Many commercial heterogeneous catalysts are complex structures that contain metal active sites promoted by multiple additives. Developing fundamental understanding about the impact of these perturbations on the local surface reactivity is crucial for catalyst development and optimization. In this contribution, we develop a general framework for identifying underlying mechanisms that control the changes in the surface reactivity of a metal site (more specifically the adsorbate-surface interactions) upon a perturbation in the local environment. This framework allows us to interpret fairly complex interactions on metal surfaces in terms of specific, physically transparent contributions that can be evaluated independently of each other. We use Cs-promoted dissociation of O_{2} as an example to illustrate our approach. We concluded that the Cs adsorbate affects the outcome of the chemical reaction through a strong alkali-induced electric field interacting with the static dipole moment of the O_{2}/Ag(111) system.

## I. INTRODUCTION

Metal surfaces act as catalysts for many important chemical processes, including commodity chemicals production, energy conversion, and pollution mitigation. The outcome of catalytic processes is governed by interactions of adsorbates with the catalytically active sites where reactions are taking place. These interactions can be modulated by the changes in the local characteristics of the active site, which can be accomplished by an introduction of various promoters/poisons or by alloying with other metal atoms.^{1} In fact, many commercial heterogeneous catalysts are very complex structures that contain metal nanoparticles promoted by multiple additives to optimize the performance of the catalysts. Most often, these additives have been discovered using a “trial and error” approach. Developing fundamental understanding about the impact of perturbations in the geometry and composition of a catalytic site on the local surface reactivity (interaction energy) is crucial for the catalyst development and optimization.

In this contribution, we attempt to develop a general framework for identifying underlying mechanisms that control the changes in the surface reactivity of a metal site (more specifically the adsorbate-surface interactions) upon a perturbation of the local environment of the surface site. We perform our analysis in a case study analyzing the impact of an alkali adatom (Cs) on O_{2} dissociation over the Ag(111) surface. We focus on this system since alkali metals are used as promoters in various heterogeneous catalytic reactions.^{2–6} There have been many contradicting mechanisms explaining their role in catalysis.^{3,4,7–11} Multiple investigators argued that alkali adsorbates act through an electrostatic mechanism by inducing a strong electric field that interacts with relevant surface intermediates through the static dipole-dipole coupling.^{3,4,7,8} Others suggested that alkali atoms affect the geometric and electronic structure of metal catalysts which influence the surface chemistry.^{5,9} Complex interplays among these interactions make the experimental identification of the dominant mode of promotion effect very difficult. Our strategy was to use an energy decomposition analysis to shed light on the problem. We note that various energy decomposition methods, originally proposed by Morokuma,^{12} have been employed to decouple the interaction of molecular fragments in chemical systems to electrostatics, exchange-repulsion, polarization, and charge transfer.^{12–17} The concepts have been extended to adsorbate-substrate and adsorbate-adsorbate interactions on surfaces,^{18–22} aiming to understanding trends and chemical origins of surface reactivity. In this context, it is important to emphasize excellent contributions by Nørskov and co-workers who developed an effective medium theory of chemisorption on metals.^{18} Our analysis is to a large degree inspired by their work.^{18} We have expanded their effort to decouple electrostatic and polarization contributions, and used the two-level interaction model to describe the one-electron energy contribution.

Below, we first introduce the computational details of Density Functional Theory (DFT) used in this study. This is followed by the description of the approach used to identify underlying mechanisms by which a surface perturbation affects the local chemical reactivity.^{18} Furthermore, we describe how these different mechanisms can be quantified and discuss the relative importance of these contributions in Cs-promoted O_{2} dissociation on Ag(111).

## II. METHOD

Quantum chemical density functional theory (DFT) calculations were performed using the ultra-soft pseudopotential^{23} plane-wave method with the generalized gradient approximation (GGA-PW91) for exchange-correlation functional^{24} implemented in the work of Dacapo.^{25} The pseudo-wavefunctions are expanded in plane-wave basis sets with an energy cutoff of 350 eV. The Ag(111) surface is modeled by a four-layer slab separated by 10 Å of vacuum space and Cesium (Cs) and/or oxygen species are placed on one side of the slab. We use the (3 × 3) and (4 × 4) unit cells to simulate the 1/9 ML and 1/16 ML adsorbate coverage, respectively. These unit cells allow us to explore a range of separation distances between the Cs and oxygen adsorbates. A dipole correction is used to decouple interactions of the slab in the *z*-direction. The adsorbates and top two layers of the substrate were fully relaxed until the force on atoms is less than 0.05 eV/Å. For the *p*(3 × 3) Ag(111) surface, a 4 × 4 × 1 Monkhorst-Pack *k*-point set is used for the Brillouin-zone integration.^{26} The equivalent *k*-point sampling is used for the calculations with different unit cells. Finite temperature Fermi function (*k _{B}T* = 0.1 eV) is utilized to facilitate the SCF convergence by smearing the band occupation around the Fermi level, and the total energy of the system is extrapolated back to

*k*= 0 eV. Transition state geometries of O

_{B}T_{2}dissociation on surfaces were identified using a Climbing-Image Nudged Elastic Band (CI-NEB) method.

