(171c) First-Principles Modelling of Photocatalytic Activation of CO2: Challenges and Approaches

Introduction

Titanium dioxide (TiO₂) is one of the most studied semiconductor materials, both experimentally and theoretically, on account of its photoactivity and a range of other potential applications. Recently, its utilization in the field of photocatalysis has become increasingly important as it represents a way to carry out catalytic reactions with lower energy consumption.

Nevertheless, pristine anatase and rutile TiO₂ have some drawbacks, such as high band gaps (above 3 eV), which means that only UV light is able to excite the electrons from the valence band (VB) to the conduction band (CB). In order to boost the photoactivity in the visible light range, modifications which decrease the band gap (utilizing visible light) are required. Moreover, other adverse phenomena must also be suppressed, such as charge recombination, while charge transfer should be increased. There are several strategies to solve these problems: doping, the deposition of co-catalysts, the integration of defects (e.g. oxygen vacancies) or using the so called Z-scheme photocatalyst.

Furthermore, in undoped TiO₂, electrons would sink into the bulk. Doping makes the material catalytically active by allowing electrons to reach the surface. In addition, metal doping controls the selectivity of the catalysts toward the desired products, which can range from CO and CH₃OH to higher hydrocarbons in the case of CO₂ photoreduction.

Since experimental testing of all possible changes is unwieldy, in-silico calculations can be performed instead. Increasing computational power has led to an increase in theoretical studies of photocatalysis in recent years. However, the vast majority of theoretical studies focus either on the calculation of catalyst properties or on phenomenological kinetic modelling of experimental results. When a reaction mechanism is studied ab initio, including all possible intermediates, activation barriers, and kinetic parameters, calculations are usually performed in the ground state. However, the explicit consideration of the excited state is crucial for the correct representation of a photocatalytic process.

An alternative approach to modelling photocatalytic reactions uses the fact that the dielectric constant of TiO2 is large enough to treat electrons and holes as free as opposed to excitons. In this approximation, the mechanism can also be investigated using electro-chemical methods (grand canonical DFT or JDFT).

Methods

We investigated a simplified mechanism of CO₂ photoreduction on Cu (111), pristine anatase (101), pristine rutile (110) and Cu/rutile (110) and Cu/anatase (101) surface. First, ground-state calculations of the reaction mechanism are performed at the DFT level. Second, excited states are accounted for following Kasha’s rule by exciting one HOMO electron from the valence band to the LUMO orbital of the conduction band. The reaction mechanism and kinetics are then compared between different surfaces in the ground and excited state.

Density functional theory (DFT) calculations were performed with the VASP-5.4.1 package. The PBE functional was used as implemented in the PAW pseudopotentials. The energy cut-off of 500 eV was shown to suffice for well converged results based. To account for strong electron localization, the Hubbard correction of (U-J) 4 eV was applied to the Ti 3d electrons in the approach by Dudarev. Long range dispersion forces were considered with the D3 correction by Grimme. Spin polarization was included for all the calculations.

To study surface phenomena, surface slabs were constructed as follows. For Cu (111), a 3-layer 6x6 supercell was prepared. A 3-layer 3x2 supercell of pristine anatase (101) and Cu/TiO₂ anatase (101) surface with one fixed layer, and a 3-layer 3x3 supercell of pristine rutile (110) and Cu/rutile (110) with two fixed layers were constructed. In all instances, 12 Å vacuum was added to the slabs to avoid spurious inter-cell interactions. A dipole correction was applied in the z-direction. The supercells were sampled with a Monkhorst-Pack mesh, at 1x1x1 (Gamma point) due to the size of the supercells. A cluster of four pre-optimized Cu atoms was deposited and allowed to relax on pristine anatase (101) and rutile (110) surfaces. All structures were relaxed until the atomic force dropped below 0.05 eV/Ã…. The nudged elastic band in conjunction with the climbing image was used to identify the transition states, which were refined with the dimer method.

