Complexes in the Photocatalytic Reaction of CO2 and H2O: Theoretical Studies

Complexes (H2O/CO2, e–(H2O/CO2) and h+–(H2O/CO2)) in the reaction system of CO2 photoreduction with H2O were researched by B3LYP and MP2 methods along with natural bond orbital (NBO) analysis. Geometries of these complexes were optimized and frequencies analysis performed. H2O/CO2 captured photo-induced electron and hole produced e–(H2O/CO2) and h+–(H2O/CO2), respectively. The results revealed that CO2 and H2O molecules could be activated by the photo-induced electrons and holes, and each of these complexes possessed two isomers. Due to the effect of photo-induced electrons, the bond length of C=O and H-O were lengthened, while H-O bonds were shortened, influenced by holes. The infrared (IR) adsorption frequencies of these complexes were different from that of CO2 and H2O, which might be attributed to the synergistic effect and which could not be captured experimentally.


Introduction
Greenhouse gas CO 2 is the primary cause of global warming. The transformation from CO 2 to fuel-like hydrocarbon is becoming one of the most important areas of chemical research, which is not only for solving the urgent greenhouse effect, but also for finding a new approach to obtain energy.
As the Earth's ultimate power supply and an environmentally friendly energy source [1][2][3][4][5], light can activate reactants and promote a reaction. While the reduction of CO 2 with H 2 O is very difficult with thermal surface catalysis, photo stimulating surface catalysis is of great theoretical and practical value. Many researches [6] have shown that CO 2 could be reduced by water vapor or solvent with photocatalysts. Among these photocatalysts, TiO 2 or modified TiO 2 may promote the photoreduction of CO 2 to useful organic compounds [7][8][9][10][11][12][13], such as formate, carbon monoxide, methane and ethanol. The optical and electronic properties of nanostructured TiO 2 can be adjusted by thermal treatments [14], supported film growth [15], and metal-ion doping [16].
During our research on the reaction of H 2 O and CO 2 over photocatalysts, we found methanol as a product [17], which meant that there must be some advantageous factors for forming C-H bond in the reaction. The photocatalytic production of CH 4 from CO 2 and H 2 O on Pt/SrTiO 3 catalysts has also been reported by Hemminger et al. [18].
H 2 O may reduce CO 2 to CH 4 , CH 3 OH, and CO over the anchored titanium oxide catalysts at 323 K under UV irradiation [19]. A reaction scheme is proposed for the photocatalytic reduction of CO 2  . Incident photons are absorbed by TiO 2 , and photo-excited electrons (e -) and positive holes (h + ) are produced in the catalyst by charge transfer to the excited state of (Ti 3+ −O − )*. Furthermore, the photo-excited electrons and holes in the lattice are separated and trapped by appropriate sites of TiO 2 to avoid recombination. The interaction of CO 2 molecules with the excited state of (Ti 3+ −O − )* leads to the formation of CO   2 radicals [5]. The semiconductor (SC) bandgap excitation leads to the formation of conduction band electrons and valance band holes, which serve as the sites for photoreduction and photooxidation, respectively [13]. The photo-oxidation of H 2 O led to the formation of hydroxyl radicals OH and H + [14].
Photocatalytic reaction is the interaction between photo-inducted electrons and holes on the photocatalyst surface with reactants. In order to know the details of the interaction among the reactants, the photo-induced electrons and holes, and the situation of activated reactants, which were referenced by Inokuchi Y. et al. [20], we calculated the interaction between photo-induced electrons and holes with H 2 O/CO 2 as complexes. There are few reports on such complexes.

Computational Details
The geometries of H 2 O, CO 2 , CO   2 , H 2 O + , H 2 O/CO 2 , e-(H 2 O/CO 2 ) and h + -(H 2 O/CO 2 ) were respectively optimized and then they were analyzed by natural bond orbital (NBO) [21] using density functional theory (DFT) (with correcting coefficient 0.96 of vibrational frequencies) [22][23][24][25] at the B3LYP [26][27][28][29] level and Møller-Plesset (MP2 (with correcting coefficient 0.92) ) perturbation theory [30] on different basis sets. Among these basis sets, 6-311 g* [31,32] was employed in calculations as the optimal one. This work was carried out with the GAUSSIAN 03 program package [33]. CO 2 and H 2 O were activated by photo-induced electrons and holes, which was confirmed by the change of geometry structure parameters and the charge distribution. NBO atomic charges and dipole moments of CO 2 and H 2 O are listed in Table 1, and the geometrical parameters are shown in Figure 1. All these data indicated great changes in the optimum geometrical parameters of H 2 O/CO 2 , e-(H 2 O/CO 2 ) and h + -(H 2 O/CO 2 ) complexes. The interaction energies when the photo-induced electrons and the holes were also taken into account. The thermochemical parameters of the system are shown in Table 2. Herein

