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Topics in Catalysis

, Volume 61, Issue 9–11, pp 763–775 | Cite as

Predicting the Electric Field Effect on the Lateral Interactions Between Adsorbates: O/Fe(100) from First Principles

  • Jacob Bray
  • Greg Collinge
  • Catherine Stampfl
  • Yong Wang
  • Jean-Sabin McEwen
Original Paper

Abstract

A density functional theory parameterized lattice gas cluster expansion of oxygen on an Fe(100) surface is developed in the presence and absence of an applied positive and negative external electric field, characterizing the heterogeneity in oxygen’s surface distribution and the effect of an external electric field on the lateral interactions between the adsorbates. We show that the presence of a negative electric field tends to weaken both attractive and repulsive interactions while the positive electric field tends to strengthen these interactions, altering surface distributions and ground state configurations. Since lateral interactions have been shown to play a critical role in defining catalytic behavior, the application of an applied electric field has the potential to be a useful tool in adjusting critical chemical properties of Fe-based hydrodeoxygenation catalysts, by decreasing the repulsive interactions between the adspecies in the presence of a negative field and thereby mitigating the formation of an oxide.

Keywords

Lattice gas model Electric field Mean field model Hydrodeoxygenation Iron Oxygen 

1 Introduction

The importance of finding a renewable replacement for transportation fossil fuels cannot be stressed strongly enough due to the harmful repercussions of their production and use. While there are many options for renewable energy sources, such as solar or wind power, only biofuels are able to act as a drop-in replacement for liquid petroleum fuels. One promising and cost effective method of biofuel production is the pyrolysis of biomass to bio-oil [1]. However, the high oxygen content (< 50 wt%) of the oils after pyrolysis causes the bio-oils to have a low heating value, poor stability, and high viscosity [1]. To address this issue, catalytic hydrotreating in the form of hydrodeoxygenation (HDO) is proposed as an effective method of selectively removing oxygen functional groups from bio-oil.

Fe catalysts are of great interest as they have been shown to be highly selective for bio-oil HDO [2]. Unfortunately, these catalysts alone are unacceptably prone to oxidative deactivation, which is due to the high oxophilicity of Fe. Since metal oxidation is due to an imbalance between surface and bulk oxygen chemical potentials, modifying one or both of these chemical potentials will correspondingly change the metal oxophilicity. Since the formation of subsurface oxygen is due to the repulsive lateral interactions between the oxygen adatoms, the formation of surface oxygen could therefore be modified if the repulsive lateral interactions between adsorbed surface species, such as oxygen, are weakened. In this regard, one method of improving oxidation resistance has been to promote Fe with a second metal (e.g., Pd, Rh, etc.). Bimetallic, especially noble metal promoted, Fe catalysts have demonstrated synergistic behavior that contributes to a more cost-effective and longer-lasting HDO catalyst, by weakening the bonding of oxygen to the metal surface and thus weakening the lateral interactions between the adspecies [2, 3, 4, 5]. Another method capable of affecting these interactions is the application of an external electric field. Both theory and experiment suggest that the latter technique can improve the performance of other catalytic processes, such as methane steam reforming [6, 7, 8, 9, 10, 11].

The most useful, experimentally relevant models are able to accurately capture the complexities that occur at the atomic level. Typical density functional theory (DFT) models only consider a periodic distribution of surface species, when in reality, this is not the case. Instead, nanoscale, attractive/repulsive lateral interactions exist between surface species, resulting in adsorbate clustering behaviors that can significantly affect larger scale catalytic properties [12], such as the tendency of the catalyst to oxidize. A lattice gas (LG) cluster expansion (CE) can be employed to account for these lateral interactions, allowing for the parameterization of the system’s total energy using DFT calculated energetic information [13, 14, 15, 16, 17, 18]. LG CEs are a concise way to represent the configuration dependence of the system’s energy, taking into account realistic surface distributions. A LG CE model can be used to extend the coverage dependence noted at the nanoscale to meso and macro scale behaviors [12]. In this work, a DFT parameterized LG CE of oxygen on an Fe(100) surface is developed in the presence and absence of an applied positive and negative external electric field, characterizing the heterogeneity in oxygen’s surface distribution and the effect of an external electric field on the lateral interactions. In doing so, we show that the presence of an electric field not only affects the lateral interactions between the adspecies, but it also alters the distribution of the adspecies in its ground state conformation at a given coverage.

2 Methodology

2.1 Theory

A LG CE is represented as a polynomial expansion where a system property of interest is fitted to a series of site–site interaction terms. A general form of a CE used to solve for the formation energy is seen in Eq. (1), valid for one site type [19, 20].
$$\begin{array}{*{20}{c}} {E\left( {\varvec{n}} \right) =\mathop \sum \limits_{i}^{{1 - body}} {V_i}{n_i}+\mathop \sum \limits_{{i>j}}^{{2 - body}} {V_{ij}}{n_i}{n_j}+\mathop \sum \limits_{{i>j>k}}^{{3 - body}} {V_{ijk}}{n_i}{n_j}{n_k}+ \ldots } \end{array}$$
(1)
Each summation term accounts for the total interaction energy of the various adsorbate clusters. The interaction coefficient associated with each type of adsorbate cluster (such as 1-body, 2-body, and 3-body clusters) is represented as V, where V i is that of an isolated adsorbate on an otherwise clean surface for which all the V i would have the same value if only one type of adsorption site is present. The adsorbate site occupation numbers are represented as n, each with a unique subscript to represent the occupation number of an adsorbate at a particular adsorption site. The n with no subscript is the vector of occupancies for each site in the lattice, i.e. it is a microstate of the adsorbate, n = (n1,n2,…,\(n_{N_s}\)), where each n i (i = 1,…,N s ) is either 0 or 1 and N s is the number of adsorption sites. The sum over multi-body interactions is written as i > j > k, and so on, to avoid the double counting of interacting adsorbates. This form of the equation lacks utility since further detail is required to be able to fully define interacting adsorbate clusters. Equation (2) represents a more useful form of Eq. (1) used to predict the surface energy of a system. As written, this is once again only applicable to a single site type for the total energy of the system.
$$\begin{array}{*{20}{c}} {E\left( {\varvec{n}} \right)=~{V_0}N+\mathop \sum \limits_{{{R_1}}}^{\infty } {V_{{R_1}}}{m_{{R_1}}}+\mathop \sum \limits_{{{R_1},{R_2},{R_3}}}^{{\infty ,\infty ,\infty }} {V_{{R_1},{R_2},{R_3}}}{m_{{R_1},{R_2},{R_3}}}+ \ldots } \end{array}$$
(2)