^{27}Different Cs–O

_{2}surface configurations (see Fig. 1) are used to probe underlying mechanisms of the variations in adsorption energies due to coadsorption of alkali promoters. Although the long-ranged van der Waals interactions are likely playing an important role for the adsorption energies of weakly adsorbed and/or highly polarizable species, we assume that the interaction energy (the change of adsorption energy due to a co-adsorbate) is less dependent on the van der Waals forces than the adsorption energies.

## III. RESULTS

### A. Variations in surface reactivity of metals with perturbations

We focus on variations in chemisorption energy of an adsorbate *A* upon a perturbation of the metal substrate (from *M* to $M\u0303$) as illustrated in Fig. 2. This perturbation of the metal can be due to the alloying of the metal or an introduction of some chemical promoters in the proximity of the active site.

Throughout this document, we followed the convention of symbols used previously.^{18} In this convention, a bare symbol (e.g., *E*) is used for the system with an adsorbate *A* on the unperturbed surface (e.g., the Ag(111) surface without Cs), a symbol with tilde for the system with a perturbation (e.g., the Ag(111) surface with Cs), and a symbol with superscript 0 for the system with the adsorbate *A* infinitely away from the surface. Symbols Δ and *δ* are used to describe the change due to an adsorbate *A* and a perturbation, respectively. Using this notation, the change in chemisorption energy *δ*Δ*E* of an adsorbate *A* due to a perturbation of the metal substrate from *M* to $M\u0303$ is

According to the Hohenberg-Kohn theorem, the total energy *E* of a system is a unique functional *E*[*n*] of the electron density $n(r\u2192)$ that determines the position and charge of nuclei and thus the Hamiltonian of the system.^{28} Such a functional can be formally written as

where *T _{HK}*[

*n*] is the kinetic energy of non-interacting electrons that have the same electron density $n(r\u2192)$ as the exact system,

*E*[

_{es}*n*] is the electrostatic energy of the system including the nucleus-nucleus repulsion, and

*E*[

_{xc}*n*] is the exchange-correlation interaction that is an explicit functional of electron density $n(r\u2192)$. Following the variational principle,

^{29}the electron density $n(r\u2192)$ can then be obtained by solving the one-electron Kohn-Sham equations (Eqs. (3)-(5)) self-consistently,

where ε_{i} and *ψ _{i}* are the one-electron eigenenergy and eigenfunction of the

*i*

^{th}Kohn-Sham orbital calculated with the one-electron effective potential

*υ*.

_{eff}*υ*is the external potential arising from the nuclei. The total energy can then be calculated by

_{ext} where the first two terms are essentially the kinetic energy *T _{HK}*[

*n*] of non-interacting electrons,

*ρ*is the sum of electron density $n(r\u2192)$ and nuclei point charges,

where *Z _{n}* is the nucleus charge and $R\u2192n$ is the nucleus position. If the true ground state electron density and effective potential for a given system are inserted in Eq. (6), the ground state energy of the system can be obtained. According to the variational principle, small inaccuracies in density and potential (away from the ground state density and potential) lead to only a second order error in energy.

^{29}Nørskov and coworkers

^{18}showed that reasonable accuracy in relative energies of chemically similar systems (i.e., in the limit of small perturbations) can be obtained if the region close to the adsorbate

*A*in Fig. 2 (region

*a*) is assumed to have a frozen charge density and potential corresponding to

*A*adsorbed on the unperturbed surface ($\rho \u0303a\u2248\rho a$ and $\upsilon \u0303a\u2248\upsilon a$), and the region outside of

*A*(region

*b*) has a frozen density and potential ($\rho \u0303b\u2248\rho b0$ and $\upsilon \u0303b\u2248\upsilon b0$), regardless of the nature and presence of adsorbate

*A*. Each energy term in Eq. (1) can now be written explicitly as a sum of kinetic, electrostatic, and the exchange-correlation energy of the two separate regions (regions

*a*and

*b*), according to Eq. (6) using these frozen densities and potentials, and the non-local electrostatic interaction energy between the two regions.

