Chinese Journal of Chemical Physics  2019, Vol. 32 Issue (6): 674-686

#### The article information

Hitler Louis, Ling-ju Guo, Shuang Zhu, Sajjad Hussain, Tao He

Computational Study on Interactions between CO2 and (TiO2)n Clusters at Specific Sites

Chinese Journal of Chemical Physics, 2019, 32(6): 674-686

http://dx.doi.org/10.1063/1674-0068/cjcp1905108

### Article history

Accepted on: August 27, 2019
Computational Study on Interactions between CO2 and (TiO2)n Clusters at Specific Sites
Hitler Louisa,b , Ling-ju Guoa , Shuang Zhua,b , Sajjad Hussaina,b , Tao Hea,b
Dated: Received on May 29, 2019; Accepted on August 27, 2019
a. Chinese Academy of Sciences Key Laboratory of Nanosystem and Hierarchical Fabrication, CAS Center for Excellence in Nanoscience, National Center for Nanoscience and Technology, Beijing 100190, China;
b. University of Chinese Academy of Sciences, Beijing 100049, China
Abstract: The energetic pathways of adsorption and activation of carbon dioxide (CO2) on low-lying compact (TiO2)n clusters are systematically investigated by using electronic structure calculations based on density-functional theory (DFT). Our calculated results show that CO2 is adsorbed preferably on the bridge O atom of the clusters, forming a "chemisorption" carbonate complex, while the CO is adsorbed preferably to the Ti atom of terminal Ti-O. The computed carbonate vibrational frequency values are in good agreement with the results obtained experimentally, which suggests that CO2 in the complex is distorted slightly from its undeviating linear configuration. In addition, the analyses of electronic parameters, electronic density, ionization potential, HOMO-LUMO gap, and density of states (DOS) confirm the charge transfer and interaction between CO2 and the cluster. From the predicted energy profiles, CO2 can be easily adsorbed and activated, while the activation of CO2 on (TiO2)n clusters are structure-dependent and energetically more favorable than that on the bulk TiO2. Overall, this study critically highlights how the small (TiO2)n clusters can influence the CO2 adsorption and activation which are the critical steps for CO2 reduction the surface of a catalyst and subsequent conversion into industrially relevant chemicals and fuels.
Ⅰ. INTRODUCTION

The enormous global significant progress in technology and the continual rise in energy demand of our modern society have stimulated the exploitation of non-renewable energy sources like natural gas, petroleum and coal as the principal energy sources to meet our industrial and societal urgent need of energy. Since these non-renewable energy sources become deficient on an increasing periodic basis, serious economic and environmental crisis emerges [1-4]. The rise in CO2 atmospheric concentration has been associated with undesirable climatic effects like global warming, desertification, rising sea level, and more erratic weather pattern [5]. Hence, the need to tackle the adverse effects of heavy CO2 emission has become a major challenge for the scientists and the modern society at large, with an envision to bring about a lasting solution [6]. The transformation of CO2 through activation and dissociation using metal and metal oxide catalysts into valuable hydrocarbon products is of significant interest as an efficient approach to relieve the consequence of CO2 on the environment [7, 8].

Atomic and molecular clusters have, for a prolonged time, been regarded as prototypes for probing the mechanism underlying the surface reactions of the semiconductor catalysts [9, 10]. Considering that the importance of clusters to the world body of knowledge cannot be overemphasized, a number of theoretical and empirical studies have been conducted on bare (TiO2)n clusters to match their behavior and structural properties to their bulk counterparts [11-16]. Berardo and coworkers have investigated the vertical and adiabatic potentials and electron affinity of bare and hydroxylated TiO2 nanoclusters in order to understand how the electronic properties of a cluster vary as a function of size and hydroxylation, besides the fundamental gap and exciton binding energy [17]. They have compared the performance and predictions calculated by using different methods, including G0W0, qsGW, EA/IP-EOM-CCSD, and DFT (BLYP, PBE). Similarly, Hamad and colleagues have employed interatomic potential to search for and predict the global minima of low-lying isomers of (TiO2)n clusters [16]. A number of cluster geometries and structures that are energetically favorable were opt-≠wpage imized by performing DFT/B3LYP order to obtain more accurate and reliable results. Woodley et al. also studied the properties of structure, electron, vibration, and stability of (TiO2)n clusters using TZVPP basis sets with GAMESS-UK software [18]. Similarly, Qu et al. investigated the properties of zero and single-charged (TiO2)n clusters employing the B3LYP/LANL2DZ DFT-based theoretical methodology [13]. Chen et al. conducted a DFT+U study of the acid-base properties of anatase TiO2 and tetragonal ZrO2 adsorbed by CO and CO2 probe molecules on both terraces and steps in the oxides [19]. More recently, Chen and Dixon predicted a series of low energy structures of the TiO2 clusters and ultra-small nanoparticles with the B3LYP/DZVP2 [20]. Dixon et al. also theoretically predicted thermodynamic possibility of chemisorption and physisorption of CO2 on the nanoclusters of Groups 4 and 6 transition metal oxides by using couple cluster (CCSD(T)) and DFT [21].

