1 Introduction

The fixation of atmospheric nitrogen has long been one of the prime challenges in chemistry and chemical engineering [1, 2]. The Haber–Bosch process has been the route of choice for performing nitrogen fixation for the past century, permitting much of the population growth over that period [3]. However, this process has significant drawbacks, including high CO2 emissions and centralized production due to large capital requirements [4]. The Haber–Bosch process’s considerable contribution to CO2 emissions has been an increasingly pressing concern for the global community, as it accounts for 340 million tonnes of CO2—fully 2% of the carbon emissions worldwide [5, 6]. For this reason, supplanting the Haber–Bosch process would represent a significant contribution to global efforts to curb climate change.

Due to the various drawbacks of the Haber–Bosch process, researchers have sought alternative means of producing fixed nitrogen [4, 7,8,9,10,11]. Two strategies that have received significant recent interest are electrocatalysis [7] and photocatalysis [12]. However, making either of these technologies viable presents a significant challenge. Electrochemical nitrogen fixation requires generating electricity and transporting electrons to the catalyst surface to perform the reaction [9]. The need for both solar and electrocatalytic cells may limit the viability of electrochemical processes in the developing world. An alternative route is photochemical nitrogen fixation, where the catalyst is placed in direct contact with sunlight, air, and water vapor to produce fixed nitrogen. The photochemical route has the potential to operate with low capital investment and simpler infrastructure, making it promising for low-resource environments [4].

The scientific community has known of photochemical nitrogen fixation for decades, but inconsistent results, questions of contamination, and low rates have discouraged further study [12, 13]. Dhar was the first to investigate photocatalytic nitrogen [14], and the first well-controlled experiments were performed decades later when Schrauzer and Guth independently re-discovered the process [15]. Schrauzer and Guth were able to establish the production of NH3 in sterilized desert sands under illumination [15], including confirmation via isotopic labeling [16]. Numerous independent experiments have been performed over the years and reported photochemical production of NH3 over titania materials [17,18,19,20,21,22], though legitimate skepticism has remained due to issues with contamination [13, 23, 24], interference [25, 26], and inconsistent results [12]. However, recent experiments utilizing ambient pressure X-ray photoelectron spectroscopy have observed reduced nitrogen compounds only under illumination [27]. These experiments provide direct experimental evidence that photoinduced nitrogen reduction occurs on titania surfaces, though the presence of carbon-based impurities was found to be a critical enabler of the process.

One route to increasing reaction rates is the inclusion of transition-metal dopants in TiO2 [28]. Transition-metal dopants can increase rates via at least two distinct mechanisms: increasing the amount of photogenerated electrons that reach the surface by improving absorption and charge separation, or by altering the kinetics of the surface reaction. Transition-metal doping has been previously explored to improve the performance of TiO2 photocatalysts [29,30,31]. In particular, early work on photocatalytic nitrogen fixation tested a variety of metal dopants. These studies found that several noble metals [32] and iron in particular increase yields [15, 16, 18, 19, 32, 33]. In these studies the dopant metals were co-precipitated with the TiO2 samples, thus having significant concentrations in the bulk. These studies were also performed without the use of isotopic labeling, and careful controls are not always included, making interpretation difficult. More recently, Hirakawa et al. used a modern photochemical setup along with isotopic labeling and found that depositing noble metals (Ru, Pt, Pd) onto an already prepared rutile (110) surface led to a decrease in reaction rates [22]. This decrease in rates, along with detailed experimental and theoretical studies on the role of iron dopants [19, 34] suggests that the primary mechanism of these previously-reported dopants is enhanced charge separation. However, transition-metal dopants are also known to affect the surface properties in a range of other materials and reactions [34,35,36,37,38,39,40]. In particular, the field of “single-atom catalysis” has revealed that isolated transition-metal sites supported on oxide materials can exhibit remarkable catalytic properties [41,42,43]. Yet, relatively little effort has focused on understanding how isolated transition-metal atom dopants affect the surface reactivity of oxides for the conversion of nitrogen to ammonia [44,45,46,47,48].