Each cluster, made up of k bodies, is defined by the pairwise distances, R n , between its adsorbates (there are \(\left( {\begin{array}{*{20}{c}} k \\ 2 \end{array}} \right)\) such distances for each k-body cluster). Here N is the number of adsorbates and the V values now correspond to each unique cluster, including the 1-body “cluster” corresponding to the adsorption energy of an isolated adsorbate at a given site, V0. These are multiplied by \({m_{{R_n}}}\), which is the number of these clusters in a given configuration. In principle, this CE would be expanded to infinite adsorbate–adsorbate distances and would also include an infinite number of n-body clusters. In practice this expansion is truncated so as to include the interactions that contribute most significantly to the energy [19, 20]. Figure 1 provides a simple example of how clusters are defined.

Fig. 1

Example of 2, 3, and 4-body clusters and the pairwise distances that define them

The two, three, and four-body interactions are defined by 1, 3, and 6 pairwise interactions, respectively. For example, \({m_{{R_1},{R_2},{R_3}}}\) in Eq. (2) corresponds to the 3-body interaction and is equal to the number of times this cluster appears in a particular surface configuration.

The accuracy, or prediction error, associated with the LG CE is typically quantified by the cross-validation (CV) score [21, 22]. In this work, the internal CV score is determined using the leave-multiple-out (LMO) method as detailed by Baumann [23]. In this method, the entire data set, or training set, is split into a construction set and a validation set. A LG model is developed by fitting the construction set to the current trial cluster expansion. This model is then used to predict the values in the validation set and an average error is determined for that split. The LMO CV score is defined as the average of these errors over multiple data splits. This approach prevents the development of an overfitted model. See Ref. [23] for further details. In this work, the validation and construction sets are fixed at 60% and 40% of the training set, respectively.

Along with the internal CV score, an external CV score is also used to assess the model’s fit. First, the current cluster expansion is used to predict the energies of new structures that have not yet been added to the training set. The external CV score is then defined as the root mean squared error of these predicted energies. Because these new structures have never been seen by the algorithm, the external CV score provides a more independent assessment of the CE’s predictiveness, whereas the internal CV score tends to be overoptimistic [23]. However, as a means of choosing the best CE, the external CV score is too dependent upon the exact nature of the external data and can amount to nothing better than a least squares fit of that small subset of data. This makes the internal CV score a much better metric for finding the best CE given the total data set. Both methods were used here to assess when an acceptable LG CE was reached.

The LG CE model employed here improves the predictiveness and reduces computational cost by also incorporating a mean field (MF) model. Such an approach was used in the past for a phenomenological model of CO/Pt(111) [24], but here we apply it based on ab initio calculations. This is accomplished by first fitting the surface energy to a MF potential. The LG model developed here is then fit to the residuals of the MF model, which tend to be relatively small and uniformly distributed about zero. Thus, the overall configurational potential developed here is represented by the following equation for the surface energy, γ:
$$\begin{array}{*{20}{c}} {\gamma =\frac{{E({\varvec{n}})}}{{{N_s}}}={V_0}\theta +c\mathop \sum \limits_{{n=1}} \frac{{V_{n}^{{mf}}}}{{n+1}}{\theta ^{n+1}}+\frac{1}{{{N_s}}}\left( {\mathop \sum \limits_{{{R_1}}}^{\infty } {V_{{R_1}}}{m_{{R_1}}}+\mathop \sum \limits_{{{R_1},{R_2},{R_3}}}^{{\infty ,\infty ,\infty }} {V_{{R_1},{R_2},{R_3}}}{m_{{R_1},{R_2},{R_3}}}+ \ldots } \right)} \end{array}$$
(3)
where the first two terms are the MF model and the remaining terms describe the LG CE, as given in Eq. (2). For the MF portion of this equation, n + 1 represents the number of adsorbates within the cluster, θ = N/Ns is the surface coverage associated with each configuration. The MF coefficients in this case are represented as \(V_{n}^{{mf}}\) while c is the coordination number of the surface. The MF model is truncated at the point where it accurately describes the trend of adsorption energy vs coverage while ensuring that it does not overfit the data or predict MF coefficients that are nonphysical. The Ab-initio Mean-field Augmented Lattice Gas Model (AMALGM) code developed within the McEwen group at Washington State University, in collaboration with the Stampfl group at the University of Sydney, is used to implement this algorithm.

2.2 Computational Details

The Alloy Theoretic Automated Toolkit (ATAT) [13, 25] works together with the Vienna Ab Initio Simulation Package [26, 27] (VASP) to build structures and determine their DFT total energies. ATAT was used here to generate structures of Fe(100) with oxygen adsorbed on the hollow site, which has been determined to be the most favorable adsorption site in previous work [28, 29]. This allows for all other sites to be ignored within the model. The Fe slab is composed of four layers with the top two layers relaxed and the bottom two fixed with a lattice constant of 2.868 Å (experimentally 2.87 Å [30]). The resulting database of structures and DFT energies is used within the AMALGM code to determine the overall configurational potential.

