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Int J Mol Sci. 2010; 11(8): 2792–2804.
Published online 2010 July 29. doi:  10.3390/ijms11082792
PMCID: PMC2996739

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

Abstract

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.

Keywords: e–(H2O/CO2), h+–(H2O/CO2), photocatalytic reaction, theoretical studies

1. Introduction

Greenhouse gas CO2 is the primary cause of global warming. The transformation from CO2 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 [15], light can activate reactants and promote a reaction. While the reduction of CO2 with H2O is very difficult with thermal surface catalysis, photo stimulating surface catalysis is of great theoretical and practical value. Many researches [6] have shown that CO2 could be reduced by water vapor or solvent with photocatalysts. Among these photocatalysts, TiO2 or modified TiO2 may promote the photoreduction of CO2 to useful organic compounds [713], such as formate, carbon monoxide, methane and ethanol. The optical and electronic properties of nanostructured TiO2 can be adjusted by thermal treatments [14], supported film growth [15], and metal-ion doping [16].

During our research on the reaction of H2O and CO2 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 CH4 from CO2 and H2O on Pt/SrTiO3 catalysts has also been reported by Hemminger et al. [18].

H2O may reduce CO2 to CH4, CH3OH, 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 CO2 with H2O as follows: TiO2hνecb-(TiO2)+hνb+(TiO2). Incident photons are absorbed by TiO2, and photo-excited electrons (e-) and positive holes (h+) are produced in the catalyst by charge transfer to the excited state of (Ti3+–O)*. Furthermore, the photo-excited electrons and holes in the lattice are separated and trapped by appropriate sites of TiO2 to avoid recombination. The interaction of CO2 molecules with the excited state of (Ti3+–O)* leads to the formation of CO2•− 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 H2O led to the formation of hydroxyl radicals OH and H+ [14].

SChν>EgSC (hνb++ecb-)
(1)
H2O+hνb+H2O+OH+H+
(2)

The hydroxyl radicals generate oxygen while H+ ions form hydrogen by capturing conduction band electrons [15,16,18].

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 H2O/CO2 as complexes. There are few reports on such complexes.

2. Computational Details

The geometries of H2O, CO2, CO2•−, H2O+, H2O/CO2, e–(H2O/CO2) and h+–(H2O/CO2) 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) [2225] at the B3LYP [2629] 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]. CO2 and H2O 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 CO2 and H2O 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 H2O/CO2, e–(H2O/CO2) and h+–(H2O/CO2) 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.

Figure 1Figure 1
Optimized geometry structure and total NBO charge distribution of the complexes by B3LYP.
Table 1
Natural Electron Configuration of the complexes.
Table 2
Thermochemistry Parameters of Complexes.

Herein, H2O/CO2-1 refers to the complex of CO2 and H2O combined by O···H···O (probable hydrogen bond between CO2 and H2O, similarly hereinafter); H2O/CO2-2, complex of CO2 and H2O combined by C···O (probable bond between the carbon atom of CO2 and the oxygen atom of H2O, similarly hereinafter); e–HC−1, the complex of CO2 and H2O combined by O···H···O captured an electron; e–HC−2, the complex of CO2 and H2O combined by C···O captured an electron, h+–HC−1, the complex of CO2 and H2O combined by O···H···O captured a hole; (h+–HC−2), the complex of CO2 and H2O combined by C···O captured a hole.

3. Results and Discussion

3.1. Geometric Parameters Analysis

As shown in Figures 1 and and2,2, the geometrical parameters of all complexes revealed that bond lengths and bond angles were almost the same in H2O/CO2-1 and H2O/CO2-2. According to both B3LYP and MP2 method, the total dipole moments of H2O/CO2 was a little greater than that of H2O, indicating that the complex H2O/CO2 could not obviously change the properties of H2O and CO2 molecules.

Figure 2
Optimized geometry structure and total NBO charge distribution of the complexes by MP2.

Calculated structural parameters of e–HC−1 and e–HC−2 by B3LYP were different from that of CO2 and H2O. The C=O bond was lengthened by 0.06–0.09 Å compared to that in CO2 while approximately equal to that in CO2•− and the length of H-O bond was also lengthened by 0.01–0.02 Å compared to that in H2O while it was shorter than that in H2O+. Therefore, CO2 was activated and the repulsion force between C and O was strengthened. The bond angle AH-O-H was reduced by 7–17 degrees compared to that in H2O/CO2, while the bond length of H–O was 3.10 Å by MP2, which indicated the dissociation of the bond. The bond length of (CO2) 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 CO2 and H2O. In e-HC−2, the bond length of (H2O) 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 H2O 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 CO2 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 CO2 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 (H2O) 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 H2O/CO2-1 and H2O/CO2-2 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.