In this work, we focus on the potential of isolated transition-metal atoms substituted into the rutile (110) titania surface (see Fig. 1) as a potential route to improve the surface kinetics of the nitrogen reduction reaction. We screen the d-block transition-metals substituted into the (110) surface in two different configurations corresponding to formal oxidation states of 2+ and 4+. We analyze the trends present across the periodic table for the dopant metal substitution energy, N2, N2H, and NH2 adsorption energy. We also map out the thermodynamics of all N2 reduction pathways and use this to assess the most favorable reaction mechanism. Finally, we assess the expected improvement in reaction rates from forming metal dopant sites on the surface. In this analysis, we consider both electrocatalytic and photocatalytic N2 reduction. The results illustrate that there are clear correlations in the metal substitution and adsorption energies with the d-band center and cohesive energies, respectively. We also find scaling relations between the surface species. These scaling relations result in an optimum in the rate-limiting potential for nitrogen reduction as a function of N2H and NH2 adsorption energies.

Fig. 1
figure 1

An example of the screened 2+ (top) and 4+ (bottom) slabs. For 2+ sites the substituent metal has replaced a sixfold Ti atom (seen in blue) and a bridging oxygen vacancy has been formed to allow the metal to enter the 2+ oxidation state. For 4+ sites the substituent metal has replaced a fivefold Ti atom (seen in blue) resulting in a 4+ formal oxidation state

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2 Results and Discussion

Rutile TiO2 (110) is chosen as a model surface based on the experimentally observed correlation between rutile content and reaction rates for photocatalytic nitrogen fixation [15]. Additionally, there is a rich literature on the surface science of rutile (110) [49,50,51,52], and recent surface-science experiments and DFT calculations indicate that carbon substitution defects on the rutile (110) surface are active for photocatalytic nitrogen reduction [27]. From this model surface, slabs containing metal dopants at the surface formally in the 2+ and 4+ oxidation states are generated for each dopant metal. These oxidation states may not represent the true oxidation state of each site, but rather represent the oxidation state the site would take on if all Ti metal atoms retained the 4+ oxidation state. We also note that these models are similar to those studied previously in the literature [39, 53]. In total, all d-block transition-metals, except Mn (24 total), are screened for their surface metal substitution energy and activity for nitrogen reduction. The binding energies of N2H and NH2 have been identified as descriptors for activity in the literature as they are typically involved in the rate-limiting steps [34, 54, 55]. Thus, these energies have been calculated to assess the activity of generated surfaces. Full details of the calculation methodology are in the Sect. 4.

2.1 Trends in Active Site Metal Substitution Energies

The stability of substituted metal surface sites is examined with respect to the position of their d-band center. In Fig. 2a, the metal substitution energy of the studied active sites has been plotted against the location of the d-band center of the corresponding transition-metal see Eq. 2. The pure metallic form is the reference for the metal substitution energy of each metal substituted site. The d-band centers are calculated from the metallic bulk state rather than the single atom [56].

Fig. 2
figure 2

a The metal substitution energy see Eq. 2 of 4+ surface sites (blue) and 2+ surface sites (orange) with respect to their bulk metallic state vs. the metallic d-band center. b The metal substitution energy of 4+ surface sites (blue) and bulk substitutions (green) with respect to their bulk metallic state vs. the metallic d-band center. d-band centers were obtained from [56]. Only metals whose d-band center was previously reported in [56] are included

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The plot indicates there is a strong correlation between the d-band center and metal substitution energy of the metal substitution (R2 = 0.91 and 0.79 for 4+ and 2+ respectively).

