Supporting Information for

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1 Supporting Information for Role of Four-Fold Coordinated Titanium and Quantum Confinement in CO 2 Reduction at Titania Surface by Donghwa Lee and Yosuke Kanai Computational Details We employ Density Functional Theory (DFT) calculations 1 to investigate the key CO 2 reduction steps proposed in the literature. 2,3 The DFT calculations were performed with the generalized gradient approximation of Perdew-Burke-Ernzehof for the exchange and correlation potential. 4 Ultrasoft pseudopotentials 5 were used to describe the valence-core interactions of electrons, including scalar relativistic effects of core electrons for transition metals. Wavefunctions and charge densities were expanded in plane waves with kinetic energies up to 25 and 200 Rydberg, respectively. Periodic boundary conditions and Γ point sampling is used for Brillouin Zone integration. In order to compensate for the charged system, the neutralizing background charge of the opposite sign is implicitly introduced in our calculations. While this does not influence the reaction energetics for a given charge state, the procedure makes it impractical to calculate the energy differences between systems of different charge states. For locating transition states and minimum energy paths, climbing-image nudged elastic band method was used with at least 12 images. 6,7 The bulk TiO 2 surface is modeled by a 15.12Åx10.22Åx13.1Å slab (4x2x2 unit-cell) with at least 15 Å of vacuum space in the direction perpendicular to the surface in order to prevent the interaction with periodic images. For the quantum-dot surface, we have used the TiO 2 nanocluster constructed by Qu et al 8. In their study, they have systematically investigated a series of TiO 2 nano-clusters computationally, and it was shown that the small 10 unit TiO 2 nano-cluster (~ 1 nm in diameter) is energetically favorable. This cluster exhibits a significant quantum confinement effect (quantum-dot) with Kohn-Sham (KS) energy gap of 3.00 ev compared to 2.08 ev for the bulk TiO2 energy gap using DFT calculations. In current study, we have used the nano-cluster with at least 15 Å of vacuum space in all three directions. In order to understand how different excess electrons affect the reaction energetics, the potential energy profile for the reactions under different charge states was also investigated (see Fig. S1 and S2). The DFT results show that the reactions are energetically highly unfavorable with no or one excess electron, resulting in the product states (formate ion or carbon monoxide) that are highly endothermic than initial physisorbed CO 2. Two electrons are necessary for CO 2 reduction to take place on either bulk TiO 2 surface or Quantum-Dot (QD) surface. For the key findings with the tetrahedral-coordinated Ti (Ti 4 ) atom, we also performed additional calculations with Hubbard correction to DFT in order to better describe the localized d-electrons 9 for validating the qualitative behavior discussed. We employed Hubbard correction with the U value of 3.5 ev to check our DFT results, using a 1-layer TiO 2 slab. DFT+U calculations show that the energy barrier reduces from 0.57 ev to 0.32 ev (formic acid mechanism) and from 1.77 ev to 0.81 ev (CO mechanism) when an oxygen vacancy is introduced, creating the Ti 4 site. The corresponding standard DFT barrier reductions are from 0.81 ev to 0.10 ev and from 1.86 ev to 0.20 ev, respectively. S1

2 (1) Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140, A1133-A1138. (2) Dey, G. R. J. Nat. Gas Chem. 2007, 16, (3) Roy, S. C.; Varghese, O. K.; Paulose, M.; Grimes, C. A. ACS Nano 2010, 4, (4) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, (5) Vanderbilt, D. Phys. Rev. B 1990, 41, (6) Jónsson, H.; Mills, G.; Jacobsen, K. W. Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions; World Scientific, (7) Henkelman, G.; Uberuaga, B. P.; Jonsson, H. J. Chem. Phys. 2000, 113, (8) Qu, Z. W.; Kroes, G. J. J. Phys. Chem. C 2007, 111, (9) Cheng, H.; Selloni, A. J. Chem. Phys. 2009, 131, S2