^{18}If it is assumed that the exchange-correlation energy is local (i.e., depends only on the local electron density and its gradient), one can conclude that the change in the adsorption energy of

*A*due to the perturbation of the metal (

*M*) can be captured by evaluating the changes of one-electron energy and the electrostatic interaction between the frozen densities of the regions

*a*and

*b*. Herein, we take this analysis a step further by considering induced charge densities in both regions. For example, in the adsorbate region

*a*, we can write

Here, *ρ _{a}* is the static charge density in the region

*a*(identical to the above discussed frozen density), while the second term on the right hand side represents an additional change in the charge density in this region due to the perturbation potential from the region

*b*. If we introduce perturbed densities in Eqs. (1) and (6), then the change in the chemisorption energy of the adsorbate

*A*induced by perturbed local environment of the active site (by having co-adsorbates or different metal atoms embedded close to the active site) can be approximated as

We note that we have neglected the changes in the exchange and correlation energy in regions *a* and *b* due to slight changes in local density away from the frozen density. Eq. (9) provides a physically transparent description for the change in chemisorption energy of an adsorbate *A* in response to any perturbation on the substrate. It suggests that variations in the adsorption energy of *A* upon a perturbation consist of three effects: (i) electronic effect (1^{st} term in Eq. (9)) that is the consequence of the change in one-electron energies of Kohn-Sham orbitals due to electronic communications between the two regions. This mechanism accounts for the energy change due to electron transfer, covalent charge sharing upon the creation of bonding and anti-bonding states, and Pauli repulsion resulting from the charge density overlap; (ii) electrostatic effect (2^{nd} term in Eq. (9)) due to the static dipole moment of *A* adsorbed on the surface interacting with an electric field set up by a perturbation potential; (iii) polarization (3^{rd} and 4^{th} terms in Eq. (9)) attributed to the interaction of the perturbation-induced dipole moment of adsorbate *A* on the surface with the electric field set up by the perturbation potential and the polarization effect of an adsorbate *A* on coadsorbates. We attempt to provide a framework for the independent evaluation of all of these contributions (i)-(iii).

### B. Impact of Cs on chemisorption of O_{2} on Ag(111)

To demonstrate how the model described above can be employed to analyze various modes of chemical promotion in chemical reactions on metal surfaces we applied it to study the impact of the atomic Cs adsorbate on the energetics of the O_{2} dissociation on Ag(111). We note that molecular O_{2} adsorbs on the Ag(111) bridge site as shown in Fig. 1. Figure 3 shows the DFT-calculated potential energy surface for the dissociation of O_{2} on clean and Cs-covered Ag(111) for different positions of Cs and O_{2} on the surface. We can see that both the molecular state O$2\u2217$ and the transition state O$2\u2021$ are stabilized by the presence of Cs and that the activation barrier is lowered on Cs/Ag(111) compared to un-promoted Ag(111). This is consistent with previous experimental observations.^{10} It is also observed that the Cs–O_{2} interaction is more pronounced for O_{2} on Ag sites closer to the Cs adsorbates. To unravel the physical origin of the Cs–O_{2} interaction on Ag(111), we first analyzed the impact of Cs adsorption on the physicochemical properties of the Ag(111) surface.^{30–32} As shown in Fig. 4(a), Cs decreases the electronic work function of the Ag(111). Compared with previous experimental measurements,^{33} DFT calculations capture very well the work function change resulting from the Cs adsorption at varying coverage. The decrease in the work function is mainly a consequence of the electron transfer from Cs to the surface as shown in Fig. 4(b), where the average alkali-induced electron density difference (*n*_{Cs/Ag111} − *n*_{Ag111} − *n*_{Cs}) in a plane perpendicular to the surface is plotted. Here the ionic core positions of separated Cs and Ag(111) systems are identical to those in the combined system. The transfer of electron density from Cs toward the Ag(111) surface results in a formation of a surface dipole.^{31}

In addition to the decrease in the work function, which is a global physical property of a surface, Cs also induces significant location-specific changes to the surface electronic structure. Figure 4(c) shows the density of states (DOS) projected onto 4*d*-orbitals of Ag atoms of the clean and Cs-promoted Ag(111) surfaces. It shows that the change in the electronic structure of Ag 4*d*-orbitals is localized only to the Ag atoms directly bonded to Cs. The projected DOS of the 2^{nd} nearest neighbor Ag atoms barely changes in response to the adsorption of Cs. We note that the projected *sp*-states onto Ag slightly move down in energy to accommodate extra electron density from Cs, but the shape does not change irrespective of surface sites.