The correlation between the d-band center, a bulk metal property, and the stability of isolated metal atoms is somewhat surprising. However, the stability of the bulk metal also plays a role in determining the stability of the isolated site, which may explain some correlation, although the d-band center was found to be a better descriptor than the cohesive energy. The observed trends are also consistent with the observation that the interaction between metal surfaces and oxygen weakens from left to right on the periodic table, as predicted by the d-band model [57]. This trend implies that the metals most able to integrate into a surface are those with the most favorable interaction with oxygen. A similar relationship has been reported previously for doped rutile oxides [58] and oxide-supported single-atom catalysts [43]. Other reports suggest that the electronegativity of the substituted metal is the relevant descriptor predicting stability [39]. The electronegativity is also correlated with the metal substitution energy (R2 = 0.81 and 0.62 for 2+ and 4+ respectively, see Fig. S3), but not as strongly as the d-band center of the metal (R2 = 0.79 and 0.91, see Fig. 2). The fact that both of these quantities correlate with the metal substitution energy is not surprising, as a lower energy d-center indicates a more favorable addition of electrons, which is similar to the concept of electronegativity. The main exceptions to this trend are Ti, Zr, Hf, and Ag. The first three can be rationalized easily since all three lie in the same column of the periodic table, which is the same as the host metal, Ti. The improved stability of substituent metals within the group lines up with the chemical intuition since these elements have the same number of valence d electrons. This chemical similarity affords approximately 1.5 eV of improved stability relative to the trend. The final outlier, Ag, is more difficult to explain. However, the d-band center of Ag is itself an outlier for its position on the periodic table. This deviation may indicate that more complex bonding interactions are involved.

These results have implications for the relative stability of single-atom sites over surface metal clusters or bulk substitutions in TiO2, and will relate to the feasibility of synthesizing metal-doped surfaces experimentally. We note that many of the metal substitution energies are exceedingly high (up to 10 eV) indicating that many of these surface sites are unlikely to be experimentally feasible. Some elements (Y, Sc, Zr, Hf) favor integration into the surface structure rather than the formation of surface metal clusters (see Tables S1 and S2). Conversely, noble metals such as Rh and Pt do not integrate into the surface favorably and will tend to form surface nano-clusters. This result agrees with TEM measurements in the experimental literature, indicating that clusters of metals such as platinum, silver, gold, nickel, rhodium form on a TiO2 surface [59,60,61,62] and rutile’s reputation as a support [63]. A metal’s ability to form surface sites is also dependent on the relative stability of bulk substitution, since a dopant that is more stable in the bulk than the surface will tend to segregate into the bulk rather than forming surface sites. Figure 2b shows that the 4+ surface sites are more stable than the bulk substitutions for all metals studied. The stability of surface sites relative to bulk integration suggests that bulk synthesis techniques such as co-precipitation should lead to a concentration of surface sites that exceeds the concentration of bulk sites for all metals considered. The correlation between the bulk metal substitution energies of dopant metals and their corresponding 4+ surface sites (Fig. 2b) is also striking, indicating that bulk and surface integration are controlled by similar electronic structure interactions.

Figure 2a also indicates that the oxidation state of the surface site that forms is dependent on the energy of the substituent metal’s d-band center. Elements with more negative d-band centers tend to favor forming 2+ surface sites, whereas more positive d-band centers favor 4+ sites, with the cross-over point being approximately 0.8 eV below the Fermi-level. This trend makes intuitive sense, as a more negative d-band center implies that the addition of electrons is more favorable, making the more negative oxidation state more stable. For most metals studied, the 2+ site is either more stable or nearly as stable, suggesting that the 2+ substitutions are generally more favorable. An alternative interpretation is that the inclusion of metal dopants favors the formation of surface oxygen vacancies, since the 2+ site involves an oxygen vacancy. The reactivity of oxygen vacancies is typically greater than the pristine surface, so promoting oxygen vacancy formation may be yet another indirect mechanism through which metal dopants affect catalytic activity.

