metal d-band and are therefore considered in the analysis of the molecule-surface bonding; the LUMO (lowest-unoccupied MO) state, which lies more than 3 eV above the valence band edge, is also considered. Two among these MOs are s-type orbitals (HOMOÀ3 and HOMO) and three are p-type orbitals (HOMOÀ2, HOMOÀ1, and LUMO). Upon interaction these molecular states downshift in energy. The downshift is larger and the molecular PDOS is more broadened for the CUS sites in accordance with the stronger moleculesurface interaction at the CUS compared to that at the CSA site. The downshift is the largest for the HOMOÀ3 s-orbital, being about 2 eV at the CSA sites and about 3 eV at the CUS sites, and its PDOS peaks are the most broadened. These PDOS peaks are located at around À5 eV for the CSA sites and at around À6 eV for the CUS sites. The ILDOS analysis clearly reveals that only these low lying molecular peaks are involved in the interaction with the copper states,88 whereas all the other molecular peaks are non-bonding with respect to the molecule-surface interaction. The MO-PDOS plots show that, in addition to HOMOÀ3, also the HOMO orbital marginally participates in the bonding low-lying peaks, but its 88 It should be noted that the ILDOS analysis shows only four plots per site, although five MOs are considered. The reason is that the HOMOÀ1 and HOMO states are located in the same energy region and cannot be separated, i.e., their PDOS peaks overlap, which is also evident from the respective MO-PDOS plots. predominant contribution is in the uppermost valence (occupied) molecular PDOS peak located at about À2.5 eV at the CSA sites and at about À3 eV at the CUS sites. The MO-PDOS plots further reveal that there is no back-donation of charge from the surface into the molecular LUMO, because the LUMO remains completely empty upon interaction, that is, the MO-PDOS shows no participation of the LUMO in the molecule-surface valence states.

Dispersion corrections
The results presented in the preceding Sections 3.1-3.3 were obtained using the PBE energy functional, which cannot describe  adsorption modes for all the three molecules; the N-Cu bonds correspondingly shorten by about 0.05 and 0.01 Å at the CSA and CUS sites, respectively. The reason that the O sub adsorption modes are stabilized stronger by dispersion interactions than the O up modes is that for the former molecules are located closer to the surface than for the latter, because they are tilted into the Cu CUS vacancies (see the respective snapshots in Fig. 1). Due to this stronger stabilization of the O sub adsorption modes, the relative stability of modes is altered for tetrazole at the CSA sites, i.e., without dispersion correction the O up adsorption mode is by 0.2 eV more stable than the O sub adsorption mode (note that for triazole the two modes are almost degenerate, while for imidazole the O sub mode is more stable). But when dispersion correction is taken into account, the O sub adsorption modes are the most stable at the CSA sites for all the three molecules. The net stabilization due to dispersion interactions at the CSA sites-calculated as the difference between the most stable PBE and PBE-D 00 adsorption modes-is therefore stronger for imidazole and triazole (about 0.5 eV) than for tetrazole (0.3 eV); see the D best column in Table 1. In contrast, at the CUS sites, which lacks the O sub adsorption modes, the stabilization is only about 0.3 eV for all the three molecules.
Dispersion interactions stabilize the adsorption structures mainly through the enhanced molecule-surface bonding. However, for the high-coverage phases the dispersion forces also affect the lateral molecule-molecule interactions due to proximity of neighboring molecules. The lateral molecule-molecule dispersion interactions were estimated*** only for imidazole at the CSA and CUS sites and amount to À0.04 eV per molecule for both sites. Given the empirical nature of the utilized dispersion correction, it can be straightforwardly inferred that it gives slightly weaker lateral molecule-molecule dispersion interactions for triazole and tetrazole compared to imidazole, because an N atom has a smaller C 6 coefficient than a C atom. The current results therefore imply that the lateral molecule-molecule dispersion interactions contribute about 10% to the overall dispersion enhancement of the adsorption energy at the high coverage.
