Mechanism of Oxygen Exchange between CO2 and TiO2(101

Article pubs.acs.org/JPCC

Mechanism of Oxygen Exchange between CO2 and TiO2(101) Anatase Dan C. Sorescu,*,† Svatopluk Civiš,‡ and Kenneth D. Jordan†,§ †

National Energy Technology Laboratory, United States Department of Energy, Pittsburgh, Pennsylvania 15236, United States J. Heyrovský Institute of Physical Chemistry, v.v.i, Academy of Science of the Czech Republic, Dolejškova 3,18223 Prague 8, Czech Republic § Department of Chemistry and Center for Molecular and Materials Simulations, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States ‡

S Supporting Information *

ABSTRACT: The mechanism of oxygen exchange between CO2 and a defective anatase (101) surface was investigated by density functional theory calculations including corrections for long-range dispersion interactions and for on-site Coulomb interactions. The calculations identify a carbonate-like configuration at a surface oxygen defect site as the key intermediate species responsible for the oxygen exchange. The stability of this species, its vibrational frequencies, and the reaction barriers involved in the oxygen exchange mechanism are found to be highly dependent on the specific value of the Hubbard U correction used to describe the on-site Coulomb interactions within the GGA+U procedure. U parameter values that result in CO2 adsorption energies and reaction barriers for oxygen exchange consistent with the results of room-temperature experiments are smaller (U ≤ 2.5 eV) than those that reproduce the experimental band gap or location of defect states in the band gap of the reduced TiO2 crystal.

1. INTRODUCTION Conversion of CO2 to marketable products via photocatalytic processes has received considerable attention in recent years, as part of the general portfolio of strategies considered to alleviate the environmental impact of greenhouse emissions.1,2 In this context, TiO2 has been identified as a promising candidate to initiate CO2 photoreduction due to its abundance, stability, and appropriate electronic absorption spectrum for such applications.3−5 To date, the synthesis of several different TiO2-based materials including dye-sensitized and doped systems as well as different titania nanocomposites and nanostructures have been reported, and analysis of their performance at CO2 photoreduction has been the subject of several review articles.2,6−8 However, the efficiencies and selectivities of these processes need to be further optimized in order to achieve economically viable solutions for CO2 conversion to useful chemicals. A prerequisite for further scientific progress in this area is enhanced understanding of the interactions between CO2 and TiO2 surfaces. Among the methods used to obtain atomic-scale insight into the evolution of the chemical intermediates on the oxide surface is oxygen isotope exchange. In the case of TiO2 catalysts, this method has traditionally considered 18O-isotopelabeled molecules interacting with regular Ti16O2 surfaces. This approach has been applied to investigate diffusion of vacancies in TiO29 and evolution of O, CO, CO2, and carbonate species on the TiO2 surface10−16 as well as evolution of photocatalytic reactions on TiO2-based materials.17−21 © 2014 American Chemical Society

Recently the isotope exchange method has been extended to consider the reverse process, in which 16O-containing molecules interact with a solid oxide that is isotopically labeled. In this context, Civiš and co-workers22 have demonstrated how isotopically pure Ti18O2 samples can be prepared from various Ti precursors via hydrolysis with heavy-oxygen water, H218O. Both anatase and rutile forms have been synthesized from either TiF4 or TiCl4 precursors, and formation of pure Ti18O2 isotopologues has been demonstrated by analysis of Raman spectra.22 Furthermore, the reactions of C16O2 with Ti18O2 anatase under both thermal excitation and photoexcitation conditions have been considered,23,24 and formation of methane and acetylene was observed in the presence of water upon UV irradiation. Following the chemical evolution of CO2 on the oxide surface, it has been demonstrated that Ti18O2 anatase samples annealed in vacuum at 450 °C can exchange oxygen with gaseous C16O2, leading to formation of C18O2 as the major product with a minor content of C16O18O.23 Isotopic oxygen exchange has been suggested to take place by adsorption of gaseous C16O2 molecules at surface oxygen defects, where they bind to surface 18O atoms and form bidentate CO3 species with subsequent thermal release of either 16 O−C− 18 O or 18 O−C− 18 O species. 23 A similar CO 3 intermediate was assumed by Yanagisawa and Sumimoto13 in Received: October 21, 2013 Revised: December 20, 2013 Published: January 10, 2014 1628