The projector-augmented wave (PAW) method [31, 32] with a plane-wave basis set and an energy cutoff of 400 eV was used for all DFT calculations. To model the electron exchange and correlation, the revised Perdew–Burke–Ernzerhof (RPBE) functional [33] has been determined to be the most suitable for this application, as detailed in the SI [34]. All systems contain Fe and are spin polarized to account for the presence of a magnetic moment. The average magnetic moment for each configuration in each of the three electric field scenarios is available in Figure S1. The Gaussian smearing [35] method was used with a smearing width of 0.1 eV. The stopping condition for the ionic relaxation and electronic relaxation was 3 × 10−2 and 1 × 10−4 eV, respectively. The first Brillouin zone of all structures was sampled using a k-point density of 1200 k-points per reciprocal atom (KPPRA). This method allows for the automatic construction of k-point meshes for similar systems of varying supercell sizes constructed by ATAT [25]. Calculations for oxygen in the gas phase were performed using a 14 × 15 × 16 Å box, and one single k-point, the Gamma point, was sufficient to span the Brillouin zone. All systems were optimized using the conjugate gradient method. Local-Orbital Basis Suite Toward Electronic-Structure Reconstruction (LOBSTER) [36, 37, 38, 39, 40] was used in conjunction with VASP to perform density of states calculations, where the k-point grid was set to (8 × 8 × 1) to increase the accuracy of the resulting density of states contributions.

DFT calculations are able to simulate a uniform electric field using the approach proposed by Neugebauer and Scheffler [41]. This method generates uniform electric fields without adding or removing any charge from the supercell [42]. An 11 Å vacuum was used to avoid field emission [43] while still eliminating the interaction between each periodic supercell in the perpendicular direction. Three sets of DFT calculations were performed on the structures generated by ATAT, one for each electric field scenario: − 0.5, 0, and + 0.5 V/Å. The VASP calculated total energy for each structure is used to calculate the surface energy, γ, and adsorption energy, Eads, as seen in Eqs. (4) and (5), respectively:
$$\gamma = \frac{{E_{{{\text{O/Fe}}(100)}} - E_{{{\text{Fe}}\left( {100} \right)}} - \frac{1}{2}{\text{N}}_{{\text{O}}} {E}_{{{\text{O}}_{2} }} }}{{\text{N}_{\text{S}} }}$$
(4)
$$E_{{{\text{ads}}}} = \frac{{E_{{{\text{O/Fe}}(100)}} - E_{{{\text{Fe}}\left( {100} \right)}} - \frac{1}{2}{\text{N}}_{{\text{O}}} {E}_{{{\text{O}}_{2} }} }}{{{\text{N}}_{{\text{O}}} }}$$
(5)
where EO/Fe(100) is the energy of the Fe slab and adsorbed oxygen, EFe(100) is the energy of the clean Fe slab, \({E_{\text{O}_2}}\) is the energy of gas phase oxygen, Ns is again the number of adsorption sites, and NO is the number of oxygen atoms per unit cell.

3 Results and Discussion

3.1 Raw Data and MF Model

The adsorption energy of oxygen on Fe(100) is used to construct the LG + MF CE models for each electric field scenario and is displayed in Fig. 2. Both the DFT calculated energies and the LG + MF CE model’s predicted energies for each electric field scenario are plotted over a full monolayer of oxygen coverages. The MF fit used to achieve the most predictive model is also provided (Fig. 2).

Fig. 2

DFT calculated adsorption energy (red circles) and LG + MF model predicted adsorption energy (crosses) alongside the MF model 2nd order fit for a system in the presence of a − 0.5 V/Å electric field (a), the absence of an electric field (b), and the presence of a + 0.5 V/Å electric field (c)

The − 0.5, 0, and + 0.5 V/Å models utilize 264, 271, and 256 structures, respectively, corresponding to the number of points on their respective graphs for both the DFT energies (red circles in Fig. 2) and the predicted energies (crosses in Fig. 2). The lowest internal CV score for each model was achieved using a 2nd order MF fit. The residuals between the MF fit and the DFT calculated adsorption energy used to construct the overall LG + MF CE model can be seen in Figure S2. The formation energy of all structures used to develop the LG models for each electric field scenario, along with the convex hull, is available in Figure S3. The criteria used in determining when each model is considered complete is based on the behavior of both the internal and external CV score. The 0 and + 0.5 V/Å electric field models were considered sufficiently predictive when the internal CV score deviated by less than 1 meV between three calculations. Each of these three final internal CV scores were calculated after introducing at least 15% additional, new structures to the database. The − 0.5 V/Å was considered sufficient when the internal CV score came within 0.1 meV of the 0 V/Å model’s internal CV score. The external CV score based on 4 new structures for the − 0.5, 0, and + 0.5 V/Å electric fields was 15.6, 9.2, and 12.0 meV, reflective of the models’ ability to predict the energetics of new structures that were not included in the existing model.

From both the raw adsorption energy data and the MF model, it is seen that oxygen binds most favorably in the 0 V/Å electric field case. This implies that the electric field has an overall destabilizing effect on oxygen’s adsorption tendencies. The MF models are very similar for each electric field scenario, implying that the effects caused by the electric field are not fully captured by the MF model alone, but require a LG model to realize the true nature of its effect.

Figure 3 illustrates the improved accuracy of a LG + MF model over a MF model alone when predicting DFT energies. The first column shows the MF predictions while the second column shows the LG + MF predictions. A parity line has been added for comparison.

Fig. 3

Comparison of DFT calculated adsorption energies to (a) MF predicted adsorption energies and (b) LG + MF predicted adsorption energies for the − 0.5 V/Å (1), 0 V/Å (2), and + 0.5 V/Å (3) electric field scenarios. A parity line (black) has been added for comparison

The MF models (a) shows more scatter and larger deviation from the parity line, where the LG + MF models show less scatter and trends more closely with the parity line. The + 0.5 V/Å LG + MF model (3b) deviates slightly more from the line of perfect fit than the − 0.5 and 0 V/Å scenario. This is likely the result of the + 0.5 V/Å model having the largest CV score of the three systems.