Cs also substantially changes the electrostatic potential above the Ag(111) surface as shown in Fig. 4(d). These changes in the potential are the result of the charge transfer from Cs to Ag, and their magnitude is governed by the extent of the charge transfer and the ability of free electrons to shield the net positive and negative charge that accompanies the charge transfer. The gradient in the electrostatic potential along the *z*-direction (surface normal), i.e., induced electric field, reaches maximum values between 1 and 3 Å above the top layer of the surface Ag nuclei, ranging from −1.3 V/Å at the near site (*A*) to −0.8 V/Å at the far site (*D*). The induced electric field interacts with the dipole moment or induced-dipole moment of an adsorbate on a substrate and so affects the surface chemistry by stabilizing or destabilizing surface intermediates or transition state species through electrostatic interaction and polarization.

### C. Evaluation of various contributions to alkali promotion

In Secs. III C 1–III C 4, we describe approaches that we devised to investigate how these Cs-induced physical changes to the Ag(111) surface impact the energetics of O_{2} dissociation. Our analysis is centered on the contribution of various terms in Eq. (9), including (1) the Cs-induced changes in the one-electron energy (electronic interaction), (2) the static dipole-dipole interaction, and (3) and the dynamic polarization interactions.

#### 1. One-electron energy contribution to the chemisorption process

To independently evaluate the impact of Cs adsorption on the one-electron energies of oxygen adsorbates (molecular and transition state), we have utilized the two-level interaction model, which neglects non-local electrostatic and dynamic polarization contributions in the analysis of molecular interactions on surfaces.^{34–36} The model is essentially an application of the tight-binding approximation to chemisorption on metal surfaces. In this model, the interaction energy between an adsorbate and the surface is separated into two terms. One term takes into account the interaction of adsorbate states (orbitals) with delocalized *sp*-electrons which leads to the formation of resonance adsorbate states. These states further interact with the *d*-state centered at the average energy of the *d*-band of the surface atoms, forming bonding and anti-bonding orbitals.^{37–39} Based on this model, the one-electron energy contribution to the total binding energy (Δ*E*_{1e}) of an adsorbate on metal surfaces is given by

where Δ*E _{sp}* is the energy contribution from the coupling of adsorbate valence states with

*sp*-electrons, and Δ

*E*is the interaction energy between the adsorbate resonance state (after interaction with

_{d}*sp*-states) with

*d*-states of the surface atoms. One way to approach the division between the contributions of the

*sp*and

*d*electrons is to view the process of chemisorption as an interaction of an adsorbate with the

*sp*-electron sea of the substrate, which is then perturbed through the interaction with the localized

*d*-states.

^{18,40,41}

We can analyze the interaction of adsorbate states with the *sp* electrons by considering the *sp* electrons as the free electron gas with varying densities. An adsorbate equilibrates at the region of the electron gas that provides an optimal electron density (most favorable embedding energy). Due to the variations in the electron density along the surface normal, this optimal electron density can be identified on any transition and noble metal surfaces. Therefore, the interaction energy of adsorbate valence orbitals with the free-electron-like *sp*-states can be assumed to be approximately constant for different transition and noble metals.^{42,43} This implies that the main difference in the electronic energy is from the interaction of the adsorbates with the *d*-band of the substrates. The interaction of the adsorbate state with the *d*-band is influenced indirectly by the *sp*-band, as the *sp*-band dictates the bond distance between the metal surface atoms and an adsorbate, which affects the adsorbate coupling to the *d*-states.^{44,45}

Below we discuss a practical application of the approach. For the chemisorption of molecular and transition state O_{2} on Ag(111), the occupied 2$\pi go$ and unoccupied 2$\pi gu$ O_{2} orbitals participate in the process. Therefore we focus on these two orbitals. The *π _{g}* orbitals are anti-bonding in nature. We use the subscript

*g*to indicate that the phase of the wavefunction is not changing in response to an inversion about the centre of symmetry. We used the superscript

*o*and

*u*to represent the occupied and unoccupied orbitals, respectively. To consider the interactions of these orbitals with the free electron

*sp*band, we performed DFT calculations analyzing the adsorption of the molecular and transition state O

_{2}on the aluminum (Al) (111) surface. We chose Al since it has no valance

*d*electrons and its density of states distribution is broad and featureless.

^{35}For the adsorbed molecular state O$2\u2217$, we found that the occupied 2$\pi go$ center at around −2.14 eV below the Fermi level, while the unoccupied 2$\pi gu$ states are around 1.32 eV above the Fermi level. For transition state O$2\u2021$, we calculated 2$\pi go$ resonance energy at −1.75 eV and 2$\pi gu$ at 0.26 eV.