One of the most important applications of TiO2 is photocatalytic reduction of CO2 to industrially relevant hydrocarbon fuels. He et al. used a periodic slab model with the GGA+U scheme to study the 2-electron reduction of CO2 on anatase (101) and observed competitive pathways to form HCOOH and CO [22]. Indrakanti et al. used both post-Hartree-Fock and DFT methods to study the transformation of CO2 on small clusters and identified that transfer of a photo-excited electron from the stoichiometric TiO2 surface to CO2 is energetically unfavorable, while the charge transfer can be facilitated in the presence of oxygen vacancy [23]. Recently Ji et al. investigated the fast hydrogenation (formaldehyde) pathway at the anatase (101) surface and proposed a new mechanism that CO replaced HCOOH in the formaldehyde pathway [24]. However, no theoretical work is available on the photocatalytic transformation of CO2 on the isolated (TiO2)n clusters. A bright and exhaustively grasp of the site specific interaction in the space separating CO2 molecules and nanosized (TiO2)n clusters has not been unfolded up hitherto. In this work, therefore, the first principle theoretical calculations based on dispersion DFT method were employed to explore the details of energetics and pathways in terms of site specific interactions between the low-lying compact (TiO2)n clusters and CO2 molecules. A theoretical electronic structure that rectifies the adsorption energy for the van der Waals long-range dispersion interaction was adopted. The computational survey was expanded to scrutinize responsiveness to different structures of the (TiO2)n clusters, correlating with different configurations of adsorbed CO2 and CO molecules.

Ⅱ. COMPUTATIONAL FRAMEWORK

DFT-based computational approach was conducted using DMol3 code as implemented in Materials Studio simulation package [25]. The exchange-correlation energy functional described by generalized gradient approximation (GGA) in the form of Becke's three-parameter exchange functional was employed along with the Lee-Yang-Parr's correction functional (BLYP) [26, 27]. All-electron Kohn-Sham wave functions were expanded in a double numerical basis set including p-polarization functional (DNP), and were utilized in this work. The self-consistent field (SCF) strategies were achieved with a convergence criterion of 10-6 a.u. on the energy and electron density. The BLYP functional was rectified to incorporate the van der Waals long-range dispersion interaction correction module, which was achieved by employing the strategy of Tkatchenko and Scheffler (TS) [28] that has been put into usage recently in the Dmol3 package [29]. This computational approach, denoted as TS-DFT, considers the atom-atom C6R-6 correction terms, with C6 coefficient being computed using frequency-dependent polarizability of the free atoms scaled by the ratios of active and free volumes. Hence, it is anticipated that the use of long-range dispersion correction in investigating CO2 adsorption on the (TiO2)n clusters will not give rise to significant inaccuracy in the computed adsorption energy. Similarly, theoretical calculation was also performed by applying the BLYP functional in the absence of the dispersion corrections so as to further confirm the significance and subsequent impact of the long-range dispersion correction on the results (supplementary matrials). The equilibrium state geometries of (TiO2)n clusters used as the model in our studies were taken from the work conducted previously [9, 30-32].

 ${E_{{\rm{ads}}}} = {E_{{\rm{adsorbate}} + {\rm{cluster}}}} - \left( {{E_{{\rm{adsorbate}}}} + {E_{{\rm{cluster}}}}} \right)$ (1)

The adsorption energy Eads was computed using Eq.(1), where Eadsorbate+cluster is the total energy of clusters covered by adsorbates, Eadsorbate is the energy of free adsorbate, and Ecluster is the total energy of clean (TiO2)n cluster. So negative and positive values of Eads refer to exothermic and endothermic adsorption, respectively. Charge transfer between the (TiO2)n cluster and adsorbed CO2 molecule was studied by using the Mulliken atomic charges approach.