Geometric Parameters Analysis
As shown in Figures 1 and 2   Calculated structural parameters of e-HC -1 and e-HC -2 by B3LYP were different from that of CO 2 and H 2 O. The C=O bond was lengthened by 0.06-0.09 Å compared to that in CO 2 while approximately equal to that in CO   2 , and the length of H-O bond was also lengthened by 0.01-0.02 Å compared to that in H 2 O while it was shorter than that in H 2 O + . Therefore, CO 2 was activated and the repulsion force between C and O was strengthened. The bond angle A H-O-H was reduced by 7-17 degrees compared to that in H 2 O/CO 2 , while the bond length of H−O was 3.10 Å by MP2, which indicated the dissociation of the bond. The bond length of (CO 2 ) O···H was 1.89 Å, which was close to that of hydrogen bond. The photo-induced electron in e-HC -1 enhanced the activation of CO 2 and H 2 O. In e-HC -2 , the bond length of (H 2 O) O···C was 1.50 Å by B3LYP and 1.45 Å by MP2, which was close to the length of C−O bond. One of the H atoms of H 2 O was dissociated from the original bonding O atom. In h + -HC -1 , it was shown by B3LYP that one C−O bond length was shortened by 0.02 Å compared to that of CO 2 and the other was lengthened 0.02 Å. The short one was near the triple bond, which might lead to CO formation. At the same time the O atom of CO 2 may form a hydrogen bond with a length of 1.51 Å. The corresponding O-H bond was lengthened 0.07 Å. In h + -HC -2 , both C−O bonds were lengthened 0.05 Å, C···O (H 2 O) bond length was 1.57 Å, while both H−O bonds were lengthened 0.02 Å, and the bond angle of O−H−O was increased by about 6−10 degrees. On the other hand, by MP2, the calculated structural parameters of h + -HC -2 were much different than from B3LYP, which indicated that the h + -HC -1 complex was not as stable as h + -HC -2. This was consistent with the following thermochemistry data. The dipole moments of both h + -HC -1 and h + -HC -2 were about three-times greater than that of H 2 O/CO 2-1 and H 2 O/CO 2-2 when calculated by B3LYP, and even greater when calculated by MP2, which indicated the breaking of symmetry in both h + -HC -1 and h + -HC -2 .

NBO Atomic Charge Analysis
The natural electron configuration of the complexes, as shown in Table 1 The population of charge in e-(H 2 O/CO 2 ) was dispersed both by B3LYP and MP2. In e-HC -1 , there was 0.06 electrons on 3s orbital of C atom, 0.04 electrons on 3p orbital, and 0.01 electrons on 3d orbital by B3LYP. In e-HC -2 , 3s orbital of C atom gained 0.00 electron, 0.05 (0.04 electrons by MP2) electron on 3p orbital and 0.02 (0.03 electron by MP2) electrons on 3d orbital by B3LYP. The contribution to the hybrid orbital from 2s orbital and 2p orbital were different in e-HC -1 and e-HC -2 .
The particular natural electron configuration of a H atom in e-HC -2 indicated that the H atom was a free radical which had 1.12 (1.00 electron by MP2) electrons on its 1s orbital, and 0.01 electrons on the 2s orbital of another H atom for the joining of the photo-induced electron by B3LYP.
The population of the charge in h + -(H 2 O/CO 2 ) was dispersed. There was not so much difference in the charge distributions of h + -HC -1 and h + -HC -2 on the C atom and H atom by B3LYP, while the charge distribution of h + -HC -2 was higher than that of h + -HC -1 by MP2. The contribution of 2p orbital in O atom of h + -HC -1 and h + -HC -2 to the hybrid orbital was different. As for H 2 O/CO 2-1 and H 2 O/CO 2-2 , the population of the charge was almost the same by both calculating methods.
The total NBO charge distribution of the complexes is presented in Figures 1 and 2. The positive charge on C was 0.460 electrons in e-HC -1 , which was lower than that in e-HC -2 . The O atom of H 2 O in e-HC -1 obtained more negative charge than that of the others in both e-HC -1 and e-HC -2 H atom was negatively charged for the effect of the photo-induced electron, where the corresponding values for the isolated CO 