2.2 Trends in Nitrogen Adsorption and Cohesive Energies

The adsorption of the inert N2 molecule is required for nitrogen fixation, and the first hydrogenation to N2H is known to be the potential-limiting step on pure TiO2 [34]. In addition, the NH2 → NH3 reaction has been identified as potential limiting on some materials [54]. This suggests that the trends in N2, N2H, and NH2 binding will provide an indication of a metal’s ability to promote nitrogen reduction. The N2 and N2H energies are calculated for both 2+ and 4+ slabs to screen the surface’s ability to reduce N2. The N2H binding energy is > 1.5 eV for all 4+ sites (see Table S2), therefore the subsequent analysis focuses exclusively on 2+ sites.

The results for N2, N2H, and NH2 adsorption on 2+ sites as a function of periodic table group are shown in Fig. 3. The results differ from the typical linear correlation that we expect from the d-band model [64], and instead, show relatively quadratic behavior with a maximum near the middle of the d-block at Os and Re for N2 and N2H respectively. Similar results are found for NH2 adsorption (Fig. 3c), though the magnitude of the adsorption energy varies, and there is small upward trend near the middle of the d-block.

Fig. 3
figure 3

The binding energies of (a) N2, (b) N2H and (c) NH2 plotted against the periodic column for 2+ metal substituent sites

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While the N2, N2H, and NH2 binding observed deviates from the near-linear correlation expected from the d-band model, we find a linear correlation between the binding energies and the d-band contributions of the cohesive energies of the corresponding bulk systems (Fig. 4) although the correlation is relatively weak in the case of N2. Cohesive energy is defined as the change in energy associated with isolated, neutrally charged atoms being brought together to form a bulk material [65]. A metal’s cohesive energy is made up of a d contribution and a s contribution. Cohesive energies have generally been a measure of the “bulk-nobleness” of a metal [66], with higher cohesive energies correlating to a more noble character. The metals with the highest “bulk-nobleness” are in the center of the d-block and resist corrosion due to the difficulty of breaking their strong metal–metal bonds. In our case, the inverse is true: the stronger the metal–metal bonds of the bulk material, the stronger the interaction between the metal and a given nitrogen species.

Fig. 4
figure 4

The d-band contribution to cohesive energies vs. the binding energies of a N2, b N2H, c NH2 for 2+ metal substituent sites. The d-band cohesive energy contributions obtained from Turchanin and Agraval [69]

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The correlation between d-band contribution to cohesive energy and binding is the strongest for N2H and NH2 (Fig. 4b, c). These two species show a relatively strong quadratic dependence (Fig. 3b, c) suggesting that the bonding of nitrogen species to these substituent metals is similar to that of forming metal–metal bonds of the original bulk material. Thus, we hypothesize that the physics of nitrogen bonding to these substituent sites is similar to the bonding between single metal atoms and a bulk metal. A similar quadratic trend is seen for N2 adsorption in Fig. 4a, though there are several outliers near the middle of the d-block (Tc, Ru, Re, Os, Ir) that bind N2 substantially stronger than predicted by the cohesive energy descriptor. The origin of this anomalously-high reactivity toward N2 is not clear, though we note that the bonding mechanism changes between physisorption for early/late metals and chemisorption for more reactive metals, indicating that the quadratic trend may still hold for chemisorption.

The trends observed for site metal substitution energy (Fig. 2) and nitrogen compound adsorption energy (Fig. 4) differ qualitatively from trends observed in bulk metals. For single transition-metal dopant atoms, the d-band center controls metal substitution energy, while the cohesive energy controls adsorption energy. In bulk metals the inverse is true: the d-band center controls a material’s ability to bind gas-phase species, whereas the cohesive energy controls how stable the material is [66]. This suggests that the origins of scaling relations for single-atom catalysts or dopant sites may differ from the case of bulk metals. However, the trend does not seem to hold in the case of 4+ sites (see Table S2), and prior work suggests that adsorption energy of oxygen on single metal atoms is correlated to the d-band center [57], so the trend is not general. The implication of different factors controlling the scaling relations of different adsorbates is that these adsorbates will also not scale with each other. This suggests that single metal atoms or dopants may be able to “break” the scaling relations between adsorbates and reach more active regions of the catalytic phase space [67, 68].