Ⅲ. RESULTS AND DISCUSSION A. Structure and stability of the clusters

The initial ground state structures of (TiO2)n clusters (n=3-10) used as the model for our study are shown in FIG. 1. All the selected clusters are characterized by the presence of 4-fold coordinated Ti atom, 2-fold coordinated O atom, and 1-fold coordinated O atom as the terminal Ti-O (titanyl). In spite of the all-inclusive behavior, there are no generic guidelines to describe the structural stability of a given cluster besides the regular pattern. Although the coordination number of O atom becomes bigger as the size increases until it approaches 3, the O atom has an average coordination of 2, while the coordination number is 4 for Ti. Nevertheless, for the O atoms possessing 2-fold coordination number (bridge O atoms), it is observed that this average estimation occasionally is responsible for the concomitant presence of terminal and 3-fold coordinated O sites, in the case of a more massive cluster or terminal and 4-fold coordination. Because the coordination number of an O atom does not surpass 3 in a covalent compound, the cluster with 4-fold coordinated O atom possesses the ionic characteristic in some sense [33]. Still more is the availability of terminal Ti-O groups (1-fold coordinated O atom) apparently in all the clusters, and the presence of terminal groups is detrimental to the cluster stability in view of the fact that its contribution to the increased average coordination is not consequential. The 1-fold coordinated O-atom centers will be chemically reactive in the oxidation reaction for a large extended titania system (surfaces and slabs) [34, 35].

 FIG. 1 Structures of the selected low-lying isomers of neutral (TiO2)n clusters.

The energy gap (Egap) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the lowest lying structures for all the clusters was calculated to study the electronic properties. The HOMO and LUMO are termed collectively as FMO (frontier molecular orbital), which are adjacent to the Fermi level that can provide qualitative information regarding the electronic states near the Fermi surface and from the transferred electrons [36]. Electronic structure of the (TiO2)n clusters can be comparable to that of an insulating material, i.e., the HOMO is comprised of O 2p level and the LUMO is primarily composed of Ti 3d. The HOMO and LUMO levels are of paramount importance altogether in magnitude and shape because both are commonly related to the chemical reactivity of the metal oxide semiconductors. Although a wide bandgap correlates with the high strength needed to alter the electronic structure, a narrow bandgap is more interesting for the chemical reactivity. For the clusters possessing under-coordinated atoms, the HOMO and LUMO are concentrated on these atoms. Using O (Ti) as an analogy, the logic is that bonding (antibonding) character of the occupied (vacant) orbital localized on this atom increases as the coordination number increases, besides the shift in its energy level downward (upward). The FMOs are thus centered on the atoms that are deficient in coordination number. Accordingly, the HOMO will be comprised primarily of such levels if a titanyl Ti-O group is available, demonstrating the chemical reactivity of a lone pair of 1-fold coordinated O atom.

1. Correlation between Egap and cluster geometry

The clusters show great structural dependence in terms of property prediction. FIG. 2(a)-(c) show the Egap of HOMO-LUMO, the dependence of HOMO (LUMO) energy level, and chemical hardness on the cluster size. From the fundamental theory of quantum confinement effect, the HOMO-LUMO Egap decreases with increase in material size. In other words, the band gap energy decreases as a material changes from nanosize to bulk. However, no obvious relationship between Egap and the cluster size can be observed. So our results are not in agreement with the quantum size confinement theory, which may be related to the strong dependence of bandgap on the structure as discussed below.

 FIG. 2 (a) HOMO-LUMO energy gap (Egap) calculated for the (TiO2)n clusters, (b) energy of the HOMO and LUMO levels of (TiO2)n clusters, and (c) variation of chemical hardness as a function of cluster size.

It is noted that the values of HOMO-LUMO Egap computed for all the structures are much dispersed with dangling oscillations (FIG. 2(a)). Hence, the cluster geometry and titanyl Ti-O play a significant role in determining the electronic properties of small titania clusters, as the associated orbitals are usually located on those atoms and, thereby, the energy is critically dependent on the surface structure. Here the stability refers to that the cluster possesses the highest negative or the least positive energy value (the lowest energy state). With the exception of n=3, 8 and 10, the primary pattern is a gradual decline for all the clusters. This unusual behavior in the Egap trend of the clusters is reported not only theoretically, but also experimentally [12, 15, 37]. Notwithstanding, the stability shows a clear relationship with Egap of the clusters. A large Egap implies high stability of a particular system. The cluster of n=4 is the most stable one, with an Egap value of 2.8 eV. In addition, no regular behavior can be observed in the change of Egap value (for instance, the so-called even and odd oscillation), as such small clusters fall to the non-scalable regime. Nevertheless, the Egap value appears to be highly dependent on the structure and far more significant as compared to cluster dimention.

2. HOMO and LUMO energy levels

The calculated HOMO and LUMO levels of (TiO2)n clusters are shown in FIG. 2(b). A situation similar to the Egap value is observed, with a trend characterized by slight decrease in value and smooth oscillation. As expected, the value of HOMO and LUMO levels, as well as their energy difference, has a substantial impact on the chemical reactivity and stability of a cluster. It is known that the interaction of a small molecule with a material surface occurs on the non-coordinated positive ions as a result of acid-base reaction [38-40]. This suggests that the LUMO energy may control the adsorption with other molecules. Moreover, it is expected that the stable clusters have high LUMO energy levels, whereas the less stable clusters have low LUMOs and are potentially more reactive. Zhai et al. reported that the electron affinity calculated as the degree of adiabatic detachment energy becomes larger with cluster size n for Ti 3d level [37], implying that the acidic property is comparatively dominant for the large-size clusters.

