DFT Modeling of CO2 Adsorption and HCOO• Group Conversion in Anatase Au-TiO2-Based Photocatalysis.

Due to the merits of carbon circulation and hydrocarbon production, solar-assisted photocatalysis has been regarded as an ideal option for securing a sustainable future of energy and environment. In the photocatalytic carbon cycle process, surface reactions including the adsorption of CO2 and the conversion of CO2 into CH4, CH3OH, etc. are crucial to be examined ascribed to their significant influence on the performance of the photocatalysis. Because the conversion reaction starts from the formation of HCOO•, the density functional theory (DFT) model was established in this study to investigate the micromechanism of CO2 adsorption and the conversion of CO2 to HCOO• group in the anatase Au-TiO2 photocatalytic system. The CO2 adsorption bonding in six configurations was simulated, on which basis the effects of the proportion of water molecules and the lattice temperature increase due to the local surface plasmon resonance (LSPR) on the photocatalytic CO2 adsorption and conversion were specifically analyzed. The results show that the experimental conditions that water molecules are released before CO2 are favorable for the formation of the adsorption configuration in which HCOO• tends to be produced without the need of reaction activation energy. This is reasonable since the intermediate C atoms do not participate in bonding under these conditions. Moreover, Au clusters have an insignificant influence on the adsorption behaviors of CO2 including the adsorption sites and configurations on TiO2 surfaces. As a result, the reaction rate is reduced due to the temperature increase caused by the LSPR effect. Nevertheless, the reaction maintains a very high rate. Interestingly, configurations that require activation energy are also possible to be resulted, which exerts a positive influence of temperature on the conversion rate of CO2. It is found that the rate of the reaction can be improved by approximately 1-10 times with a temperature rise of 50 K above the ambient.

Introduction

In recent years, inspired by the carbon sequestration by the photosynthesis of green plants, artificial photosynthesis, which utilizes solar energy based on photocatalysts to enable the conversion of CO2 into methanol, methane, and other hydrocarbon fuels, has become a research hotspot in the field of frontier science and technology.[1−4] On the one hand, the increasingly severe environmental problems caused by the greenhouse effect can be partly resolved using the photocatalytic technology.[5,6] On the other hand, energy crisis and carbon reduction issues can be effectively alleviated due to the value-added hydrocarbon fuels through catalytic hydrogenation.[7,8] Therefore, the emerging photocatalytic technology is of significance to achieve a clean and sustainable future, which fulfills the goal of carbon neutrality.[9]

In the process of photocatalytic carbon cycle, surface reaction is an important factor to be considered for the evaluation of efficiency. However, the reaction is based on the adsorption of CO2 molecules on the catalyst surface.[10,11] With no adsorption of molecules, the catalytic reaction cannot be activated. Therefore, it is crucial to study the adsorption behaviors of CO2 on the surface of the photocatalyst.

In anatase TiO2, the (101) surface is the most stable and the most exposed surface. Comparatively, the anatase (001) surface has the advantage of higher catalytic activity despite relatively weaker features in stability and exposure area. Consequently, the anatase (001) surface has been widely involved in photocatalytic studies.[12] For example, Vittadini et al.[13] investigated the dissociation behavior of molecules on (001) surfaces using the density functional theory (DFT). It was reported that the (001) surfaces were ideal sites for water to be dissociated. In addition, Ye et al.[14] successfully prepared TiO2(001), (101), (010) surfaces and studied the catalytic reduction of CO2 to CH4 when the exposure ratio of these three surfaces reached 90%. According to the fluorescence spectra, it was speculated that the electron–hole separation ability of the (001) surfaces was stronger than the other two crystal faces.

In the specific adsorption process, CO2 molecules are first adsorbed on the (001) surface to absorb photogenerated electrons for the formation of HCOO•. As the first step of the conversion, it is necessary to be examined as it is the basis of the subsequent reactions that convert the intermediates into hydrocarbon fuels such as CO, CH4, CH3OH, and HCOOH, affecting the whole reaction rate. It is worth mentioning that a series of subsequent reactions occur with the participation of water, which is oxidized by photogenerated holes to produce O2. Apparently, there is certain competition between the water reduction and the CO2 reduction in this step,[15] which is a unique step of photocatalytic reduction of CO2 compared with others. Moreover, input energy is required to activate the reaction since the structure of CO2 is highly stable and inert. As reported, the first-step reaction can only be realized at the potential of −1.05 eV, which is difficult to happen spontaneously without the addition of energy to overcome the reaction barrier in the uphill process. Nevertheless, CO2 tends to be activated as a strong electron acceptor under the condition that hot electrons are promptly provided.