3.2. NBO Atomic Charge Analysis

The natural electron configuration of the complexes, as shown in Table 1, revealed the population of charges in H2O/CO2, which was different from that of H2O (O: 2s(1.75)2p(5.11)3d(0.01), H: 1s(0.56)) and CO2 (C: 2s(0.64)2p(2.31)3p(0.03)3d(0.02); O: 2s(1.72)2p(4.76)3d(0.01)). This was evidence for the formation of a London dispersion complex [34]. The natural electron configuration of CO2•− and H2O+ were shown as follows: the natural electron configuration of the C atom was 2s(0.97)2p(2.39)3s(0.06)3p(0.04)3d(0.01) and that of the O atom was 2s(1.74)2p(5.00) by B3LYP, while 2s(0.94)2p(2.20)3s(0.05)3p(0.04)3d(0.02) of the C atom and 2s(1.75)2p(5.12)3d(0.01) of the O atom by MP2 in CO2•− The natural electron configuration of the O atom was 2s(1.81) 2p(4.26) and that of the H atom was 1s (0.46) by B3LYP, while 2s(1.79)2p(4.28)3d(0.01) of the O atom and 1s(0.46) of the H atom by MP2 in H2O+.

The population of charge in e–(H2O/CO2) 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+–(H2O/CO2) 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−1and h+–HC−2 to the hybrid orbital was different. As for H2O/CO2-1 and H2O/CO2-2, 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 and2.2. 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 H2O in e–HC−1obtained more negative charge than that of the others in both e–HC−1and e–HC−2 H atom was negatively charged for the effect of the photo-induced electron, where the corresponding values for the isolated CO2•− and H2O+ are shown as follows: 0.513 e for C and −0.756 e for O by B3LYP while 0.753 e for C and −0.877 e for O by MP2 in CO2•− −0.070 e for O and 0.535 e for H by B3LYP, and −0.082 e for O and 0.541 e for H by MP2 in H2O+. It is interesting that the charge of O atom from H2O in h+–HC−1 was different from that in h+–HC−2 by both methods for different chemical environment around them. The unbalanced charge distribution of the two O atoms from CO2 in h+–HC−1 was because of the tendency to form hydrogen bond. This phenomenon also existed in H2O/CO2-2.

The total NBO charge distribution in H2O/CO2-2 was different from that of H2O (O: −0.870 e, H: 0.435 e), CO2 (C: 1.000 e, O: −0.500 e) and H2O/CO2-1 because of the interaction between C atom and O atom (from H2O). The greatest difference of the two calculating method is shown in e-HC−1and e-HC−2, especially for C and H atoms, while the tendency of the H dissociation was almost the same by B3LYP and MP2.

3.3. Thermochemistry Parameters Analysis

Thermochemistry parameters of the system are presented in Table 2. The interaction energies of CO2 and H2O molecule including photo-induced electrons and corresponding holes were calculated using the following equations:

ΔEHC=EHC-ECO2-EH2O
(3)
ΔEe-HC=Ee-HC-ECO2--EH2O
(4)
ΔEh+HC=Eh+HC-ECO2-EH2O+
(5)

In the equation (1), ΔEHC could represent the calculated interaction energy values of the sum of electronic and thermal energies (Etot), the sum of electronic and thermal enthalpies (H) and the sum of electronic and thermal free energies (G) of HC−1 and HC−2. In the equation (2) ΔEe–HC represents the same items of e–HC−1 and e–HC−2, and then in the equation (3) ΔEh+HC represents that of h+–HC−1 and h+–HC−2. The corresponding entropy values were calculated by the following equation:

ΔS=ΔH-ΔGT
(6)

T refers to the reaction temperature of our experiment 333 K [17].

H2O/CO2-2 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 (ΔEtot = −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 (ΔEtot = 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 H2O/CO2-2 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 CO2 and H2O, the sum of CO2 and H2O+, and the sum of H2O and CO2•− 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 CO2 and H2O, the sum of CO2 and H2O+, and the sum of H2O and CO2•−, 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 [3540], we did not included them in Table 2.

