Ambient pressure XPS has demonstrated its great potential in probing the solid/liquid interface, which is a central piece in electrocatalytic, corrosion, and energy storage systems. Despite the advantage of ambient pressure XPS being a surface sensitive characterization technique, the ability of differentiating the surface adsorbed species (∼Å scale) and bulk electrolyte (∼10 nm scale) in the spectrum depends on the delicate balance between bulk solution concentration (C), surface coverage (θ), bulk liquid layer thickness (L), and inelastic mean free path (λ) as a function of photon energy. By investigating a model system of gold dissolving in a bromide solution, the connection between theoretical prediction at the atomic resolution and macroscopic observable spectrum is established.

The research interests of physicists, chemists, and materials scientists have shifted significantly from the study of bulk properties of materials to the system behaviors at the interfaces.1 The interactions and exchange of ions and electrons occurring at the solid/liquid interface are ubiquitous scenarios in electrocatalytic systems, e.g., CO2 reduction,2–4 hydrogen evolution reaction,5–9 oxygen evolution reaction,10–15 oxygen reduction reaction,16,17 nitrogen fixation, and18,19 corrosion, as well as in energy storage systems, e.g., lithium ion battery.20,21 In order to expedite understanding, controlling, and optimizing the design of these systems, it is crucial to capture the electron transfer, ion transfer, and breaking and remaking of chemical bonds with the effect of solvation environment at the interface, ideally through the integration of advanced characterization techniques and theoretical models.

Characterization instrumentations possessing the power of atomic resolution can be divided into two classes: imaging (e.g., SEM, TEM, etc.) and spectroscopy [e.g., x-ray photoelectron spectroscopy (XPS), x-ray absorption spectroscopy (XAS), IR, etc.]. Both classes of techniques have profound history in surface science applications, which are usually conducted at Ultra-High Vacuum (UHV). With the increasing demand for in situ and operando measurements, which are orders of magnitude higher in pressure than UHV, advanced spectroscopy with a state-of-the-art modification22–25 is continuously bridging the pressure gap and is gaining an upper hand in the research of solid/liquid interface. For example, ambient pressure XPS26,27 demonstrated its ability in the direct observation of the electrical double layer28 and catalytic mechanism,29operando XAS has been employed to study the molecular scale electrode/electrolyte interface,30 and infrared nanospectroscopy enables studies of the molecular structure of graphene/liquid interfaces with nanoscale spatial resolution.31 

Despite the exciting development and improvement of ambient pressure XPS in the application of probing solid/liquid interfaces, fundamental questions regarding the sensitivity of these measurements to interfacial features have not been well addressed in the previous literature. A special yet central request in understanding the solid/liquid interface is to detect and to differentiate surface species from their bulk counterparts. Achieving this atomic scale sensitivity is challenging because such surface species are at the scale of ∼Å, and furthermore, their signals are buried underneath a bulk liquid layer at the scale of ∼10 nm, as illustrated in Fig. 1. To answer the questions regarding sensitivity, as well as to demonstrate a procedure of connecting atomic understanding to experimental observables, we chose to look at a typical scenario in electrochemistry and corrosion: Br ion dissolving gold. It is a well-studied system with established understanding;32,33 therefore, the goal here is not to repeat the electrochemical findings, but rather to leverage the past knowledge as an excellent opportunity for us to address the sensitivity of this ambient pressure XPS measurement unambiguously. With a special focus on connecting the atomic level picture [Fig. 1(b)] and experiment (Fig. 2), we intend to provide a general framework (ab initio MD → DFT → analytical model → ab initio constructed spectrum) for a solid/liquid system revealing the relationship of realistic experimental conditions [photon energy (PE), concentration, coverage (Fig. 3), etc.] vs the expected spectrum from ab initio (Fig. 4), therefore providing insights into the understanding of distinct spectroscopic features. Finally, we arrived at the conclusion that the ability of differentiating the surface adsorbed species (∼Å scale) and bulk electrolyte (∼10 nm scale) on spectroscopy depends on the delicate balance (Fig. 5) between solution concentration (C), surface coverage (θ), bulk liquid layer thickness (L), and inelastic mean free path (λ) as a function of photon energy (PE).

FIG. 1.