dx.doi.org/10.1021/jp410420e | J. Phys. Chem. C 2014, 118, 1628−1639

The Journal of Physical Chemistry C

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their study of the oxygen exchange of C18O2 with vacuumannealed Ti16O2 powders; however, specific details of the mechanism were not elaborated. Formation of surface oxygen defects (VO) on the anatase surface is a topic that has been reviewed several times over the past decade.25−28 It has been noted25 that there is a smaller tendency for formation of VO defects on the anatase (101) surface (the most stable surface of this polymorph) than on its counterpart, the (110) surface of rutile. This finding has been attributed to the lower stability of adjacent 4-fold Ti3+ sites on the anatase (101) surface than of adjacent 5-fold-coordinated Ti3+ sites on the rutile (110) surface. Density functional theory (DFT)27 calculations indicate that the energy for forming an oxygen surface defect is about 0.5 eV greater than for forming a bulk vacancy. More recently, the distribution of surface oxygen defects created nonthermally by electron bombardment and monitored as a function of temperature by use of a scanning tunneling microscope (STM) was reported.28 In that study, it was found that surface defects start to migrate to subsurface sites at temperatures above 200 K. However, after an initial decrease in the density of surface defects, some surface defects reappeared either at the same sites or at different locations on the surface, indicating a back-and-forth movement of the oxygen defects between surface and subsurface sites. As noted by the authors of ref 28, the results of the DFT calculations are hard to reconcile with the thermal equilibrium between subsurface and surface oxygen defects observed in the STM experiments. However, it was also noted that the calculations did not consider the effect of subsurface defects upon the stability of the VO defect, located on the surface. Very recently, Setvin et al.29 have demonstrated theoretically that when O2 is adsorbed on TiO2 anatase (101) having a subsurface oxygen vacancy, there is an energetic favorable driving force for the subsurface vacancy to diffuse to the surface with subsequent filling of the vacancy by an O2 molecule to give a peroxo (O22−) species. The possibility of creating surface oxygen defects and Ti3+ sites on anatase TiO2 nanocrystals under mild conditions has also been reported. Specifically, work done in the Praserthdam group has shown that such surface defects can be created at mild temperatures either by changing the amount of oxygen fed during calcination30 or by varying the water/alkoxide ratio during a sol−gel synthesis.31 For samples synthesized via the latter method, temperature-programmed desorption (TPD) measurements give broad peaks centered at 175 and 200 K for CO2 desorption. These peaks were assigned, respectively, to CO2 adsorbed at regular Ti4+ and at Ti3+ vacancy sites.31 This assignment was based on comparison with the 170 and 200 K TPD peaks recorded for CO2 desorption from oxidized and reduced rutile (110), respectively.32 Given the close correspondence between the TPD data for CO2 desorption from the anatase and rutile surfaces, it can be expected that the binding energies of CO2 on the anatase (101) surface are close to those on the rutile (110) surface. For the rutile (110) surface, the zero-coverage adsorption energies of CO2 are 11.59 and 12.90 kcal/mol from the fully oxidized and reduced surfaces, respectively.32 In the present study we extend our previous theoretical investigation33 of the adsorption of CO2 on oxidized and defective anatase (101) surfaces to examine oxygen exchange between gaseous CO2 and surface oxygen atoms. As shown in previous studies of adsorption of CO2 on the rutile34−37 and anatase33 surfaces, near quantitative agreement between

experimental and calculated adsorption energies can be obtained, provided that corrections for long-range dispersion interactions are included in the DFT calculations. Due to self-interaction error (SIE),38 commonly used DFT methods have difficulties describing the unpaired electrons left behind after removal of an oxygen atom from the oxide surface.39 This problem is partially remedied by use of hybrid functionals40−43 or dynamical mean-field theory.44 However, for the system sizes employed in this study, the computational cost of such methods would be prohibitive. An alternative, computational tractable approach is to include on-site Coulomb corrections by use of the GGA+U procedure.45,46 The main limitation of this method in the case of the heterogeneous gas− surface interactions investigated in this study is the identification of an appropriate U value. In previous computational studies47−52 of anatase, U values ranging from 2.5 to 8.5 eV were employed in connection to the Perdew−Burke−Ernzerhof (PBE) exchange−correlation functional. Different U values result depending on the experimental property, band gap, location of the Vo defect level in the band gap, relative stabilities of different TiO2 polymorphs, or measured phase stability under compression one is trying to reproduce. In catalytic applications, one is confronted with the problem of accurately describing the energy differences between different configurations. In recent work, Hu and Metiu53 have shown that for redox reactions involving the TiO2/Ti2O3 species, U parameters in the range 2−3 eV give reaction energies in best agreement with experiment. Similarly, Bell and co-workers54 found that the experimental reaction energy for oxidation of TiO2 to Ti2O3 is best matched by use of U = 2.3 eV. On the other hand, larger U parameters result from fits to the band gap of TiO2 or to the energies of states in the band gap of partially reduced TiO2. For example, a U value of 4.2 eV gives good agreement for the calculated band gap with the corresponding experimental value for rutile.55 These findings are not limited to TiO2: similar results have been reported by Bell and co-workers54 for oxidation reactions of vanadium, molybdenum, and cerium oxides. This reinforces the need to evaluate the effect played by the choice of U parameter in analysis of catalytic reactions, and this is one of the goals of the current study. The organization of the paper is as follows: Section 2 describes the computational methods used. Results of the theoretical analysis are reported in section 3. Section 4 summarizes our main conclusions.

2. COMPUTATIONAL METHODS Density functional theory calculations were carried out with the Vienna ab initio simulation package (VASP)56,57 in conjunction with periodic slab models. Plane-wave basis sets were employed together with the PBE functional58 and projector-augmented wave (PAW) method.59,60 The electrons in 3s, 3p, 3d, and 4s shells for Ti and in 2s and 2p shells for C and O were treated as valence. A cutoff energy of 400 eV was used for the plane-wave basis set. As in our previous studies addressing adsorption of CO2 on rutile (110)34,36,37 and anatase (101)33 surfaces, the PBE functional was corrected to include long-range dispersion interactions by the Tkatchenko and Scheffler (TS) method61 as implemented in the VASP code.62 Hereafter, this approach will be referred to as PBE-TS. Corrections for on-site Coulomb interactions by use of the GGA+U procedure46 were done with effective U parameters for Ti ranging from 0 to 4 eV. 1629



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errors of only 0.32% and 0.59% for the a and c lattice parameters, respectively. As noted in our previous study,33 inclusion of the dispersion corrections improves the performance of the calculations at predicting the lattice constants. With increasing value of the U parameter, there is a systematic expansion of the lattice and a growing deviation of the calculated lattice constants from the experimental values. Simultaneously, the bulk modulus decreases, reflecting a softening of the lattice. These trends are similar to those reported by other authors52 using the GGA+U method but without inclusion of corrections for dispersion. The anatase (101) surface was modeled with a (1 × 3) supercell along the [101̅] and [010] crystallographic directions, respectively. The supercell contains 8 Ti and 16 O atomic layers, and for each value of U it was constructed starting from the optimized bulk parameters. A 12 Å vacuum layer was used to minimize the interactions between surfaces of adjacent slabs, and a 2 × 2 × 1 Monkhorst−Pack64 grid of k-points was used to sample the Brillouin zone. The minimum energy reaction pathways for oxygen exchange were mapped out via the climbing-image nudged elastic band (CI-NEB) method.65,66 The nature of various extremal points on the potential energy surface was characterized by calculation of the harmonic vibrational frequencies of the surface CO2 or CO3 species in the frozen phonon mode approximation but including explicitly the Ti atoms directly bonded to the CO2 or CO3 species. In these calculations, the Hessian matrix was

