changes.txt

Figures 2, 3, 7, and 8 have been updated. 

Revised abstract:
OLD
<     the BEEF-vdW functional and computational hydrogen electrode is applied
<     in order to analyze the expected dinitrogen coverage at the surface as
<     well as the overpotentials for electrochemical reduction and oxidation.
<     The results indicate that the thermodynamic limiting potential for
<     nitrogen reduction on rutile (110) is considerably higher than the
<     conduction band edge of rutile TiO$_2$, even at oxygen vacancies and
<     iron substitutions, indicating that this is unlikely to be the relevant
<     surface for nitrogen reduction. However, the limiting potential for
<     nitrogen oxidation on rutile (110) is significantly lower, indicating
<     that oxidative pathways may be relevant on rutile (110). These findings
<     suggest that photocatalytic dinitrogen fixation may occur via a complex
<     balance of oxidative and reductive processes.
---
NEW
>     the Bayesian error estimation functional (BEEF-vdW) and computational
>     hydrogen electrode is applied in order to analyze the expected
>     dinitrogen coverage at the surface as well as the overpotentials for
>     electrochemical reduction and oxidation. This is the first application
>     of computational techniques to photocatalytic nitrogen fixation, and the
>     results indicate that the thermodynamic limiting potential for nitrogen
>     reduction on rutile (110) is considerably higher than the conduction
>     band edge of rutile TiO$_2$, even at oxygen vacancies and iron
>     substitutions. This work provides strong evidence against the most
>     commonly reported experimental hypotheses, and indicates that rutile
>     (110) is unlikely to be the relevant surface for nitrogen reduction.
>     However, the limiting potential for nitrogen oxidation on rutile (110)
>     is significantly lower, indicating that oxidative pathways may be
>     relevant on rutile (110). These findings suggest that photocatalytic
>     dinitrogen fixation may occur via a complex balance of oxidative and
>     reductive processes.

Addition of new references in introduction:
OLD
< [@Stodt2013; @Sorescu2000; @Cheng2011]. Two comprehensive computational
< studies on nitrogen oxides were performed by Stodt et al. [@Stodt2013]
< and Sorescu et al. [@Sorescu2000]. These studies examined N$_x$O$_y$
< compounds on TiO$_2$ (110) surfaces both experimentally under UHV
< conditions and theoretically using DFT at the GGA[@Sorescu2000] and
< hybrid [@Stodt2013] levels of theory. This work showed that DFT is able
< to accurately obtain the vibrational frequencies of intermediates on the
---
NEW
> [@Stodt2013; @Sorescu2000; @Cheng2011; @H_skuldsson_2017; @Xie_2017].
> Two comprehensive computational studies on nitrogen oxides were
> performed by Stodt et al. [@Stodt2013] and Sorescu et al.
> [@Sorescu2000]. These studies examined N$_x$O$_y$ compounds on TiO$_2$
> (110) surfaces both experimentally under ultrahigh vacuum (UHV)
> conditions and theoretically using density functional theory (DFT) at
> the generalized gradient approximation (GGA)[@Sorescu2000] and hybrid
> [@Stodt2013] levels of theory. This work showed that DFT is able to
> accurately obtain the vibrational frequencies of intermediates on the

Added discusson of 2 new references to introduction:
OLD
< and monoclinic [@Guo_2012] polymorphs of TiO$_2$.
---
NEW
> and monoclinic [@Guo_2012] polymorphs of TiO$_2$. Very recently Xie et.
> al. used DFT to calculate the energetics of nitric oxide reduction on
> TiO$_2$ [@Xie_2017], and Höskuldsson et. al. utilized GGA DFT to screen
> rutile oxides for electrochemical ammonia synthesis, and found a
> relatively large limiting potential of ca. 2 V for the (110) surface of
> rutile TiO$_2$ [@H_skuldsson_2017].