The most stable structures within the CE are associated with the most negative adsorption energy at each given coverage, known as the ground state configuration (GSC). A sampling of these GSCs can be seen in Fig. 4. The minimum energy hull over the entire coverage range for each electric field scenario is seen in Figure S2.

Fig. 4

Ground state configurations associated with three different coverages for the − 0.5, 0, and + 0.5 V/Å models. The associated unit cell for each ground state is also indicated

The three electric field scenarios share identical GSCs at 0.57 ML. The + 0.5 V/Å system has different GSC at 0.25 ML, while the − 0.5 V/Å system has a different GSC at 0.71 V/Å. Previous experimental work indicates that the Fe(100) surface can reach a full monolayer of oxygen coverage, in agreement with their simulated scanning tunneling microscope (STM) images [44]. Not only will the application of an applied electric field alter the CE, but it also impacts the GSCs.

3.2 LG + MF Model Comparison Using Unique CEs

Figure 5 shows the most predictive LG + MF CE models developed for the − 0.5, 0, and + 0.5 V/Å systems, detailing each oxygen atom cluster along with the cluster’s effective cluster interaction (ECI). Errors for each ECI were estimated using the method developed by Collinge et al. [45] and are provided as error bars.

Fig. 5

Clusters and ECIs for each LG + MF CE of oxygen (red circles) on Fe(100) (white circles) in the presence of a − 0.5 V/Å electric field (a), no electric field (b), and + 0.5 V/Å electric field (c)

Because the CE for each system is allowed to be unique in order to find the most predictive model, the 0 V/Å CE does not contain any 2-body clusters. This indicates that the MF model adequately captures the contribution of 2-body interactions in the 0 V/Å electric field system’s configurational potential. The MF portion of the − 0.5 and + 0.5 V/Å system must therefore not sufficiently capture 2-body interactions as the LG CE portion of the model includes 2-body interactions. A list of all possible clusters, including those presented here, can be found in Table S2.

Negative and positive ECI values indicate attractive (energy lowering) and repulsive (energy raising) interactions, respectively. It is important to note that the true, total interaction tendencies associated with each cluster requires a closer look at the cluster’s configuration. For example, the ECI for cluster 36 should be interpreted as a correcting factor to cluster 4 since cluster 36 is essentially cluster 4 but with one extra oxygen atom in its presence. Summing the ECI of cluster 4 and 36 (17.7 meV) accounts for the overall repulsive behavior of cluster 36. The effect of the MF model must be accounted for when trying to interpret these ECIs as well, which is less repulsive than would be expected given the repulsive nature of cluster 4. The addition of an extra O atom to cluster 4 to create cluster 36 corresponds to an increase in coverage, accounted as a repulsive effect in the MF portion of the model. In this way, the negative (attractive) ECI of cluster 36 shows a mitigating effect against this mean field repulsion.

A closer look at the attractive clusters in the negative electric field CE can help explain the difference in GSCs. Figure 6 highlights the most attractive cluster in the 0.71 ML GSC of the − 0.5 V/Å electric field scenario.

Fig. 6

The strongest attractive cluster present in the GSC of the − 0.5 V/Å at 0.71 ML

Cluster 75 of the − 0.5 V/Å electric field CE is the most attractive cluster among all the clusters in each electric field CE and appears in the − 0.5 V/Å electric field GSC at 0.71 ML (highlighted in white). The presence of this highly attractive cluster helps to explain the differences observed between the GSCs of the − 0.5 and 0 V/Å systems. The 0 V/Å GSC at 0.71 ML includes all of the attractive clusters in its CE; however, none of these clusters are as attractive as cluster 75 in the − 0.5 V/Å electric field CE.

A detailed analysis of each LG + MF CE is seen in Table 1. The average ECIs for each CE are shown along with the error in each cluster’s ECI. Two chief factors in determining the importance of a particular cluster used within a CE are the magnitude of the ECI and the cluster’s multiplicity, or the number of times the cluster appears on a fully covered surface. Thus, a multiplicity-weighted ECI for each cluster can be defined as the product of the cluster’s ECI and multiplicity. The impact each cluster has on the model’s overall fit is assessed as the percent contribution of the cluster’s multiplicity-weighted ECI to the absolute sum of the CE’s multiplicity-weighted ECIs. For example, removing a cluster with a high weight percent from the CE would have a larger impact on the model’s CV score than removing a cluster with a lower weight percent.

Table 1

Comparison of CE characteristics for the − 0.5, 0, and + 0.5 V/Å LG + MF models showing both the unweighted ECI and multiplicity-weighted ECI (Wtd ECI) in meV and percentage contribution to the CE’s total ECI

− 0.5 V/Å electric field

Cluster ID

Multiplicity

ECI (meV)

Wtd ECI (meV)

Weight (%)

Error (%)

50

8

18.7

149.7

14.7

8.2

57

2

70.2

140.3

13.8

8.1

36

8

− 16.9

− 135.4

13.3

6.1

54

8

− 13.7

− 109.4

10.8

9.0

17

4

− 25.6

− 102.3

10.1

21.6

8

4

− 23.1

− 92.4

9.1

31.2

12

2

40.7

81.4

8.0

9.8

4

2

34.6

69.2

6.8

10.3

32

8

6.8

54.7

5.4

14.0

75

1

− 50.5

− 50.5

5.0

6.1

35

4

8.0

32.1

3.2

8.7

Average weighted ECI:

92.5 meV

  

Average weighted repulsive ECI:

87.9 meV

  

Average weighted attractive ECI:

− 98.0 meV

  

CV score:

11.8 meV/site

  