Mapping of the simple schematic model to the atomic scale ab initio model. (a) Schematic illustration of the homogeneous layer model. This model consists of an averaged layer of surface species and an averaged layer of solution species. The x-ray source is from the liquid layer side. The bulk liquid layer thickness is estimated experimentally in Ref. 28 to be 10 nm–30 nm. The interfacial layer thickness is calculated by taking the average height of the surface Br ion in the last 200 equilibrated Molecular Dynamics (MD) trajectory snapshots. The solid electrode thickness does not contribute to the signal of the Br ion. (b) Atomic scale illustration of the surface species layer and solution species layer, from an equilibrated snapshot of ab initio MD (AIMD) calculation. More frames are provided in Fig. 7. Using the ab initio approach, we can calculate the interfacial layer thickness, as well as calculating the BE difference of the surface Br ion and solution Br ion, as explained in detail in the section titled Parameter space.

FIG. 1.

Mapping of the simple schematic model to the atomic scale ab initio model. (a) Schematic illustration of the homogeneous layer model. This model consists of an averaged layer of surface species and an averaged layer of solution species. The x-ray source is from the liquid layer side. The bulk liquid layer thickness is estimated experimentally in Ref. 28 to be 10 nm–30 nm. The interfacial layer thickness is calculated by taking the average height of the surface Br ion in the last 200 equilibrated Molecular Dynamics (MD) trajectory snapshots. The solid electrode thickness does not contribute to the signal of the Br ion. (b) Atomic scale illustration of the surface species layer and solution species layer, from an equilibrated snapshot of ab initio MD (AIMD) calculation. More frames are provided in Fig. 7. Using the ab initio approach, we can calculate the interfacial layer thickness, as well as calculating the BE difference of the surface Br ion and solution Br ion, as explained in detail in the section titled Parameter space.

Close modal
FIG. 2.

Comparison of the Br[3d] spectrum at the condition of 0.6 V vs Ag/AgCl and the Br 3d spectrum in a reference solution of 1M AuBr4. (a) Raw spectrum of Br 3d at 0.6 V vs Ag/AgCl shows a symmetrical feature. (b) Raw spectrum of Br 3d in a reference solution of 1M AuBr4 shows an asymmetrical feature, which has an obvious concave feature at 69.3 eV, indicated by the blue arrow. (c) Fitted spectrum of Br 3d with background subtracted at 0.6 V vs Ag/AgCl has an emerging surface species, which contributes to the symmetrical feature. The black thick line is the experimental data with background noise subtracted, and this is what we want to reproduce from ab initio. (d) Fitted spectrum of Br 3d with subtracted background in a reference solution of 1M AuBr4 shows the 2:3 spin–orbit splitting, which is 1 eV apart.

FIG. 2.

Comparison of the Br[3d] spectrum at the condition of 0.6 V vs Ag/AgCl and the Br 3d spectrum in a reference solution of 1M AuBr4. (a) Raw spectrum of Br 3d at 0.6 V vs Ag/AgCl shows a symmetrical feature. (b) Raw spectrum of Br 3d in a reference solution of 1M AuBr4 shows an asymmetrical feature, which has an obvious concave feature at 69.3 eV, indicated by the blue arrow. (c) Fitted spectrum of Br 3d with background subtracted at 0.6 V vs Ag/AgCl has an emerging surface species, which contributes to the symmetrical feature. The black thick line is the experimental data with background noise subtracted, and this is what we want to reproduce from ab initio. (d) Fitted spectrum of Br 3d with subtracted background in a reference solution of 1M AuBr4 shows the 2:3 spin–orbit splitting, which is 1 eV apart.

Close modal
FIG. 3.

(a) Adsorption isotherms at various bulk solution concentrations at different potentials. Surface Br coverage θ quickly saturated as the bulk solution concentration of Br increases, reaching an equilibrium concentration of 0.4 ML at the realistic condition of 0.6 V vs Ag/AgCl. (b) Surface coverage of the Br ion in the electrolyte as a function of the applied potential at different solution concentrations of Br.

FIG. 3.

(a) Adsorption isotherms at various bulk solution concentrations at different potentials. Surface Br coverage θ quickly saturated as the bulk solution concentration of Br increases, reaching an equilibrium concentration of 0.4 ML at the realistic condition of 0.6 V vs Ag/AgCl. (b) Surface coverage of the Br ion in the electrolyte as a function of the applied potential at different solution concentrations of Br.

Close modal
FIG. 4.