As a feasible approach, the local surface plasmon resonance (LSPR) effect can be utilized to generate hot electrons for the activation of CO2. This is because significant surface heating by LSPR enables the molecules to overcome the high potential barriers in photocatalytic reactions.[16] The LSPR effect can be formed by loading Au, Ag, and other particles on TiO2. With the combined effect of LSPR and the thermal confinement in the nano volume, the lattice temperature can be augmented in a few picoseconds as a result of the coupling of hot electrons and metal lattice phonons.[17,18] Jain et al.[19] studied the effect of femtosecond laser heating on gold nanoparticles attached to DNA ligands via thiol groups. The results showed that a Au–S bond could be destroyed, which was proven by the SPR peak shift of the Au NP.

In this study, the adsorption of CO2 on a Au-TiO2 porous catalyst was considered based on a newly established model based on the density functional theory (DFT) for the LSPR-supported photocatalysis. The micromechanism of CO2 adsorption bonding in six configurations was studied. In addition, the effects of the proportion of water molecules and lattice temperature on CO2 adsorption and conversion in the anatase Au-TiO2 photocatalytic system were specified.

DFT Modeling for CO2 Adsorption and Conversion

The first-principles method based on DFT was used in the simulation. Since the periodic solid system on the surface of TiO2 was considered, the periodic boundary conditions and the plane-wave basis set were applied. In the specific calculation, Vienna Ab initio Simulation Package (VASP) and the generalized gradient approximation (GGA) were adopted to describe the system. Moreover, the exchange-correlation interaction of the system was described by PBE functional.[20] For the description of the electron in the nucleus of the system, the pseudopotential method and PAW were used to approximate the inner electrons and check the role of valence electrons. The expansion of the wave function was controlled by the plane-wave base set, the size and energy of which were truncated. For structural optimization, the truncation energy of the plane-wave basis set was 400 eV.[21] A plane-wave base set with truncation energy as twice as that of the optimized structure was used to perform high-precision electronic step self-consistent calculation. The conditions for the end of structural optimization were that the force of all nuclei was less than 0.01 eV/A. The conditions for the end of the electron self-consistent cycle were that the total energy difference between the two steps was less than 1.0 × 10–6 eV. The reciprocal space was sampled with (2 × 2 × 1) k-point meshes. Periodic boundary conditions were set to simulate the surface of TiO2 using supercells.[22] The (110) direction was defined as the X direction, the (010) direction was defined as the Y direction, and the (001) direction was defined as the Z direction in the model. In the X and Y directions, the periodic expansion was assumed to be infinite, while in the Z direction, a vacuum layer with a thickness of 15 Å was inserted for the periodic expansion. During the structural optimization, other atoms in the bulk phase were fixed and the O–Ti–O atomic layer on the surface of (001) was released for the relaxation to the equilibrium position. Therefore, the slab model of the anatase TiO2(001) surface was obtained, which was conducive to the description of plane waves.[23]

First, the crystal plane model of anatase phase TiO2(001) was established, as shown in Figure . The Ti atom in the bulk phase is 6-fold coordination, while the O atom is 3-fold coordination. Suspend bond exists when the TiO2 crystal plane is peeled off from the solid-phase titanium dioxide; therefore, the unsaturated bond can be observed. The atoms on the TiO2(001) crystal plane are divided into five-coordination Ti atom, two-coordination O atom, and three-coordination O atom, which are expressed as Ti*5c, O*2c, and O3c, respectively. Herein, the stars represent unsaturated O and Ti atoms.

Figure 1

Crystal faces and atomic coordination relations of anatase TiO2(001).

To further understand the reactive activity of TiO2(001), the surface electrostatic potential distribution was plotted, as shown in Figure . It can be seen from the figure that the electrostatic potential of O*2c is larger than that of O3c. This shows that the reactive activity of O*2c on the TiO2(001) surface is comparatively higher. It has also been observed in the simulation that when the initial CO2 molecule is placed above O*2c, the adsorption configuration of C (CO2) bonded to the surface O*2c will be formed after the geometric optimization, as shown in Figure . The (b)–(d) configurations, with higher binding energies, belong to chemisorption. When the initial CO2 molecule is placed above O3c, the linear physisorption configuration (f) as shown in Figure will be formed after the geometric optimization. The corresponding binding energy is calculated as 0.603 eV, which is far smaller than other chemical adsorption configurations. Therefore, when the reactant is adsorbed on the TiO2(001) surface, the hydrogen atom in the hydroxyl group will first bond with O*2c.