Added justification of (110) model surface:
OLD
< TiO$_2$(110) surface. The availability of adsorbed nitrogen is
< investigated under aqueous and gas-phase conditions, and the
---
NEW
> TiO$_2$(110) surface. The rutile (110) surface is hypothesized to be the
> active surface due to the fact that photocatalytic nitrogen fixation
> rates have been observed to correlate with the amount of rutile in
> TiO$_2$ samples [@Schrauzer_2011]; the (110) surface is the lowest
> energy surface on rutile and is likely to provide a model for other
> rutile surfaces. Furthermore, the rutile (110) surface has been
> explicitly hypothesized to be the active surface in recent experimental
> work [@Hirakawa_2017]. The availability of adsorbed nitrogen on rutile
> (110) is investigated under aqueous and gas-phase conditions, and the

Revised figure 2 caption to be clearer:
OLD
< respectively. Nitrogen pressure at aqueous conditions is estimated using
< Henry’s law. The probability of various coverages (c,f) given the
< uncertainty in the BEEF-vdW functional is calculated using Eq.
---
NEW
> respectively. Graphs a-c use constant N$_2$ chemical potential set at
> atmospheric pressure of N$_2$ (0.8 atm) and d-f use constant water
> chemical potential set at 100% relative humidity of H$_2$O. Nitrogen
> pressure at aqueous conditions is estimated using Henry’s law. The
> probability of various coverages (c,f) given the uncertainty in the
> BEEF-vdW functional is calculated using Eq.

Modified discussion of Fig. 2 to be consistent with proper relative humidity:
OLD
< available at ambient gas-phase conditions (H$_2$O, N$_2$, O$_2$, OH).
< The results show that the bare TiO$_2$ surface is dominant at gas-phase
< conditions. The ensemble of energies from the BEEF-vdW functional can be
< exploited to evaluate the sensitivity of these coverages to DFT error.
< The probability analysis (Fig \[fig:surface\_diagram\]a, bottom)
< suggests that there is a probability of $\approx$ 10% of having a N$_2$
< coverage $>$ 0.25 ML. One interpretation of this probability is that the
---
NEW
> available at ambient gas-phase conditions (H$_2$O, N$_2$, O$_2$, OH) (a
> similar analysis including all reactants, products and intermediates is
> available in the Supporting Information). The results show that the bare
> TiO$_2$ surface is dominant at gas-phase conditions. The ensemble of
> energies from the BEEF-vdW functional can be exploited to evaluate the
> sensitivity of these coverages to DFT error. The probability analysis
> (Fig \[fig:surface\_diagram\]a, bottom) suggests that there is a very
> low probability of having appreciable N$_2$ coverage at 100% RH, but
> under dry conditions there is a probability of $\approx$ 10% of having a
> N$_2$ coverage $>$ 0.25 ML. This suggests that arid environments may
> favor N$_2$ adsorption, though it is noted that water also acts as a
> proton source so nitrogen reduction cannot occur if the humidity is too
> low. One interpretation of the surface coverage probability is that the

Added citation to Fig. 3 caption:
OLD
< required driving force ($\Delta$V). The difference between hydrogen
< evolution and nitrogen reduction ($\mathrm{\Delta \Delta V_{HER}}$) is
< shown to highlight the selectivity challenge for nitrogen reduction.
< Band edges for rutile TiO$_2$ are shown (black bar) for reference (note
< scale break at 1.75
---
NEW
> required driving force ($\Delta$V) [@Medford_2017]. The difference
> between hydrogen evolution and nitrogen reduction
> ($\mathrm{\Delta \Delta V_{HER}}$) is shown to highlight the selectivity
> challenge for nitrogen reduction. Band edges for rutile TiO$_2$ were
> obtained from literature [@Nozik_1996] and are shown (black bar) for
> reference (note scale break at 1.75

Added discussion of why selectivity is remarkable despite known fact that
TiO2 is not a good HER catalyst:
OLD
< [@Schrauzer_1977; @Schrauzer_1983; @Schrauzer_2011; @Augugliaro_1982].
< This suggests that identification of the active site for photocatalytic
< nitrogen reduction may enable the development of improved nitrogen
< reduction electrocatalysts. In this section we hypothesize that the
< active site is pristine rutile (110), and examine the binding free
< energies of intermediates for the dissociative and associative nitrogen
< reduction pathways.
---
NEW
> [@Schrauzer_1977; @Schrauzer_1983; @Schrauzer_2011; @Augugliaro_1982],
> indicating that TiO$_2$ is capable of dissociating the strong N-N bond
> more easily than the much weaker H-H bond. This suggests that
> identification of the active site for photocatalytic nitrogen reduction
> may enable the development of improved nitrogen reduction
> electrocatalysts. In this section we hypothesize that the active site is
> pristine rutile (110), and examine the binding free energies of
> intermediates for the dissociative and associative nitrogen reduction
> pathways.

