The Effect of Excess Electron and hole on CO2 Adsorption and Activation on Rutile (110) surface

CO2 capture and conversion into useful chemical fuel attracts great attention from many different fields. In the reduction process, excess electron is of key importance as it participates in the reaction, thus it is essential to know whether the excess electrons or holes affect the CO2 conversion. Here, the first-principles calculations were carried out to explore the role of excess electron on adsorption and activation of CO2 on rutile (110) surface. The calculated results demonstrate that CO2 can be activated as CO2 anions or CO2 cation when the system contains excess electrons and holes. The electronic structure of the activated CO2 is greatly changed, and the lowest unoccupied molecular orbital of CO2 can be even lower than the conduction band minimum of TiO2, which greatly facilities the CO2 reduction. Meanwhile, the dissociation process of CO2 undergoes an activated CO2− anion in bend configuration rather than the linear, while the long crossing distance of proton transfer greatly hinders the photocatalytic reduction of CO2 on the rutile (110) surface. These results show the importance of the excess electrons on the CO2 reduction process.

than the TiO 2 conduction band minimum (CBM) about 0.4 eV above the Fermi level 28 . Thus, such relatively high potential prevents the efficient electron transfer process from TiO 2 to CO 2 , which is a necessary for the photo-catalytic reduction reaction.
On the other side, several experiments have shown that the CO 2 can be triggered on the pure TiO 2 6,29 . The vibrational spectroscopic techniques have shown that CO 2 − anions is identified on pure TiO 2 surface, indicating electron can be transferred from TiO 2 to CO 2 23 . Additionally, Tan et al. found that CO 2 molecule can be activated by one electron and reduced to CO on the reduced rutile (110) surface based on scanning tunneling microscopy 30 . How to reconcile this paradox as most of the experimental results appear CO 2 can be converted, while lowest unoccupied molecular orbital (LUMO) value of CO 2 molecule is extremely high 28 . On the theoretical side, He et al. reported the CO 2 − anion is one of the important species on the charged anatase (101) surface, and the reduction of CO 2 into HCOOH or CO mainly it takes 2e − reaction on anatase TiO 2 (101) 31,32 . Thus, it is urgency to know how the excess electrons effect on the CO 2 adsorption and activation during the reduction process at the molecular level.
In this paper, we explore excess electrons effect on the structure and reactivity of CO 2 on the perfect and reduced rutile (110) by first-principles calculations. Spin moment and density calculations show that the CO 2 anion can exist in the TiO 2 (110) containing excess electrons, and a new configuration of CO 2 cation exists in the hole system. Furthermore, the electronic density of various CO 2 adsorptions show that the LUMO of CO 2 can be tuned by the excess electrons or hole. Especially, the LUMO of the activated CO 2 can even be lower than the TiO 2 CBM, which can effectively lower the reaction barrier. Our results show that the CO 2 activation and reduction processes on the rutile (110) surface are greatly affected by the excess electrons and holes.

Results
In the present study, we examine the effect of excess electrons on the CO 2 adsorption and activation on the perfect/reduced rutile (110) surfaces. We firstly focus on the role of excess electrons on the CO 2 adsorption configurations adsorbed on perfect rutile (110) surface. Later, intrinsic oxygen vacancy (O v ) defect is further explored. Further, we explore reaction pathway of CO 2 dissociation into CO on O v rutile (110) surface and mechanism involves photo-catalytic reduction of CO 2 to form a HCOOH.
The excess electrons effect on CO 2 adsorption on the perfect rutile (110) surface. In this section, we initially focus on the possible CO 2 adsorption configurations in the case of excess electrons on the perfect rutile (110) surface. Before discussing the detailed CO 2 adsorption, it should be emphasized that the linear molecular CO 2 is firstly physically adsorbed on the rutile (110) surface. And according to the previous our results 33 , the molecular CO 2 linearly adsorbed at five-fold Ti 5f in a tilted style is the most stable one. Based on this adsorption, the molecular CO 2 will undergo a translation into bend through activation or reduction. As a result, the molecular adsorbed CO 2 changes to the bend chemical adsorption. Five different binding configurations of CO 2 exist on rutile (110) surface. All possible adsorption configurations are examined, which are labeled as M 1 , C 1 , C 2 , I 1 and I 2 (see Fig. 1). M 1 is a physical adsorption, where the CO 2 linearly adsorbs at five-fold Ti 5f in a tilted style. Except M 1 , all other four C 1 , C 2 and I 1 , I 2 configurations are chemical adsorptions: In C 1 configuration, one O atom of CO 2 bonds to the fivefold Ti 5f , and the C atom of CO 2 interacts with the bridge oxygen, forming a bent CO 2 configuration; As for C 2 , the two O atoms of CO 2 adsorbs at two adjacent Ti 5f sites, and the C atom directly bonds with the O 3f atom of TiO 2 ; Quite similar to C 2 , the C atom of I 1 does not interact with surface oxygen atom; As for I 2 , the CO 2 adsorbs on the top of the bridging oxygen, forming a new C-O 2f bond.