2.3 Trends in Catalytic Activity for Nitrogen Reduction

The photocatalytic activity of doped TiO2 surfaces can be assessed by computing the maximum thermodynamic barrier with electrons at the conduction band edge potential [34], while the electrocatalytic activity of doped TiO2 surfaces can be assessed by computing the thermodynamic limiting potential [39, 70]. The computational hydrogen electrode (CHE) provides a route to computing the thermochemical potential of electrons at the TiO2 surface (Sect. 4.3), and the resulting analysis provides only a thermodynamic picture of the reaction pathway. This analysis establishes a lower bound on the kinetics and correlates well with experimental trends in the literature [71].

Computing the maximum barrier or limiting potential requires the free energies of each state along a given reaction pathway. The full thermodynamics of the N2 reduction reaction pathways on all 2+ sites were calculated, allowing the generation of free energy diagrams for all possible reaction pathways (Figs. S4–S109, Table S1). H¨oskuldsson et al. [54] also previously found strong scaling relations between the binding of nitrogen compounds and the N2H binding energy for rutile metal oxides. The binding energies of all species are fit to linear scaling relations with N2H and NH2 as descriptors to assess the scaling relations for this system (Fig. S1). The scaling relations have a root mean squared error on the order of 0.2 eV (see Figures S1 and S2), consistent with general scaling relations for other reactions [72]. The N2H and NH2 were also used to fit scaling relationships for all electrochemical steps, yielding similar accuracy to scaling relations for individual species (Fig. S2). These scaling relations directly predicting reaction energies are used for subsequent analyses.

A primary consideration when assessing the electrocatalytic activity of a surface is the largest thermochemical barrier. Thermochemical steps do not involve electron transfers, so they are not considered when computing the limiting potential. However, they may still present a substantial barrier that will affect the overall rate. The largest thermochemical barriers for each surface can be seen in Table S4. The three steps with significant thermochemical barriers are N2 adsorption, NH2–NH2 scission, and NH3 desorption. For the case of the most promising dopant, Mo, the adsorption of N2 is exergonic by − 0.27 eV, which is large enough to yield reasonable to N2* coverages. However, competitive adsorption with H2O and O2 have not been considered. Moreover, there is a substantial thermochemical barrier of 0.83 eV for NH3 desorption. Desorption of NH3 is the thermochemical limiting step for most dopants, suggesting that NH3 may exist at high coverages or even poison the surface. However, solvation effects have been neglected, and the free energy is computed at a chemical potential of NH3 equivalent to 1 bar, suggesting that NH3 desorption may not be limiting in aqueous solutions with low NH3 concentrations. Some of the noble dopants (Pd, Ag, Au, and Cu) also show substantial thermochemical barriers of 0.5–1.5 eV for NH2–NH2 scission, indicating that rates for these metals will be low even at the limiting potential. A more detailed kinetic analysis of both electrochemical and thermochemical activation energies is required to predict the electrocatalytic rate for any dopant, but this thermochemical analysis provides lower bound for the kinetic barrier.