We start with the parameters that generate the spectrum from ab initio (black thick line in Fig. 4) that best resembles the symmetrical feature, see the black thick line of Fig. 1(c) and direct comparison in Fig. 6. We then used these parameter combinations (C = 2M, θ = 0.4 ML, L = 10 nm, and λ = 11 nm) as our basis (black thick line) and show how different the spectroscopic features we expect to see varying an individual parameter. The gray areas are the signals from the solution Br ion, and the red areas are the signals from the surface Br ion. The solution Br ion signal and surface Br ion signal together adds to the total intensity (black line). With the calculated binding energy BE, intensity, and a uniform gaussian broadening, we can create the spectra from ab initio. (a) We fix C, θ, and λ and vary the bulk liquid layer thickness L from 5 nm (left) to 10 nm (middle) and then to 30 nm (right), and we found that the effect of L is shifting the spectrum left and right. (b) We fix C, θ, and L and vary the inelastic mean free path λ from 5 nm (low) to 11 nm (middle) and to 15 nm (high). (c) We fix θ, L, and λ and vary the solution Br ion concentration from 1M (low) to 2M (middle) and to 4M (high), and the 4M has the same concentration in the experimental reference spectrum [Fig. 1(d)]. (d) We fix C, L, and λ and vary the surface Br ion coverage from 0.1 ML (low) to 0.4 ML (middle) and to 0.6 ML (high).

FIG. 4.

We start with the parameters that generate the spectrum from ab initio (black thick line in Fig. 4) that best resembles the symmetrical feature, see the black thick line of Fig. 1(c) and direct comparison in Fig. 6. We then used these parameter combinations (C = 2M, θ = 0.4 ML, L = 10 nm, and λ = 11 nm) as our basis (black thick line) and show how different the spectroscopic features we expect to see varying an individual parameter. The gray areas are the signals from the solution Br ion, and the red areas are the signals from the surface Br ion. The solution Br ion signal and surface Br ion signal together adds to the total intensity (black line). With the calculated binding energy BE, intensity, and a uniform gaussian broadening, we can create the spectra from ab initio. (a) We fix C, θ, and λ and vary the bulk liquid layer thickness L from 5 nm (left) to 10 nm (middle) and then to 30 nm (right), and we found that the effect of L is shifting the spectrum left and right. (b) We fix C, θ, and L and vary the inelastic mean free path λ from 5 nm (low) to 11 nm (middle) and to 15 nm (high). (c) We fix θ, L, and λ and vary the solution Br ion concentration from 1M (low) to 2M (middle) and to 4M (high), and the 4M has the same concentration in the experimental reference spectrum [Fig. 1(d)]. (d) We fix C, L, and λ and vary the surface Br ion coverage from 0.1 ML (low) to 0.4 ML (middle) and to 0.6 ML (high).

Close modal
FIG. 5.

Contour plot shows the region of visibility at various experimentally controllable conditions. No visibility of the surface species if the liquid layer thickness is over 35 nm or photon energy is less than 2 keV. [(a) and (d)] Visible area is shown as the red triangular area, which is taken as the intersection of the upper limit of the adsorption isothermal (black horizontal line at coverage = 0.4 ML); the lower limit of visibility of the Br 3d core level (black vertical line at bulk concentration = 2M); and, finally, a high I(bulk)/I(surface) ratio (the black and dark gray regions, underneath the red dotted line). (b) The upper limit of the layer thickness is estimated to be around 35 nm at PE = 5 keV, corresponding to λ = 15 nm. (c) Above 35 nm, for example, L = 40 nm, there is no intersection satisfying the constraints defined in text, and therefore, no visibility for the surface Br ion even if it is presented at the interface. (e) The lower limit of the photon energy is estimated to be around 2 keV, corresponding to λ = 6.5 nm, at the typical layer thickness of 20 nm. (f) Below 2 keV photon energy, there is no visibility of the surface Br ion even if it is presented at the interface.

FIG. 5.

Contour plot shows the region of visibility at various experimentally controllable conditions. No visibility of the surface species if the liquid layer thickness is over 35 nm or photon energy is less than 2 keV. [(a) and (d)] Visible area is shown as the red triangular area, which is taken as the intersection of the upper limit of the adsorption isothermal (black horizontal line at coverage = 0.4 ML); the lower limit of visibility of the Br 3d core level (black vertical line at bulk concentration = 2M); and, finally, a high I(bulk)/I(surface) ratio (the black and dark gray regions, underneath the red dotted line). (b) The upper limit of the layer thickness is estimated to be around 35 nm at PE = 5 keV, corresponding to λ = 15 nm. (c) Above 35 nm, for example, L = 40 nm, there is no intersection satisfying the constraints defined in text, and therefore, no visibility for the surface Br ion even if it is presented at the interface. (e) The lower limit of the photon energy is estimated to be around 2 keV, corresponding to λ = 6.5 nm, at the typical layer thickness of 20 nm. (f) Below 2 keV photon energy, there is no visibility of the surface Br ion even if it is presented at the interface.

Close modal
FIG. 6.