In Fig. 2, the positive digit in the transverse axis represents the number of excess electron, while the negative digit denotes the number of hole. When the system does not contain any excess electron or hole, three different binding configurations of CO 2 on the perfect TiO 2 were identified after the geometry relaxation, namely M 1 , C 1 and C 2 . The others, I 1 and I 2 , are unstable. The corresponding binding energy shows that M 1 has the largest binding energy of − 0.23 eV as the system does not contain excess electron, which is a little smaller than the earlier reported pure PBE value of − 0.35 eV 33,34 . This is because PBE+U functional treats the d-orbital of Ti in a more localization.
As an electron is introduced to TiO 2 , I 1 can exist with a binding energy of 1.02 eV. Therefore, the CO 2 adsorption in I 1 is meta-stable. It should be noted that the same kind configuration is also reported on the anatase (101) surface, and the corresponding adsorption energy of CO 2 is 0.78 eV 31 , which is quite close the current one. When more electrons are included in TiO 2 , no new configuration appears, and the corresponding binding energy are also not sensitive to the number of excess electrons. When the TiO 2 surface is charged with holes, the configuration of I 2 can exist with a binding energy of − 0.05 eV.
The detailed geometrical parameters, net charge, and spin polarized moment of the CO 2 adsorption configurations are also calculated as shown in Table 1. Among these five states, the configurations of M 1 , C 1 and C 2 adsorbed on the perfect without excess electron or hole are chosen as they are not sensitive to the excess electrons. While the configurations of I 1 and I 2 are shown for the system containing one electron or hole. Compared with the single CO 2 molecule, the C-O bond length of CO 2 in M 1 is almost similar, and the ∠ O-C-O angle slightly decreases by 2.38°. The net charge and spin polarized moment of adsorbed CO 2 are the same to that of single CO 2 molecule. A keen look into the structures of the C 1 /C 2 , the C-O bond length in C 1 /C 2 increases by 0.08/0.14 Å, while the ∠ O-C-O bond angle decreases by 53.76/47.45°. In case of C 1 and C 2, owing to the strong interaction between the CO 2 and rutile (110) surface, charge transfer occurs from TiO 2 to CO 2 by about 0.29e − . The spin polarized moment of these two adsorbed CO 2 states is zero, demonstrating that there is no unpaired electron existing in both C 1 and C 2 .   As we mentioned above, when the system contains the excess electron, the I 1 becomes metastable. As for the I 1 , the relaxed geometric parameters (Ti-O, C-O and ∠ O-C-O) of I 1 and net charges are quite close to C 2 , but the spin polarized moment is 0.74 μ B , indicating an unpaired electron is located on the CO 2 forming a activated state of I 1 . The corresponding spin densities as shown in Fig. 3. The excess electron is mainly localized on the C atom of the CO 2 , suggesting that an excess electron is transferred from TiO 2 to CO 2 and to form a CO 2 − anion 31 . It should be mentioned that although this configuration is rather unfavorable, the extra electron is shown to be critical to stabilize this binding configuration. When it comes to I 2 , the C-O bond length is little elongated to 1.27 Å, and the ∠ O-C-O angle enormously decreases to 120.27°. The spin polarized moment is about 0.90 μ B , indicating an unpaired electron is located on CO 2 . Further spin density calculation demonstrates that the electron in I 2 is localized at the two O atoms instead of C atom in the CO 2 forming a activated CO 2 + cation as shown in Fig. 3, which is different from the previous reported result only forming CO 2 − state 31 . From the above results, we clearly observe that various CO 2 adsorptions appear on the perfect rutile (110) surface in the case of excess electrons or holes.   The corresponding binding energies, geometrical parameters, net charge, and spin polarized moment of the CO 2 adsorption on reduced TiO 2 are also summarized in Table 1 Further spin density calculation reveals that the electron is localized on the C atom of the CO 2 as shown in Fig. 3. Thus, the CO 2 in O v-2 indeed converts into an activated CO 2 − anion. Although O v-2 has a relatively lower binding energy than other configurations, the extra electron at "C" atom is crucial to stabilize the binding configuration.