Added discussion of possible hybrid dissociative/associative mechanism:
OLD
< barrier is not sensitive to the BEEF-vdW XC approximation, and is
< expected to be prohibitively large even in the presence of solvent
< stabilization since each adsorbed N\* would need to be stabilized by
< $>$3 eV, significantly more than typical solvent stabilization
< values[@Karlberg_2007; @He_2017; @Hellman2017]. This provides strong
< evidence against direct dissociation of the N-N bond on the pristine
< rutile TiO$_2$ surface.
---
NEW
> barrier is not sensitive to the BEEF-vdW exchange-correlation
> approximation, and is expected to be prohibitively large even in the
> presence of solvent stabilization since each adsorbed N\* would need to
> be stabilized by $>$3 eV, significantly more than typical solvent
> stabilization values[@Karlberg_2007; @He_2017; @Hellman2017].
> Furthermore, this step is not electrochemically driven, so even the
> application of large overpotentials will not enable direct N-N scission.
> This provides strong evidence against direct dissociation of the N-N
> bond on the pristine rutile TiO$_2$ surface. The same stabilization
> would be required for NH\* species, effectively eliminating any pathway
> involving NH\* (e.g. dissociation of NNH). Adsorbed NH$_2$ species are
> somewhat more stable, and may exist under solvated conditions, opening
> the possibility of mechanisms involving dissociation of
> N$_2$H$_{\mathrm{x}>2}$ species, similar to the associative mechanism
> that will be discussed subsequently.

Added comparison of limiting potential to new reference:
OLD
< potential of 2.5 V due to the unstable NNH\* adsorbed intermediate. This
< barrier is significantly higher than the conduction band potential,
< making the route improbable unless the adsorbates are stabilized
< significantly ($\approx$ 2 eV) by solvent/dipole effects. The
< rate-limiting hydrogenation of N$_2$ is consistent with studies of
< electrochemical nitrogen reduction on metals [@Skulason_2012] and
< nitrides [@Abghoui_2016], indicating a general trend for photo- and
---
NEW
> potential of 2.5 V due to the unstable NNH\* adsorbed intermediate,
> which is consistent with previous work [@H_skuldsson_2017]. This barrier
> is significantly higher than the conduction band potential, making the
> route improbable unless the adsorbates are stabilized significantly
> ($\approx$ 2 eV) by solvent/dipole effects. The rate-limiting
> hydrogenation of N$_2$ is consistent with studies of electrochemical
> nitrogen reduction on metals [@Skulason_2012], nitrides [@Abghoui_2016],
> and oxides [@H_skuldsson_2017] indicating a general trend for photo- and

Fixed equations for reaction mechanism:
OLD
<     N_2^* + ^*  & \rightarrow 2N^*\\
<     2N^* + 2(H^+ + e^-) & \rightarrow 2NH^* \\
<     2NH^* + 2(H^+ + e^-) & \rightarrow 2NH_2^* \\
<     2NH_2^* + 2(H^+ + e^-) & \rightarrow 2NH_3^* \\
<     NH_3^*  & \rightarrow NH_3(g) + ^{*}
---
NEW
>     N_2^* + H^+ + e^-  & \rightarrow NNH^* \\
>     NNH^* + H^+ + e^- & \rightarrow HNNH^* \\
>     HNNH^* + H^+ + e^- & \rightarrow  HNNH_2^* \\
>     HNNH_2^* + H^+ + e^- & \rightarrow H_2NNH_2^* \\
>     H_2NNH_2^* + ^* + H^+ + e^- & \rightarrow NH_2^* + NH_3^* \\
>     NH_2^* + NH_3^* + H^+ + e^- & \rightarrow 2NH_3^*  \\
>     2NH_3^*  & \rightarrow 2NH_3(g) + 2^{*} 