Direct comparison of the experimental and theoretical spectrum. The blue arrow points out the concave and asymmetrical feature of the reference spectrum, which does not show the signal from surface Br. (a) Experimental spectrum of the 1M AuBr4 (4M [Br]) bulk solution. (b) Theoretical spectrum of the 1M AuBr4 (4M [Br]) bulk solution, created using parameters C = 4M, θ = 0.0 ML, L = 10 nm, and λ = 11 nm at PE = 4 keV. (c) Experimental spectrum of Au dissolved in the 1M KBr solution at 0.6 V vs Ag/AgCl, and the increased Br 3d signal is due to the dissolution of Au and the formation of AuBr4, therefore increasing the local concentration of the solution Br ion to more than 1M. (d) Theoretical spectrum derived from ab initio that best resembles the spectrum in (c), and the parameters used to create this spectrum (d) are C = 2M, θ = 0.4 ML, L = 10 nm, and λ = 11 nm at PE = 4 keV.

FIG. 6.

Direct comparison of the experimental and theoretical spectrum. The blue arrow points out the concave and asymmetrical feature of the reference spectrum, which does not show the signal from surface Br. (a) Experimental spectrum of the 1M AuBr4 (4M [Br]) bulk solution. (b) Theoretical spectrum of the 1M AuBr4 (4M [Br]) bulk solution, created using parameters C = 4M, θ = 0.0 ML, L = 10 nm, and λ = 11 nm at PE = 4 keV. (c) Experimental spectrum of Au dissolved in the 1M KBr solution at 0.6 V vs Ag/AgCl, and the increased Br 3d signal is due to the dissolution of Au and the formation of AuBr4, therefore increasing the local concentration of the solution Br ion to more than 1M. (d) Theoretical spectrum derived from ab initio that best resembles the spectrum in (c), and the parameters used to create this spectrum (d) are C = 2M, θ = 0.4 ML, L = 10 nm, and λ = 11 nm at PE = 4 keV.

Close modal
FIG. 7.

Atomic scale illustrations of the surface species layer and solution species layer, from equilibrated snapshots of the ab initio MD calculation. From left to right are snapshots at the last 100, 200, and 400 frames.

FIG. 7.

Atomic scale illustrations of the surface species layer and solution species layer, from equilibrated snapshots of the ab initio MD calculation. From left to right are snapshots at the last 100, 200, and 400 frames.

Close modal

After dip and pull (schematic, see Ref. 28), a meniscus liquid layer forms with a thickness of L on the electrode in the probing area. X rays arrive through the bulk liquid region, which is assumed to contain a homogeneously distributed solution Br ion of concentration C. Another surface adsorbed Br ion with a concentration expressed in terms of coverage θ has a 0.8 eV higher binding energy (BE) than solution Br. A schematic illustration, especially mapping the ideal model to an ab initio atomic-scale description, is provided in Fig. 1.

Measured photoelecton signals due to x-ray excitation attenuate exponentially, I(x) = I0 * exp(−x/λ), where I0 is the intensity of the signal at the depth x = 0 and λ is the inelastic mean free path of the excited photoelectron. The inelastic mean free path of the excited photoelectron generally follows the universal curve, which is a numerical relationship between the inelastic mean free path with the electron kinetic energy KE, where KE is the kinetic energy of the excited photoelectron, KE = PE − BE − Φ. PE is the photon energy of the x-ray beam, and BE is the binding energy of the specific element in a specific chemical environment (for example, Br in solution and Br on the surface), which could be calculated quantum mechanically. Φ is the work function of the system of interests, which is canceled out when calculating the relative binding energy shift. In our experiment, KE is in the range of 4 keV, which gives us λ in the range of 5 nm for the metallic system. However, the inelastic mean free path of the excited photoelectron in liquid could deviate from that predicted from the universal curve, yielding an approximate λ of 10 nm using a tender x ray, shown in Table S1 of Ref. 34, which is calculated using the TPP-2M formalism.35 A recent study36 using the relativistic full Penn algorithm (FPA) indicated that the inelastic mean free paths (IMFPs) for liquid water at 4 keV could reach 11 nm.

Surface Br species is assumed to be homogeneously covering the Au surface, with a coverage, θ, given as a fraction of a monolayer. To summarize, the intensity of the surface Br ion and solution Br ion, depend on the combination of L, C, θ, elemental cross section or resolution, and λ. Because the surface Br ion and the solution Br ion are made from the same element, the intensity ratio of these two species is independent of the elemental cross section. Given the BE of the surface Br ion and solution Br ion, as well as the intensity of signals for the surface Br ion and solution Br ion, we can, in principle, construct the ab initio Br 3d spectrum, as shown in Fig. 4.