We assess the ability of dopant metals to improve photocatalytic nitrogen reduction. This is calculated based on the largest thermodynamic barrier at a reductive potential equal to the conduction band edge of TiO2 (approximately − 0.15 V vs. RHE [73]). This approach assumes that the conduction band edge of TiO2 is not significantly affected by the presence of the dopant, and neglects improvements in other photochemical properties such as introduction of defect levels, charge separation or carrier lifetime. Nonetheless, it provides a good starting point for assessing the impact of dopant metals on the surface catalytic properties. The highest thermodynamic barrier for the best reaction pathway is plotted vs. the NH2* binding energy in Fig. 5. The results are qualitatively similar to the electrochemical limiting potentials in Fig. 6, but there are some deviations that occur for two reasons. The first is that the photochemical analysis includes both thermochemical and electrochemical steps. The desorption of NH3* is a thermochemical step that becomes rate-limiting for reactive surfaces. For less reactive surfaces the electrochemical step of N2 hydrogenation is rate-limiting, which becomes slightly more favorable under the applied bias, effectively shifting the right side of the volcano downward. The second reason for deviation is that multi-electron transfers are less sensitive to small potentials, so dopants such as Re which have relatively unstable N2Hx>2 states are not as favorable under photocatalytic conditions. Overall, the results suggest that the minimum thermodynamic barriers of 1.06 eV, 0.97 eV, 0.96 eV, 0.90 eV, 0.82 eV, for Mo, V, Hf, Ir, and Rh, respectively. This represents a substantial improvement over the 1.26 eV limiting potential for pure Ti, indicating that these metals may act as surface promoters for photocatalytic nitrogen reduction if kinetic barriers are low.

Fig. 5
figure 5

The highest barrier observed vs the NH2 binding energy with the potential set to band edge of rutile. The data for this plot can be seen in Table S5. Any surface for which a full path was not available has been excluded

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Fig. 6
figure 6

a The limting potential vs the NH2 binding energy. The data for this plot can be seen in Table S3. b A two dimensional volcano plot for electrochemical limiting potential using N2H and NH2 as descriptors for the studied systems. Points are colored in with the limiting potential calculated from DFT. Any surface for which a full path was not available has been excluded

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The electrochemical limiting potential is calculated for all surfaces to assess their ability to reduce N2 under applied bias. The results are plotted against the NH2 binding energy in Fig. 6a. This plot reveals a clear volcano relationship between the NH2 binding energy and the limiting potential. In contrast to prior work by H¨oskuldsson et al. [54] and Montoya et al. [55], we find that the NH2 binding energy is a slightly more reliable descriptor than N2H binding; however these quantities are linked by scaling relations, indicating that either descriptor will provide consistent trends. In this case, the limiting step shifts from NH2 desorption on the left to N2 hydrogenation on the right, with most dopants being limited by NH2 desorption. This means that NH2 adsorption energy directly controls the reactive side of the volcano, and explains why it is an accurate descriptor in this case.

To better understand the relationship between the descriptors, limiting potential, and limiting steps, the fits of the scaling relations (see Fig. S2) were used to generate a two dimensional volcano plot (Fig. 6b).We note that the points on this plot are filled in with their calculated limiting potential from DFT, but placed based on their predicted limiting potential from the scaling relations, enabling direct assessment of the error due to scaling relations. As with the scaling relations, the root mean squared error of the predicted limiting potential in Fig. 6b is roughly 0.2 V. The results confirm the findings from Fig. 6a, but provide additional insight into the limiting steps. The results also show that the optimal limiting potential is still relatively large (∼ − 0.8 V), and that Mo is near-optimal. There are also a few dopants that deviate from the trend. Notably, Os, Ir, and Hf are on the reactive side of the volcano, but the potential limiting step is N2H formation [34, 54]. Nonetheless, these elements fortuitously fall close to the trend predicted by the volcano plot.

Overall, the results suggest that several dopants are capable of improving the performance over pure TiO2. The elements that show significant improvement are Mo, Rh, and Re. Mo is relatively inexpensive and abundant, whereas Re and Rh are relatively scarce [74]. Moreover, synthesis may be a challenge since the metal substitution energy of the surface sites is generally positive relative to the bulk metals (Fig. 2). Nonetheless, the results indicate that Mo is the most promising dopant for reducing the thermodynamic limiting potential of ammonia synthesis on TiO2. This is also interesting since Mo is known to play a role in biological nitrogen fixation [75], and Mo-based transition-metal complexes are known to reduce nitrogen in homogeneous catalysis [76]. We also note that for metals that are not predicted to improve the rate of reaction relative to Ti the observed reaction rates would appear very similar to the rate of pure Ti, as Ti sites would dominate observed turnovers. Thus, suppression of rates observed experimentally is likely related to other effects such as reduced charge generation/transport in the bulk and near-surface region.