Added discussion of multiple Fe defect sites considered:
OLD
< energetics of the process. The latter hypothesis was tested by
< substituting the 5-fold titanium with an iron atom and repeating the
< analysis. Fig. \[fig:FED\_FE\_assoc\] shows the energetics of the
< associative pathway with an iron-substituted rutile (110) surface. The
< limiting potential is comparable to that of the defected surface in Fig.
< \[fig:FED\_defect\_assoc\] ($\approx$ 1.7V). This supports the
< hypothesis of Soria et al.[@Soria_1991] that the primary role of iron is
< to promote charge separation in the bulk structure. The energy required
< to form this defect was calculated to be 2 eV relative to bulk rutile
< and BCC iron. The energetic penalty of creating this surface site is
< high and the improvement to the stability of surface intermediates is
< moderate, indicating this is unlikely to be an active site for nitrogen
< reduction. The energetics of the associative pathway on Fe-substitution
< defects is compared to O-br defects and pristine rutile (110) in Fig.
< \[fig:defect\_effects\]a, illustrating that the Fe-substitution defect
< has a significantly smaller effect than the O-br vacancy.
---
NEW
> energetics of the process. The latter hypothesis was tested by computing
> the energetics of the associative mechanism on a slab with an iron
> substitution defect. Two defects were considered, an Fe$^{4+}$ defect
> arising from direct substitution of the 5-fold Ti atom, and an Fe$^{2+}$
> defect formed by substitution of a Ti atom beneath a bridging O and
> removal of the bridging O, effectively forming a O-br defect and Fe
> substitution (see the Supplementary Information for visualization of the
> slab). The Fe$^{2+}$ defect was found to be more stable, and Fig.
> \[fig:FED\_FE\_assoc\] shows the energetics of the associative pathway
> with an iron-substituted rutile (110) surface (a comparison of the free
> energy path for the Fe$^{4+}$ defect is available in the Supplementary
> Information). This mechanism is very similar to the mechanism on the
> pristine and O-br vacancies, with the slight difference that N-NH$_2$ is
> more stable than HNNH on the Fe defect. The limiting potential of 2.2 eV
> is comparable to that of the defected surface in Fig.
> \[fig:FED\_defect\_assoc\] (1.7 eV), but is slightly higher due to the
> stronger adsorption of N$_2$. The energetics of the associative pathway
> on Fe-substitution defects are compared directly to O-br defects and
> pristine rutile (110) in Fig. \[fig:defect\_effects\]a, illustrating
> that the Fe-substitution defect has a similar effect to the O-br
> vacancy. The energy required to form this defect was calculated to be
> 1.1 eV relative to bulk rutile and BCC iron. This moderate formation
> energy is lower than that of the O-br defect, and N$_2$ adsorbs with a
> relatively strong binding energy of -0.5 eV. This suggests that Fe
> surface defects promote the formation of O-br vacancies and adsorption
> of N$_2$. Nonetheless, the high limiting potential of 2.2 V indicates
> that the Fe-substitution defect is not active for photocatalytic
> nitrogen reduction.