At 0.6 V vs Ag/AgCl, dissolution of Au in Br forming AuBr4 in the liquid phase is observed through a sharp increase in the cyclic voltammetry curve as well as an obvious Br 3d signal at 67 eV–71 eV. On the contrary, at a negative potential or positive potential less than 0.6 eV, the thermodynamic driving force for the dissolution of gold is too small, and no signal of Br 3d is observed due to the low concentration of the solution Br ion in the liquid phase and low cross section for the Br 3d core-level.

It is interesting to point out that the Br 3d spectrum collected at 0.6 V vs Ag/AgCl [Figs. 2(a) and 2(c)] showed a comparatively symmetrical peak, in contrast to the expected 2:3 [Figs. 2(b) and 2(d)] peak feature of the 1M reference AuBr4 solution (4M Br in the liquid phase) spectrum due to the spin–orbit splitting of the 3d orbital. This change in the spectroscopic feature from asymmetric [Fig. 2(b)] to symmetric [Fig. 2(a)], together with the weakening concave feature [blue arrow in Figs. 2(b) and 2(d)] at 69.3 eV, indicates the possibility of a surface species at a higher binding energy [Fig. 2(c)]. Given the fact that signals of such surface species within ∼Å of the interface are buried underneath a bulk liquid layer at the scale of ∼10 nm, it is important to address at what conditions such weak signals of surface species can be observable. Furthermore, one should, in principle, be able to recreate the spectrum [black thick line in Fig. 2(c)] ab initio if given the right combinations of the experimental conditions.

In order to recreate the spectrum, especially the interesting symmetrical featured spectrum of Br 3d at 0.6 V vs Ag/AgCl, we need to define the lower limit and the upper limit of the parameters relevant in Fig. 1, namely, the solution Br ion concentration C, surface Br ion coverage θ, bulk liquid layer thickness L, and inelastic mean free path λ. We grouped these four parameters into chemically relevant one (C and θ) and measurement relevant one (L and λ). In the following, we will describe the upper and lower limits of the parameters with supports from either experiment or theory.

  • Layer thickness L is between 10 nm and 30 nm in a typical solid/liquid Ambient Pressure XPS (APXPS) experimental setup.28,37 By assuming that the electrolyte covering the working electrode surface is in the form of a thin layer after the electrochemical treatment, the liquid layer thickness can be obtained from the attenuation of the working electrode signal. To show an extreme version of the effect of bulk liquid layer thickness on the spectrum, we plotted in Fig. 4(a) using a thickness L from 5 nm to 30 nm.

  • Inelastic mean free path λ is 11.7 nm using the relativistic full Penn algorithm (FPA) at a photon energy of 4 keV. To get more intuition of the effect of the inelastic mean free path on the features of the spectrum, we chose to vary the mean free path from 5 nm to 15 nm in Fig. 4(b).

  • Solution Br ion concentration C is estimated to fall within 2M–4M. It has been observed experimentally that the Br 3d in a 1M KBr solution at 0 V vs Ag/AgCl did not show observable intensity, and the Br 3d at 0.6 V vs Ag/AgCl intensity is not as strong as that in a reference 4M solution. The effect of solution Br ion concentration C on the spectrum is investigated in Fig. 4(c).

  • Surface Br coverage θ can be derived theoretically from the continuum model described in Ref. 38 as a function of the applied potential and bulk solution concentration and then be fitted on the Frumkin isotherm. Here, we exploit the experimental guidance and use the “Hurwitz-Parsons” method (Hurwitz, 1965; Dutkiewicz and Parsons, 1966) to construct the adsorption isotherms shown in Fig. 3. The saturation coverage is on the order of 0.4 monolayer. In order to visualize the effect of surface coverage, we selected a range of surface coverage θ from 0.1 ML to 0.6 ML and plotted the corresponding ab initio generated spectrum in Fig. 4(d).

Three pieces of information are needed for constructing the spectrum from ab initio: binding energy (BE), which determines the center of individual peak; gaussian broadening, which is assumed to be universal for each species as the commonly observed 1.1 eV full width at half maximum (FWHM); and intensity I, which can be calculated, given the parameters (L, λ, C, θ) defined in the Parameter space section. The solution Br ion and surface Br ion intensity can be calculated using the following formulas assuming the exponential decay of signals:

Ibulk=I0*Cbulk*h=0h=Lexphλdh,
Isurface=I0*Csurface*expLλ*h=0 Åh=2.6 Åexphλdh.