Calculations with the U correction are referred to as PBE-TS +U. Relaxed lattice parameters for bulk anatase obtained by use of the PBE-TS functional61 with and without the U correction are reported in Table 1. In the absence of the U correction, the Table 1. Comparison of Calculated and Experimental Lattice Parameters and Bulk Modulus for Bulk Anatasea U (eV) 0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0

a, Å (error, %) 3.794 3.807 3.813 3.819 3.825 3.831 3.836 3.841 3.782

(0.32) (0.65) (0.82) (0.98) (1.13) (1.28) (1.43) (1.57)

c, Å (error, %) PBE-TS+U 9.558 (0.59) 9.570 (0.72) 9.576 (0.78) 9.583 (0.85) 9.588 (0.91) 9.596 (1.00) 9.603 (1.06) 9.612 (1.16) Experimentalb 9.502

ΔV, % 1.23 2.04 2.43 2.83 3.21 3.60 3.98 4.36

B0, GPa (error, %) 174.7 174.5 174.4 173.6 172.9 172.8 172.8 172.6

(−2.41) (−2.48) (−2.56) (−2.99) (−3.37) (−3.45) (−3.43) (−3.55)

179 ± 2

a

Calculations include dispersion corrections and are reported for different values of the on-site Coulomb correction. bExperimental values of the lattice parameters are from ref 63, and those for the bulk modulus are from ref 73.

calculated lattice parameters are in good agreement with the low-temperature experimental data from ref 63 with relative

Figure 1. General scheme representing initial, intermediate, and final configurations involved in oxygen exchange between CO2 and a defective anatase (101) surface. (Left panels) Side and top views of adsorption configurations of CO2 at a VO site on the surface. The CO2 molecule remains linear in L(1) and L(2) but is bent in B(1) and B(2), with formation of new bonds with Ti(5f) and O(2f) surface atoms. (Middle panels) Side and top views of C(0) configuration. (Right panels) Side and top views of a CO2 molecule with an exchanged O atom adsorbed in a linear L(3) configuration, which is symmetrically equivalent to L(1) with respect to C(0). For easy identification, O and C atoms of the original CO2 molecule are depicted in yellow and green, respectively, while O and Ti atoms of the surface are colored in red and gray, respectively. The location of the VO site is indicated in light blue in the top left panel. For the C(0) configuration, OI denotes the O atom of CO2 molecule closest to the surface, which is bonded to a Ti(5f) atom, while OII indicates the nonbonded O atom of the CO2 molecule. 1630



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Table 2. Adsorption Energies, Representative Geometric Parameters, Vibrational Frequencies, and Bader Charges of a CO2 Molecule Adsorbed at Different Sites on a Defective Anatase (101) Surfacea configb gas phase B(1) B(2) L(1) L(2) C(0) B(1) B(2) L(1) L(2) C(0,α) C(0,β)

bonding typec

μ1-η2 μ1-η2

μ1-η2 μ2-η3 μ2-η3

μ2-η3 μ2-η3

r(Ti−O), Å

2.157 2.017 2.387 2.628 1.996 2.234, 2.116, 2.410 2.539 2.162, 2.196,

r[O(s)−C],d Å

1.399 1.391

1.361 2.269 2.258

1.406 1.410

2.208 2.120

1.350 1.320

r(C−O), Å U = 0 eV 1.176, 1.176 1.238, 1.304 1.298, 1.264 1.187, 1.164 1.183, 1.170 1.360, 1.224 U = 2.5 eV 1.248, 1.285 1.274, 1.247 1.188, 1.164 1.183, 1.168 1.311, 1.267 1.320, 1.280

ν(CO2),e cm−1

α(OCO), deg

Eads, kcal/mol

180.0 129.4 133.1 177.3 178.4 120.8

14.7 15.2 15.8 9.1 14.6

2365, 1640, 1706, 2368, 2357, 1651,

1318, 1179, 1215, 1320, 1316, 1030,

633, 811, 810, 706, 708, 961,

129.8 134.6 177.6 178.2 121.1 119.5

14.1 8.2 14.0 9.8 16.2 19.5

1634, 1694, 2367, 2369, 1463, 1407,

1224, 1239, 1312, 1322, 1209, 1263,

814, 739 798, 842 680, 595 681, 624 986, 758 1023, 771

633 743 739 607 629 756

Δq(CO2)

0.295 0.292 0.011 0.012 0.110 0.298 0.400 0.035 0.012 0.362 0.207

a

As determined from PBE-TS+U calculations with U = 0 and 2.5 eV. bPictorial views of the indicated configurations are provided in Figure 1. Bonding notation based on Gibson convention.74 The first index μn indicates the number of bonds to the metal centers, whiles the second index ηm gives the total number of bonds. dThe O(s) label refers to a generic surface O atom. eVibrational frequencies calculated for the 16O isotope for the gas-phase and adsorbed CO2 molecules. c

determined via finite differences with a step size of 0.02 Å for displacement of individual atoms along each Cartesian coordinate. Charge transfer between adsorbates and the anatase surface was analyzed from Bader charges67 determined by the charge density decomposition method of Henkelman and coworkers.68