At the computational levels we employed, the skeletal bending vibration of CO2•− was at 711.03 cm−1, the symmetrical stretching vibration and the asymmetrical stretching vibration of C=O at 1277.34 cm−1 and 1621.78 cm−1 respectively by B3LYP, while the corresponding absorption frequencies of CO2•− by MP2 were at 689.17 cm−1, 1232.93 cm−1 and 1613.98 cm−1, respectively.

The infrared absorption spectra of complexes herein became more complicated for the interaction between H2O and CO2 and the effect of photo-induced electrons and holes as shown in Figures 3 and and4.4. In H2O/CO2-1, the asymmetrical stretching vibration of O–C[equivalent]O at 2342.28 cm−1 by B3LYP and 2261.42 cm−1 by MP2, respectively.

Figure 3
IR Spectrum of the complexes at B3LYP/6–311G* Level (GV 4). (a) H2O/CO2-1B; (b) H2O/CO2-2B; (c) e–HC−1B; (d) h+– HC−1B; (e) e–HC−2B; (f) h+– HC−2B.
Figure 4Figure 4
IR Spectrum of the complexes at MP2/6–311G* Level (GV 4). (a) h+–HC−2M; (b) H2O/CO2-2M; (c) h+–HC−1M; (d) e–HC−1M; (e) H2O/CO2-1M; (f) e–HC−2M.

There was no different infrared absorption between H2O/CO2-1 and H2O/CO2-2 by MP2. In e–HC−1, the stretching vibration of H–O (O–H···O=C) was at 3390.72 cm1 by B3LYP, and the other stretching vibration of H–O at 3590.40 cm−1, the scissoring rocking vibration of C=O at 710.40 cm−1, the symmetrical stretching vibration and the asymmetrical stretching vibration of C=O at 1253.76 cm−1 and 1648.32 cm−1, respectively. By MP2, the infrared absorption frequencies of e–HC−1 were somewhat red shifted. In e–HC−2, the stretching vibration of C···O was at 546.72 cm−1 by B3LYP, the symmetrical stretching vibration and the asymmetrical stretching vibration of C=O at 1242.24 cm−1 and 1782.72cm−1, respectively. There are many differences of which by MP2, the skeletal rocking vibration at 513.47 cm−1, the in-plane rocking vibration and the out-of-plane rocking vibration of H–O at 1137.10 cm−1 and 531.10 cm−1, respectively, the stretching vibration of H–O at 3525.12 cm−1, the in-plane bending vibration and the out-of-plane bending vibration of C=O at 765.76cm−1 and 805.19cm−1, the symmetrical stretching vibration and the asymmetrical stretching vibration of C=O at 1225.77 cm−1 and 1716.58 cm−1, the stretching vibration of C···O at 587.59 cm−1.

There are some synergistic effects in h+–HC−1 by B3LYP. The symmetrical stretching vibration of O···H–O was at 2182.68 cm−1, the out-of-plane bending vibration and the in-plane bending vibration of O–C[equivalent]O at 603.19 cm−1 and 612.05 cm−1, respectively, the symmetrical stretching vibration of O–C[equivalent]O at 1322.16 cm−1, the synergistic effect of the asymmetrical stretching vibration of O···H–O and O–C[equivalent]O at 2384.96 cm−1. While by MP2 in h+–HC−1, the out-of-plane bending vibration of O···H–O was at 538.36 cm−1, the symmetrical stretching vibration and asymmetrical stretching vibration of O–C[equivalent]O at 1356.56 cm−1 and 2275.21 cm−1. The asymmetrical stretching vibration of O···H–O was at 2507.93 cm−1, the stretching vibration of H–O at 3309.60 cm−1. 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+–(H2O/CO2) had only one stable structure h+–HC−1.

4. Conclusion

The charge distribution of H2O and CO2 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 H2O and CO2 herein. H2O has been known to exist as –OH group on the surface of catalysts by our experiment and the literature [12]. H2O was activated for the lengthened O–H bond in h+–(H2O/CO2). The possible hydrogen bond and CO in h+–(H2O/CO2) indicated that the hole was advantageous during the photoreduction of CO2 by H2O. The IR absorption of e–(H2O/CO2) and h+–(H2O/CO2) 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 H2O/CO2 was stronger than the interaction between H2O and CO2, therefore CO2 was activated in e–(H2O/CO2) and h+–(H2O/CO2), the bond length of RO=C lengthened in e-(H2O/CO2), the charge on C and O changed greatly, the density of electron cloud on C strengthened in e–(H2O/CO2), and the probability for C to combine with –OH or H increased, which might be favorable for forming CH3OH.

Acknowledgement

Financial supports of Natural Science Foundation of Jiangxi Province, China (2007GZH2643) is gratefully acknowledged.