The interaction of these resonance oxygen 2*π*^{∗} orbitals with the *d*-band of Ag(111) can be described, using the tight binding approximation as

The first term in each bracket describes the covalent attraction, while the second term describes the Pauli repulsion between metal *d*-states and the adsorbate orbitals. The coefficient in front of the bracket is the degeneracy of the corresponding adsorbate 2*π* states. *f* and ε_{d} are the respective filling and center of the *d*-band projected onto the surface metal atoms. $\epsilon 2\pi gu$ and $\epsilon 2\pi go$ are the energy levels of the renormalized adsorbate orbitals formed after the interaction with the broad, free-electron-like substrate *sp*-band. These are computed in the calculations of the adsorbate on the Al(111) surface as described above. *S* and *V* are the overlap integral and interatomic coupling matrix element describing the interaction between renormalized adsorbate orbitals and metal *d*-orbitals.^{46}

To gain confidence that this simple model can capture variations in adsorption energy due to changes in one-electron energies, we first demonstrate that the model can capture the interactions of the molecular and transition state O_{2} on various transition and noble metal surfaces. We note that in these systems, in the limit of a low adsorbate coverage (1/16 ML), the difference in the chemisorption energies on different metal surfaces is mainly due to one-electron energies. The first step is to evaluate various variables in Eq. (11). The interatomic coupling matrix element *V* and overlap integral *S* for 2$\pi go$ and 2$\pi gu$ resonance orbitals interacting with the *d*-state of the substrate are assumed to be identical because they are derived from molecular orbitals of the same symmetry and for the same geometry.^{35} Furthermore, we approximate that the coupling matrix element *V* is linearly related to the overlap integral *S*, i.e., *S* = − *αV*, where *α* is an adsorbate dependent parameter related to the repulsive interaction between coupling orbitals.^{46} We treat *α* as a fitting parameter. It should not be confused with the symbol of polarizability defined in Section III C 3.

To obtain the absolute value of *V*, we used the relationship, $V2=\beta Vad2$. Here, *V _{ad}* is the relative coupling matrix element squared that is a property of the metal. $Vad2$ can be calculated in an LMTO (linear muffin-tin orbital) framework. We used $Vad2$ tabulated in the solid state tables.

^{46}In the calculations below, we treat

*β*as another adsorbate-dependent fitting parameter.

The *α* and *β* variables in the model can be estimated by fitting the Eqs. (10) and (11) with DFT-calculated adsorption energies of molecular and transition state O_{2} on five transition metal surfaces. The data in Fig. 5(a) show that this model based on the changes in one-electron energy can capture the trend of chemisorption for molecular and transition state O_{2} on various metal surfaces.^{35}

The model in Eq. (11) also allows us to estimate the change in one-electron energy of molecular and transition state O_{2} on the Ag(111) surface in response to the presence of Cs. For Cs promoted Ag(111) surface, the adsorbate bond distance to the surface atoms changes due to variations in *sp* electron density induced by Cs adatoms. For example, as Cs is introduced to the surface, it donates electron density to Ag, and as a consequence an oxygen adsorbate at an adsorption site of Ag(111) moves away from the surface to obtain the optimal electron density. This change in the bond distance *d* affects the interatomic matrix element *V* and the overlap integral *S*, and therefore the contribution of one-electron energy to the chemisorption energy of the oxygen species. We note that based on the muffin-tin orbital theory, the *V* and *S* for coupling between *d*-orbitals of metal atoms and *p*-orbitals of adsorbates are proportional to 1/*d*^{7/2}, where *d* is the metal-adsorbate bond distance.^{46} Using DFT-calculated adsorbate bond distance to the surface along with Eq. (11), the one-electron energy contribution to the interaction energy between Cs adatom with the adsorbed oxygen species can then be evaluated. Those values at varying Cs coverage and Cs–O_{2} separations plotted against DFT calculated interaction energies are shown in Fig. 5(b) (see Table I for detailed data). Figure 5(b) shows that the one-electron effect on the Cs-induced changes in the adsorption energy of O_{2} is rather small and it cannot capture the interaction energy between the O_{2} species and Cs. We also note that the electronic effect of oxygen species on Cs adsorption on Ag(111) is negligible since the oxygen induced changes of metal electronic *sp*- and *d*-states are highly localized.