In addition, reactivity of the clusters is also associated to the high energy of the HOMOs centered on the non-coordinated single O atom, while the values for the most stable isomers do not constitute the utmost scenario. On the other hand, the HOMO levels that depart strongly from the average value are in accord with the isomers with inferior stability. As previously discussed, the clusters with narrow HOMO-LUMO gap are almost always unstable. The common pattern slightly declines with smooth swinging, and the values for n=3, 6, and 7 appear above the other clusters. Because stabilization of the O 2p level in concurrence with the computed HOMO level shows a decrease in n values, experimental adiabatic energy becomes bigger as the size of the cluster increases [37].

3. Cluster chemical hardness

The chemical hardness is a quantity that determines or controls chemical reactivity. It would thus seem that chemical hardness should be the energy, or at least potential. Pearson has proposed that an operational definition of the absolute hardness can be obtained using the finite difference approximation?·=0.5(I-A) [41], where I is the ionization potential and A the electron affinity. This expression implies that the chemical hardness is proportional to the band gap of a chemical system when a gap exists. In addition to the bandgap, the computed DFT-based descriptors for (TiO2)n nanoclusters (namely electronegativity, global hardness, molecular softness and electrophilicity index) are outlined in Table S1 of supplementary materials, while the correlation of cluster size with global hardness is presented in FIG. 2(c). The general trend shows an oscillating behavior of the chemical hardness as a function of the cluster size, which is also observed for the clusters of Al-Au [42] and Pd [43]. In this work the clusters of size n=4 and 3 have the maximum and minimum chemical hardness of 1.41 and 0.93 eV, respectively (FIG. 2(c)). So the (TiO2)4 cluster possesses the highest tendency to release or exchange electrons, while the (TiO2)3 cluster has the least likelihood of exchanging electrons during chemical reactivity. Similarly, the (TiO2)5 and (TiO2)8 clusters also have the propensity to interchange electrons in which the respective chemical hardness is 1.33 and 1.35 eV, which is close to the highest value.

B. Adsorption and activation of CO2 on (TiO2)n clusters

CO2 can interact with a cluster or surface in two basic configurations, one is physisorbed configuration, where the CO2 binds to Ti atom of the cluster through one of the O atom in CO2, while remaining geometric property of gas phase isolated CO2, and the other one is chemisorbed configuration, where it forms a monodentate carbonate by binding to the bridge O atom (O2c) of the cluster via C atom in CO2, meanwhile being deformed geometrically (bent and activated). Here the specific interaction sites of CO2 on the (TiO2)n clusters are investigated by setting up three possible initial adsorption sites on a cluster surface, i.e., 4-fold coordinated Ti atom (Ti4c), 2-fold coordinated O atom (O2c) and 1-fold coordinated O atom in the terminal Ti-O (O1c). Various adsorption modes and configurations are presented in FIG. 3, while all of the optimized Cartesian coordinates and total energies of clusters are shown in Tables S4- S11 of supplementary matrials.

 FIG. 3 (a) CO2 adsorption geometry on Ti4c site of the clusters. The CO2 molecule was initially introduced onto the cluster surface in a vertical configuration, while it moved away slightly during energy minimization perpendicularly from the surface but remaining in a linear conformation. (b) CO2 adsorption on O2c site. The CO2 molecule was initially introduced onto the cluster surface in a horizontal configuration, while it was strongly adsorbed on the cluster surface after geometry optimization but deviating from a linear to bent conformation. (c) CO2 adsorption on O1c site. The CO2 molecule was adsorbed in a horizontal configuration with C atom on the 1-fold coordinated O atom at the terminal Ti-O (titanyl). The red and grey colors represent O and Ti atoms of the clusters, respectively; black and blue colors represent O and C atoms of the CO2, respectively.
1. CO2 adsorption on Ti4c sites

