Core electron binding energies of adsorbates on Cu(111) from first-principles calculations

Core-level X-ray Photoelectron Spectroscopy (XPS) is often used to study the surfaces of heterogeneous copper-based catalysts, but the interpretation of measured spectra, in particular the assignment of peaks to adsorbed species, can be extremely challenging. In this study we demonstrate that first principles calculations using the delta Self Consistent Field (delta-SCF) method can be used to guide the analysis of experimental core-level spectra of complex surfaces relevant to heterogeneous catalysis. Specifically, we calculate core-level binding energy shifts for a series of adsorbates on Cu(111) and show that the resulting C1s and O1s binding energy shifts for adsorbed CO, CO2, C2H4, HCOO, CH3O, H2O, OH and a surface oxide on Cu(111) are in good overall agreement with the experimental literature. In the few cases where the agreement is less good, the theoretical results may indicate the need to re-examine experimental peak assignments.


I. INTRODUCTION
Metallic copper and copper nanoparticles play an important role in industrially relevant catalytic processes, such as the low-temperature water gas shift reaction [1][2][3] and the synthesis of methanol from CO 2 and H 2 [4][5][6].Considerable efforts have been directed towards understanding the mechanisms that operate in these systems and X-ray photoemission spectroscopy (XPS) has been the tool of choice in many experimental studies [7][8][9][10][11][12][13][14][15][16][17].XPS is particularly attractive for the characterization of surfaces because it provides information about the elemental composition of the surface as well as the chemical states of the elements.
However, despite nearly forty years of research, many gaps remain in our understanding of the correspondence between features in the experimental XPS spectra and the composition of the sample surface.For example, O1s peaks at binding energies of 531.4 eV, 533.4 eV, 534.2 eV and 535.5 eV have been assigned to physisorbed CO 2 on Cu(111), polycrystalline Cu, Cu(211) and Cu(100), respectively [12,[18][19][20].It is surprising that the reported values differ by as much as 4 eV as physisorbed CO 2 is expected to interact only weakly with any of these surfaces.The situation is similar for many other species: for HCOO − (formate) on Cu(111), C1s binding energies ranging from 287.3 eV to 289.8 eV have been reported [13][14][15]21], and values between 288.2 eV and 291.0 eV have been assigned to the C1s peak of "surface carbonates" on various copper surfaces [8,20,21].Importantly, the reported binding energy ranges for these species also overlap with reported binding energies of "chemisorbed CO 2 " which range from 287.9 eV to 289.8 eV [8,9,12,15,19].This clearly shows that there is a need for additional insights to analyze and interpret experimental photoemission spectra of adsorbed species on Cu surfaces.
First-principles calculations based on densityfunctional theory (DFT) or the GW approach are routinely used to guide the interpretation of valence electron photoemission spectra [22][23][24][25][26][27].In contrast, the vast majority of experimental core-level photoemission spectra are currently interpreted without the aid of computational simulation of the spectroscopic process.For example, none of the twenty experimental XPS studies of Cu surfaces that we reviewed when writing the manuscript used comparisons to theoretical core level binding energies to guide peak fitting [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][28][29][30][31][32].However, a number of approaches for calculating core level bindings energies have been developed over the years, including the frozen-orbital method [33], the Z+1 approximation [34], the Slater-Janak transition state method [35][36][37][38][39], the GW method [40] and the ∆-SCF scheme [41][42][43].In the ∆-SCF scheme, the core-level binding energy is calculated as the total energy difference between the ground state and the fully screened final state.Benchmark calculations on molecular systems indicate that ∆-SCF calculations based on DFT yield binding energies shifts within 0.3 eV of the experimental values [41][42][43].This accuracy is significantly higher than reported binding energy ranges for many adsorbates on Cu surfaces and therefore insights from theoretical calculations should be very useful for the interpretation of experimental core level spectra.
In this paper we use the ∆-SCF method to calculate core-electron binding energies of various adsorbed species on Cu(111), which is the lowest energy surface of metallic copper.In particular, we determine C1s and O1s binding energy shifts for CO, CO 2 , ethene, formate, methoxy, water, OH, and a surface oxide on Cu(111).We compare our calculations in detail with the available experimental literature and highlight cases where experimental peak assignments need to be re-examined.arXiv:1806.03895v1[cond-mat.mtrl-sci]11 Jun 2018