. | Cs site . | δΔE
. | $\epsilon Csave$ . | δε_{d}
. | δΔE_{1e}
. | δΔE
. _{es} | $\delta \Delta Epe\delta \upsilon 0$ . | $\delta \Delta Epe\Delta \upsilon $ . |
---|---|---|---|---|---|---|---|---|

O$2\u2217$ | 1 | −0.48 | −0.92 | −0.06 | −0.10 | −0.22 | −0.13 | −0.01 |

2 | −0.46 | −0.92 | −0.06 | −0.10 | −0.20 | −0.13 | −0.01 | |

3 | −0.45 | −0.90 | −0.06 | −0.10 | −0.20 | −0.12 | −0.01 | |

4 | −0.42 | −0.88 | −0.06 | −0.09 | −0.19 | −0.12 | −0.01 | |

5 | −0.17 | −0.60 | −0.02 | −0.03 | −0.10 | −0.05 | 0.00 | |

6 | −0.14 | −0.54 | −0.02 | −0.02 | −0.09 | −0.04 | 0.00 | |

7 | −0.13 | −0.54 | −0.02 | −0.02 | −0.08 | −0.04 | 0.00 | |

8 | −0.13 | −0.52 | −0.02 | −0.02 | −0.08 | −0.04 | 0.00 | |

9 | −0.12 | −0.51 | −0.02 | −0.02 | −0.08 | −0.04 | 0.00 | |

O$2\u2021$ | 1 | −0.95 | −0.88 | −0.09 | −0.19 | −0.65 | −0.06 | −0.04 |

2 | −0.68 | −0.61 | −0.09 | −0.16 | −0.37 | −0.04 | −0.04 | |

3 | −0.67 | −0.58 | −0.06 | −0.16 | −0.35 | −0.03 | −0.03 | |

4 | −0.71 | −0.62 | −0.06 | −0.16 | −0.39 | −0.04 | −0.03 | |

5 | −0.22 | −0.34 | −0.06 | −0.04 | −0.18 | −0.01 | −0.01 | |

6 | −0.25 | −0.37 | −0.02 | −0.05 | −0.18 | −0.01 | −0.01 | |

7 | −0.22 | −0.35 | −0.02 | −0.04 | −0.18 | −0.01 | −0.01 | |

8 | −0.27 | −0.39 | −0.02 | −0.05 | −0.20 | −0.02 | −0.01 | |

9 | −0.27 | −0.40 | −0.02 | −0.05 | −0.20 | −0.02 | −0.01 |

. | Cs site . | δΔE
. | $\epsilon Csave$ . | δε_{d}
. | δΔE_{1e}
. | δΔE
. _{es} | $\delta \Delta Epe\delta \upsilon 0$ . | $\delta \Delta Epe\Delta \upsilon $ . |
---|---|---|---|---|---|---|---|---|

O$2\u2217$ | 1 | −0.48 | −0.92 | −0.06 | −0.10 | −0.22 | −0.13 | −0.01 |

2 | −0.46 | −0.92 | −0.06 | −0.10 | −0.20 | −0.13 | −0.01 | |

3 | −0.45 | −0.90 | −0.06 | −0.10 | −0.20 | −0.12 | −0.01 | |

4 | −0.42 | −0.88 | −0.06 | −0.09 | −0.19 | −0.12 | −0.01 | |

5 | −0.17 | −0.60 | −0.02 | −0.03 | −0.10 | −0.05 | 0.00 | |

6 | −0.14 | −0.54 | −0.02 | −0.02 | −0.09 | −0.04 | 0.00 | |

7 | −0.13 | −0.54 | −0.02 | −0.02 | −0.08 | −0.04 | 0.00 | |

8 | −0.13 | −0.52 | −0.02 | −0.02 | −0.08 | −0.04 | 0.00 | |

9 | −0.12 | −0.51 | −0.02 | −0.02 | −0.08 | −0.04 | 0.00 | |

O$2\u2021$ | 1 | −0.95 | −0.88 | −0.09 | −0.19 | −0.65 | −0.06 | −0.04 |

2 | −0.68 | −0.61 | −0.09 | −0.16 | −0.37 | −0.04 | −0.04 | |

3 | −0.67 | −0.58 | −0.06 | −0.16 | −0.35 | −0.03 | −0.03 | |

4 | −0.71 | −0.62 | −0.06 | −0.16 | −0.39 | −0.04 | −0.03 | |

5 | −0.22 | −0.34 | −0.06 | −0.04 | −0.18 | −0.01 | −0.01 | |

6 | −0.25 | −0.37 | −0.02 | −0.05 | −0.18 | −0.01 | −0.01 | |

7 | −0.22 | −0.35 | −0.02 | −0.04 | −0.18 | −0.01 | −0.01 | |

8 | −0.27 | −0.39 | −0.02 | −0.05 | −0.20 | −0.02 | −0.01 | |

9 | −0.27 | −0.40 | −0.02 | −0.05 | −0.20 | −0.02 | −0.01 |

#### 2. Electrostatic Interaction

The evaluation of electrostatic contribution (the second term on the right of Eq. (9)) is restricted to the local region of adsorbate *A*, where the adsorbate-induced charge density interacts with the perturbation potential set up by coadsorbate-induced density outside this region. Since there is no clear boundary between the regions dominated by the adsorbate *A* and by the perturbation potential, we evaluate the electrostatic contribution over the entire supercell and divide by 2 as in Eq. (12),

The division by 2 is needed since by employing the integration over the entire cell, we are essentially double-counting the electrostatic interaction between the two regions (*a* and *b* in Fig. 2). The Eq. (12) is valid as long as the charge density overlap between the region *a* and *b* is small.