Initial stages of the CO2 interactions are carried out on the Ti4c sites for all the selected clusters. A physisorption phenomenon characterized by a relatively large bond distance is observed, implying a weak interaction between the surface and adsorbate molecule (CO2). Considering that CO2 binds to the Ti4c site of a cluster via one of its O atom, the CO2 molecule is initially placed onto the surface in a standing configuration, while it moves slightly away perpendicularly from the surface during geometry optimization and, meanwhile, retaining its linear configuration. The fully optimized CO2 adsorption configurations on the Ti4c sites are displayed in FIG. 3(a), with the summary of adsorption energy, adsorption distance, bond length, and bond angle listed in Table Ⅰ. The interaction of CO2 with the Ti4c after geometry optimization is observed to be in a physisorbed state, while the gas phase property of CO2 remains (C=O bond length of 1.18 Å and O=C=O bond angle of 180.0°). The Mulliken partial atomic charge on the adsorbed CO2 is calculated to further confirm this (Table Ⅰ). It is found that the total charge on the adsorbed CO2 is partially positive, suggesting that there is no electron transfer from the (TiO2)n surface to CO2 molecule. The weak interaction between the CO2 molecule and Ti4c sites is electrostatic in nature, where the Ti4+ ion polarizes the neutral CO2 molecule. This observation is consistent with previous report using CO and CO2 to probe the acid-base properties of TiO2 surface [19]. The most stable and the least stable physisorption modes are clusters of size n=6 and 3, respectively.

Table Ⅰ The adsorption energy (Eads, in eV), C=O bond length (d(C=O) in Å), bond adsorption distance (in Å), CO2 bond angle (in (°)), and net charge transfer (∆ q(CO2)) for different sites of Ti4c, O2c and O1c. n=0 represents an isolated CO2 molecule without adsorbing on the cluster.
2. CO2 adsorption on O2c sites

Different from the Ti4c sites, a strong interaction is observed between the CO2 adsorbate molecules with the O2c sites in all the clusters, as displayed in FIG. 3(b). Here, the CO2 molecule is originally placed on the O2c sites of a cluster in a horizontal configuration, whereas the CO2 molecule is observed to be strongly adsorbed on the cluster surface via binding its C atom to form carbonate complex, while deviating from a linear to bent conformation. The CO2 bond length and angle, CO2 adsorption energy and distance, and variation in the total charge of the chemisorbed CO2 molecule (∆ q(CO2)) are summarized in Table Ⅰ. The elongation in C=O bond length, decrease in O=C=O bond angle, and subsequent charge transfer are the evidence for CO2 activation on the bridge O atom of the clusters. The CO2 activation can be attributed to the movement of electrons from valence orbitals of the cluster to anti-bonding orbitals of the CO2 molecule [44]. Clusters with size of n=8 and 9 are found to be the most and the least stable chemisorbed structures, both of which have chemisorptive adsorption energy of -1.00 and -0.29 eV, respectively. Some factors responsible for the cluster stability are the geometry type, presence of 4-fold coordinated Ti atom, and the absence of terminal dangling T=O bond. Since Ti has the electron configuration of [Ar]3d24s2, experiments have demonstrated that it can form +3 and +4 oxidation states. So it can lose 3 or 4 electrons to form the corresponding ions. The +4 state is the most common and stable one as it is able to form an octet, while the +3 state is less stable (more reactive) because it leaves a single d electron in the valence orbital. As shown in Table Ⅰ, the clusters of n=8 and 9 appear to have similar geometrical shape, whereas the different number of Ti4+ bonds may be responsible for the different stability. In comparison with other experimental and theoretical studies involving TiO2, it is understood that adsorption on the surface of TiO2 results in the formation of a partially charged species CO2δ·- through the reaction of the CO2 molecule with the surface atoms or bare clusters. This adsorbate (activated CO2 molecule) no longer has the linear symmetry of the free CO2 molecule and thus has a lower barrier for accepting an electron because the LUMO level of CO2 decreases as the molecule bends. Compared to the fact-finding predicted by He and colleagues, the trends in the adsorption energy and structural parameters for the adsorption energy on the perfect surface are similar for the cluster of sizes (TiO2)4 and (TiO2)5 [45, 46].

3. CO2 adsorption on O1c sites

The optimized adsorption configurations of CO2 on O1c sites are shown in FIG. 3(c). The bond length, adsorption distance and energy, and variation in the total charge of the chemisorbed CO2 molecule (∆ q(CO2)) are summarized in Table Ⅰ. As implied in Table Ⅰ, the CO2 molecule is adsorbed favorably in a horizontal configuration with C atom on the 1-fold coordinated O atom as the terminal Ti-O bond (titanyl). Physisorption is observed for all the clusters after geometry optimization. The C=O bond length and O=C=O bond angle are similar to those of a gas phase CO2. However, a partial charge transfer is observed from the O1c sites to CO2 molecule after optimization. However, the degree of electron transfer is not sufficient to induce CO2 activation. This can be explained by the defect state of terminal O atom and, thus, no sufficient electron is available for transfer.