0 V/Å electric field

Cluster ID

Multiplicity

ECI (meV)

Wtd ECI (meV)

Weight (%)

Error (%)

57

2

72.1

144.2

17.6

6.2

17

4

− 34.5

− 137.9

16.9

5.6

50

8

16.9

135.3

16.5

22.4

36

8

− 11.5

− 92.3

11.3

15.1

12

2

43.2

86.4

10.6

16.8

65

8

− 10.8

− 86.6

10.6

24.8

35

4

16.4

65.4

8.0

12.3

33

4

− 10.2

− 40.6

5.0

5.8

43

4

− 7.2

− 28.7

3.5

21.0

Average weighted ECI:

74.3 meV

  

Average weighted repulsive ECI:

107.8 meV

  

Average weighted attractive ECI:

− 77.2 meV

  

CV score:

11.0 meV/site

  

+ 0.5 V/Å electric field

Cluster ID

Multiplicity

ECI (meV)

Wtd ECI (meV)

Weight (%)

Error (%)

11

4

47.0

188.1

21.7

15.4

41

8

− 18.4

− 147.0

16.9

8.2

35

4

30.8

123.1

14.2

15.3

26

8

− 15.4

− 122.9

14.2

19.9

77

4

− 20.9

− 83.8

9.7

14.7

57

2

36.9

73.8

8.5

17.8

5

4

− 16.7

− 67.0

7.7

15.0

34

2

31.2

62.3

7.2

13.3

Average weighted ECI:

78.9 meV

  

Average weighted repulsive ECI:

111.8 meV

  

Average weighted attractive ECI:

− 105.2 meV

  

CV score:

16.1 meV/site

  

The clusters in each model’s CE seen in Table 1 are ranked according to the cluster’s weight percent. The − 0.5 and 0 V/Å systems share similar clusters having the most impact on the models’ overall fit, such as clusters 50 and 57, while the + 0.5 V/Å system differs, with clusters 11, 41, and 35 having the most impact on the model’s overall fit.

The − 0.5 V/Å electric field increases the average ECI by 18.2 meV, while the + 0.5 V/Å electric field increases the average ECI less significantly, by 4.6 meV. The − 0.5 V/Å field reduces the overall repulsive interaction strength by 19.9 meV, while the + 0.5 V/Å field increases the repulsive interaction strength 4.0 meV. The − 0.5 V/Å electric field strengthened the attractive interactions by 20.7 meV, while the + 0.5 V/Å strengthened the attractive interactions by 27.9 meV. The CV scores for the − 0.5 and 0 V/Å models (11.8 and 11.0 meV, respectively) are lower than that of the + 0.5 V/Å model (16.1 meV), indicating that the + 0.5 V/Å model may be overall slightly less predictive than the others. Overall, both the − 0.5 and + 0.5 V/Å electric fields strengthen the attractive interactions, while the repulsive interactions are weakened by the − 0.5 V/Å electric field and strengthened by the + 0.5 V/Å electric field.

3.3 LG + MF Model Comparison Using Identical CEs

The unique CE associated with each electric field scenario makes it difficult to directly determine the effect of the electric field on the adsorbate interactions. To allow for direct comparison, the CE developed in absence of an electric field is used as the CE for the − 0.5 and + 0.5 V/Å models, seen in Fig. 7. The − 0.5, 0, and + 0.5 V/Å ECIs are plotted side by side for each cluster.

Fig. 7

− 0.5 V/Å (black), 0 V/Å (blue), and + 0.5 V/Å (red) systems both using the 0 V/Å cluster expansion to allow for direct comparison of the electric field effect on ECIs

The electric field has the most statistically significant impact on clusters 12, 35, and 57, all of which exhibit repulsive interactions. The error associated with the remaining clusters washes out the effect of the electric field on their ECI. Table 2 provides more details regarding the interactions for each electric field scenario.

Table 2

Comparison of CE characteristics using a common CE for each electric field scenario, showing both the unweighted ECI and multiplicity-weighted ECI in meV and percentage contribution to the sum of the CE’s absolute weighted ECIs

Cluster ID

Multiplicity

ECI (meV)

Weighted ECI (meV)

− 0.5 V/Å

0 V/Å

+ 0.5 V/Å

− 0.5 V/Å

0 V/Å

+ 0.5 V/Å

12

2

73.1

43.2

55.0

146.2

86.4

110.0

17

4

− 33.3

− 34.5

− 42.7

− 133.2

− 137.9

− 170.8

33

4

− 11.5

− 10.2

− 12.1

− 46.0

− 40.6

− 48.3

35

4

8.3

16.4

28.8

33.3

65.4

115.1

36

8

− 11.9

− 11.5

− 9.7

− 94.9

− 92.3

− 77.5

43

4

− 7.2

− 7.2

− 9.9

− 28.8

− 28.7

− 39.4

50

8

9.0

16.9

19.8

71.6

135.3

158.1

57

2

53.8

72.1

50.8

107.5

144.2

101.6

65

8

− 2.6

− 10.8

− 14.1

− 20.6

− 86.6

− 112.5

Cluster ID

Multiplicity

Weights (%)

Error (%)

− 0.5 V/Å

0 V/Å

+ 0.5 V/Å

− 0.5 V/Å

0 V/Å

+ 0.5 V/Å

12

2

21.4

12.7

11.8

4.2

11.5

8.4

17

4

19.5

20.2

18.3

6.6

10.4

6.5

33

4

6.7

6.0

5.2

20.2

28.8

27.5

35

4

4.9

9.6

12.3

34.0

21.8

13.6

36

8

13.9

13.5

8.3

14.4

25.4

32.0

43

4

4.2

4.2

4.2

30.9

30.4

31.6

50

8

10.5

19.8

16.9

23.7

20.4

14.2

57

2

15.8

21.1

10.9

9.5

7.9

9.3

65

8

3.0

12.7

12.1

102.9

33.0

27.6

Average weighted repulsive ECI, meV:

75.8

90.8

103.7

 

Average weighted attractive ECI, meV:

89.7

107.8

121.2

 

Average weighted ECI, meV:

− 64.7

− 77.2

− 89.7

 

CV score, meV/site:

12.4

11.0

16.8

 

The application of the + 0.5 V/Å electric field results in the average magnitude of the multiplicity-weighted ECI increasing by 12.9 meV, while the − 0.5 V/Å electric field lowers the average ECI magnitude by 15.1 meV when compared to the 0 V/Å system. The − 0.5 V/Å electric field weakens both the average repulsive and attractive interactions by 18.2 and 12.6 meV, respectively, while the + 0.5 V/Å electric field strengthens the average repulsive and attractive ECIs by 13.4 and 12.5 meV, respectively. Cluster 17 is shared across each electric field scenario as one of the most important clusters to the model’s overall fit. The − 0.5 and 0 V/Å systems share cluster 57 as one of their top three contributing clusters, while the + 0.5 and − 0.5 V/Å systems share cluster 50 as one of their top three contributing clusters. The CV score increases by less than 1 meV for the − 0.5 and + 0.5 V/Å electric field systems even when forcing their CE’s to that of the 0 V/Å CE, indicating that the models maintain their predictiveness.

The use of identical CEs for each electric field scenario elucidates a more consistent electric field effect observed on attractive and repulsive interactions. The negative electric field tends to weaken both attractive and repulsive interactions and the positive electric field tends to strengthen these interactions, while overall the repulsive interactions are the most strongly affected. This was not the case for the negative electric field when using unique CEs, where our analysis was implying that the interactions were greatly strengthened (see Fig. 7). This indicates that the use of a common cluster expansion allowing for direct CE comparison may be a more appropriate analysis. Overall, it is clear that the application of an electric field is capable of altering the lateral interactions between adsorbed oxygen atoms, impacting both repulsive, attractive, and overall interaction strength.

3.4 Density of States

Donati et al. have investigated the density of states of the p(1 × 1)–O/Fe(100) surface using scanning tunneling spectroscopy (STS) [44]. They show the STS spectra to be dominated by two peaks: one at 0.5 eV below the Fermi level and the other at 1.0 eV above the Fermi level. DFT-based density of states are presented here as a means to ensure our models’ align with experimental results. Figure 8 displays the density of states for both a surface Fe and O atom on a p(1 × 1) (or 1 ML) surface. The total density of states is shown as the black line, while the relevant projected valence contributions are represented as the dotted blue and red lines, respectively.

Fig. 8

Density of states for p(1 × 1)–O/Fe(100) for a the surface Fe atom and b an oxygen atom

The surface Fe atom (a) exhibits a peak around 1 eV above the Fermi level, dominated by a d-orbital contribution. The surface O atom exhibits a peak around 0.5 eV below the Fermi level, which is dominated by the p-orbital contribution. The two peaks in the DOS are in agreement with the experimental results obtained by Donati et al. providing experimental validity to the simulated electronic interactions captured in the LG + MF models’ presented here.

4 Conclusion

This work provides a thorough investigation of oxygen’s coverage behavior on Fe(100) in the presence and absence of an applied electric field. The configurational potential energy has been characterized by combining both MF and LG methods to develop predictive surface coverage models. This work shows that a MF model alone is insufficient in capturing the effects of the electric field, but requires a LG approach to realize the true effect. LG + MF CE models were built for three electric field scenarios (− 0.5, 0, and 0.5 V/Å), revealing the effect of electric fields on surface coverage behavior. An analysis of both adsorption energy data (from 0 to 1 ML) and the data’s corresponding MF model indicates that oxygen binds most favorably in the absence of an electric field, implying that the electric field has an overall destabilizing effect on oxygen’s adsorption tendencies. In addition, the application of a negative electric field results in different ground state configurations. We acknowledge that other methods can be used to construct a CE, such as machine learning approaches where graph-theoretical cluster expansions can be constructed [18]. However, the ease of transferability of the lattice gas Hamiltonian to a corresponding kinetic model and the physical insight obtained from the determination of the lateral interactions makes the construction of such a Hamiltonian highly desirable.

When a common CE is used for each electric field scenario it is observed that the negative electric field tends to weaken both attractive and repulsive interactions while the positive electric field tends to strengthen these interactions. Overall, it is clear that the application of an electric field is capable of altering both repulsive and attractive lateral interactions between adsorbed oxygen atoms. Since lateral interactions have been shown to play a critical role in defining catalytic behavior, the application of an applied electric field has the potential to be a useful tool in adjusting critical chemical properties of Fe based HDO catalysts, by decreasing the repulsive interactions between the adspecies in the presence of negative electric fields and thereby mitigating the formation of an oxide.

To this end, the nanoscale atomic interactions characterized in this work can manifest into important catalytic properties when observed on the macroscale. Multi-scale modeling techniques, such as Monte Carlo methods, can be used to extend the coverage dependence noted at the nanoscale to real-material, macroscale behaviors, capable of being directly compared to experiment. As such, the work presented here provides the first ingredients necessary to build realistic, multi-scale kinetic models of an Fe-based HDO catalyst from first principles while incorporating the effect of applied electric fields. Ultimately, this study, combined with future Monte Carlo simulations, will incorporate the effect of realistic surface configurations into a multi-scale model of an Fe catalyst, which can be used to determine experimentally useful kinetic properties such as rates, rate orders, and activation energies [20] allowing for the improved design of inexpensive Fe based HDO catalysts.