It is well known that the LUMO value of an isolated CO 2 molecule is very high, and the electron is very difficult to transfer to the CO 2 molecule from the TiO 2 conduction band 3 . In order to know whether the above CO 2 adsorptions can affect the LUMO of CO 2 in the presence of excess electron or hole, the partial density of states (PDOS) of the adsorbed CO 2 is calculated. The results are shown in Fig. 5. As for M 1 , the LUMO value is located above the TiO 2 CBM onset by 3.4 eV. This value is in consistent with the estimated value of 3.5 eV by Indrakanti et al., and a little larger than the value of 2.3 eV by Tan et al. 3,30 .Thus, the electron in the TiO 2 CBM is rather difficult to be transferred to the CO 2 in molecular state. When the CO 2 is changed to bending adsorption configurations (C 1 and C 2 ), the localized LUMO of CO 2 molecule becomes delocalized state, and the LUMO onset shifts down to 2.3 eV. Therefore, the energy level can be modified by CO 2 adsorption mode. Whereas this value is still too large for the electron transfer from the TiO 2 conduction band to the CO 2 molecule. When the CO 2 adsorptions with the configurations of I 1 , I 2 , and O v-2 on TiO 2 (110) containing excess electron or hole, the PDOS shows the LUMO of CO 2 shifts further downward, which can even be lower than the TiO 2 CBM. Hence, the electron or hole can easily transfer from TiO 2 CBM to the CO 2 with I 1 , I 2 , and O v-2 .
Dissociation of CO 2 into CO on O v rutile (110) surface. As discussed above, the CO 2 adsorption on the O v rutile (110) surface can be activated, and the corresponding LUMO is even lower than TiO 2 CBM. Thus it is interesting to know how the CO 2 adsorption on O v rutile (110) can be further converted into the other species. The activation process can be expressed as: 2 2 From the equation (2), we can clearly observe that the activation of CO 2 process needs an excess electron in the system. Scanning tunneling microscopy experiment suggested that the conversion of CO 2 to CO is relative to  30 . However, the detailed dissociation of CO 2 mechanism at molecular level is still unknown. Here, we start the study from configuration O v-1 with intrinsic excess electrons in reduced TiO 2 , and the dissociation of CO 2 into CO are explored. The detailed reaction pathway and calculated energy barriers are shown in Fig. 6.
As shown in Fig. 6, the CO 2 molecule firstly adsorbs at the oxygen vacancy, forming the linear adsorption as O v-1 . In this step, there is no electron transfer from reduced TiO 2 to linear CO 2 , which is a different from the previous result where the linear CO 2 can form an electron attachment state 36 . Then, the linear adsorbed CO 2 molecule initiates to bent, which undergoes a transition state transition state 1 (TS1) with an energy barrier 1.12 eV to form O v-2 structure. Subsequently, the excess electron in the TiO 2 transfers to the CO 2 , forming CO 2 − anion (see Fig. 3). On the basis of CO 2 − anion, the C-O bond breaks to form CO, leaving an O atom at the oxygen vacancy site. The energy barrier of this process is about 0.61 eV. From the whole process, the CO formation undergoes an activation state of O v-2 rather than a direct C-O bond breaking of linear CO 2 .
Photo-catalytic reduction of CO 2 to form HCOOH. Apart from the CO formation in the reduced TiO 2 , photo-catalytic reduction of CO 2 can also form synthetic fuels such as formaldehyde (HCHO), formic acid (HCOOH), methanol (CH 3 OH), and methane (CH 4 ) on the TiO 2 based materials. However, the formation of these useful fuels through activated CO 2 is still rare, and most of the theoretical researches mainly focus on the anatase phase 32 . Here, on the basis of configuration I 1 , the reduction of CO 2 to form HCOOH is investigated, which can be expressed as:  (3) to (5), we can clearly understand that the reaction involves two electrons and two protons in the system. The complete reduction process can be divided into five steps as follows: The molecular CO 2 firstly adsorbs on the rutile (110) surface as C 1 ; Following this, excess electron injects into CO 2 , and the corresponding CO 2 becomes CO 2 − anion as I 1 ; Then, one proton and electron transfer to the CO 2 − anion, forming HCO 2 − ; Finally, the other proton transfers to HCO 2 − , forming HCOOH. According to the above reaction processes, the transition states and corresponding energy barriers of CO 2 reduction to HCOOH are summarized in Fig. 7. On the basis of configuration C 1 , the two O atoms of CO 2 begin to bend towards the adjacent fivefold Ti 5f in plane through TS1, the two O atoms of CO 2 is adsorbed by Ti 5f in nature as shown step-3 in Fig. 7. Consecutively, the electron spontaneously transfers to the CO 2 forming the CO 2 − anion. This process needs to overcome an energy barrier of 1.28 eV, which is much higher than the case in anatase (101) of 0.87 eV 32 . Consecutive proton and electron move to the "C" atom of CO 2 − anion to form HCO 2 − . These findings are very different from the case in anatase (101). In anatase case, proton transfer occurs with no energy barrier, but the proton transfer on rutile needs to overcome an energy barrier of 0.93 eV. The calculated energy barrier is relatively higher, because the proton should move about 3.10 Å between the adsorbed proton and the CO 2 − anion, which is larger than the one in anatase (about 2.60 Å). Further, the other proton moves to the "O" atom of HCO 2 − , resulting in HCOOH. This process needs a moderate energy barrier of 0.75 eV. From the complete reduction process, the formation of CO 2 − anion is the rate limiting step, and also the proton transfer step is much difficult than the earlier reported anatase (101) surface 32 . Activation of CO 2 by a hole. On the basis of configuration I 2 , the activation of CO 2 by the hole is also investigated, which can be expressed as: In the CO 2 activation process (Eq. 6), a hole is transferred to the O atom of CO 2 in configuration I 2 . The detailed reaction process and activation barrier of hole to CO 2 with I 2 are calculated (Fig. 8). The molecular CO 2 adsorbs on the top of bridge oxygen on TiO 2 with a C-O b distance of 2.71 Å. Then the C atom of the CO 2 moves towards the bridge-site oxygen. In the transition state geometry, the C-O b distance decreases from 2.71 Å to 1.74 Å. Finally, the "C" atom of CO 2 adsorbed with the bridge oxygen forming a bent like CO 2 , and the C-O b distance decreases to 1.34 Å. Simultaneously, the hole is transferred to the two "O" atoms of CO 2 forming a CO 2 + as shown in Fig. 3. Formation of cation need to overcome a relatively lower energy barrier (about 0.75 eV) than that of anions.