Added more discussion of possible implications of hybrid mechanism:
OLD
< mechanism at the O-br vacancy. Furthermore, we note that the free energy
< diagram in Fig. \[fig:defect\_effects\]b requires two O-br vacancies,
< since each N\* is adsorbed at a vacancy. The relatively high formation
< energy of O-br vacancies suggests that this is improbable, and the
< experimental investigation of Hirakawa et. al. [@Hirakawa_2017] shows a
< linear dependence on oxygen vacancies, rather than the quadratic
< dependence that would be indicative of direct N-N scission. This finding
< strongly refutes the proposed hypothesis that direct N-N scission by
< O-br vacancies is the mechanism of photocatalytic nitrogen fixation on
< TiO$_2$. However, the fact that the O-br vacancy significantly
< stabilizes NH$_{\mathrm{x}}$ species, making NH$_{\mathrm{x}}$ binding
< close to exothermic suggests that it can promote nitrogen reduction and
< ammonia formation after the N-N bond has been cleaved.
---
NEW
> mechanism at the O-br vacancy. An alternative possibility is a mixed
> mechanism proceeding through dissociaton of partially hydrogenated
> species, since the NH$_{\mathrm{x}}$ species are stable at the O-br
> vacancy; however, this would still necessitate the formation of the
> potential-limiting HNNH\* species from the associative mechanism and
> would be thermodynamically (though not kinetically) equivalent.
> Furthermore, we note that the free energy diagram in Fig.
> \[fig:defect\_effects\]b requires two O-br vacancies, since each N\* (or
> NH$_{\mathrm{x}}$) is adsorbed at a vacancy. The relatively high
> formation energy of O-br vacancies suggests that this is improbable, and
> the experimental investigation of Hirakawa et. al. [@Hirakawa_2017]
> shows a linear dependence on oxygen vacancies, rather than the quadratic
> dependence that would be indicative of direct N-N (or HN-NH) scission by
> two vacancy sites. This finding strongly refutes the proposed hypothesis
> that direct N-N scission by O-br vacancies is the mechanism of
> photocatalytic nitrogen fixation on TiO$_2$. However, the fact that the
> O-br vacancy significantly stabilizes NH$_{\mathrm{x}}$ species, making
> NH$_{\mathrm{x}}$ binding close to exothermic suggests that it can
> promote nitrogen reduction and ammonia formation after the N-N bond has
> been cleaved.

Revised discussion of oxidative route to address direct N2O* formation:
OLD
< than the case of nitrogen reduction. When the significant driving force
< provided by the photo-excited hole (1.22 V overpotential) is taken into
< account (Fig. \[fig:FED\_oxid\]b) the oxidative path becomes extremely
< favorable, with the highest energy state being adsorbed N$_2$. We note
< that this analysis considers only the thermodynamics of adsorbed states,
< and neglects activation barriers that will ultimately govern the
< kinetics of the process. These barriers could potentially be significant
< for N-O coupling, although the strong driving force under photocatalytic
< conditions will improve the kinetics of any electrochemical step.
---
NEW
> than the case of nitrogen reduction. In addition, the direct adsorption
> of N$_2$ to this reactive surface oxygen is exergonic by 0.3 eV,
> indicating that adsorption of N$_2$ is favored by oxygen-rich surfaces.
> When the significant driving force provided by the photo-excited hole
> (1.22 V overpotential) is taken into account (Fig. \[fig:FED\_oxid\]b)
> the oxidative path becomes extremely favorable, with all steps being
> exergonic with the exception of N$_2$O$_2$ dissociation which is very
> slightly ($<0.1$eV) uphill. We note that this analysis considers only
> the thermodynamics of adsorbed states, and neglects activation barriers
> that will ultimately govern the kinetics of the process. These barriers
> could potentially be significant for N-O coupling, although the strong
> driving force under photocatalytic conditions will improve the kinetics
> of any electrochemical step.

Fixed typo of conduction/valence band in figure caption:
OLD
< ($\eta$) of zero (a) and at the overpotential due to the conduction band
---
NEW
> ($\eta$) of zero (a) and at the overpotential due to the valence band

Added discussion of implications of selectivity on NO reduction:
OLD
< the band gap of TiO$_2$[@Medford_2017]. Titania photocatalysts have been
< reported to reduce nitrates under aqueous conditions, although
< selectivity to dinitrogen vs. ammonia varies widely based on preparation
< conditions and metal dopants
---
NEW
> the band gap of TiO$_2$[@Medford_2017], and has been reported
> experimentally[@Ranjit_1997] and studied theoretically[@Xie_2017]. The
> thermodynamic feasibility of this pathway on rutile (110) has been
> computed and the most thermodynamically favorable path is shown in Fig.
> \[fig:FED\_oxid\_red\]. The mechanism and energetics are consistent with
> prior work[@Xie_2017], and indicate that this is indeed
> thermodynamically feasible. However, reduction of nitrogen oxides is a
> complex process that can also form partially reduced species such as
> N$_2$O or N$_2$. In particular, the reaction of NO to N$_2$O and the
> reaction of N$_2$O to N$_2$ has been observed under UHV conditions by
> Yates and colleagues[@Rusu2000; @Rusu2001]. Fully understanding the
> selectivity of photocatalytic NO reduction on TiO$_2$ is beyond the
> scope of this work, but selectivity should be considered in future
> studies of NO reduction.
> 
> Experimentally, titania photocatalysts have been reported to reduce
> nitrates under aqueous conditions, although selectivity to dinitrogen
> vs. ammonia varies widely based on preparation conditions and metal
> dopants