The proportionality is defined in I0, which is a function of the cross section of the element of interest, the incident angle, and an equipment-dependent constant. In the current study, the incident angle and equipment are the same, and I0 is the same for surface Br and solution Br. Csurface is in the same unit (mol/m3) as Csolution. Csurface can be easily converted from θ (in unit of monolayer) using the area of unit area (2.96 × 2.96 Å2) of the Au surface and the average height (2.6 Å) of surface Br, which were obtained from density functional theory (DFT) and ab initio MD calculations, whereas the relative position of the peaks (BE difference) is obtained from the average binding energy (BE) differences between the surface Br ion and the solution Br ion in the 200 equilibrated ab initio MD frames. We found that the surface Br ion is 0.8 eV higher in binding energy than the solution Br ion. The spin–orbit splitting is 2:3 eV and 1.0 eV apart. Details of the binding energy calculation are described in the  Appendix. The constructed spectrum from ab initio is shown in Fig. 4.

While the spectroscopic feature from the Br 3d solid/liquid APXPS measurement depends on the 4-dimensional space of bulk solution concentration (C), surface coverage (θ), bulk liquid layer thickness (L), and inelastic mean free path (λ), it is worthwhile to predict and provide a general guidance of the visibility region for the surface Br ion or other solid/liquid systems alike. In Fig. 5, we investigated the influence of two measurement related parameters [bulk liquid layer thickness (L) and inelastic mean free path (λ)] and plotted the idealized landscape of visibility for such solid/liquid interfacial systems. The visible region (outlined using the red dashed line in Fig. 5) must satisfy the following constraints:

  • In order to differentiate surface species from that in the bulk solution, the intensity ratio of I(bulk)/I(surface) must be sufficiently small. In this case, we define ten times as the threshold, as indicated by the red dotted line on the color bar of Fig. 5. The visible area must be black or gray.

  • The experimental evidence of no obvious solution Br ion signal before 0.6 V vs Ag/AgCl indicates that there is an absolute minimum value for the detection of the Br 3d core-level signal, which is estimated to be 2M and represented as the black vertical line at x = 2M in Fig. 5. The visible area must be to the right of the black vertical line. The cross section for the Br 3d core-level is comparatively low, and for other elements and their corresponding core levels, this vertical line will shift to the left, resulting in a bigger visible area.

  • The adsorption isotherm, as discussed in Fig. 4, puts an upper limit on the maximum surface coverage of the surface Br ion, which is in the range of 0.4 ML–0.5 ML. For simplicity, we represented this limit as a black horizontal line at y = 0.4 ML in Fig. 5. The visible area must be below the black horizontal line.

To summarize, the visible area is outlined by the red dotted triangle in Fig. 5. For maximum visibility, it is suggested to collect the spectrum at a thinner liquid layer thickness although technically difficult to get the analyzer cone to be too close to the interface, as shown in Figs. 5(a)–5(c). In addition, it is also suggested to collect the spectrum at a higher photon energy within the limit of the tender x ray (1 keV–5 keV) due to a longer inelastic mean free path, as shown in Figs. 5(d)–5(f). However, if the photon energy increases too much to the region of the hard x ray, we may suffer from a decrease in the cross section.37 

Generalizing from the present example of Au dissolution with the Br ion, we wish to provide a workflow that allows the construction of the solid/liquid APXPS spectrum ab initio. The common practice in the field is usually “fitting the experimental spectrum” rather than “constructing the spectrum ab initio.” However, there is a fundamental difference between “fitting the experimental spectrum” and “constructing the spectrum ab initio.” The former is not generalizable, and it is system specific. A much harder, yet impactful question is how to predict a spectrum, given any chemical system and reaction condition, if no experimental spectrum is readily available for fitting. With that said, this latter goal of “construct the spectrum ab initio” is generalizable to other systems and reaction conditions because the workflow that we described and elaborated (ab initio MD → DFT → analytical model → ab initio constructed spectrum) in the Parameter space and Expected spectrum from ab initio calculations sections for constructing the spectrum ab initio is universal. First, the ab initio molecular dynamics calculation provides the atomic level structures with thermal fluctuations in the equilibrated frames. Second, the DFT level calculation on the representative, thermodynamically equilibrated structure [shown in Fig. 1(b)] predicts the binding energy (BE) of the surface and bulk solution species. Every signal of the chemical species is expected to be a gaussian distribution. The binding energy (BE) is the center of the gaussian distribution. The same broadening of 1.1 eV was used to account for thermal fluctuations. Third, the analytical model (with parameter space derived and defined in the Parameter space section) allows us to get the scaling of signal intensity (gaussian area) of each species. Finally, we arrive at the ab initio constructed spectrum (Fig. 4), which could then be used to compare with the experimentally observed spectrum.