II. COMPUTATIONAL DETAILS
The calculations of core-electron binding energies of adsorbed molecules on Cu(111) were performed in two stages, as described below.
Firstly, adsorption geometries for all of the adsorbed species in the ground state were obtained by using a slab model of the surface.To generate starting configurations, the results of previously published experimental and theoretical studies on the adsorption of CO [44,45], CO 2 [46][47][48] [52,53].For the case of adsorbed CO, we have considered two distinct adsorption sites: the "top" site, directly above a surface Cu atom, and the "three-fold" site, in the valley between three surface Cu atoms (see Figure 1 and Supplementary Figure 2).The Cu slabs were cut with the (111) faces exposed and are four atomic layers thick.In order to minimize the interactions between periodic images, the slabs were built from orthorhombic supercells with a total of 64 Cu atoms per cell, except for the case of the surface oxide for which a 4 × 4 supercell of the hexagonal Cu(111) surface unit cell was used.
The structures were relaxed until the forces on the atoms were less than 10 −3 Ry/bohr and the total energy change between the last two optimization steps was less than 10 −4 Ry.These calculations were carried out using DFT as implemented in the Quantum Espresso software package [57], which employs a plane-wave basis set.Cut-off energies of 40 Ry and 200 Ry were used for the wavefunctions and the charge density, respectively, and the interaction between core and valence electrons is described via ultrasoft pseudopotentials from the Garrity-Bennett-Rabe-Vanderbilt (GBRV) Pseudopotential Library [58].The slabs were separated by ∼ 14 Å of vacuum and a dipole correction [59] was used to minimize spurious interactions between adjacent layers.We employed the PBE exchange-correlation functional [60] with the Grimme-D2 correction to capture the effect of van der Waals interactions [61].The relaxed geometries are shown in Supplementary Figure 2 and the corresponding atomic positions are also provided in the supplementary materials.† Secondly, photoelectron binding energies were calculated using the ∆-SCF approach, i.e. as the total energy difference between the ground state and the ionized state where one electron is removed from a core orbital.This corresponds to the assumption of a fully screened core hole.In these calculations, the surfaces were modelled as clusters cut from the relaxed slabs generated in the first step.The clusters, comprising 88 Cu atoms and the adsorbate, were cut such that the adsorbed species sits approximately at the centre of the top (111) face.The geometries of the adsorbed species on the clusters are illustrated in Figure 1 and the corresponding atomic positions are provided in supplementary information.† The total energies of the clusters were calculated using DFT with a Gaussian orbital basis set as implemented in the all-electron quantum chemistry code NWChem [62].For simulating the final states, an explicit core hole was generated by constraining the occupancy of one of the core orbitals, whilst all other electrons were allowed to relax in the presence of the core hole.The basis sets used in the cluster calculations are provided in the supplementary information.†Briefly, effective core potentials with the associated basis sets from reference [63] were used for the Cu atoms with the following modifications: for the Cu atoms in the top layer, the exponents of the two most diffuse sp-type basis functions were increased to 0.1619 and 0.074, respectively; for the Cu atoms which are not in the top layer, the sp-type basis function with the smallest exponent was removed and the exponent of the sp-type basis function with the second smallest exponent was reduced to 0.1119.These changes were required to prevent numerical instabilities during the self-consistent field procedure.The pcseg-2 all-electron basis sets developed by Jensen [64] were used for the light elements H, C and O, except for the atoms with a core hole, for which a special basis set with uncontracted core orbitals was used (derived from the pcJ-3 2006 basis sets from reference [65]), in order to allow full relaxation of the other electrons on the same atom in the presence of a core hole.All ∆-SCF calculations of Cu(111) clusters with adsorbates were carried out using the PBE exchange-correlation functional.
In order to assess the accuracy of our calculations, additional C1s binding energy calculations were carried out for the free molecules CH 4 , C 2 H 6 , CO, CO 2 , CCl 4 , and CF 4 , and the O1s binding energy was calculated for H 2 O, CO, CO 2 , CH 3 OH, and HCOOH (both O sites).In these calculations both the initial structure relaxation as well as the subsequent ∆-SCF calculation were carried out using both the M06 hybrid functional [66] as well as PBE [60].
We observed in our calculations that the localization of a core hole onto a single atomic site may fail when there are two or more atoms of the same element in the molecule (or cluster).For such systems, it was possible to guide the core hole to the desired site by (i) introducing a fictitious additional atomic charge of +0.1 e (with e being the proton charge) at that site only for the initialization of the Kohn-Sham wavefunctions, and (ii) ensuring that the basis set with uncontracted core wavefunctions that is best suited to accommodate the core hole is only used at that site.