Figure 2

Surface electrostatic potential distribution of TiO2(001).

Figure 3

Adsorption configuration of CO2 on TiO2 surface: (a) linear chemisorption (η1); (b) monodentate carbonate (η1); (c) bidentate carbonate (η2); (d) bridged carbonate (μ3−η3); (e) bridged configuration (μ2−η2); (f) linear physisorption.

The CO2 adsorbed on the crystal face of anatase phase TiO2(001) has different configurations. In this simulation, six models were established for the CO2 adsorption, which determines the different adsorption energy of the system, as shown in Figure .[10,24,25] The first one is that the CO2 molecule is linearly adsorbed (η1) on the surface via the Oa atom (a). The second is that the CO2 molecule is absorbed via the C atom to generate a monodentate carbonate (η1) species (b). In the third, a bidentate carbonate (η2) species is generated through the interaction of a CO2 molecule with the surface via both the Oa and C atoms (c). The fourth is the generation of a bridged carbonate (μ3−η3) geometry with the C atom of CO2 pointing downward, forming a C–O bond; and two O atoms of CO2 bind with two metal atoms to form a Ti–O bond with the Ti atom on the surface (d). In the fifth, a bridged configuration (μ2−η2) with the C atom of CO2 pointing upward and two O atoms of CO2 binding with two metal atoms is formed (e). The presence of a Ti–O–Ti bond on the surface is contributed to the formation of the fourth or fifth model. The sixth is a linear physisorption that is not bonded (f). In the chemisorption configurations, they all have the common characteristic that C in CO2 bonds with O*2c in TiO2, and O in CO2 bonds with Ti in TiO2. The dividing line between physisorption and chemisorption of CO2 on the anatase TiO2(001) surface is approximately 2.4 Å above Ti5c on the surface of TiO2.

Results and Discussion

Bond Length, Bond Angle, and Adsorption Energy

The bond lengths, bond angles, and adsorption energies of CO2 before and after adsorption in the six adsorption configurations are given in Tables and 2. The adsorption energies are all negative (1), indicating that the adsorption process is exothermic and the adsorption structure is stable. In configurations (a)–(e), molecules form chemical bonds with the surface to reduce energy, leading to relatively stable chemisorption. In comparison, configuration (f) belongs to physisorption, with the adsorption energy significantly lower than that of the chemisorption.

Table 1

CO2 Parameters before Adsorption

CO2 bond angle before adsorption (deg)	CO2 bond length before adsorption (Å)
180	1.18, 1.18

Table 2

CO2 Parameters after Adsorption

	adsorption configurations	CO2 bond angle after adsorption (deg)	CO2 bond length after adsorption (Å)	adsorption energy Ead (eV)
(a)	linear chemical adsorption (η1)	170.344	1.259, 1.297	–3.75
(b)	monodentate carbonate (η1)	136.808	1.266, 1.266	–4.61
(c)	bidentate carbonate (η2)	136.026	1.225, 1.281	–4.36
(d)	bridged carbonate (μ3−η3)	139.722	1.267, 1.267	–5.57
(e)	bridged carbonate (μ2−η2)	140.214	1.267, 1.267	–4.01
(f)	linear physisorption	179.226	1.179, 1.181	–0.60

In the bending adsorption configurations of (b), (c), (d), and (e), it is found that the bond angle after adsorption decreases significantly compared with that before adsorption, which is roughly between 135 and 140°. The bond length of CO2 increases significantly and is approximately 1.26 Å after the adsorption process. In the linear physisorption configuration F, the bond length barely changes after the adsorption. In contrast to the linear chemisorption, the bond angle is between the linear adsorption configuration and the curved configuration, which is slightly curved compared with the completely linear adsorption. This indicates that the chemical bonding on the surface of CO2 and TiO2 causes the redistribution of CO2 charge. It breaks the original stable high symmetry of CO2, which causes the electron cloud arrangement to converge to one side, thus causing slight local deformation on the surface of TiO2.