Notes

Acknowledgements

J.B. and J.-S.M. were primarily funded by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Biosciences and Geosciences (DE-SC0014560). G.C., NSF Graduate Research Fellow, gratefully acknowledges financial support from the National Science Foundation Graduate Research Fellowship Program. G.C. also acknowledges the NSF EAPSI fellowship program under award number 1613890. J.B., Seattle Chapter ARCS Fellow, gratefully acknowledges financial support from the Achievement Rewards for College Scientists Foundation. The Pacific Northwest National Laboratory is operated by Battelle for the U.S. DOE.

Supplementary material

11244_2018_944_MOESM1_ESM.docx (1.3 mb)
Supplementary material 1 (DOCX 1285 KB)

References

  1. 1.
    Wang H, Male J, Wang Y (2013) Recent advances in hydrotreating of pyrolysis bio-oil and its oxygen-containing model compounds. ACS Catal 3(5):1047–1070CrossRefGoogle Scholar
  2. 2.
    Sun J, Karim AM, Zhang H, Kovarik L, Li XS, Hensley AJR, McEwen J-S, Wang Y (2013) Carbon-supported bimetallic Pd–Fe catalysts for vapor-phase hydrodeoxygenation of guaiacol. J Catal 306:47–57CrossRefGoogle Scholar
  3. 3.
    Hong Y, Zhang H, Sun J, Karim AM, Hensley AJR, Gu M, Engelhard MH, McEwen J-S, Wang Y (2014) Synergistic catalysis between Pd and Fe in gas phase hydrodeoxygenation of m-cresol. ACS Catal 4(10):3335–3345CrossRefGoogle Scholar
  4. 4.
    Nie L, de Souza PM, Noronha FB, An W (2014) Selective conversion of m-cresol to toluene over bimetallic Ni–Fe catalysts. J Phys Chem C 388:47–55Google Scholar
  5. 5.
    Sitthisa S, An W, Resasco DE (2011) Selective conversion of furfural to methylfuran over silica-supported Ni Fe bimetallic catalysts. J Catal 284(1):90–101CrossRefGoogle Scholar
  6. 6.
    Che F, Ha S, McEwen J-S (2016) Elucidating the field influence on the energetics of the methane steam reforming reaction: a density functional theory study. Appl Catal B 195(1):77–89CrossRefGoogle Scholar
  7. 7.
    Che F, Gray JT, Ha S, McEwen J-S (2016) Improving Ni catalysts using electric fields: a DFT and experimental study of the methane steam reforming reaction. ACS Catal 7(1):551–562CrossRefGoogle Scholar
  8. 8.
    Che F, Ha S, McEwen J-S (2017) Hydrogen oxidation and water dissociation over an oxygen-enriched Ni/YSZ electrode in the presence of an electric field: a first principles-based microkinetic model. Ind Eng Chem Res 56(5):1201–1213CrossRefGoogle Scholar
  9. 9.
    Che F, Gray JT, Ha S, McEwen J-S (2015) Catalytic water dehydrogenation and formation on nickel: dual path mechanism in high electric fields. J Catal 332:187–200CrossRefGoogle Scholar
  10. 10.
    Che F, Ha S, McEwen J-S (2017) Catalytic reaction rates controlled by metal oxidation state: C–H bond cleavage in methane over nickel-based catalysts. Angew Chem Int Ed 129(13):3611–3615CrossRefGoogle Scholar
  11. 11.
    Che F, Gray JT, Ha S, McEwen J-S (2017) Reducing reaction temperature, steam requirements, and coke formation during methane steam reforming using electric fields: a microkinetic modeling and experimental study. ACS Catal 7(10):6957–6968CrossRefGoogle Scholar
  12. 12.
    Hong Y, Hensley AJR, McEwen J-S, Wang Y (2016) Perspective on catalytic hydrodeoxygenation of biomass pyrolysis oils: essential roles of Fe-based catalysts. Catal Lett 146(9):1621–1633CrossRefGoogle Scholar
  13. 13.
    Van De Walle A, Ceder G (2002) Automating first-principles phase diagram calculations. J Ph Equilib 23(4):348–359CrossRefGoogle Scholar
  14. 14.
    Stampfl A, Kreuzer HJ, Payne SH, Pfnür H, Scheffler M (1999) First-principles theory of surface thermodynamics and kinetics. Phys Rev Lett 83(15):2993CrossRefGoogle Scholar
  15. 15.
    McEwen J-S, Eichler A (2007) Phase diagram and adsorption-desorption kinetics of CO on Ru(0001) from first principles. J Chem Phys 129(9):094701CrossRefGoogle Scholar
  16. 16.
    McEwen J-S, Payne SH, Stampfl C (2002) Phase diagram of O/Ru(0001) from first principles. Chem Phys Lett 361(3):317–320CrossRefGoogle Scholar
  17. 17.
    Bray JM, Skavdahl IJ, McEwen J-S, Schneider WF (2014) First-principles reaction site model for coverage-sensitive surface reactions: Pt(111)–O temperature programmed desorption. Surf Sci 622:L1–L6CrossRefGoogle Scholar
  18. 18.
    Vignola E, Steinmann SN, Vandegehuchte BD, Curulla D, Stamatakis M, Sautet P (2017) A machine learning approach to graph-theoretical cluster expansions of the energy of adsorbate layers. J Chem Phys 147(5):054106CrossRefPubMedGoogle Scholar
  19. 19.
    Reuter K, Stampfl C, Scheffler M (2005) Ab initio atomistic thermodynamics and statistical mechanics of surface properties and functions. In: Yip S (ed) Handbook of materials modeling, vol. 1. Springer, Dordrecht, pp 149–194CrossRefGoogle Scholar
  20. 20.
    Asthagiri A, Janik MJ (eds) (2013) Computational catalysis. Royal Society of Chemistry, CambridgeGoogle Scholar
  21. 21.
    Zhang P (1993) Model selection via multifold cross validation. Ann Stat 21(1):299–313CrossRefGoogle Scholar