III. RESULTS: TESTS
To assess the accuracy of our calculations for corelevel binding energies of adsorbates on Cu(111) surfaces, we have carried out test calculations of (i) core-electron binding energies of free molecules, (ii) stabilization energies of a point charge above a metallic cluster, (iii) coreelectron binding energies of adsorbed small molecules at different quasi-equivalent adsorption sites on Cu clusters and (iv) the density of states (DOS) of the Cu cluster and bulk Cu metal.
The results of the calculations on free molecules are summarized in Table I and Figure 2. The theoretical binding energy shifts (referenced to methane for the C1s core level and methanol for the O1s core level) have been compared to experimental values compiled by Cavigliasso [41].Good agreement between theory and experiment is found for both functionals, with M06 performing somewhat better than PBE: the mean unsigned errors are 0.08 eV and 0.13 eV for M06 and PBE, respectively, and FIG. 2. Theoretical core level binding energy shifts for free molecules, plotted against the corresponding experimental shifts from gas phase measurements [41].
the maximum errors are 0.23 eV (C1s binding energy of CO) for M06 and 0.79 eV (C1s binding energy of CF4) for PBE.Despite the small quantitative difference with the M06 results, the results obtained with PBE are sufficiently accurate to interpret experimental spectra.It is also possible to compare the absolute values of the theoretical binding energies to the experimental data for the free molecules, and for the C1s and O1s core levels considered in this work, we find that the values agree to within ∼ 0.3 % for M06 and ∼ 0.5 % for PBE.
Next, we studied how the finite size of the cluster affects the calculated core-electron binding energies.For this, a series of calculations were performed using clusters of a "model metal".This "model metal" was chosen to enable the simulation of large clusters and consists of lithium atoms in a cubic close-packed structure with a lattice parameter of 4.39 Å, similar to the high pressure fcc phase of lithium [67,68].The shapes of the Li 42 , Li 88 and Li 162 clusters used in these calculations are shown in Figure 3.For maximum computational efficiency, a primitive STO-2G basis set was used.A test charge of +1 e located above the cluster surface was used to simulate the effect of a core hole in an adsorbed molecule.Table II shows the calculated stabilization energies, i.e. the difference of total energies with and without the test charge, for three different cluster sizes and different heights of the test charge defined as the distance of the point charge from the plane of Cu nuclei in the top layer.The test charge was placed above either a 3-fold site or a "top" site of the close-packed surface.We find that the stabilization energies calculated using the Li 88 cluster are within ∼ 0.16 eV of those obtained using the larger Li 162 cluster.If the relative stabilization energies for different  sites close to the surface of the cluster are considered, the errors are even smaller.This finding suggests that the finite-size error in our calculations of adsorbates on Cu clusters consisting of 88 atoms are small enough to allow meaningful interpretation of experimental spectra.
We have not been able to perform calculations on bigger Cu clusters because of the required computational expense of the calculations and the numerical instabilities that are common in simulations of metallic systems using a local orbital basis set that includes "diffuse" (i.e.small exponent) Gaussian basis functions.We also calculated the C1s and O1s binding energies for the CO and CO 2 molecules adsorbed at two different adsorption sites on the top surface of the Cu 88 cluster that are equivalent with respect to the underlying lattice, but distinguishable by their position relative to the finite sized cluster, see Figure 1.Large differences in the obtained binding energies at different quasi-equivalent sites on the cluster surface would indicate that the calculated values are strongly affected by finite size effects.The results of these tests are shown in Table III.Amongst the tested positions, the calculated binding energies vary by less than 0.05 eV indicating that finite-size effects are small.
Finally, in order to verify that the effective core po- tential and the Gaussian basis set from reference [63] are suitable for simulations of metallic Cu, we calculated the DOS of bulk Cu using this basis set and the CRYSTAL14 software package [69].Figure 4 shows that the resulting DOS is in excellent agreement with the DOS of bulk Cu obtained from plane-wave DFT.For comparison, we have also included the DOS of the bare Cu 88 cluster in Fig- ure 4.