Bonding Mechanism Analysis

CO2 forms two stable π34 delocalized bonds. Each π bond has two π electrons located on the lower bonding delocalized π orbital π(2px)1 or π(2py)1, and the other pair of π electrons are located on the higher nonbonding molecular π orbital π(2px)2 or π(2py)2, i.e., half-full, which shows that it has a certain electron giving ability and a certain electron receiving ability. The first ionization energy (13.79 eV) of CO2 is significantly larger than that of the isoelectronic configuration of COS, CS2, and N2O; therefore, it is relatively difficult for CO2 to give electrons. However, CO2 is more receptive to electrons because of its lower half-full orbital (2π) and higher electron affinity (38 eV). The bond delocalization π orbitals are composed of two 2p orbitals provided by two O atoms.

After the adsorption, the internal bond length of CO2 changes from 1.18 to 1.26 Å, and the covalency of the internal bond is weakened and the ionicity is enhanced. Figure shows the sp hybrid orbital (σ orbital) and 1π orbital (highest energy occupied molecular orbital, HOMO) of CO2 before adsorption and the 2π* orbital (lowest energy unoccupied molecular orbital, LUMO) peak at the Fermi level. After the adsorption, hybridization occurs between the Ti-d and O-p orbitals, indicating that the bonding happens between the Ti-d and O-p orbitals. However, the 2π* orbital shifts to the left due to the gain of electrons because Ti atoms give the d orbital electrons back to the 2π* antibonding orbital of CO2 (Figure ), which strengthens the degree of wave function offset between the CO2 antibonding orbital and the bonding orbital. Consequently, the internal bonding of CO2 is weakened and the internal bond length of CO2 becomes longer.

Figure 4

Partial density of states of CO2 before and after adsorption.

Figure 5

Outer electron orbital cloud (d orbital) of Ti atoms.

As the surface of titanium dioxide is irradiated by light, electron–hole pairs are generated. The electrons and holes migrate to different positions on the surface of TiO2, and REDOX reactions occur with the substances adsorbed on the surface of TiO2.[26][26] When an electron is transferred to the lowest unoccupied molecular orbital (LUMO) of CO2, CO2 is reduced to CO2•- species. At this point, the bond angle of CO2 decreases from 180° due to the repulsion between the two unshared electron pairs on the oxygen atom and the unshared electron pairs on the carbon atom.[27] For example, the bond angle of the bent configuration (b)–(e) mentioned above is approximately 135–140°. Before adsorption, the energy gap between HOMO (highest molecular vacant orbital) and LUMO of CO2 is as large as 13.7 eV, and the reduction potential of CO2 molecule is a negative value of 0.6 ± 0.2 eV. Therefore, the chemical properties of CO2 are relatively stable. As electrons are transferred to the LUMO, the gap between HOMO and LUMO decreases, and the excitation of electrons from HOMO to LUMO becomes easier. Consequently, the reaction energy barrier is reduced, and the reactivity is improved.[28,29] Therefore, the CO2 reduction adsorbed on the surface of the photocatalyst is extremely important. As multiple electrons migrate from the interior of the photocatalyst to the surface, the electrons and the corresponding number of protons are possible to participate in the reaction. For example, the formation of CH4 requires eight electrons and eight protons. Therefore, the process of photocatalytic CO2 reduction to generate organic compound fuel is bound to involve a multicomponent reaction. It is speculated that the regulation of thermochemical reduction potential exerts a significant effect on the generation of hydrocarbon fuels. This can be achieved by the selection of photocatalyst preparation and variations of reaction conditions. Typically, there are two common CH4 formation pathways[30](i) CO2 → HCOO• → HCHO → CH3OH → CH4and(ii) CO2 → CO → C• → CH2 → CH4However, it is worth mentioning that the reaction could be multipath due to the combined influence of multiple factors as mentioned above. For this reason, the first step of CO2 transformation to the HCOO• group in the first reaction path was simulated using the established model.

Influence of the Ratio of Water Molecules

It can be seen from Figure that the HCOO• group is obtained by connecting the H atom to the C atom. The linear CO2 molecule is extremely stable and contains two C=O double bonds. The bond energy of the C=O double bond is 750 kJ/mol. The reduction of CO2 starts from the formation of HCOO•.[10,25] However, this process can only be realized at the potential of −1.05 V, which is difficult for many semiconductors to be fulfilled. Therefore, the first-step reaction is the main factor limiting the reaction rate.

Figure 6

Diagram of CO2 conversion to the HCOO• group.