Scientific advancement in applications such as catalysis, batteries, and energy related materials involves characterization and understanding fundamental atomic level behaviors at the solid/liquid interface. The users of synchrotron-based facilities normally have a materials science, synthesis, or engineering background, and they rely on the surface-sensitive ambient pressure XPS technique to probe the interface of interest. The calendar for conducting these experiments is very limited (one day a month or 3–4 consecutive days every 6 months), and normally, there is no chance to iteratively perform the experiments with adjusted or updated experimental settings. Despite all the advantages (e.g., improved coherence, better resolution, increased flux, tunable probing depth, and ambient pressure) at synchrotron-based facilities, this working style of the synchrotron-based measurement makes prior experimental planning pivotal for success. Experimental planning includes sample preparation, and more importantly, selecting the right parameters (photon energy, probing liquid layer thickness) beforehand because these parameters are tunable at soft x-ray synchrotron-based facilities, whereas they are not always tunable in the lab-based system. As a result, we decided to explicitly depict the role of such experimental parameters and their relationship with respect to the observed spectrum.

Finally, we want to make the point that even though the chemistry did not change, the observed spectrum can be different because of different experimental parameters. Unfortunately, the natural and potentially undesirable tendency is to interpolate these differences as a change in chemistry. Showing this procedure of “constructing the spectrum ab initio” and encouraging others to go through the same type of procedure (ab initio MD → DFT → analytical model → ab initio constructed spectrum) for their own system of interest helps address a fundamental challenge to definitively distinguish a new spectroscopic feature that represents truly new chemistry from an artifact of a specific set of experimental parameter choices.

Most of the chemical reactions in catalysis, electrocatalysis, corrosion, and energy storage systems are happening at the solid/gas or solid/liquid interface, and the goal of characterization is naturally differentiating and identifying the surface species and bulk solution species through the distinctive spectroscopic features. However, the setup for the solid/liquid ambient pressure XPS experiment generally has the surface adsorbed species (∼Å scale) buried underneath a bulk electrolyte (∼10 nm scale) layer, yielding a weak signal of the target surface adsorbed species. In this example system of Br ion dissolving gold, we demonstrated a procedure of connecting electronic structure information, chemical information, and electrochemical information from ab initio calculations (DFT and MD) to the experimentally obtained x-ray photoelectron spectrum. This workflow of constructing the spectrum ab initio (ab initio MD → DFT → analytical model → ab initio constructed spectrum) is universal, and we are merely using the Au/Br system as an example. First, the ab initio molecular dynamics calculation provided the atomic level structures with thermal fluctuations in the equilibrated frames. We used the average of the last 200 equilibrated frames to extrapolate the structural coordinates for the surface species and solution species. Second, we conducted the DFT level calculation using the final state approach on the representative, thermodynamically equilibrated structure [shown in Fig. 1(b)] to extrapolate the binding energy (BE) of the surface species and solution species in the bulk solution. The result from DFT is that the binding energy (BE) of these two species is 0.8 eV apart. Every signal of the chemical species is expected to be a gaussian distribution, and naturally, information needed for the construction of this gaussian includes the center, the broadening, and the scaling/area. The binding energy (BE) is the center of the gaussian distribution. The same broadening of 1.1 eV was used to take thermal fluctuations into account. Third, the analytical model (with parameter space derived and defined) allows us to get the scaling of signal intensity (gaussian area) of each species. Finally, we arrive at the ab initio constructed spectrum (Fig. 4).

Walking through this procedure of constructing the spectrum ab initio allows us to advance the experimental planning knowledge at synchrotron facilities by illustrating the delicate balance of experimental conditions, including the chemical condition [bulk solution concentration (C), surface coverage (θ), as well as measurement condition (bulk liquid layer thickness (L), and inelastic mean free path (λ)] that would lead to the desired spectroscopic features with clear visibility for differentiating the surface Br and solution Br ions, and the same framework can be extended to other systems, given the specific parameters of the interested systems.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

This work was supported by a user project at the Molecular Foundry and its compute cluster (vulcan), managed by the High Performance Computing Services Group, at Lawrence Berkeley National Laboratory (LBNL), and portions of this work used the computing resources of the National Energy Research Scientific Computing Center (NERSC), LBNL, both of which are supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The Advanced Light Source is supported by the Director, Office of Science, Office of BES, of the US DOE under Contract No. DE-AC02-05CH11231. J.Q. and E.J.C. were supported by an Early Career Award in the Condensed Phase and Interfacial Molecular Science Program, in the Chemical Sciences, Geosciences, and Biosciences Division of the Office of Basic Energy Sciences of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