IV. RESULTS: ADSORBATES ON CU(111)
The results of the C1s and O1s binding energy calculations for the various adsorbed species on Cu(111) are compared to experimental data in Figures 5 and 6 and in Tables IV and V. Whenever possible, we compare our results to measured binding energies of adsorbates on Cu(111).However, because of the limited availability of experimental data for this surface, we also compare to results obtained on other Cu surfaces as well as polycrystalline Cu. Figure 5 and Table IV show good overall agreement between the calculated O1s binding energy shifts and experimental measurements.In our calculations, the top O atoms in the surface oxide structure, see Figure 1, exhibit the smallest binding energy and we use this energy as reference for all O1s binding energy shifts.The binding energy shift of the lower O atom in the surface oxide is 0.78 eV.To compare this result to experimental data, we have grouped together all peak assignments that are referred to as "adsorbed oxygen", "oxygen adatom" or "surface oxide" in the experimental literature, see Table IV.The corresponding experimental binding energy shifts are calculated relative to a reference energy of 530.0 eV and range from -0.50 to +1.00 eV [8,12,16,19,21,32].For an adsorbed methoxy (CH 3 O) group we obtain a binding energy shift of 1.40 eV in good agreement with the experimental result of 1.20 eV for methoxy on Cu(110) [21].The calculated binding energy shifts of adsorbed hydroxyl (OH) and formate (HCOO) are 1.63 eV and 1.66 eV, respectively, in very good agreement with the measured values of 1.50 eV for OH on Cu(111) [9] and 1.50 eV for formate on Cu(111) [13,14].
For the case of CO on Cu(111), it is important to note that the top adsorption site is found to be the most favourable one by experiment [70] and also in calculations using the DFT+U method [45], hybrid functionals [71] and the Random Phase Approximation (RPA) [72].In contrast, standard functionals based on the Generalized Gradient Approximation (GGA) predict adsorption at the 3-fold site to be most stable [73,74].In our calculations, a core level binding energy shift of 2.91 eV is obtained for the molecule on the top site, whereas a value of 1.67 eV is obtained for the molecule at the three-fold site.The value obtained for the top site is in reasonable agreement with the experimental value of 3.40 eV reported in reference [9] for CO on the Cu(111) surface.In contrast, a much smaller binding energy shift of 1.5 eV has been reported in reference [7], also for CO on Cu(111), and this value is similar to our calculated result for the three-fold site.Whilst this result might be interpreted to mean that both adsorption sites can be occupied under the measurement conditions, further work on this matter is desirable because to the aforementioned limitations of GGA functionals which we employ in our ∆-SCF calculations in describing the adsorption of CO on Cu(111).
For H 2 O on Cu(111), both the isolated molecule and the monolayer have similar binding energy shifts of 3.41 eV and 3.24 eV, respectively.Both of these values are in good agreement with the experimental studies that report a binding energy shift of 3.0 eV for adsorbed water on Cu [8,32].Finally, CO 2 on Cu(111) exhibits the largest binding energy shift of 4.39 eV of all oxygen-containing molecules in our study.We find that this molecule is not chemically bonded to the surface.Experimental findings for O1s binding energies of physisorbed CO 2 on Cu surfaces range from 1.40 eV to 5.50 eV [12,[18][19][20], making it difficult to assess the agreement between theory and experiment.It is interesting to compare our results also to experimental measurements for physisorbed CO 2 on different metals as the binding energy shifts which are dominated by electrostatic image charge effects should only weakly depend on the chemical composition of the metal.In particular, O1s binding energy shifts of 4.7 eV and 5.0 eV have been reported for physisorbed CO 2 on Ni(110) and polycrystalline Fe, FIG. 5. A comparison of calculated and experimental O1s binding energy shifts for various surface species on copper.For the surface oxide, the square indicates the theoretical value obtained for the higher (surface) oxygen site, and the diamond shows the value for the lower (buried) oxygen site.For CO, the square indicates the theoretical value obtained for the "top" adsorption site, and the diamond shows the value for the "3-fold" site.For water, the square indicates the theoretical value obtained for a surface water molecule hydrogen bonded to two other water molecules, and the diamond shows the value for an isolated water molecule on Cu(111).Full details and references for the experimental datapoints are given in Table IV.FIG. 6.A comparison of calculated and experimental C1s binding energy shifts for various surface species on copper.For CO, the square indicates the theoretical value obtained for the "top" adsorption site, and the diamond gives the value for the "3-fold" site.Full details and references for the experimental datapoints are given in Table V.
respectively [75].This, combined with the theoretical results, suggests that the peaks at much lower binding energies that have been assigned to physisorbed CO 2 on Cu may actually correspond to some other chemical environments.
The calculated C1s binding energy shifts are compared against the available experimental data in Figure 6 and Table V.In our calculations, adsorbed ethene is used as a model of "adventitious carbon", and we use the C1s binding energy of this species as the reference for all theoretical C1s binding energy shifts.Experimental C1s binding energy shifts are calculated relative to a reference energy of 285.0 eV.In Figure 6 and Table V, we have grouped together all peak assignments that are referred to as "adventitious carbon", "carbon contamination", "graphitic carbon", "C 0 " or "C x H y " in the experimental literature.The corresponding experimental binding energy shifts range from -0.6 eV to 0.2 eV [8,9,12,19,20].
For CO on Cu(111), the theoretical binding energy shift obtained for the 3-fold adsorption site (1.40 eV) is slightly closer to the experimental values reported for the (111) surface (1.1-1.2 eV) [7,9] than the theoretical value for the top site (1.75 eV).However, as discussed before, further work is required to assess the influence of the choice of exchange-correlation functional in the ∆-SCF calculation on the core-level binding energy of CO on Cu(111).For the formate species, the theoretical binding energy of 2.81 eV agrees well with the majority of the published experimental values for formate on various Cu surfaces that range from 2.3 eV to 3.2 eV [8,[12][13][14][15]21].The outlier amongst the experimental datapoints (at 4.75 eV [29]) is also the one that lies furthest from the calculated value.For methoxy on Cu(111), we note that unfortunately neither of the detailed photoelectron diffraction studies of this species [30,76] report the experimental C1s binding energy.The binding energy shift that has been reported for C-O(H) environments on Cu(111) (1.3 eV) is relatively similar to our calculated value for methoxy on Cu(111) (1.82 eV), whereas the shifts that have been reported for the methoxy species on Cu(110) and polycrystalline Cu (0.8 eV and 0.2 eV [8,21]) are much smaller.However, we believe that all of these experimental values should be taken with a note of caution, because they come from studies where complex surface chemical processes were investigated [8,12,21], making the interpretation of the experimental spectra extremely challenging.
For physisorbed CO 2 on Cu(111), we have obtained a theoretical C1s binding energy shift of 4.92 eV.Favaro et al. [12] have reported a binding energy shift of 3.4 eV for CO 2 on Cu(111), but the binding energy shifts reported for physisorbed CO 2 on other Cu surfaces and polycrystalline copper are significantly larger and range from 6.0 eV to 7.0 eV [18][19][20].Similarly large shifts of 6.2 eV and 6.5 eV have been reported for physisorbed CO 2 on Ni(110) and polycrystalline iron [75], respectively.This suggests that the theoretical binding energy shift value of 4.92 eV is probably too low by approximately 1-2 eV.We note that in the calculations of free molecules, the C1s binding energy shift in CO 2 is also underestimated by ∼ 0.5 eV when using the PBE functional, but this is not sufficient to explain the discrepancy of more than 1 eV for the adsorbed species.In order to account for the remaining part of the disagreement, we hypothesize that CO 2 molecules may not physisorb onto Cu as a uniform monolayer.In particular, since the adsorption energy for CO 2 on Cu (∼ 24 kJ/mol [47]) is similar to the enthalpy of sublimation of solid CO 2 (∼ 26 kJ/mol [77]), the formation of three-dimensional ad- sorbed clusters may be favourable even at monolayer or sub-monolayer coverage.For CO 2 molecules in adsorbed clusters, it is reasonable to expect that the O1s binding energy is higher than for a single adsorbed molecule because the screening of the core hole in the final state is weaker when the molecule is located further away from the metal surface.
Finally, we note that we have not been able to calculate theoretical photoelectron binding energies for chemisorbed CO 2 .In agreement with previous experimental [10,47,78,79] and theoretical [46,47] investigations we have found that CO 2 does not chemisorb on defect-free Cu(111), which is the surface that has been considered throughout this work.In fact, the theoretical calculations of Muttaqien et al. suggest that the chemisorption of CO 2 is also unfavourable on ideal stepped and kinked Cu surfaces that expose the Cu(111) face [80], and very recently it has been proposed that the chemisorbed state can only occur on Cu(111) in the presence of sub-surface oxygen atoms [12].