First, the wettability needs to be introduced to the surface of TiO2. In previous studies on the molecular adsorption of water, the oxygen atom of the water molecule binds to a Ti5c atom, while in dissociative adsorption, there is an additional proton transferring from the chemisorbed water molecule to a bridging surface O2c atom in the adjacent row.[31] This type of dissociative adsorption can lead to the cleavage of Ti5c–O2c bonds on anatase (001), by the formation of Ti–OH (H2O) bonds and O (TiO2)–H (H2O) bonds, as shown in Figure . Here, H atoms on the surface O2c and OH groups on the surface Ti5c are directly connected.

Figure 7

Dissociative adsorption of H2O on the TiO2 surface.

Then, different adsorption configurations were introduced to optimize the adsorption structure. As a consequence, the configurations of CO2 and H2O molecules were obtained. The effect of the ratio of CO2 and water molecules on adsorption was studied by changing the ratio of CO2 and water molecules (3:1, 2:1, 1:1, 1:2, 1:3).

In the adsorption of water, there are four basic conclusions as follows: first, H of water will form a hydrogen bond with O of TiO2, thus occupying this adsorption site, increasing the difficulty of bonding between C (CO2) and O (TiO2); second, H of water will form a hydrogen bond with O of CO2, thus increasing the difficulty of bonding O (CO2) with Ti; third, O of hydroxyl will bind to the Ti on the surface, reducing the configuration of Ti bonding with CO2; fourth, O of hydroxyl will combine with C (CO2) to form −OOCOH, thus reducing the adsorption configuration of C (CO2) to participate in bonding.

The effect of the H atom implies that the bridge carbonate adsorption configuration (d) of CO2 on the dry surface may be transformed into bidentate carbonate η2 (c) and monodentate carbonate η1 (b) in the presence of water molecules. Part of the effect of increasing the proportion of water molecules is that it increases the probability that water will form hydrogen bonds with O in CO2. The premise of this discussion is that CO2 first approaches the O2c point on the surface of TiO2, which may correspond to the actual conditions that CO2 is first released prior to that of water. However, under the condition that CO2 and water also compete for Ti adsorption sites, the occurrence probability of adsorption configurations without C bonding with TiO2 surface may increase, including linear chemisorption η1 (a), bridged carbonate μ2−η2 (e), linear physisorption (f), etc. In the reaction path of CO2 to CH4, the first step involves the bonding of C; therefore, the exposed adsorption configuration of C (i.e., the reaction conditions under which CO2 and water are released simultaneously or water is released before CO2) may be favorable for this subreaction.

However, it should be noted that hydrogen bonds formed by H atoms are weaker than those formed by C(CO2) and Ti and O(−OH), so the influence of hydroxyl groups on CO2 adsorption may need to be considered. Simulation results show that when C(CO2) does not bond with TiO2 surface and O(−OH) does not bond with Ti, C(CO2) will rapidly combine with O(−OH) to form a strong bond of −OOCOH. Under the condition that C(CO2) bonds with TiO2 surface and O(−OH) does not bond with Ti, C(CO2) will break away from the existing bond and combine with O(−OH) alternatively. Therefore, it is speculated that simultaneous release of CO2 and water has a negative influence on the conversion of CO2 to HCOO• group.

Effect of Au on CO2 Adsorption

The structure of Au-TiO2 with the LSPR effect is different from that of Au-TiO2 with doping modification. For the former, gold particles exist in the form of clusters, which are deposited on the surface of TiO2 with a size in the range of 1–10 nm, For the latter, Au is doped in the lattice of TiO2 in the form of metal ions.

In the study, gold nanoclusters of 5 nm are used to be adsorbed on the surface of TiO2, occupying approximately 800 active adsorption sites of O3c, O*2c, and Ti*5c, respectively. In the simulation, the influence of Au deposition (i.e., shape and size of Au clusters) on the preferred adsorption sites of CO2 has been extensively investigated. This can be studied by featuring the adsorption behaviors of gold clusters in a small volume. Figure presents the schematics of Au clusters and the simulated adsorption preference on the TiO2 surface. As seen from the figure, the TiO2 surface and Au clusters with lengths of 10 and 6 Å, respectively, were intercepted in the simulation to examine the adsorption behaviors as mentioned above. As adsorption sites on the TiO2 surface can be typically recognized as the upper space of O3c, O*2c, and Ti*5c, respectively, the proportions of different types of adsorption sites are analyzed in the simulation. Specifically, the ratios of O3c:O*2c:Ti*5c of 2:2:1, 1:2:2, and 1:3:2 are considered in the study.