Thermochemistry Parameters Analysis
Thermochemistry parameters of the system are presented in Table 2. The interaction energies of CO 2 and H 2 O molecule including photo-induced electrons and corresponding holes were calculated using the following equations: T refers to the reaction temperature of our experiment 333 K [17]. H 2 O/CO 2-2 had the maximum value of the entropy (ΔS = -128.80 J/mol·K ) for its loose structure and poor symmetry. h + -HC -1 had the highest energy (ΔE tot = -84.70 KJ/mol) for the existence of dissociative H atom among the six complexes, while e-HC -2 had the minimum entropy (ΔS = -243.75 J/mol·K ) and the lowest energy (ΔE tot = 14.54 kJ/mol) compared to the other five for its relatively stable skeletal structure as well as its good symmetry by B3LYP. This result was different from that by MP2, where HC -1 and H 2 O/CO 2-2 had the maximum values of the entropy (ΔS = -264.23 J/mol·K) and h + -HC -1 had the highest energy (ΔEtot = -77.75 kJ/mol).
The enthalpy values of most of the six complexes were higher than that of the sum of CO 2 and H 2 O, the sum of CO 2 and H 2 O + , and the sum of H 2 O and CO   2 for the forming of new bond and radicals.
The Gibbs free energy values of most of the six complexes were lower than that of the sum of CO 2 and H 2 O, the sum of CO 2 and H 2 O + , and the sum of H 2 O and CO   2 , where the necessary energy for photo-induced electrons and holes to charge the reactants from the environment of the photoreaction system is available. It is interesting that the highest ΔG was in h + -HC -2 , which indicated the instability of h + -HC -1 . This was consistent with the structural parameters at the same level. No thermochemistry experimental data now for these complexes were available for the complicated photocatalytic reaction environment. Counterpoise calculations at the B3LYP/6-311G*//6-311++G** level and the MP2/6-311G*//6-311++G** level suggested that basis set superposition errors (BSSE) were nearly the same (2.09 kJ/mol) for all conformers. Since it is not clear that such corrections improved the reliability of the results [35][36][37][38][39][40], we did not included them in Table 2.  In h + -HC -2 by B3LYP the in-plane bending vibration of C=O was at 540.22 cm -1 , the stretching vibration of C···O at 601.69 cm -1 , and the synergistic effect of the asymmetrical stretching vibration of C=O at 722.74 cm -1 , the asymmetrical stretching vibration of H···O=C at 1012.45 cm -1 . While by MP2 the stretching vibration of C···O at 685.57 cm -1 , the scissoring rocking vibration of C=O at 511.11 cm -1 , and the symmetrical stretching vibration of C=O at 1334.48 cm -1 . It indicated that both the two calculating method revealed the unreasonable data to h + -HC -2 , therefore the complex was unstable, therefore h + -(H 2 O/CO 2 ) had only one stable structure h + -HC -1 .

Conclusion
The charge distribution of H 2 O and CO 2 was changed because of the joining of the photo-induced electrons and holes both by MP2 and by B3LYP. The effect from photo-induced electrons and holes in complexes activated H 2 O and CO 2 herein. H 2 O has been known to exist as -OH group on the surface of catalysts by our experiment and the literature [12]. H 2 O was activated for the lengthened O-H bond in h + -(H 2 O/CO 2 ). The possible hydrogen bond and CO in h + -(H 2 O/CO 2 ) indicated that the hole was advantageous during the photoreduction of CO 2 by H 2 O. The IR absorption of e-(H 2 O/CO 2 ) and h + -(H 2 O/CO 2 ) could not be captured experimentally, and some synergistic effect appeared in IR adsorption spectra which were consistent with the state of complexes and their geometric parameters, therefore the result of calculations revealed useful information for understanding the reaction system.
The results of calculations indicated that the action of photo-induced electrons and holes to H 2 O/CO 2 was stronger than the interaction between H 2 O and CO 2 , therefore CO 2 was activated in e-(H 2 O/CO 2 ) and h + -(H 2 O/CO 2 ), the bond length of R O=C lengthened in e-(H 2 O/CO 2 ), the charge on C and O changed greatly, the density of electron cloud on C strengthened in e-(H 2 O/CO 2 ), and the probability for C to combine with -OH or H increased, which might be favorable for forming CH 3 OH.