energy of the isolated CO2 molecule was calculated by use of a cubic cell with sides of 12 Å. As seen from the data in Table 2, the most stable configurations, B(1), B(2), and L(1), have similar binding energies, ranging from 14.7 to 15.8 kcal/mol. These values are only slightly larger than that reported for the defective rutile (110) surface of 12.9 kcal/mol,32 consistent with the close resemblance of the TPD spectra of CO2 on anatase and rutile surfaces found by Praserthdam et al.30 In addition to the four configurations discussed above and which we reported previously in ref 33, we present a new configuration C(0) with the CO2 bound to the surface by 14.6 kcal/mol. This corresponds to a bent CO2 molecule adsorbed at a VO site with the CO2 molecule forming a bond to a surface Ti(5f) atom and a bond to a nearby bridging O(2f) atom. This CO3-like species is symmetrically bonded to two consecutive Ti(5f) atoms located in the top layer. As shown in the top-view representation of C(0) in Figure 1, the resulting CO3 entity has axial symmetry with respect to an axis passing through the C− OII bond of the original CO2 molecule. Due to the axial symmetry, the OI atom (represented in yellow in Figure 1) bonded to the Ti(5f) atom becomes practically symmetrically equivalent to the surface bridging O(2f) atom (represented in red). The OII end of the molecule remains nonbonded to surface atoms as seen from the side-view representation. Thus, this configuration is an ideal candidate for promoting oxygen exchange. Indeed, as shown in Figure 1, starting from the C(0) configuration, the system can rearrange to the L(3) configuration with the CO2 molecule composed of OII−C− O(2f). During this process the OI atom becomes incorporated into the surface as a regular bridging oxygen atom. From L(3), the CO2 molecule can desorb from the surface or continue to diffuse on the surface and become involved in a subsequent oxygen exchange at a VO site. From the data in Table 2, it can be seen that sizable differences exist among the calculated vibrational frequencies of the various binding configurations. The least affected (compared to the gas-phase molecule) are the linear binding L(1) and L(2) configurations. In contrast, the CO stretch vibrations of the CO2 molecule in the bent B(1), B(2), and

3. RESULTS AND DISCUSSION 3.1. CO2 Adsorption and Oxygen Exchange Reactions on the Defective (101) Anatase Surface for U = 0 eV. It was proposed in earlier experimental studies13,23 that oxygen atom exchange between gaseous CO2 and the anatase surface is mediated by formation of a carbonate species upon CO2 adsorption at a surface VO defect site. In order to test this hypothesis, we consider possible adsorption configurations of CO2 at or near a Vo site on the anatase (101) surface, in an attempt to identify promising candidate configurations for formation of the CO3 species. In this section, we consider results obtained in the absence of the Hubbard U term correction; the effect of nonzero U corrections will be considered in the following section. A summary of the CO2 binding configurations on the defective anatase (101) surface is presented in the left-hand inset panels of Figure 1. As can be seen, near a surface VO site, CO2 can adsorb in either bent (B) or linear (L) configurations. In the former case [configurations B(1) and B(2)], covalent bonds between the adsorbed CO2 molecule and surface atoms are formed, while in the latter case [configurations L(1) and L(2)], the molecule is physisorbed on the surface. A select set of geometrical parameters and vibrational frequencies, together with the corresponding adsorption energies for the indicated configurations, are presented in Table 2. The adsorption energies were calculated as Eads = (nECO2 + Eslab − ECO2+slab)/n, where ECO2 is the energy of the CO2 molecule at its optimized gas-phase geometry, n represents the number of adsorbate molecules in the simulation cell, Eslab is the total energy of the slab, and ECO2+slab is the total energy of the adsorbate/slab system. With this sign convention, positive adsorption energies correspond to stable configurations. The 1631



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Figure 2. Minimum energy pathways for (a) B(1) ⇄ C(0), (b) B(2) ⇄ C(0), and (c) L(2) ⇄ C(0) conversion as determined from calculations using the PBE-TS method (U = 0 eV). Atomic configurations for specific images along the reaction pathway are also indicated. The color legend for the atoms is the same as in Figure 1

conversion process. In Figure 3, we present results for the L(1) → C(0) → L(3) sequence, leading to the exchange of one of

C(0) configurations are strongly red-shifted relative to the gas phase values, with frequency ranges of 1640−1706 and 1030− 1215 cm−1. Consistent with the vibrational frequency changes, there are also small increases in the amount of excess negative charge on the CO2 molecule upon adsorption. Having analyzed the adsorption energies and binding configurations of CO2 in the surface region around the VO site, we turn our attention toward description of the reaction profiles for conversion of CO2 to CO3-like species. Specifically, using the CI-NEB procedure, we have calculated the minimum energy reaction pathways for interconversion of bent [B(1), B(2)] or linear [L(1), L(2)] binding configurations to the C(0) species. Minimum energy pathways for B(1) → C(0), B(2) → C(0), and L(2) → C(0) interconversion are represented in panels a− c of Figure 2, respectively. All three reaction profiles have calculated barriers of 12.5 kcal/mol or less. Additionally, it appears that, independent of the initial configuration, the reaction proceeds through a common intermediate before reaching the C(0) configuration. Visual inspection of this intermediate represented by images 7 in panel a, 10 in panel b, and 12 in panel c indicates that it corresponds to the linear binding configuration L(1) described above. This finding suggests that, independent of the initial location of the adsorbed CO2 molecule or the initial binding type (i.e. bent or linear), formation of the carbonate configuration at the surface defect takes place through the common intermediate L(1), in which the molecule adsorbs just above the defect site in a linear configuration. Given the importance of the L(1) configuration, in the following we focus exclusively on analysis of the L(1) → C(0)

Figure 3. Minimum energy pathways for oxygen exchange between a CO2 molecule and the anatase (101) surface via L(1) → C(0) → L(3) as determined from PBE-TS calculations with U = 0 eV. Atomic configurations for specific images along the reaction pathway are indicated. The color legend for the atoms is the same as in Figure 1

the O atoms of CO2 molecule with a surface O atom. As seen from this figure, upon formation of the C(0) configuration, one of the oxygen atoms of the starting CO2 molecule (depicted in yellow) remains adsorbed on the surface, while a new CO2 molecule containing the second O atom of the original CO2 and a surface oxygen atom breaks apart and evolves toward the L(3) configuration, symmetrically oriented relative to the VO site as the initial L(1) configuration. As shown in Figure 3, the energy profiles for L(1) → C(0) and L(3) → C(0) are essentially equivalent. The barriers for the entry L(1) → C(0) 1632