Figure 8

Schematics of Au clusters and the simulated adsorption preference on TiO2 surface: (A) TiO2 of 5 nm; (B) Au cluster of 5 nm; (C) Au cluster of 6 Å; and (D, E, F) Au adsorbed at different adsorption sites of TiO2.

Based on the simulation, the adsorption of Au clusters is regarded as chemisorbed due to the provision of electrons to the TiO2 surface. As a result, the catalytic performance in the photocatalytic reaction is promoted under the LSPR effect of Au clusters. This can be verified by the observed coexistence of the second LUMO, which indicates the transfer of thermal electrons evidenced by the strong coupling between Ti 3d orbital and Au sp orbital. Meanwhile, it is found that adsorption configurations as shown in Figure D–F change insignificantly after the simulation. This indicates that the adsorption of Au clusters has no preference on TiO2 surfaces. Consequently, the adsorption sites of CO2 on TiO2 surfaces are reduced with no preference.

In an attempt to observe whether Au clusters would affect the adsorption configurations of CO2, first, Au clusters as shown in Figure C are added to the TiO2 surfaces adjacent to CO2 with a distance of 1–2 Ti–O bond lengths. Subsequently, the adsorption behaviors of CO2 with six configurations are specifically analyzed. In terms of the simulation results, Au clusters have an insignificant effect on the adsorption behaviors of CO2 because of the no variation of the spatial positions of atoms in the CO2 molecules.

The simulation results show that Au clusters have an insignificant influence on the adsorption behaviors of CO2 including the adsorption sites and configurations on TiO2 surfaces. These results are consistent with the literature. For example, according to the TPD analysis by Zeng et al.,[32] most CO2 is adsorbed on TiO2 of the Au-TiO2 photocatalyst. Moreover, in terms of the study by Hussain et al.,[33] Au has weak interactions with CO2 and H2O in the catalytic system.

Transition-State Search and the Effect of Temperature

In the theory of reaction kinetics, the energy barrier of the catalytic reaction is an index to describe the degree of difficulty of chemical reactions. Therefore, it is significant to search for transition states and calculate the reaction energy barrier when studying the conversion between CO2 adsorption configurations and the reaction path of CO2 to the HCOO group. Transition-state structure refers to the highest energy point on the reaction path on the potential energy surface. It connects the structures of the reactants and products (including intermediates in the case of multistep reactions) through a minimum energy path (MEP).[34] This is beneficial to identify the adsorption configurations favorable for the catalytic reaction, providing a dimensional assessment for the selection of experimental conditions. In this step, complete LST/QST method was adopted to provide the structures of reactants (CO2 and H atoms were adsorbed on the surface of TiO2, respectively) and products (HCOO groups were adsorbed on the surface of TiO2) under different adsorption configurations, and the parameters related to the structure optimization of the transition state were consistent with the adsorption structure optimization. The initial adsorption sites of the H atom were all approximately one Ti–O bond distance from the middle C atom after the CO2 adsorption. To calculate the reaction barrier as accurately as possible, the number of interpolations of the transition states was augmented from the least to the most until the change in the reaction barrier was less than 0.01 eV. It is noted that the barrier is evaluated by the free energy of the transition-state structure and the free energy of the reactant structure.

Figure shows the transition-state search curve of the reactant structure changing into the product structure under six adsorption configurations. The data of reaction energy and reaction barrier are shown in detail in Table . It can be seen that the reaction energies of all of the adsorption configurations are negative, which indicates that the reaction is exothermic. Among them, the reaction energies of most adsorption configurations are between −0.03 and −0.045 Ha, while the reaction energies of (e) and (f) configurations are larger, which are −0.0758 and −0.0904 Ha, respectively. It is inferred that the structure of the product is more stable than that of the reactants. The reaction barriers of (b)–(d) configurations are all positive, that is, the transition structure of the reactants is the most unstable at a certain moment during the transition to the product structure. Without energy input, the molecule tends to maintain the original reactant structure and the energy across this reaction barrier is provided by photoexcited TiO2 electrons and the LSPR effect of Au. The energies of (a), (e), and (f) configurations decrease throughout the process of the transformation of the reactant structure to the product, which indicates that there is no transition state because the energy of the transition state is lower than that of the reactant. To ensure the situation, for the first step, the configurations are maintained the same transition-state structures. The results show that the energies of configurations (a), (e), and (f) from reactants to products still tend to decrease with no transition points in the middle. For the second step, the reactant and product structures of (a), (e), and (f), the calculation level, and the upper limit of small step length are changed for repetitive simulations. It is found that no transition state appears and the results are not affected by the above conditions. Therefore, it is concluded that for configurations (a), (e), and (f), there are no transition states. It is speculated that the structure of the reactant in configurations (a), (e), and (f) is more unstable and has a tendency to spontaneously transit to the product structure. It is noted that for the adsorption configurations of (a), (e), and (f), the C in the middle of CO2 does not bond with TiO2; therefore, it does not need to undergo the process of bond breaking and re-bonding of the middle C atom when it is transformed into the product structure bonded by the middle C and H, which may be the reason for the avoidance of the reaction barrier.