V. CONCLUSIONS
In this work, we have shown that accurate core-level binding energy shifts of various adsorbed molecules on Cu(111) can be obtained from ∆-SCF calculations on a cluster model of the surface.For the majority of the studied adsorbates (H 2 O, OH, HCOO, C 2 H 4 and CO), the calculated binding energy shifts agree well with published experimental data.In the few cases where the agreement is less good (CH 3 O, CO 2 ), the theoretical results may indicate the need to re-examine experimental peak assignments.
The ability to calculate core-level binding energy shifts from first principles is highly desirable due to the commonly encountered difficulties in the interpretation of experimental spectra.In particular, theoretical modelling may be the only practical way for estimating core-level binding energies of atoms in complex chemical environments, such as those that are formed under non-UHV conditions, under irradiation or in electrochemical setups.
On the other hand, the results presented in this work Monolayer physisorbed CO2 on Cu(poly) [19] 291.00 6.00 Physisorbed CO2 on Cu(poly) [18] 291.306.30 Monolayer physisorbed CO2 on Cu(211) [19] 291.50 6.50 Physisorbed CO2 on Cu(100) [20] 292.00 7.00 a All energies are given in eV. also highlight the difficulty of assessing the accuracy of a method for calculating XPS binding energy shifts for surface species which stems from the scarcity of reliable reference data.To make progress in this direction, it would be highly desirable to combine XPS measurements with other experimental techniques, such as scanning tunnelling microscopy or surface X-ray diffraction, to establish detailed structural models for several adsorbed species which could then inform first-principles calculations of core-level binding energies.