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and for the exit C(0) → L(3) steps are calculated to be 12.5 and 11.4 kcal/mol, respectively. Overall, the results presented in this section based on PBETS DFT calculations give CO2 binding energies that are consistent with the TPD experiments.30 Additionally, the calculated barriers for the proposed sequence of steps L(1) → C(0) → L(3) have moderate values, indicating that oxygen exchange could be initiated by thermal excitation at ambient conditions, in agreement with experimental measurements.22 3.2. Dependence of Energetic, Geometric, and Vibrational Properties of Adsorbed CO2 on the U Parameter in PBE-TS+U Calculations. A limitation of the calculations described in the previous section is the improper description of the localization of excess electrons formed upon creation of a VO defect. In this section we consider the results of the PBE-TS +U calculations that improve the description of electron localization in the case of the defective oxide surface. U values ranging from 1 to 4 eV are considered. In the case of the bare surface, the increase of U has an important effect on the electronic properties. This can be seen from analysis of the density of states for the bare surface and of the corresponding spin density distributions, shown in Figure S1 in the Supporting Information. At U = 0, the PBE calculations predict that excess electrons are highly delocalized and that the levels associated with the Vo defect are located at the bottom of the conduction band, similar to the conclusions of previous studies.27 Increasing U to the range 1.5−2.5 eV leads to the appearance of a new level in the band gap. In this case one of the excess electrons of VO becomes localized on a Ti atom near the defect. For U values equal or larger than 3.5 eV, the excess electrons of the VO defect become localized on two undercoordinated Ti atoms (see Figure S1g, Supporting Information), and correspondingly two well-defined levels can be identified in the band gap. These levels shift down to lower energies upon increasing U to 4.0 eV. Overall, it can be concluded that, in the case of the bare anatase (101) surface containing a VO defect, increasing the U parameter leads to a systematic increase of the band gap between the valence and conduction bands, an enhanced localization of the defect levels, and a shift of their energies down in the gap. It should be noted that the use of a too-large value of the Hubbard U parameter (e.g., > 3 eV) can be detrimental, as it can lead to appearance of midgap band levels that do not have an experimental correspondent, as was recently demonstrated for the case of Nb-doped anatase.69 Figure 4 summarizes the results of adsorption calculations performed at different U values for the L(1) and C(0) binding configurations. For U < 1.5 eV, the optimized L(1) and C(0) configurations as well as the bare surface with the VO site remain in the singlet state, due to the highly delocalized nature of the two excess electrons. When U is increased above 1.5 eV, the triplet state becomes energetically favored. In the spin singlet region, there is little difference between the adsorption energies of the linear L(1) and bent C(0) configurations, as seen from Figure 4. This situation changes dramatically when U is increased above 1.5 eV. In the triplet region, the adsorption energy of the L(1) configuration displays only a weak dependence on U, while the binding energy of the C(0) configuration increases continuously as the U parameter is increased. The variations are moderate for 1.5 ≤ U ≤ 2.5 eV, but they increase sharply to unrealistically high values for U ≥ 3 eV. We recall that, according to Praserthdam and co-workers,30 the experimental

Figure 4. Variation of adsorption energy of a CO2 molecule adsorbed at L(1) and C(0) sites for various U parameters. For U ≤ 1 eV the system is in a singlet state, while for U ≥ 1.5 eV it is in a triplet state. For the C(0,α) configuration, the excess electrons are localized at Ti atoms located on different rows and in different atomic layers, while for the C(0,β) configuration, they are localized in the same row at successive Ti atoms in the top layer. Specific locations of the excess spins are indicated as top and side views in the right inset panels. For the L(1) configuration, the spins are located on Ti atoms located in different rows and in different layers around the defect site.

binding energy of the physisorbed CO2 on reduced anatase surface should be close to 12.9 kcal/mol32 as determined on rutile (110) surface.32 A binding energy of this magnitude is achieved in our calculations only for U values ≤ 2.5 eV. For the C(0) binding configuration in the spin triplet region, multiple solutions are possible even when the CO2 molecule occupies approximately the same physical location at the defect site. These differ in the Ti sites at which the excess electrons are localized. The right inset panels of Figure 4 show top and side views of the two most stable configurations for C(0), hereafter denoted as C(0,α) and C(0,β). In these two configurations, the molecule is located essentially at the same site on the surface but the excess electrons are localized on different sets of Ti atoms: diagonally positioned in different layers in C(0,α) or on Ti atoms located in the top layer on the same row in C(0,β). The adsorption energies of C(0,α) and C(0,β) configurations depend strongly on the value of U but show a preference for the C(0,β) configuration. For completeness, we also indicate in the lowest set of inset panels in Figure 4 the localization of the two electrons in the case of the spin triplet state for the L(1) configuration. In this case, the unpaired electrons are located on Ti atoms located in different rows and in different layers. We note that the spin localization indicated in the inset panels in Figure 4 is generally observed for U values larger than 2.5 eV. For 1.5 < U < 2.5 eV, solutions in which one electron is localized on the Ti atom in the top layer near the defect and the other electron is partially delocalized over several subsurface atoms are also observed, particularly for the bare surface and for the L(1) configuration. In these cases, configurations in which both electrons are fully localized are also possible but they are slightly less stable than configurations with fully localized spins. Further increase of U leads to an increased stabilization of the arrangements where both excess electrons are fully localized, in agreement with previous findings for reduced bulk anatase.48 As U is increased, the amount of charge transferred from the surface to the adsorbed CO2 increases, particularly for the case of most stable chemisorbed states. For example, the total charge (determined via Bader analysis) of the adsorbed CO2 molecule increases systematically from 0.07e (U = 0 eV) to 0.21e (U = 2.5 eV) and further to 0.32e (U = 3.5 eV) and to 0.35e (U = 4.0 eV) for the C(0,β) configuration. Further insight into the 1633