Experimental observations can provide further insight into the computational predictions. Several prior reports have investigated transition-metal dopants for enhancing photocatalytic ammonia production on TiO2 [15, 22, 32]. Interestingly, Schrauzer et al. report increases in ammonia yield in the presence of Mo dopants [15], though this report comes from the early literature and rigorous controls [77] or isotopic labeling studies [78] were not included. Moreover, the same report revealed enhanced rates for Fe and Ni, so the confirmation of the prediction regarding the former two should be treated with caution. The rate enhancement for noble metals such as Ru, Rh, and Pd is conflicting even in the early literature, with Schrauzer and Guth reporting no enhancement [15]. However, Ranjit et al. reported enhancement for all noble metals with the most significant improvement for Ru [32]. In all of these systems, the metal dopants were incorporated via coprecipitation, and catalysts were polycrystalline TiO2, indicating that the metals may also enhance yields via charge separation, mediation of crystallization, or other mechanisms [12]. Hirakawa et al. added Ru, Pt, and Pd to pre-synthesized TiO2 particles and reported no significant improvement in the reaction rates [22]. These experiments are more consistent with the computational model system used in this study since only surface properties are affected, and the results are consistent with the prediction that these noble metals will not improve the rate. However, further systematic and well-controlled experiments that characterize the state of the metal incorporation in the TiO2 surface are required to validate the predicted trends.

3 Conclusions

The stability of metal dopant surface sites and their effects on the reaction thermodynamics of N2 reduction on rutile (110) are studied using DFT. We find that the metal substitution energy of these doped surface states is strongly related to the location of the d-band center of the substituted metal, with a trend consistent with the d-band model. We also find a correlation between the cohesive energy of metals and their N2H and NH2 binding energy on the surface, suggesting that the bonding of nitrogen species is similar to that of bulk metals. Finally, we investigate the effects of dopant sites on the full reaction pathways for 2+ sites on all studied metals. We find a clear volcano relationship between NH2 binding and both the electrochemical limiting potential and the highest thermodynamic barrier for photocatalytic reactions. The formation of Rh 2+ sites is proposed to yield a slight improvement of reaction rates in both electrocatalysis and photocatalysis. Other metals commonly used in catalysis, such as Pt and Pd are predicted to have a limited or detrimental effect on the surface catalytic properties of TiO2 for nitrogen reduction. This suggests that the role of metal dopants in photocatalytic ammonia synthesis by TiO2 is likely related to modifications of bulk properties in most cases. However, the existence of clear trends in the metal substitution energy and reactivity of single metal atom dopants toward nitrogen intermediates suggests that computational design of metal-doped oxide materials is a promising strategy for other oxide systems and/or other nitrogen conversion reactions.

4 Methods

4.1 Density Functional Theory Calculations

All first principles calculations are performed in the Quantum Espresso software package [79]. The TiO2 slabs and atomistic images are created using the Atomic Simulation Environment (ASE) package [80]. Spin polarization is used in all simulations to ensure the lowest energy spin state is obtained for each site. The BEEF-vdW functional [81] is used with plane wave cutoff of 550 eV and a Monkhorst–Pack k-point grid spacing of 4 × 4 × 1 [82]. The efficiency versions of the standard solid state psuedopotentials [83] (SSSP) are used for all calculations because of their high reported accuracy [84]. The convergence threshold is set at 10−6 eV and Fermi- Dirac smearing of 0.1 eV is used. All structures are converged to a maximum force smaller than 0.05 eV/A using the BFGS line search algorithm. Adsorption energies are obtained from the DFT calculations by subtracting the energy of a clean slab and the energy of the free gas molecule from the energy of the gas adsorbed to the slab:

$$E_{adsorption} = E_{slab + adsorbate} - E_{slab} - E_{adsorbate}$$
(1)

For all calculations the magnetic moments have been perturbed. Most elements the magnetic moments were perturbed near zero. However, for elements known to show complex magnetic states (Ni, Fe, Co, Cr) the magnetic moments have been initialized to the natural magnetic moment of these elements in the bulk metal form. All obtained magnetic moments for the unit cells may be seen in Table S6. It should be noted that non-integer values were obtained for several spin states, which is likely a result of the GGA approximation.