3 [TiO 2 ] 0 -H + (b) [TiO 2 ] 0 [TiO 2 ] 1- -H + [TiO 2 ] 1- [TiO 2 ] 2- [TiO 2 ] 2- -H + Figure S. 1. Comparison of potential energy profiles with excess electrons: formic acid and (b) carbon monoxide pathways. The reaction energetics on TiO 2 anatase (101) bulk surface are calculated in three different oxidation states: no excess electron ([TiO 2 ] 0, red square), one excess electron ([TiO 2 ] 1-, green circle), two excess electrons ([TiO 2 ] 2-, blue triangle) [TiO 2 ] 0 -H + (b) [TiO 2 ] 0 -H + [TiO 2 ] 1- -H + [TiO 2 ] 1- -H + [TiO 2 ] 2- -H + [TiO 2 ] 2- -H + Figure S. 2. Comparison of potential energy profiles with excess electrons: formic acid and (b) carbon monoxide pathways. The reaction energetics on TiO 2 quantum dot (QD) surface are calculated in three different oxidation states: no excess electron ([TiO 2 ] 0, red square), one excess electron ([TiO 2 ] 1-, green circle), two excess electrons ([TiO 2 ] 2-, blue triangle) S3

4 !"#$ (e) (c)!%#$ Relative Energy (ev) [TiO 2 ] [TiO 2 ] (b) (c) (d) Figure S. 3. Four different CO 2 adsorption geometries on TiO 2 anatase (101) bulk surface and their relative energetics with respect to the physisorbed state in Configuration. The comparison shows that the physisorbed configuration is energetically the most stable configuration without any excess electrons present. With two excess electrons, however, configuration (b) is energetically more favorable slightly than the physisorbed state. In order to characterize the oxidation state of the adsorbed CO 2 molecule, Bader charge analysis was employed, and all CO 2 configurations are shown to be essentially in the neutral state. While a previous study has reported a CO 2 anion at the bulk surface with oxygen atoms pointing toward the surface [22], our study shows that this configuration lies much higher in energy (1.10 ev) with respect to Configuration. TiO 2 CO 2!"#$% %&"% 0.23 ev 0.37 ev 0.06 ev TiO 2 CO 2 %!"#$% ' () $%! E=-0.27 ev Figure S. 4. Metastable CO 2 - configuration formed at Ti4 on the QD surface. It is located 0.06 ev higher than the physisorbed state. Projected densities of states are plotted for the spin-up and spin-down electrons on the right panels. Small reaction barrier (0.23 ev) is associated with the formation of CO 2 - configuration on the QD surface. S4

5 - Figure S. 5. CO 2 anion configuration located in presence of tetrahedrally-coordinate Ti atoms. Bader charge analysis shows that the charge on CO 2 molecule is electron for on TiO 2 anatase bulk surface with an oxygen vacancy and electron at the TiO 2 QD surface. S5

6 Exothermic Formate ion High barrier Physisorbed CO 2 Bent CO 2 Monkey saddle Endothermic Carbon monoxide Figure S. 6. Geometries along the reaction path on bulk TiO 2 surface Highly Exothermic Formate ion Low barrier Physisorbed CO 2 Bent CO 2 Monkey saddle Exothermic Carbon monoxide Figure S. 7. Geometries along the reaction path on TiO 2 QD surface S6

7 HCOOH (b) HCOOH Bulk QD CO 2 +2H CO+OH+H CO 2 +2H CO+OH+H Figure S. 8. Ternary energy diagram for the reaction pathways on anatase (101) bulk surface and (b) TiO 2 QD surface. On the bulk surface, formic acid (HCOOH) formation is an exothermic reaction while carbon monoxide (CO) formation is an endothermic reaction. Both HCOOH and CO formation encounter a significant energy barrier. For TiO 2 QD surface, both reactions are exothermic and the energy barrier is much smaller than that on the bulk surface. Figure S. 9. CO 2 - anion configuration at four-folder coordinated Ti atom (Ti 4 ) site of Ti-MCM41. DFT calculation predicts that the bending angle of and the O-Ti 4 distance of 1.92Å. DFT+U calculation predicts the bending angle of and the O-Ti 4 distance of 1.96 Å. S7

8 Top View (b) Side View Figure S. 10. TiO 2 ribbon structure, which is periodically repeated in one direction and surrounded by vacuum regions in other two directions. Blue box represents the periodic box of our simulation cell. S8

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