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temperature and value of U is shown in Figure 6 for the L(1) and C(0,β) configurations. For the L(1) configuration, the condition for surface desorption (see Figure 6a), that is, ΔGads = 0, is satisfied for temperatures in the range 150−177 K when 0 < U < 3.0 eV. This range of desorption temperatures agrees well with the lower value determined experimentally.31 The weak sensitivity of the desorption temperature of L(1) to the value of U is consistent with the relatively weak dependence of the adsorption energy of L(1) on the value of U (Figure 4). In contrast, for the C(0,β) configuration (see Figure 6b) the predicted desorption temperature increases sharply from 151 K (U = 0 eV) to 196 K (U = 2.5 eV) to 247 K (U = 3.0 eV) to 266 K (U = 3.5 eV). For this configuration, the calculated desorption temperatures for U values larger than 2.5 eV are inconsistent with experiment. The increased binding for the C(0,α) and C(0,β) configurations for nonzero U values is associated with changes of key geometrical parameters. The changes upon going from U = 0 to U = 2.5 eV are reported in Table 2. Increasing U from 0 to 2.5 eV causes the OICOII plane to tilt toward the surface with a corresponding change of the angle between the COII bond and the surface normal from 56° to 68°. As a result, the OII end of CO2 molecule, which is not bonded at U = 0 eV, becomes bonded at U = 2.5 eV to a Ti(5f) atom located in the next row. The corresponding Ti(5f)−OII separation decreases from 2.971 Å at U = 0 eV to 2.208 Å for C(0,α) and to 2.120 Å for C(0,β) at U = 2.5 eV. This new Ti(5f)−OII bond is apparent by comparing the side-view panel of C(0) configuration in Figure 1 with the corresponding views in Figure 4 for configurations C(0,α) and C(0,β). Concomitant with formation of the Ti(5f)−OII bond, the C−OII bond of CO2 increases from 1.224 Å at U = 0 eV to 1.267 Å for C(0,α) and to 1.280 Å for C(0,β), indicating a weakening of this bond. In contrast, the second C−OI bond of CO2 is compressed from 1.360 Å at U = 0 eV to 1.311 Å for C(0,α) and to 1.320 Å for C(0,β) at U = 2.5 eV, indicating bond strengthening. Overall as U changes from 0 to 2.5 eV, the bonding scheme of the adsorbed CO3 species changes from a bridged bidentate to a tridentate, with all three O atoms anchored to Ti(5f) atoms. Adoption of a nonzero value of the U parameter also leads to geometrical changes for the B(1) and B(2) bent configurations. Again, the use of a U parameter of 2.5 eV leads to the formation of an additional bond between the OII end of the adsorbed CO2 and a surface Ti(5f) atom. In particular, for B(1) the separation between OII end and the closest Ti(5f) atom decreases from

charge transfer is provided by analysis of the charge difference map shown in Figure 5, from which it is seen that charge is

Figure 5. Top and side views of the charge difference map for a CO2 molecule adsorbed in the C(0,β) configuration as determined from calculations with U = 2.5 eV. The two isosurfaces correspond to values of +0.05 e−/Å3 (yellow) and −0.05 e−/Å3 (blue). The indicated TiI and TiIII atoms are located in the same row in the top surface layer, while TiII is located in a neighbor row in a subsurface layer.

depleted from the subsurface TiII site, where electron localization was favorable in the case of the bare surface, and accumulates primarily on the adsorbed CO2 molecule and on TiIII (see Figure 5b), located in the top layer and in the same row as the TiI atom. Additional insight into the role played by the U parameter in the GGA+U calculations can be obtained by comparing predicted CO2 desorption temperatures to those observed experimentally. As indicated in the Introduction, Praserthdam and co-workers31 have established by TPD measurements that desorption of CO2 from anatase nanocrystals is characterized by broad peaks at 175 and 200 K. We have estimated desorption temperatures for the L(1) and C(0,β) configurations described above from the temperature dependence of the Gibbs free energy of adsorption (ΔGads). These calculations were done at a pressure of ∼10−12 atm, which is representative of the TPD experiments under ultrahigh vacuum (UHV) conditions. The entropic and enthalpic contributions were obtained by assuming ideal gas behavior for the CO2 molecules Additionally, for evaluation of the free energy contributions of the slab, the vibrational terms of surface atoms either directly bonded or located in close proximity to the adsorbed CO2 molecule were included. The variation of ΔGads as a function of

Figure 6. Variation with temperature of the calculated Gibbs free energy for adsorption of a CO2 molecule at (a) L(1) and (b) C(0,β) sites for various U values. A pressure of 10−12 atm was assumed. 1634



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2.414 Å at U = 0 eV to 2.269 Å at U = 2.5 eV, while for B(2) it decreases from 2.391 Å at U = 0 eV to 2.258 Å at U = 2.5 eV. On the basis of these geometry changes, it follows that for U = 2.5 eV the adsorbed CO2 molecule is bonded through both its O and C atoms, giving a tridentate carbonate-like structure. Consistent with the energetic and geometric changes of the C(0) configuration upon adsorption of a nonzero value of the U parameter, there are also modifications of the vibrational frequencies of the adsorbed species. These are detailed in Figure 7 for the two highest frequencies (denoted as ν1 and ν2)