  22. 22.
    Shao J (2012) Linear model selection by cross-validation. J Am Stat Assoc 88(422):486CrossRefGoogle Scholar
  23. 23.
    Baumann K (2003) Cross-validation as the objective function for variable-selection techniques. TrAC 22(6):395–406Google Scholar
  24. 24.
    McEwen J-S, Payne SH, Kreuzer HJ, Kinne M, Denecke R, Steinrück HP (2003) Adsorption and desorption of CO on Pt(111): a comprehensive analysis. Surf Sci 545(1):47–69CrossRefGoogle Scholar
  25. 25.
    Van De Walle A, Asta M, Ceder G (2002) The Alloy Theoretic Automated Toolkit: a user guide. arXivorg 26(4):539–553Google Scholar
  26. 26.
    Kresse G, Furthmüller J (1996) Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6(1):15–50CrossRefGoogle Scholar
  27. 27.
    Kresse G, Hafner J (1993) Ab initio molecular dynamics for liquid metals. Phys Rev B 47(1):558–561CrossRefGoogle Scholar
  28. 28.
    Błoński P, Kiejna A, Hafner J (2005) Theoretical study of oxygen adsorption at the Fe (110) and (100) surfaces. Surf Sci 590(1):88–100CrossRefGoogle Scholar
  29. 29.
    Freitas RRQ, Rivelino R, de Brito Mota F, de Castilho CMC (2012) Dissociative adsorption and aggregation of water on the Fe(100) surface: a DFT study. J Phys Chem C 116(38):20306–20314CrossRefGoogle Scholar
  30. 30.
    Kittel C (2004) Introduction to solid state physics, 8 edn. Wiley, New YorkGoogle Scholar
  31. 31.
    Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50(24):17953CrossRefGoogle Scholar
  32. 32.
    Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59(3):1758–1775CrossRefGoogle Scholar
  33. 33.
    Hammer B, Hansen LB, Nørskov JK (1999) Improved adsorption energetics within density-functional theory using revised Perdew–Burke–Ernzerhof functionals. Phys Rev B 59(11):7413–7421CrossRefGoogle Scholar
  34. 34.
    Hensley AJR, Ghale K, Rieg C, Dang T, Anderst E, Studt F, Campbell CT, McEwen J-S, Xu Y (2017) DFT-based method for more accurate adsorption energies: an adaptive sum of energies from RPBE and vdW density functionals. J Phys Chem C 121(9):4937–4945CrossRefGoogle Scholar
  35. 35.
    Stevens ED, Rys J, Coppens P (1978) Quantitative comparison of theoretical calculations with the experimentally determined electron density distribution of formamide. J Am Chem Soc 100(8):2324–2328CrossRefGoogle Scholar
  36. 36.
    Maintz S, Deringer VL, Tchougréeff AL, Dronskowski R (2016) LOBSTER: a tool to extract chemical bonding from plane-wave based DFT. J Comput Chem 37(11):1030–1035CrossRefPubMedPubMedCentralGoogle Scholar
  37. 37.
    Maintz S, Deringer VL, Tchougréeff AL, Dronskowski R (2013) Analytic projection from plane-wave and PAW wavefunctions and application to chemical-bonding analysis in solids. J Comput Chem 34(29):2557–2567CrossRefPubMedGoogle Scholar
  38. 38.
    Deringer VL, Tchougréeff AL, Dronskowski R (2011) Crystal orbital hamilton population (COHP) analysis as projected from plane-wave basis sets. J Phys Chem A 115(21):5461–5466CrossRefPubMedGoogle Scholar
  39. 39.
    Dronskowski R, Bloechl PE (1993) Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculations. J Phys Chem 97:8617–8624CrossRefGoogle Scholar
  40. 40.
    Maintz S, Esser M, Dronskowski R (2016) Efficient rotation of local basis functions using real spherical harmonics. Acta Phys Pol B 47(4):1165–1175CrossRefGoogle Scholar
  41. 41.
    Neugebauer J, Scheffler M (1992) Adsorbate-substrate and adsorbate-adsorbate interactions of Na and K adlayers on Al(111). Phys Rev B 46(24):16067–16080CrossRefGoogle Scholar
  42. 42.
    Deshlahra P, Wolf EE, Schneider WF (2009) A periodic density functional theory analysis of CO chemisorption on Pt(111) in the presence of uniform electric fields. J Phys Chem A 113(16):4125–4133CrossRefPubMedGoogle Scholar
  43. 43.
    Feibelman PJ (2001) Surface-diffusion mechanism versus electric field: Pt/Pt(001). Phys Rev B 64(12):2491CrossRefGoogle Scholar
  44. 44.
    Donati F, Sessi P, Achilli S, Li Bassi A, Passoni M, Casari CS, Bottani CE, Brambilla A, Picone A, Finazzi M, Duò L, Trioni MI, Ciccacci F (2009) Scanning tunneling spectroscopy of the Fe(001)—p(1 × 1)Osurface. Phys Rev B 79(19):195430–195436CrossRefGoogle Scholar
  45. 45.
    Collinge G, McEwen J-S (2018) Estimation of errors in effective cluster interactions of lattice gas models based on ab initio calculations. (In Preparation)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Jacob Bray
    • 1
  • Greg Collinge
    • 1
  • Catherine Stampfl
    • 2
  • Yong Wang
    • 1
    • 5
  • Jean-Sabin McEwen
    • 1
    • 3
    • 4
    • 5
  1. 1.The Gene & Linda Voiland School of Chemical Engineering and BioengineeringWashington State UniversityPullmanUSA
  2. 2.The School of PhysicsThe University of SydneySydneyAustralia
  3. 3.Department of Physics and AstronomyWashington State UniversityPullmanUSA
  4. 4.Department of ChemistryWashington State UniversityPullmanUSA
  5. 5.Institute for Integrated CatalysisPacific Northwest National LaboratoryRichlandUSA

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