For the excited-state calculations, we applied the delta self-consistent field (∆SCF) approach. Firstly the structures of the initial, final and transition states were optimized in the ground state. Subsequently, the density of states was analyzed for each structure to identify the orbital for electron insertion. Then, an electron was moved from the valence band maxima (VBM) into the conduction band minima (CBM), leaving a hole in the VBM. A triplet spin state was used to force the population of the LUMO and depopulation of HOMO. After the change in orbital population, orbitals are reoptimized, and the energy is computed from these orbitals.

To evaluate the time evolution of the heterogeneous photocatalytic process, we created a microkinetic model using DFT-calculated reaction parameters. The model assumes an ideal batch reactor with the following: constant temperature and pressure, no mass transfer limitations, ideal mixing, no lateral interactions. Since the microkinetic model was set up to compare the differences in reaction kinetics in the photoactivated and dark regime, the exact reactor parameters was less of a concern. To mathematically describe the transformation, we constructed and solved a system of differential equations for the gas and surface reactions along with a balance for the active sites.

Results

We explicitly considered the excited states during CO₂ photoreduction with the ∆SCF method. Due to Kasha’s rule, we only considered the first excited state. For Cu (111), no differences were observed on account of its metallicity. Consequently, the rutile and anatase crystal phases of TiO₂ were chosen as benchmark and the most researched photocatalysts in the literature. We showed that photo-excitation has a significant impact on the activation barriers, which can be significantly reduced. Nevertheless the pristine facets are rather inactive for the CO₂ reduction. Lastly, we deposited four Cu atoms on the rutile (110) and anatase (101) surfaces as a computationally tractable model of the Cu/TiO₂ formulation.

On Cu (111), surface we can expect the direct dissociation of CO₂ to form CO and hydrogenation of CO₂ under thermocatalytic conditions. The relatively high CO adsorption energy might hints that it is unlikely to desorb and indeed Cu is a well-known catalyst for the formation of C₂₊ products. There is little change in its photocatalytic performance due to the overlapping valence and conduction bands (no band gap).

On the other hand, pristine anatase (101) exhibits a high band gap of 2.36 eV. The ground state calculations reveal CO₂ would be reduced through direct hydrogenation, but this is unlikely due to a high activation barrier. Inclusion of the excited states significantly reduces the barriers. CO adsorption strength is rather weak, which is also the case for pristine rutile (110) surface. A direct CO₂ dissociation is again impossible due to unfavourable thermodynamics. The most likely reaction pathway is the direct hydrogenation to HOCO, which then likely reacts further towards methane or methanol. The reaction rates in all cases are negligible.

Finally, we deposited four Cu atoms on rutile and anatase. Contrary to pristine anatase (101) surface, the Cu/anatase (101) surface has much lower activation energies in the ground state, where results suggest that hydrogenation and dissociation of CO₂ are almost equally likely to happen. After the formation, HOCO can then react further or dissociate to CO and OH. Inclusion of excited states furthermore reveals that the activation barriers are further lowered. In the case of Cu/rutile (110), it was found that in the ground state the direct dissociation of CO₂ is likely the predominant pathway, whereas hydrogenation has a higher barrier. Due to low adsorption energies of CO, it is also likely to be the major product. The inclusion of excited states even further lowers the E_A.

It should be noted that Cu-clusters on a TiO2 surface introduce cluster states in the band gap, which themselves do not significantly influence it as shown in Figure 2. This is expected as cluster states do not have a sufficient cross section to influence an optical measurement but they can function as recombination sites. Consequently, the photo-excited electrons have substantial energy inside TiO2 but the overall efficiency of the system can be lowered by the recombination sites.

Conclusion

Subsequently, a microkinetic model was constructed to investigate the evolution of the participating species on all five photocatalytic surfaces. In the ground state, CO₂ reduction did not proceed at the mild reaction conditions of 1 bar and 298 K, which was expected. However, accounting for the excited states revealed that Cu/rutile (110) and Cu/anatase (101) surfaces are active. The former was active for water splitting, forming predominantely H₂, whereas Cu/anatase (101) favored the production of CO. The results were found to agree with other experimental studies, reinforcing the importance of including excited states in DFT calculations and subsequent macro-scale models.