Fixed typo of conduction/valence band in figure caption:
OLD
< ($\eta$) of zero (a) and at the overpotential due to the conduction band
---
NEW
> ($\eta$) of zero (a) and at the overpotential due to the valence band

Clarified reference state at atmospheric conditions in methods:
OLD
< pristine surface. All thermodynamics were evaluated at 300 K and set to
< their atmospheric values (0.8 atm N$_2$, 0.2 atm O$_2$). Liquid water
< was approximated as an ideal gas at saturation pressure at 300 K (0.031
< atm). Relative (formation) energies were computed with respect to
< reference states using the equation: $$\begin{aligned}
---
NEW
> pristine surface. All thermodynamics were evaluated at 300 K and gas
> partial pressures were set approximate atmospheric conditions (0.8 atm
> N$_2$, 0.2 atm O$_2$). Liquid water was approximated as an ideal gas at
> saturation pressure at 300 K (0.035 atm). Relative (formation) energies
> were computed with respect to reference states using the equation:
> $$\begin{aligned}

Clarified reference states at atmospheric conditions in methods:
OLD
< reference for oxygen is O$_2$ ($\mu_O = \frac{1}{2} G_{O_2}^o$) and the
< reference for hydrogen is H$_2$O
< ($\mu_H = \frac{1}{2} (G_{H_2O}^o - \frac{1}{2} G_{O_2}^o$)). In this
< work no gas-phase corrections (e.g. O$_2$ [@Norskov_2004], CO$_2$
< [@Peterson_2010]) are applied since it is difficult to rigorously
< correct the BEEF-vdW ensembles; the quantification and propagation of
< error with the BEEF-vdW ensembles will capture these errors to some
< extent, and overpotentials are defined relative to the equilibrium
< potential computed by DFT in order to minimize the influence of
< inaccurate equilibrium potentials from DFT (see subsequent section).
---
NEW
> reference for oxygen is H$_2$O
> ($\mu_{H_2O} = \frac{1}{2} G_{H_2O}^o - \mu_H$) and the reference for
> hydrogen is set by the computational hydrogen electrode
> ($\mu_H = \frac{1}{2} G_{H_2}^o$ + eU). In this work no gas-phase
> corrections (e.g. O$_2$ [@Norskov_2004], CO$_2$ [@Peterson_2010]) are
> applied since it is difficult to rigorously correct the BEEF-vdW
> ensembles; the quantification and propagation of error with the BEEF-vdW
> ensembles will capture these errors to some extent, and overpotentials
> are defined relative to the equilibrium potential computed by DFT in
> order to minimize the influence of inaccurate equilibrium potentials
> from DFT (see following section).

Clarified method of calculating overpotential in methods:
OLD
< and holes. The potential of holes was set to -0.1V and the potential of
< excited electrons was set to 2.9V, conserving the experimental value of
< the band gap at 3 eV [@Scanlon_2013].
---
NEW
> and holes relative to a the redox couples of the relevant reactions so
> that the overpotential is equivalent to the experimentally expected
> overpotential. This approach causes the *absolute* potential of
> electrons/holes to depend on the reaction in question (due to DFT errors
> in the reaction energies), while the *relative* energy of
> electrons/holes to a given redox couple is equal to the experimental
> value. The computed (and experimental) equilibrium potential of a given
> reaction is provided in the caption of each figure.


Added description of SI contents:
NEW:
> 
> The Supporting Information is available and contains:
> 
> All adsorption energies, vibrational frequencies, and structure images;
> surface free energy, coverage, and probability diagrams including all
> species under oxidizing and reducing conditions; reaction equations for
> all mechanisms and defect formations; comparison of free energy pathway
> for different Fe substitution models.
>