In summary, we note that analysis of the calculated energies, geometries, and vibrational frequencies of CO2 molecules adsorbed at a surface defect of anatase with formation of a carbonate-like species provides a consistent picture: namely, that U values less than 2.5 eV provide the best overall agreement of calculated results with experiment. As noted in the Introduction, these U values are significantly smaller than those generally used to describe the band gap properties or the location of defect states in the band gap. 3.3. Variation of Activation and Reaction Energies for Oxygen Exchange with the Value of the U Parameter. Another topic addressed in this study is the sensitivity of the activation energies for oxygen exchange to the value of the U parameter when the PBE-TS+U method is used. We focus on the L(1) → C(0) → L(3) pathway, which we concluded (see section 3.1) is responsible for the observed exchange. As described in section 3.2, adsorption of CO2 at a VO defect with formation of a CO3 species is characterized by configuration C(0) for U < 1 eV and by configurations C(0,α) and C(0,β) for larger U values. Consequently, we have analyzed the particular pathways for oxygen exchange for each of these configurations. The minimum energy pathways for L(1) → C(0,α) → L(3) and L(1) → C(0,β) → L(3) obtained from calculations with U = 2.5 eV are presented in Figure 8. These energy profiles differ

Figure 7. Variation of calculated vibrational frequencies for the two highest frequency modes of CO2 in the carbonate-like C(0,α) and C(0,β) structures as a function of U. The experimental vibrational frequencies for the bridged bidentate [ν(bb)] carbonate from ref 70 and for bidentate carbonate [ν(bi)] from refs 71 and 72 are included for comparison. (Insets) Eigenvectors for the vibrations.

of the C(0,α) and C(0,β) species. As seen from this figure, the frequencies of the ν1 and ν2 modes undergo significant shifts as U is increased from 0 to 2.0 eV, while smaller frequency shifts are found for U > 2 eV. The calculated values can be compared against experimental data, and, for this purpose, we used two different sets of values. The first set corresponds to the observed infrared bands of the bridged bidentate [ν(bb)] carbonate species at 1215−1245 and 1670−1671 cm−1, obtained from ref 70. The second set at 1315−1355 and 1566−1589 cm−1 is based on the work of Grassian and coworkers71 and Su et al.72 for the bidentate carbonate [ν(bi)] species. From Figure 7 it is seen that for no single choice of U are the calculated frequencies of both ν1 and ν2 vibrations in good agreement with the experimentally measured frequencies. For the high-frequency mode, the calculated frequency for U values below 2 eV is close to both the measured ν(bb) and ν(bi) values. However, for the lower frequency bands, the calculated frequency is close to the measured ν(bb) frequency at 1219− 1243 cm−1 only when the calculations use U ≥ 2 eV. It should be noted that the experimental results reported in Figure 7 were obtained for samples with combinations of different anatase and rutile phases or nanopowders having a distribution of particle sizes and shapes. Additionally, the experiments used mixtures of different gases, in some cases including water, and consequently, differences between the calculated and measured values of the vibrational frequencies are expected. Nevertheless, the data in Figure 7 show that a tentative match between calculated and observed frequencies is obtained only for U values below 2.5 eV.

Figure 8. Minimum energy pathways for oxygen exchange between a CO2 molecule and the anatase (101) surface for (a) L(1) → C(0,α) → L(3) and (b) L(1) → C(0,β) → L(3) interconversion steps, as determined from PBE-TS+U (U = 2.5 eV) calculations.

in important ways from that obtained for U = 0 eV (see Figure 3). The major change resulting from the use of a nonzero U parameter is the increased stabilization of C(0,α) and C(0, β) local minima relative to the initial L(1) and final L(3) configurations. The L(1) → C(0) reaction, which is slightly endothermic for U = 0 eV, becomes exothermic at U = 2.5 eV by 2.3 kcal/mol for L(1) → C(0,α) and by 5.6 kcal/mol for L(1) → C(0,β). Correspondingly, there is a small decrease in the activation barriers from 12.5 to 10.9 kcal/mol. The 1635



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values determined from analysis of TPD data.31 Additionally, for U = 0 eV the calculated activation energies for the oxygen exchange mechanism between CO2 and solid TiO2 are small enough (Ea < 12.5 kcal/mol) to support initiation of the oxygen exchange at ambient temperature as seen by Civiš and coworkers.23 The use of U parameters in the range 1.5−2.5 eV leads to modest increases of CO2 adsorption energies and of activation energies for oxygen exchange, such that overall the calculated values remain consistent with experimental data. However, U values of 3.0 eV or larger give energies inconsistent with experiment. In particular, there is a large increase of the adsorption energy of CO2 at the defect site to unphysically large values (>24 kcal/mol). Correspondingly, the vibrational frequencies are shifted to values very far from those measured experimentally. Additionally, the calculated barriers for the oxygen exchange mechanism become too large to be consistent with the observation of the reaction at ambient temperature conditions.23 These findings reconfirm the point raised previously by Hu and Metiu53 that values of U that give electronic band gaps close to experiment are less useful for prediction of chemisorption properties. Indeed, in the present case we have seen that U values in the range 3.5−4 eV, typical of those used to give a band gap close to experiment for reduced anatase,47,48 lead to a poor description of CO2 adsorption and reaction properties on the surface. The U value that is the best compromise for the set of geometric, energetic, and activation energies of CO2 on the anatase (101) surface as found in this study is U = 2.5 eV. As noted in the Introduction, a U value of about 2.3 eV is necessary to obtain a calculated energy for oxidation of TiO2 (rutile) → Ti2O3 in agreement with experiment.53,54 This U value is also much smaller than those (4.5 eV or larger53,55) generally used to predict the band structure of reduced rutile. Moreover, these trends are not limited to reactions involving TiO2. Indeed, as shown by Lutfalla et al.,54 calculation of the energies for oxidation of molybdenum, vanadium, and cerium oxides in agreement with experimental data requires use of a U value significantly smaller than those used to reproduce experimental electronic properties. Overall, these results indicate a limitation of the GGA+U method. This limitation can be partially solved by using hybrid functionals that incorporate a portion of exact exchange but also require a significant increase in computational cost. A final comment pertains to the oxygen-exchange mechanism. As shown in this work, a carbonate-like species C(0) can be formed at a surface VO site on the anatase (101) surface, with the exchange taking place via a bridging O atom directly bonded to the CO2 species. If the location of the vacancy on the crystal were to remain fixed during the experiments, only a limited number of CO2 molecules could undergo oxygen exchange. However, experiments have shown that oxygen exchange between C16O2 molecules and solid Ti18O2 can convert a high fraction of the C16O2 molecules to C18O2.22 This requires a continuous supply of Vo sites on the oxide surface. As shown recently by Scheiber et al.,28 following equilibration there is an exchange of defects between surface and subsurface sites of anatase. Such a process would replenish 18O atoms on the surface at defect sites, allowing for conversion of a large fraction of the C16O2 molecules to C18O2.