For our system, the perturbation potential *δυ*^{0} is calculated as the electrostatic potential of Cs/Ag(111) minus that of clean Ag(111). The oxygen species induced charge density, Δ*ρ*, was obtained by subtracting the charge density of Ag(111) from the charge density of oxygen adsorbed on Ag(111) with the inclusion of electron density and nuclei point charges. The external potential within the core region (*r _{c}*, 3.41 a.u. for Cs and 1.00 a.u. for O defined in the Vanderbilt ultra-soft pseudopotentials) of an atom

*i*, was calculated by

where *Z _{eff}* is the effective nucleus charge taken as the number of valence electrons which is 7 for Cs and 6 for O with the pseudopotentials used in this study. We note that the potential outside of core regions is directly obtained from the sum of the external potential defined by the pseudopotential, the Hartree potential, and the exchange-correlation potential (see Eq. (5)). Only by including such corrections at core regions, the numerical value of the electrostatic interactions obtain using Eq. (12) is insensitive to taking either Cs or O

_{2}species as a perturbation and the other as an adsorbate. The impact of the ionic core potentials of the substrate Ag atoms in Eq. (12) cancels for calculating

*δυ*

^{0}because we used fixed substrate atoms.

Figure 6(a) shows the electrostatic interaction energy between Cs and O_{2} species on the surface of Ag(111) obtained using Eq. (12) for different Cs–O_{2} surface configurations (see Fig. 1). The energies are plotted as a function of DFT calculated interaction energies. The diagonal line corresponds to a situation where the electrostatic contribution would completely capture the interaction between the two adsorbates. At low Cs coverage (1/16 ML), electrostatic model (Eq. (12)) captures very well the Cs–O_{2} interaction for varying configurations. At higher Cs coverage (1/9 ML), electrostatic contribution is still a relatively large part of the Cs–O_{2} interaction. The data also show that the electrostatic model captures nicely the qualitative trend of interaction energies.

In Fig. 6(b), we also compared the electrostatic interaction values, calculated as described above using Eq. (12), to the values obtained using a simple analytical expression that multiplies alkali adatom induced maximum electric field $\epsilon Csmax$ at the O_{2} adsorption site, and the O_{2}-induced static dipole moment on the surface.^{7} The adsorbate *A* (e.g., O_{2}) induced static dipole moment on the slab is calculated by

where

The *ρ*_{O2/slab} and *ρ _{slab}* include electronic and ionic charge density contributions, and

*z*is the Cartesian coordinate in the surface normal direction.

^{7}Figure 6(b) shows that the simple model captures the trends in the electrostatic interaction energy relatively well. The drawback of this analytic model is that the estimation of the electrostatic effect depends on the perspective of adsorbates and perturbation potential, i.e., if we multiplied the dipole moment induced by the adsorption of Cs with the O

_{2}induced maximum electric field at the adsorption site of Cs, we would get values that are different from the values plotted in Fig. 6(b).

#### 3. Polarization

The polarization contribution (the last two terms in Eq. (9)) is estimated by introducing a constant, artificial electric field (ε), and evaluating the change of the chemisorption energy of O_{2} on Ag(111) referenced to the Ag(111) surface with the same artificial electric field and the gas phase O_{2} in vacuum. We will label this interaction energy as the field-adsorbate interaction energy. This artificial electric field can be manipulated so that the introduced electrostatic potential profile matches closely the Cs-induced electrostatic potential (see Fig. 4(d)) around the adsorbed oxygen species on the specific adsorption site.