References

1. Subrahmanyam M, Kaneco S, Alonso-Vante N. A Screening for the Photo Reduction of Carbon Dioxide Supported on Metal Oxide Catalysts for C1–C3 Selectivity. Appl. Catal. B. 1999;23:169–174.
2. Tseng IH, Chang WC, Wu JCS. Photoreduction of CO2 Using Sol-Gel Derived Titania and Titania-Supported Copper Catalysts. Appl. Catal. B. 2002;37:37–48.
3. Xie TF, Wang DJ, Zhu LJ, Li TJ, Xu YJ. Application of Surface Photovoltage Technique in Photocatalysis Studies on Modified TiO2 Photo-catalysts for Photo-reduction of CO2. Mater. Chem. Phys. 2001;70:103–106.
4. Linsebigler AL, Lu GJ, Yates JT. Photocatalysis on TiO2 Surfaces: Principles, Mechanisms, and Selected Results. Chem. Rev. 1995;95:735–758.
5. Sasirekha N, Basha S, Shanthi K. Photocatalytic Performance of Ru Doped Anatase Mounted on Silica for Reduction of Carbon Dioxide. Appl. Catal. B Environ. 2006;62:169–180.
6. Yamashita H, Fujii Y, Ichihashi Y, Zhang SG, Ikeue K, Park DR, Koyano K, Tatsumi T, Anpo M. Selective Formation of CH3OH in the Photocatalytic Reduction of CO2 with H2O on Titanium Oxides highly Dispersed within Zeolites and Mesoporous Molecular Sieves. Catal. Today. 1998;45:221–227.
7. Zhang SG, Fujii Y, Yamashita K, Koyano K, Tatsumi T, Anpo M. Photocatalytic Reduction of CO2 with H2O on Ti-MCM-41 and Ti-MCM-48 Mesoporous Zeolites at 328 K. Chem. Lett. 1997;7:659–660.
8. Rasko J, Solymosi F. Infrared Spectroscopic Study of the Photoinduced Activation of CO2 on TiO2 and Rh/TiO2 Catalysts. J. Phys. Chem. 1994;98:7147–7152.
9. Lin WY, Han HX, Frei H. CO2 Splitting by H2O to CO and O2 under UV Light in TiMCM-41 Silicate Sieve. J. Phys. Chem. B. 2004;108:18269–18273.
10. Anpo M, Yamashita H, Ikeue K, Fujii Y, Zhang SG, Ichihashi Y, Park DR, Suzuki Y, Koyano K, Tatsumi T. Photocatalytic Reduction of CO2 with H2O on Ti-MCM-41 and Ti-MCM-48 Mesoporous Zeolite Catalysts. Catal. Today. 1998;44:327–332.
11. Anpo M, Yamashita H, Ichihashi Y, Fujii Y, Honda M. Photocatalytic Reduction of CO2 with H2O on Titanium Oxides Anchored within Micropores of Zeolites: Effects of the Structure of the Active Sites and the Addition of Pt. J. Phys. Chem. B. 1997;101:2632–2636.
12. Anpo M, Yamashita H, Ichihashi Y, Ehara S. Photocatalytic Reduction of CO2 with H2O on Various Titanium Oxide Catalysts of Special Interest. J. Electroanal. Chem. 1995;396:21–26.
13. Xu YJ, Chen FM, Jiang L, Zhou LD. Photoreduction of CO2 in the Suspension System of Semiconductor Catalyst TiO2 Modified by Palladium. Photogr. Sci. Photochem. 1999;17:61–65.
14. Banfield JF, Navrotsky A. Reviews in Mineralogy and Geochemistry. Mineral. Soc. Am. 2001;44:293–349.
15. Huang D, Xiao ZD, Gu JH, Huang NP, Yuan CW. TiO2 Thin-Films Formation on Industrial Glass through Self-Assembly Processing. Thin Solid Films. 1997;305:110–115.
16. Li W, Shah SI, Hunag CP, Jung O, Ni C. Metallorganic Chemical Vapor Deposition and Characterization of TiO2 Nanoparticles. Mater. Sci. Eng. B. 2002;96:247–253.
17. Luo DM, Chen C, Zhang N, Hong SG, Wu HW, Liu ZH. Characterization and DFT Research of Nd/TiO2: Photocatalyst for Synthesis of Methanol from CO2 and H2O. Z. Phys. Chem. 2009;223:1470–1476.
18. Hemminger JC, Carr R, Somorjai GA. The Photoassisted Reaction of Gaseous Water and Carbon Dioxide Adsorbed on the SrTiO3 (111) Crystal Face to form Methane. Chem. Phys. Lett. 1978;57:100–104.