increased stabilization of the carbonate species, however, leads to larger barriers for the exit channel, that is, 13.4 kcal/mol for C(0,α) → L(3) and 16.5 kcal/mol for C(0,β) → L(3). Calculated activation energies for the L(1) → C(0,α) and L(1) → C(0,β) steps for all U values considered are reported in Figure 9. For each U value, the relative energy (taken as

Figure 9. General scheme representing the variation of adsorption, activation, and reaction energies for L(1) → C(0). Results are reported as a function of the Hubbard U parameter. For each barrier profile, three sets of data are indicated: relative energy of the initial configuration with respect to the energy of the isolated slab and isolated gas phase CO2 molecule is given in parentheses, barrier height is shown at the top of the reaction profile, and the value indicated at the bottom of the reaction profile without parentheses represents the reaction energy. For U ≥ 1.5 eV, the reaction profile in black corresponds to L(1) → C(0,α) while the reaction profile in red represents the L(1) → C(0,β) reaction. The corresponding energy variations for the singlet state (U ≤ 1) are indicated in blue.

negative of the adsorption energy) of the initial L(1) configuration (provided in parentheses), activation energy, and reaction energy with respect to the initial configuration are reported. For U > 1.5 eV, two sets of results for L(1) → C(0,α) (represented in black) and L(1) → C(0,β) (represented in red) are shown. Inspection of the results presented in Figure 9 allows identification of three important trends as the U value is increased from zero. First, the barriers for the reactions to form the carbonate species decrease slightly. Second, there is a systematic stabilization of the carbonate configuration. As a result, the reverse reaction corresponding to formation of L(1) [or L(3)] species starting from the carbonate configuration acquires larger barriers. As found by Civiš and co-workers,22 the isotopic oxygen exchange reaction of C16O2 with reduced Ti18O2 anatase occurs at ambient temperature. As seen from the data in Figure 9, for U > 2.5 eV the calculations give large barriers (20.4−24.2 kcal/ mol) for CO2 elimination from the carbonate-like state. A barrier of this magnitude would make the exchange mechanism unlikely under thermal excitation at room temperature. Only in the case of U < 2.5 eV are the calculated barriers low enough to be consistent with oxygen exchange taking place at ambient temperature. Interestingly, the PBE-TS method without the +U correction48 provides good agreement of the calculated bulk lattice parameters and bulk modulus with the experimental data63,73 and gives CO2 adsorption energies consistent with 1636



4. CONCLUSIONS The adsorption of a CO2 molecule at a VO defect site on the anatase (101) surface and the mechanism of oxygen exchange between molecule and surface have been analyzed by DFT calculations with inclusion of corrections for long-range dispersion, with and without on-site Coulomb interactions. The main findings are as follows: (1) CO2 adsorption at a VO site is found to take place either in linear L(1)−L(3) or bent B(1), B(2), or C(0) configurations. For the C(0) configuration, adsorption of CO2 at a VO site involves simultaneous bonding to surface Ti(5f) and O(2f) atoms, giving a carbonate-like structure. This configuration is predicted to be an intermediate in the oxygen exchange reaction as it allows direct extraction of a surface bridging oxygen followed by CO2 elimination. (2) The calculated adsorption energies of CO2 molecules in the linear L(1)−L(3) configurations show only a weak dependence on the value of U. In contrast, for the bent B(1), B(2), and C(0) species, the adsorption energies increase with increasing U. The changes are moderate for 1.5 < U < 2.5 eV, but they become unphysically large for U ≥ 3.0 eV. For U > 1.5 eV, the adsorption energies depend on the details of localization of the excess electrons at Ti sites. Consistent with the increase in the adsorption energies with increasing U, there are also sizable geometry changes and vibrational frequency shifts. U values of 3 eV or larger lead to vibrational frequencies that deviate significantly from the available experimental data. The calculated adsorption free energy for the strongest binding configuration C(0,β) is consistent with the experimental results under UHV conditions only for U ≤ 2.5 eV. (3) Analysis of the minimum energy reaction pathways for the L(1) → C(0) reaction as a function of U reveals two major trends as U is increased. The first is a slight decrease of the activation energy for formation of the C(0) intermediate, while the second is an increase of exothermic character of the reactions. The increased stabilization of the carbonate-like C(0) structure leads to larger exit barriers, which for U ≥ 3.0 eV are too large to be compatible with room-temperature experiments. (4) Overall, the collection of geometries, vibrational frequencies, and energies calculated as a function of U indicate that the best agreement with experimental data is obtained for a U value around 2.5 eV. This value is smaller than those generally used to reproduce the band structure or the energies of the states in the gap for reduced anatase (U ≥ 3.5 eV). On the other hand, a U value of 2.5 eV is consistent with that required to describe the catalytic properties of other TiO2 phases53 or other oxides.54

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ACKNOWLEDGMENTS

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REFERENCES

We acknowledge a grant of computer time at Pittsburgh Supercomputer Center and on the NETL HPCEE supercomputer system. The work at University of Pittsburgh was performed in support of the National Energy Technology Laboratory’s Office of Research and Development under Contract DE-FE0004000.2.661.251.001. Disclaimer: reference in this work to any specific commercial product is to facilitate understanding and does not necessarily imply endorsement by the United States Department of Energy.

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S Supporting Information *

One figure showing variation of total density of states and spin density for a defective anatase (101) surface as a function of U in GGA+U calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

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The authors declare no competing financial interest. 1637



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