C. Comparison of CO2 and CO adsorption using pure DFT and TS-DFT methods

The optimized adsorption energy and associated geometrical structure parameters of CO adsorption on the Ti4c, O2c and O1c sites are shown in Table Ⅱ. The geometrical adsorption configurations considered in this work are also shown in FIG. 4. The O1c (i.e., CO adsorption at the O atom of terminal Ti-O) has the strongest adsorption with an adsorption distance around 1.18 Å (for comparison, C=O bond length in CO2 is 1.18 Å too), implying that CO adsorbed at the O atom of terminal Ti-O can regenerate CO2 molecule. This explains why CO is adsorbed more favorably at the Ti atom of terminal Ti-O. So neither electron transfer nor C=O bond length elongation can be observed upon energy minimization.

Table Ⅱ The adsorption energy (Eads, in eV), C=O bond length (in Å), bond adsorption distance (in Å), and net charge transfer (∆ q(CO)) for different sites of Ti4c, O2c and O1c. n=0 represents an isolated CO molecule without adsorbing on the cluster.
 FIG. 4 CO adsorption geometry and configuration for Ti4c, O2c and O1c sites of the clusters. The red color and grey color represent O and Ti atoms of the clusters, respectively; black and blue color represents O and C atoms of the CO, respectively.

As discussed earlier, CO2 prefers to bind strongly on the bridge O site (O2c), while for CO the most preferable and stable adsorption site is at the O atom of terminal Ti-O (O1c). This observation is significant, as competitive adsorption will not occur during co-adsorption of CO and CO2 molecules on the same surface. Moreover, catalytic poison during the CO2 reduction, one major issue in catalysis, will be greatly avoided because the reactant and product will be adsorbed at different sites on the catalytic surface.

The variation in CO2 and CO adsorption energy considered for all the possible adsorption sites (Ti4c, O2c and O1c sites) are shown in FIG. S1 and FIG. S2 as well as in Tables S2 and S3 for those calculated using pure DFT, and in FIG. S3 and FIG. S4 for those computed using TS-DFT (see details in supplementary materials). The adsorption configuration of CO2 and CO calculated using DFT functional are presented in FIG. S5 and FIG. S6 (see details in supplementary materials). Comparing the results shown in FIG. 3 and FIG. 4 as well as in Tables Ⅰ and Ⅱ, it is found that the general adsorption energy trend determined using the TS-DFT method is also observed for that derived from the pure DFT approach. The adsorption energy for CO2 adsorption on the O2c site of the clusters is predicted to be more stable (negative) using the TS-DFT method, while pure DFT predicts the adsorption energy to be positive and hence energetically unfavorable. Similar result is also observed for the CO molecular adsorption using both methods. Sorescu et al. [47] reported that the optimized adsorption energy of CO2 is close to the experimental value when the van der Waals long-range dispersion correction term is used alongside the selected functional. Recently, this long-range dispersion correction term has achieved tremendous significance for precisely forecasting the properties of solids, and the application is not limited to the simulation of soft matter or rare-gas solids only [48, 49], but also including the hard matter or alkali-metals, insulators, ionic compounds and metals [50, 51]. For instance, recently modified van der Waals functional with optimized exchange has precisely predicted the adsorption energy for gas-phase clusters, surfaces and systems [51].

D. Electronic and vibrational analysis

Understanding the underlying catalytic properties responsible for the CO2 activation is of paramount significance for developing catalysts with enhanced efficiency. Therefore, the electronic density distribution, frontier molecular orbitals (HOMO-LUMO), electronic density of states (DOS and PDOS), vibrational frequency and ionization potential (IP) are investigated as the cluster descriptors for the calculated adsorption pattern.

1. Ionization potential

It has been previously reported that the IP of a catalyst is one of the ideal parameters for describing the adsorption phenomena [52], especially for the systems involving migration of electrons, such as CO2 chemisorption on O2c sites of the clusters as shown in FIG. 3(b). The correlation between the IP and adsorption energy of CO2 adsorbed on the O2c site is displayed in FIG. 5. It is found that the IP of chemisorbed carbonyl complex decreases with increase in the binding energy of CO2 on the cluster (Table S12 of supplementary materials). In view of the fact that the IP is the ability to remove the valence electron from an atom, with the exception of clusters n=8 and 9, all clusters possess the ability to donate electrons to CO2 molecule to form the carbonate species. Given that IP is the catalytic property viable for the measure of charge transfer to CO2 that induces activation of the adsorbate molecule, the deviation of clusters n=8 and 9 may reveal the least ability to donate electrons to the adsorbate species [53].