Figure 9

Transition-state search of six adsorption configurations transforming to HCOO•.

Table 3

Energy States of Different Adsorption Configurations in Transition

configurations	ΔE (Ha, reaction, Epr – Ere)	ΔEb (Ha, barrier, Etr – Ere)
a	–0.0365
b	–0.0436	0.0134
c	–0.0398	0.0157
d	–0.0410	0.0197
e	–0.0758
f	–0.0904

The frequency analysis of the change of structures of the reactants and products to the first-step products in photocatalysis was conducted for the six adsorption configurations. This is to obtain the relationship between the Gibbs free energy, a thermodynamic parameter, and the temperature (0–500 K). Equations and 3 were used to calculate the Gibbs free energy change of the temperature-corrected reactionwhere Gtotal(T) is the Gibbs free energy difference corrected by temperature T for each structure, including the zero-point vibrational energy (ZPVE); Etotal is the total energy of each structure, obtained from the frequency calculation output document; Etcorr(T) denotes the Gibbs free energy of each structure under specific temperatures; and ΔG(reaction, T) represents the change of Gibbs free energy in the transformation to the products in the first step of photocatalysis at various temperatures for the six adsorption configurations, as shown in Figure .

Figure 10

Change of Gibbs free energy of the transformation reaction of six adsorption configurations.

As can be seen from the transition-state search chart (Table ), the reaction in which CO2 is transformed into HCOO• group is exothermic. It is shown from the chart that the Gibbs free energy change of the reaction is all negative and the reaction tends to be spontaneous. However, except for configurations (a), (e), and (f), all of the other reactions require certain reaction activation energy. Due to the consumption of CO2 gas, this reaction is a reaction of entropy reduction. Therefore, with the increase of temperature, the molecular motion is strengthened and the thermal stability difference between CO2 and HCOO• group becomes smaller. This results in a positive slope in the curve of Figure , indicating that the absolute value of Gibbs free energy change of the reaction becomes smaller with the increase of temperature.

For a long time, there are three hypotheses for the explanation of the enhancement of catalytic activity by surface plasmas, which are temperature rise, molecular photoexcitation, and hot electron injection.[33] Plasma resonance energy causes the local lattice temperature to increase sharply in a few picoseconds.[35] In this study, the tunneling effect and variational transition state theory (VTST) are not considered in the simulation.[36] Instead, it is assumed that the concentrations of CO2 molecules and H atoms of the reactants are maintained in the process and are both in the gas phase. The classical transition-state theory was used to investigate the influence of temperature on the degree of difficulty of the reaction. Based on the assumptions, the half-life of the reaction T1/2 (the time required to reduce the reactant concentration to half of the initial concentration) was calculated according to the TST formula, as given in eqs –6 [37]where k is the reaction rate constant in s–1·(molecules/cm3)−1; σ is the degeneracy of reaction path, which is 1; KB is the Boltzmann constant, which is 1.3806503 × 1023 J/K; T is the temperature in K; h is Planck’s constant, which is 6.6260696 × 10–34 J·s; P0 is the standard atmospheric pressure, 1 bar; Δn is related to the number of reactant molecules N, which is equal to N – 1; ΔG0,≠(T) denotes the temperature-adjusted free energy difference between the transition structure GTS0(T) and the reactants at standard atmospheric pressure Greactant0(T) in kJ/mol; T1/2 represents the half-life, which is the time required to reduce the concentration of the reactants to half the initial concentration, in s; and [A0] is the initial concentration of the reactants, which is assumed to be 1 M in the calculation.