1. Experimental method

Beamline 9.3.1 at Advanced Light Source (ALS, Lawrence Berkeley National Laboratory) is equipped with a bending magnet and a Si (111) double crystal monochromator having a total energy range between 2.1 keV and 6.0 keV (“tender” x-ray range). We followed the same experimental procedure as described in Ref. 28. For the electrochemical interface, the electrolyte was comprised of a 1M KBr + 6M KF aqueous solution. For the bulk, the AuBr4 solution was from a 1M Au2Br6 aqueous solution.

2. Adsorption isotherm of Br ions

Following early ideas of Grahame39 and Parson’s analysis of the double layer capacitance,40 the surface coverage of specifically adsorbed species can be estimated using the “Hurwitz–Parsons” method.41 According to this method, the excess surface concentration ΓBr (mol/area) can be obtained from the thermodynamic relationships,

1kBTσ0σlnxφ=ΓBrφx,

or

1kBTφ0φlnxσ=ΓBrσx,

where σ0 or φ0 are surface charge densities or electrode potentials of a reference system (no specifically adsorbing ions in the solution of the same ionic strength) and x is the molar fraction of the specifically adsorbing species (Br ions). In practice, ΓBr is determined as a slope of the surface tension γ with respect to ln x: ΓBr=1kBTγlnxφ and γ(φ; cbuk(Br)) = ∬Cdif(φ; cbuk(Br))d2φ, where Cdif(φ; c) is the differential capacitance of the double layer at a fixed solution concentration of Br ions, and the integration constants are the potentials of the zero charge (PZC) and a sufficiently negative electrode potential where no adsorbed Br ions are expected [a potential at which all differential capacitance curves coincide, e.g., φ = −1.0 V (vs Ag/AgCl)].

3. Ab initio MD calculation

The input AIMD structure (i.e., a set of atomic coordinates) of the equilibrated electrolyte is obtained from the classical MD trajectory using the TIP3P-CHARMM force field. The slab of the electrolyte was then combined with the slab of gold (111 surfaces, 3 layers) with the top layer pre-optimized. The parameters of the simulation cells are listed in Table I. Using a sampling of 0.5 fs, we performed AIMD simulations within the canonical NVT ensemble at 300 K with the Nose–Hoover thermostat42 (with a characteristic time step of 100 fs with the Nose–Hoover chain of length 3), and periodic boundary conditions were carried out using the Quickstep module of the CP2K package.43 The total energy was sampled at the Γ-point only. The valence electrons were treated explicitly at the DFT level using the revPBE parameterization functional and a triple-ζ basis set with two additional sets of polarization functions (TZV2PX),44 and the energy grid cutoff was set as 320 Ry. The core electrons on all atoms were treated using norm-conservative Goedecker–Teter–Hutter (GTH) pseudopotentials.45 Long-range dispersive forces were treated with the DFTD3 empirical Grimme correction.46 5 ps equilibration was followed by a 25 ps AIMD trajectory.

TABLE I.

Parameters of ab initio MD simulations.

SystemNo. of molecules in the boxEquilibrated box parameters (Å)
∼6M KBr in water next to the Au (111) surface 16 K, 16 Br, 108 Au, 119 H217.63 × 15.58 × 28.0 
SystemNo. of molecules in the boxEquilibrated box parameters (Å)
∼6M KBr in water next to the Au (111) surface 16 K, 16 Br, 108 Au, 119 H217.63 × 15.58 × 28.0 

4. Binding energy calculation

Equilibrated frames of the ab initio MD trajectory were taken as the structures for binding energy (BE) calculations. The relative XPS core-level shift of the surface Br and solution Br ions is calculated in Vienna Ab initio Simulation Package (VASP)47 at the PBE-D3 level.48 There are two approaches for the calculation of the relative core-level shift: the initial and final approximation. In the initial state approximation, Kohn–Sham eigenvalues of the core states are subsequent to the self-consistent determination of the charge density associated with the valence electrons.49 Theoretical studies report that the initial approach often reproduces the experimental observations very well for metallic surfaces,50,51 especially if the adsorbates are far from the metal surfaces, where the relaxation time is longer than the near metal core-hole pair. The binding energy of the Br ion is calculated to be the same in the KBr solution, AuBr3 solution, and AuBr solution, which are all possible sources for the solution Br ion.

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