FIG. 1 .
FIG. 1.The clusters used for the calculation of core level binding energies of adsorbates on Cu(111).

FIG. 3 .
FIG.3.The clusters used for calculating the stabilization energy of a test charge near a surface of a "model metal" with the electronic configuration of lithium and a face-centered cubic structure.

FIG. 4 .
FIG. 4. Left: The Cu88 cluster used for the ∆-SCF calculations.Right: The density of states of bulk Cu calculated using a plane-wave basis set, bulk Cu calculated using a Gaussian basis set and of the Cu88 cluster.The curve of Cu88 has been offset for clarity.The energies are referenced to the respective calculated Fermi energies.
, C 2 H 4 [49], H 2 O [50-53], HCOO − [13, 29], CH 3 O − [30, 54, 55] and OH − [50] on Cu(111), as well as the study of Lian et al. on the formation of surface oxides on low-index Cu surfaces [56], were used.For the case of adsorbed water, we have considered two distinct models: an isolated H 2 O molecule on Cu(111) and an H 2 O molecule hydrogen bonded to two other surface H 2 O molecules, with a similar local environment to what is found in water hexamers on Cu(111)

TABLE I .
A summary of the results of core-level binding energy calculations of free molecules.Atom a Exp B.E. b Exp shift M06 shift M06 error PBE shift PBE error

TABLE II .
Stabilization energies of a test charge of +1 proton charge at various distances above the top face of a cluster of a "model metal" with the electronic configuration of lithium.

TABLE IV .
A summary of the results of O1s binding energy calculations of various adsorbates on Cu(111), as well as the surface oxide.Exp.species Ref. Exp.B.E. a Exp.shift Theor.species Theor.shift a All energies are given in eV.

TABLE V .
A summary of the results of C1s binding energy calculations of various adsorbates on Cu(111).Exp.species Ref. Exp.B.E. a Exp.shift Theor.species Theor.shift Graphitic carbon on Cu(111)