Discussions
In summary, by the first-principles calculations, structural and reactivity behavior of CO 2 on rutile TiO 2 are greatly affected by excess electrons. The computed results show that various CO 2 adsorption configurations appear in the case of excess electrons, and activated CO 2 adsorption configurations can be exist in the not only excess electron system as I 1 and O v-2 , but also in the hole system as I 2 . Further electronic density calculation shows that the LUMO of CO 2 can be modified by varying the CO 2 adsorption states, and it can even be lowered and below the TiO 2 conduction band. The detailed CO 2 activation and reduction processes are also explored. The mechanism of CO 2 reduction to CO on oxygen vacancy rutile (110) surface is revised, the reduction process involves the formation of CO 2 anion in bend type structure with an energy barrier of 1.12 eV. The results also suggest that, the energy barrier of rate limitation step to form HCOOH is about 1.28 eV. In addition, the process for the formation of CO 2 + cation in the hole system is also investigated, and it needs a much lower energy barrier of 0.75 eV.

Method
The calculations are performed based on the spin-polarized density functional theory (DFT) in periodic boundary conditions, as implemented in the CP2K/Quickstep package 37 . This simulation code employs hybrid Gaussian and plane wave (GPW) basis sets and norm conserving Goedecker-Teter-Hutter (GTH) pseudo-potentials to represent the ion-electron interactions 38,39 . The Gaussian functions consisting of a double-ζ plus polarization (DZVP) basis set was employed to optimize the structures 40 . The energy cutoff for the real space grid was 500 Ry, which yields total energies converged to at least 0.001 eV per atom. For the exchange-correlation functional, we have used the Perdew-Burke-Ernzerhof (PBE) functional of generalized gradient approximation (GGA) 41 . The Figure 7. Illustration of reaction pathway via I 1 configuration to form HCOOH. The sum of energies of the CO 2 and 2H is the zero reference for energy. The sign of " + " indicates non-interacting species (e.g. CO 2 + OH), and the transition state denotes by TS. vdW correction is considered with the Grimme approach (DFT-D3) 42 . Since the standard GGA functional has the limitation to calculate the d-band electrons of transition metal, GGA+U functional is used to treat Ti 3d electron with U = 4.2 eV 43 . In order to avoid the interaction between the adjacent images, a vacuum spacing of 15 Å is employed for all the systems. Transition states along the reaction pathways are searched by the Climbing Image Nudged Elastic Band (CI-NEB) approach 44 .
The interaction between the adsorbed molecule and the substrate, which can be characterized by the binding energy, which is defined as, where E ad/sub is the total energy of the molecule adsorbed on the substrate, E ad is the energy of the isolated molecule in the same box, and the E sub is the energy of the substrate. In the present study, a (4 × 2) supercell is used to represent rutile TiO 2 (110) substrate containing four tri-layers. In the rutile TiO 2 (110) features three types of under coordinated atoms: five-fold Ti ionic (Ti 5f ), bridge oxygen atom in two-fold (O 2f ), and planar three-fold oxygen atom (O 3f ). The excess electrons in the system are simulated by adding hydrogen atoms or hydroxyls, and one hydrogen/hydroxyl corresponds to one electron/hole 45 . All the CO 2 adsorption configurations studied in the text, only one CO 2 molecule is considered to adsorb on the (4 × 2) supercell, corresponding to 1/8 ML coverage.