Previous literature suggests that Hubbard + U corrections are needed to properly capture the behaviour of d-electrons within DFT [85]. However, we have chosen not to include these corrections in this work. This was done to avoid issues created by selecting + U values for all metals, for which there is no accepted universal method [53, 58]. Additionally, the primary concern of this work is capturing trends in the surface adsorption properties, which may change with the addition of + U corrections. However, previous work has been performed on rutile oxides [58] and doped rutile TiO2 [53], finding that the trends observed with the addition of + U corrections are preserved by GGA for those systems for oxygen evolution reactions.

4.2 Thermochemistry

To calculate the adsorption energy at standard temperature and pressure, the thermochemistry package from ASE is used [80]. The contributions of zero point energy (ZPE) have been included for all systems. Free gasses are approximated in the ideal gas limit, and adsorbed gasses in the harmonic limit [86]. A frequency cutoff of 33 cm−1 for low frequency modes was selected. The vibrational mode for all metals were assumed to be approximately the same as those of the respective species adsorbed to the oxygen vacant TiO2 (110) surface, thus the same thermodynamic correction values are applied to all species of the same type.

Site metal substitution energies were calculated based on the energy of displacing the metal dopant atom from it’s bulk metallic form into the position of a titanium atom, and placing the titanium atom into a bulk metallic titanium form. The following formula was used:

$$\Delta {E_s}\; = \;{E_{Ti}}_{_{n - 1}}{O_y}M\; + \;{E_{Ti}}_{_{(m)}}\; - \;{E_{{M_{(m)}}}}\; - \;{E_{T{i_n}}}{O_y}$$
(2)

where ∆Es is the metal substitution energy of the dopant metal site, ET in−1Oy M is the energy of the doped surface, ET i(m) is the per atom energy of bulk Ti, EM(m) is the per atom energy of the dopant metal, and ET inOy is the energy of the undoped surface.

4.3 Photochemistry

The photochemistry has been treated using the methods outlined by Hellman et al. [87]. Within this framework, the effects of excited states are neglected allowing the treatment of excited electrons and holes using the computational hydrogen electrode model (CHE). In this formalism, the reference electrode is set by setting the free energy of hydrogen evolution reaction (HER) to zero:

$$H^{ + } + e^{ - } \to H_{2} ; \;\;\;\Delta G = \, 0\;\;at \, \;\;U = 0$$
(3)

The potentials of electrons and holes are set at the value of the band edges of the rutile [73].

4.4 Model Surface Generation

The surfaces are constructed with 4 TiO2 tri-layers (bottom two layers constrained to bulk positions), with a 1 × 2 supercell repeat. The pristine slab totals 48 atoms, with 4 Ti and 8 O per tri-layer. 6 Ǻ of vacuum are added on both top and bottom of the slab and a dipole corrections is applied in the z direction [88]. The lattice parameters of the unit cells are fixed at the calculated value for pure rutile TiO2. 2+ sites were created by replacing the six-fold titanium site with the substituent metal and removing a single bridging oxygen (see Fig. 1) 4+ sites were generated by replacing the five-fold titanium site with the substituent metal. The adsorption site was selected to directly over the substituent metals.

4.5 Adsorption Structure Optimization

To obtain reasonable initial guesses for structural optimization, all calculations were first performed using using Fe as the dopant metal. In these initial runs multiple adsorbate geometries were used as initial guesses. These converged structures were then used as initial guesses for all other dopant metals by replacing Fe with the corresponding metal. These structures were then allowed to relax to obtain the new lowest energy structure. All structures may be obtained from the provided SI.