19. Ikeue K, Nozaki S, Ogawa M, Anpo M. Characterization of Self-standing Ti-containing Porous Silica Thin Films and Their Reactivity for the Photocatalytic Reduction of CO2 with H2O. Catal. Today. 2002;74:241–248.
20. Inokuchi Y, Kobayashi Y, Muraoka A, Nagata T, Ebata T. Structures of water-CO2 and methanol-CO2 cluster ions: [H2O•(CO2)n]+ and [CH3OH•(CO2)n]+ (n = 1–7) J. Chem. Phys. 2009;130:1–12. [PubMed]
21. Hohenberg P, Kohn W. Inhomogeneous Electron Gas. Phys. Rev. B. 1964;136:B864–B871.
22. Kohn W, Sham LJ. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965;140:A1133–A1138.
23. Gerratt J, Mills IM. Force Constants and Dipole-Moment Derivatives of Molecules from Perturbed Hartree–Fock Calculations. J. Chem. Phys. 1968;49:1719–1729.
24. Pulay P. Second and Third Derivatives of Variational Energy Expressions-application to Multi-configurational Self-consistent Field Wave-functions. J. Chem. Phys. 1983;78:5043–5051.
25. Vosko SH, Wilk L, Nusair M. Accurate Spin-dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis. Can. J. Phys. 1980;58:1200–1211.
26. Lee CT, Yang WT, Parr RG. Development of the Colle-Salvetti Correlation-energy Formula into a Functional of the Electron Density. Phys. Rev. B. 1988;37:785–789. [PubMed]
27. Becke AD. Density-functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993;98:5648–5652.
28. Becke AD. Density-functional Exchange-Energy Approximation with Correct Asymptotic Behaviour. Phys. Rev. A. 1988;38:3098–3100. [PubMed]
29. McLean AD, Chandler GS. Contracted Gaussian-basis Sets for Molecular Calculations. 1. 2nd Row Atoms, Z = 11–18. J. Chem. Phys. 1980;72:5639–5648.
30. M[slash in circle]ller C, Plesset MS. Note on an Approximation Treatment for Many-electron Systems. Phys. Rev. 1934;46:618–622.
31. Krishnan R, Binkley JS, Seeger R, Pople JA. Self-Consistent Molecular Orbital Methods. 20. Basis set for Correlated Wave-functions. J. Chem. Phys. 1980;72:650–654.
32. Frisch MJ. Gaussian 94. Gaussian; Pittsburgh, PA, USA: 1995. Revision E.2.
33. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA, Jr, Vreven T, Kudin KN, Burant JC, et al. Gaussian 03. Gaussian Inc; Wallingford, CT, USA: 2004. Revision E.01.
34. Li Z, Wang L, Ran H, Xie D, Blinov N, Roy PN, Guo H. Path integral Monte Carlo study of CO2 solvation in 4He clusters. J. Chem. Phys. 2008;128:224513:1–224513:7. [PubMed]
35. DelBene JE. Ab initio Molecular Orbital Study of the Structures and Energies of Neutral and Charged Bimolecular Complexes of Water with the Hydrides AHn (A = nitrogen, oxygen, fluorine, phosphorus, sulfur, and chlorine) J. Phys. Chem. 1988;92:2874–2880.
36. Binkley JS, Pople JA. M[slash in circle]ller-Plesset Theory for Atomic Ground State Energies. Int. J. Quantum Chem. 1975;9:229–236.
37. Feller D. Application of Systematic Sequences of Wave-functions to the Water Dimer. J. Chem. Phys. 1992;96:6104–6114.
38. Kim KS, Mhin BJ, Choi US, Lee K. Ab-initio Studies of the Water Dimer using large Basis set: The Structure and Thermodynamics Energies. J. Chem. Phys. 1992;97:6649–6662.
39. Szalewicz K, Cole SJ, Kolos W, Bartlett RJ. A Theoretical Study of the Water. Dimer Interaction. J. Chem. Phys. 1988;89:3662–3673.
40. Frisch MJ, DelBene JE, Binkley JS, Schaefer HF., III Retical Studies of the Hydrogen-bonded Complexes (H2O)2, (H2O)2H+, (HF)2, (HF)2H+, F2H, and (NH3)2. J. Chem. Phys. 1986;48:2279–2289.

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