The variation of the reaction half-life with temperature is shown in Table and Figure . It can be seen that the curves are divided into two categories, one is configurations (b)–(d), which are the adsorption configurations requiring reaction activation energy, and the other is configurations (a), (e), and (f), which represent the adsorption configurations without reaction activation energy. The reaction half-life of the former is very large at low temperatures (0 K to approximately 100 K), which implies the impossibility of the reaction. However, as the temperature gradually increases, it provides energy to overcome the reaction barrier, and the half-life decreases rapidly. At the room temperature of 298.15 K, the half-life can reach the order of nanoseconds to picoseconds. As the temperature continues to increase, the reaction rate accelerates continuously, but the change of the time order is not dramatic. The reaction rate of the latter is extremely fast at low temperatures. With the increase of temperature in the exothermic reaction, both the positive reaction and the reverse reaction are accelerated. However, the reverse reaction is more intense, leading to a slower positive reaction rate and longer half-life. Compared with (b)–(d) configurations, their half-lives still have a prominent advantage of tens of orders of magnitude. The effect of the temperature rise caused by plasma resonance is discussed based on room temperature. It is found that the reaction rate of (a), (e), and (f) configurations is insignificantly reduced. However, the reaction still proceeds at a high rate within picoseconds. Interestingly, the temperature rise is beneficial for (b)–(d) configurations, which need to overcome the reaction barrier. Above the room temperature, the half-life decreases by 0–1 order of magnitude with every 50 K increase of temperature, resulting in an increase of the reaction rate by 1–10 times. It is worth mentioning that the above analysis is in the premise that the influence of the TiO2 catalyst which provides the activation energy required for the reaction is not considered.

Table 4

Variation of the Half-Life (T1/2) of the Reaction with Temperature

temperature (K)	a	b	c	d	e	f
50	7.103 × 10–213	1.205 × 104	6.245 × 1012	2.954 × 1020	7.265 × 10174	1.233 × 10171
100	1.879 × 10115	2.904 × 106	2.855 × 10	5.559 × 102	8.416 × 1095	8.787 × 1094
150	3.584 × 1083	1.831 × 109	1.073 × 105	6.954 × 104	8.545 × 1069	3.523 × 1068
200	4.032 × 1067	5.025 × 1011	7.338 × 108	8.501 × 107	4.933 × 1056	1.278 × 1055
250	1.490 × 1057	6.181 × 1012	3.960 × 109	1.617 × 108	1.552 × 1048	3.041 × 1048
298.15	2.038 × 1051	1.651 × 1012	6.229 × 1010	1.296 × 109	8.567 × 1044	1.398 × 1043
350	1.497 × 1048	5.798 × 1013	1.537 × 1010	1.902 × 1010	3.382 × 1040	4.524 × 1040
400	4.977 × 1046	2.904 × 1013	5.671 × 1011	4.856 × 1011	1.095 × 1037	1.336 × 1037
450	2.087 × 1043	1.709 × 1013	2.633 × 1011	1.693 × 1011	8.970 × 1036	1.019 × 1035
500	2.587 × 1041	1.123 × 1013	1.432 × 1011	7.312 × 1012	2.843 × 1034	3.053 × 1034

Figure 11

Half-life (T1/2) of the reaction as a function of temperature.

Concluding Remarks

In this study, we focus on the adsorption mechanism of CO2 on the anatase phase Au-TiO2(001) crystal plane and examine the behavior of the first step reaction for converting to the HCOO• group in the photocatalytic reduction of CO2 to the CH4 path. The influence of the water molecules ratio and the temperature rise due to LSPR are specifically discussed. Based on the model, it is concluded that the role of adsorption in CO2 reduction is to weaken the internal bonding of CO2 and activate CO2 molecules. Moreover, the way CO2 is converted to HCOO• group is that the middle C atom bonds with an H from H2O; therefore, the adsorption configuration for which the middle C atom does not participate in the bonding is conducive to this step reaction. Due to the competitive relationship of adsorption sites, this corresponds to the experimental conditions that water molecules are released prior to CO2. Au clusters have an insignificant influence on the adsorption behaviors of CO2 including the adsorption sites and configurations on TiO2 surfaces. The conversion of CO2 to HCOO• group is an exothermic reaction, and the adsorption configurations in which the intermediate C atom does not participate in bonding do not require activation energy in the reaction. For these configurations that do not require activation energy, the reaction rate is reduced due to the temperature increase caused by the LSPR effect of Au. However, the reaction continues at a very high rate, which occurs within picosecond magnitude. However, the activation energy is indispensable in other adsorption configurations and can be provided by the catalytic action of TiO2 in the photocatalysis. Comparatively, the reaction rate for these configurations is approximately 1–10 times improved with every 50 K increase of temperature above the ambient.