Dispersion corrections affect the adsorption phase-diagrams of  Table 1 Comparison of PBE and PBE-D 00 adsorption energies for high coverage (1 Â 1) adsorption phases. Only the most stable adsorption mode is considered at the CUS sites, whereas for the CSA sites two modes are considered, because dispersion correction alters the relative stability of modes in some cases (the most stable adsorption energies are emphasized in bold). The label D stands for the difference between the PBE-D 00 and PBE adsorption energies for a given mode, whereas D best is the difference between the most stable PBE and the most stable PBE-D 00 adsorption modes for a given molecule, i.e., the difference between the two energies written in bold and where E lateral is calculated with both the PBE-D 00 (E PBE-D 00 lateral ) and PBE (E PBE lateral ) functionals. E (1Â1) mol is the total energy of the (1 Â 1) layer of molecules with structure kept the same as in the adsorption system and E mol is the total energy of the isolated molecule having the same structure as the molecule in the (1 Â 1) layer. The reason that the lateral molecule-molecule dispersion interactions are calculated by eqn (11) and not simply by E PBE-D 00 lateral of eqn (12) is due to a large permanent molecular dipole moment of azoles. Hence the E PBE-D 00 lateral also contains the lateral dipole-dipole contributions, which are canceled out by the E PBE lateral term in eqn (11). triazole the border between (1 Â 1)-mol@Cu 2 O(111) [green region] and (1 Â 1)-mol@CSA [yellow region] shifts to the left, i.e., to lower values of m O , because the dispersion bonding enhancement is larger at the CSA sites (E0.5 eV) than at the CUS (E0.3 eV) sites. In contrast, for tetrazole the dispersion bonding enhancement is almost the same at the two sites and the pertinent border remains unaffected. The resulting, dispersion corrected phase diagrams are presented in Fig. S3 in the ESI. † Finally, some caution is in place concerning the currently used semi-empirical dispersion correction. Namely, PBE-D was currently reparametrized (PBE-D 00 ) to match the experimental adsorption energy of flat lying benzene on Cu(111), because the original PBE-D often overestimates the molecule-surface bonding. 27,29,30,50 However, the current adsorption systems consist of Cu 2 O oxide surfaces and molecules that bond perpendicularly or tilted to the surface. For this reason the current dispersion corrected results may be taken more qualitatively than quantitatively.

Conclusions
Adsorption bonding of imidazole, triazole, and tetrazole to Cu 2 O(111)-w/o-Cu CUS and Cu 2 O(111) was characterized by means of DFT calculations. The difference between these two surfaces is that the Cu 2 O(111)-w/o-Cu CUS lacks the reactive CUS sites and is consequently thermodynamically more stable than Cu 2 O(111). We showed that the bonding of current azole molecules at CUS sites on Cu 2 O(111) is by about 1 eV stronger than at CSA sites on Cu 2 O(111)-w/o-Cu CUS . The bonding at CUS sites is so strong that it compensates the thermodynamic deficiency of Cu 2 O(111), making it more stable than Cu 2 O(111)-w/o-Cu CUS , provided the conditions are not too oxygen rich and/or azole lean. This finding, together with the previously observed trend that azoles bond significantly stronger to low coordinated defects on metallic Cu surfaces than to high coordinated flat facets, 32,33 indicates that azoles have a strong affinity to preferentially adsorb at reactive undercoordinated or unsaturated surface sites, which in turn tentatively suggests that their corrosion inhibition capability may, at least in part, stem from their ability to passivate reactive surface sites.
As for the chemical nature of the molecule-surface interaction, we showed that the current azole molecules preferentially bind to Cu 2 O surfaces via a single s-type N-Cu bond and concomitantly form a hydrogen bond with a nearby surface O ion. Adsorption bonding is further enhanced by van der Waals dispersion interactions, in the range 0.23-0.53 eV, depending on specifics of the adsorption structure. This is a sizable enhancement, because it represents about 50-60% of the total adsorption bonding at the CSA and about 15-20% at CUS sites. At large intermolecular separations (or at a low coverage), where the lateral dipole-dipole effects are sufficiently small, the magnitude of adsorption energy follows the imidazole E triazole 4 tetrazole order, but at a high coverage the trend is altered, because imidazole displays repulsive and tetrazole attractive lateral dipole-dipole interactions. Despite these differences in lateral interactions, atomistic thermodynamics analysis reveals that for all the three molecules only three among the considered phases appear in the phase diagrams: high coverage (1 Â 1)-mol@Cu 2 O(111) and (1 Â 1)-mol@Cu 2 O(111)-w/o-Cu CUS molecular phases, and clean Cu 2 O(111)-w/o-Cu CUS .