The stability of an adsorbed oxygen species in this artificial electric field (the field-adsorbate interaction energy) will change due to the interaction of static and induced dipole moments with the artificial electric field. To determine the polarization energy contribution as a function of the electric field intensity, we subtract out the energy due to the electrostatic interaction of the artificial homogeneous electric field with the adsorbate static dipole from the first-principles calculated field-adsorbate interaction energies. This electrostatic energy is calculated using −*μ* ⋅ ε, where *μ* is the adsorbate dipole moment of an adsorbate on the surface ($\mu O2\u2217=\u22120.25$ eÅ, $\mu O2\u2021=\u22120.40$ eÅ) and ε is the applied electric field (V/Å). The polarizability (*α*) of oxygen adsorbates can then be calculated based on the polarization energy contribution obtained for a series of artificial electric fields ε as shown in Fig. 7(a) by quadratic fitting of the polarization energy with respect to applied electric field using

With this approach, we obtained the polarizabilities of adsorbed oxygen species, $\alpha O2\u2217=0.30$, and $\alpha O2\u2021=0.14e\xc52/V$. The Cs induced polarization energy on oxygen adsorbates at any arbitrary configurations can then be calculated using Eq. (16) with corresponding Cs induced electric field at a specific site. Here we approximated Cs induced electric field $\epsilon Csave$ as the average of Cs induced maximum electric field at the adsorption site in *z*-direction and that at the positions of adsorbate nuclei. We did the same analysis for the oxygen species induced polarization energy on adsorbed Cs. The static dipole moment of Cs adsorbed on Ag(111) is *μ*_{Cs∗} = 1.28 eÅ. The polarizability of adsorbed Cs is *α*_{Cs∗} = 0.60 eÅ^{2}/V, calculated based on the energy response of Cs adsorbed on Ag(111) with a series of artificial electric fields. Since the oxygen induced electric field is relatively weak, the polarization energy of adsorbed Cs atoms is small compared to the polarization energy of O_{2}, as can be seen in Fig. 7(b) and Table I.

#### 4. Identification of the dominant mode of interactions

We demonstrated above a way to evaluate independently different modes of interactions for O_{2} and Cs adsorbed in various configurations on the Ag(111) surface. Figure 8(a) shows the comparison between the DFT-calculated interaction energies and the interaction energies computed using the independent evaluation of the various terms in Eq. (9). The data show that there is an excellent quantitative agreement for different Cs surface coverage (1/16 ML and 1/9 ML) and varying Cs–O_{2} configurations (A summary of data is shown in Table I). In Fig. 8(b), we show the values of different interaction energies for a specific surface configuration (the closest Cs–O_{2} separation with 1/9 ML Cs, site 1 in Fig. 1). These data are qualitatively representative of all examined Cs–O_{2} separations and configurations. We can see that the electrostatic interaction is the dominant mode of interactions between Cs and the O_{2} species. This mode of interactions is characterized by the interaction of the Cs-induced static potential with the static dipole moment of oxygen adsorbates. This effect is more pronounced for the transition state than for the molecular adsorbed O_{2} due to the larger dipole moment of the transition state O_{2} resulting from a more significant charge transfer from the metal to the transition state adsorbate. This ultimately leads to the lowering of the activation barrier of O_{2} dissociation.

The analysis above leads to a simple theoretical argument that might explain observations that alkali adsorbates can impact dramatically the stability of reacting intermediates and the rates of chemical transformations on metal surfaces. It is clear that alkali-induced electric fields are relatively large, and that these fields play a significant role. If an adsorbate (the reactant or transition state in an elementary reaction) are characterized by larger dipole moments (due to the electronic charge donation to the adsorbate from the metal) then alkali atoms will stabilize these adsorbates. The degree of the adsorbate stabilization is governed by the magnitude of the field, and it can decrease the activation barrier for an elementary step if the dipole moment of the transition state is larger than the dipole moment of the initial state.^{47} Such conceptual arguments can shed light on a number of experimental observations. For example, the adsorption of many diatomic molecules (H_{2}, CO, NO, N_{2}, etc.) on metal surfaces proceeds via a mechanism characterized by the donation of electronic charge to the anti-bonding molecular orbitals.^{48} As the molecule propagates along the reaction coordinate through a transition state, this electron donation is increased. This charge transfer from the metal to the transition state results in a large dipole moment, which can be stabilized in the alkali-induced electric field, and consequently decreases the activation barrier associated with the dissociation of these diatomic molecules.

## IV. CONCLUSION

In conclusion, we have established a theoretical framework allowing us to interpret fairly complicated interactions on metal surfaces in terms of tractable formulations of energy, i.e., one-electron interaction, electrostatic interaction, and polarizations. The advantage of this theoretical framework is that these terms can be evaluated independently, which provides a fundamental understanding of physical mechanisms governing variations in the surface reactivity of TMs upon a perturbation, such as the introduction of promoters, or through alloying. By applying the model, we have shown that the dominant contribution to alkali promotion effect for O_{2} activation on Ag(111) in the limit of low oxygen chemical potential is electrostatic in nature, arising from the alkali-induced electric field.

## Acknowledgments

We acknowledge support from the US DOE Office of Basic Energy Sciences, Division of Chemical Sciences (No. FG-02-05ER15686).