 FIG. 5 Relationship between ionization potential (IP) and CO2 binding energy for the most stable adsorption configuration. The numbers 4, 5, 6, 7, 8, 9, and 10 are the cluster size respectively.
2. Electronic density distribution

The iso-surface graphic description of the complete charge density distribution of the bent (activated) CO2 is shown in FIG. 6. The charge density is computed as the difference between the total charge density of the whole system (cluster+bent CO2) and the charge density of the discrete atomic component. It can be seen that charge surplus in the area between the C and underlying O atoms is present to some degree for all the O2c sites under computation. This agrees well with the findings reported by Rodriguez [54] who concluded that the deformed (bent and activated) species is an effective electron acceptor, in spite of the fact that the spot of CO2 adsorbed molecule, where the C atom is centered on the apex of a surface C atom, is not limited to this study. Nevertheless, the migrated electron charge for the most stable activation configuration is calculated to be about 0.07 |e| with some small charge density beneath the C atom.

 FIG. 6 Electronic density distribution of the most stable CO2 adsorption configurations.
3. Electronic density of states

The density of states (DOS) and projected density of states (PDOS) of the C and O atoms in CO2 molecule, along with the surface O2c combined with the C atom in the CO2, are computed to study the properties of bonding formed between the CO2 and (TiO2)n clusters. The DOS and PDOS of CO2 adsorbate molecule and clean (TiO2)n clusters for the chemically adsorbed configurations are shown in FIG. 7. The orbital overlaps between O 2s and C 2p in light of the DOS and PDOS of CO2 molecule indicate the actuality of sp orbital hybridization and C-O bond. It also reveals that the HOMO is a π orbital that constitutes primarily of the O 2p orbital and the LUMO is a π* orbital that is mainly contributed from 2p orbitals of C and O. The DOS and PDOS of (TiO2)n clusters are shown in FIG. 7. The valence band of (TiO2)n clusters mainly consists of O 2p, while the conduction band is mainly made up of Ti 3d. Here only the O2c adsorption site is essentially considered for all the (TiO2)n clusters. As a result of the interaction with the CO2 molecule, the electronic levels of the isolated cluster drift to a relatively high energy (close to the Fermi level). The measure of such a shift declines as the cluster grows in size, which is a factor that accounts for the increasing adsorption power of CO2 molecule. Above and overall, the electronic DOS can be regarded as a perfect parameter to describe the CO2 adsorption and activation pattern.

 FIG. 7 DOS and PDOS of the CO2 and clusters with n=4-10, respectively.
4. Frontier molecular orbitals

The highest occupied molecular orbital energy and lowest unoccupied molecular orbital energy are widely termed as the frontier molecular orbitals (FMOs), which dictate the pathways that the molecules chemically react with the others. HOMO is the orbital that serves as the electron donor, as it is the valence orbital (the highest energy) containing electrons. LUMO is the orbital that is often regarded as the electron acceptor because it is the innermost orbital (the lowest energy) that has room to accept electrons. According to the FMO theory, the evolution of a transition state is due to the chemical combination between the FMOs of the reactant species. The HOMO energy is associated directly with the ionization potential, and LUMO energy is a direct measure of the electron affinity. According to Koopmansa€?s theorem [55, 56] for the closed shell systems, the FMO method is suitable for describing the stability and chemical interaction of the species.

Charge density designation in the HOMO advocates a peculiar site to be nucleophilic, while the site is electrophilic in nature where LUMO is centered. The optimized structure with corresponding HOMO and LUMO electron density distribution of the preferred stable CO2 adsorption configurations are presented in FIG. 8. Upon examining the FMOs of the cluster complex, the HOMO of cluster size n=7 is the most stable cluster complex (cluster+CO2), and n=4 is the least stable one. Furthermore, the HOMO of all the (TiO2)n clusters is the lowest in energy in contrast to the LUMO of CO2. Because CO2 is electrophilic in nature, the HOMO of the clusters can chemically interact with the LUMO of the CO2 adsorbate molecule [57]. The cluster complex that possesses a large HOMO-LUMO gap is considered a hard molecule and is comparatively more stable than the soft molecule (more reactive) that possesses a narrow HOMO-LUMO gap [58]. Clusters with size n=5-8 have comparably wide bandgap and are known as hard clusters (less reactive), while clusters with size n=4, 9 and 10 are known as soft clusters since they exhibit relatively narrow bandgap. Chemical hardness is associated with the stability and interaction of a chemical system, which is the degree opposite to change in the electron charge dissemination or electron migration.

 FIG. 8 Electron distribution of HOMO and LUMO levels, and the corresponding bandgap values.
E. Vibrational frequency analysis

Analyzing the CO2 vibrational frequency on the surface of (TiO2)n clusters can provide an in-depth intuition into the critical bond feature of the adsorbate molecule and, thereby, can provide a useful roadmap for interpreting the experimental vibrational spectra. Here the vibrational frequency for the chemisorption complex is calculated by performing the zero-point vibrational energy, where the CO2 is adsorbed to the bridge O atom (O2c) via its C atom to form a monodentate carbonated species on the surface of (TiO2)n clusters. The computed frequencies are displayed in Table Ⅲ, where νa, νs, and νb are the asymmetric stretching, symmetric stretching and bending mode of the CO2, respectively. More important, it is known that the specific vibrational modes can be used to describe the crucial geometric and electronic parameters that are directly critical for the CO2 activation [59]. The deviation in the vibrational frequency from neutral CO2 to the carbonate CO2δ·- can be ascribed to the possession of electrons in the adsorbate species as a result of binding to the Ti4+ metal center. Although the asymmetric stretching of carbonyl for all the clusters remains comparatively similar, the symmetric and bending modes are not the same. The clusters n=4, 5, 6, 8 and 10 have a carbonyl vibrational frequency of ~1200 cm-1 for the symmetric stretching, with the exception of cluster n=9 at ~1000 cm-1. Conversely, clusters n=4 and 6 have carbonyl vibrational bending mode at ~1500 cm-1, clusters n=5, 8 and 10 at ~1600 cm-1, while the clusters n=7 and 9 are at ~1800 cm-1. Here the computed carbonyl vibrational frequencies are similar to other theoretical and experimental results conducted on the surface of TiO2 [60, 61]. Furthermore, our DFT bending vibrational frequency modes (~1200 cm-1) are similar to the results obtained by Guo et al. on the surface of Ti(0001) for the CO2 bending vibrational mode (1296.8 cm-1). Interestingly, our DFT predicted value is close to the experimentally observed value of 1351 cm-1 [62].

Table Ⅲ The calculated vibrational frequency for the strong adsorption of CO2 on the surface of (TiO2)n cluster. n=0 represents an isolated CO2 molecule without adsorbing on the cluster.
Ⅳ. CONCLUSION

In this work, we have focused on a detailed TS-DFT and DFT study of the energetics underlying the adsorption, activation of CO2 on low-lying (TiO2)n clusters (n=3-10). We found that the size and, more important, structure of the clusters have a significant impact on the stability, electronic and chemical properties of these low-lying structures. The computed HOMO/LUMO orbital energy and HOMO-LUMO gap are dependent on the size and conformation, but do not possess a customary sequence. Basically, the bandgap of a nanosized material is larger than its bulk counterpart as a result of quantum size effect, which approaches to the value of a bulk material as the size becomes bigger. However, here the observed behavior pattern has a small decrease with smooth swinging, and the values for n=3, 6 and 7 appear above the other clusters.

The site specific interaction of the CO2 with (TiO2) clusters was investigated by setting up all possible initial adsorption configurations on the cluster surface and three possible adsorption sites were considered, i.e., 4-fold coordinated Ti-atom (Ti4c), 2-fold coordinated O-atom (O2c) and terminal Ti-O coordination (O1c). The results indicate that CO2 prefers to be adsorbed on the O2c site and CO intends to be adsorbed at Ti atom of the terminal Ti-O. The various adsorption energies obtained for CO2 reaction on the O2c site of the clusters was predicted to be more stable. Consequently, the adsorption of CO2 on the O2c site of the clusters leads to activation (bending) of the CO2 molecule, which is characterized by deviation from the gas phase CO2. The computed vibrational frequency values clearly indicate that the CO2 is deviated slightly from its linear shape in the complex, which agrees well with the experimental results. Furthermore, the results of electronic parameters, HOMO/LUMO and its difference, electronic density, ionization potential and DOS confirm the charge transfer and interaction between the CO2 and clusters.

Supplementary materials

The results of the DFT study without the dispersion correction are presented along with all the geometry parameters. Furthermore, the optimized Cartesian coordinates for all the clusters are available therein.

Ⅴ. ACKNOWLEDGMENTS

This work was partially supported by the National Natural Science Foundation of China (No.11404074) and the Belt and Road Initiative by Chinese Academy of Sciences. Louis Hitler also thanks the Chinese Scholarship Council Fellowship for International Master Students.

Supporting Information
Table S1 Calculated DFT-based descriptors of (TiO2)n clusters
Table S2 Adsorption energy of CO2 calculated with DFT computational method.
Table S3 Adsorption energy of CO calculated with DFT computational method.
 FIG. 1 Variation of the CO2 adsorption energy with adsorption sites, calculated with DFT computational method.
 FIG. 2 Variation of the CO adsorption energy with adsorption sites, calculated with DFT computational method.
 FIG. 3 Variation of the CO2 adsorption energy with adsorption sites, calculated DFT-TS computational method.
 FIG. 4 Variation of the CO adsorption energies with adsorption sites, calculated DFTTS computational method.
 FIG. 5 CO2 adsorption geometry and configuration calculated with DFT computational method. (a) CO2 adsorption on 4-fold coordinated Ti atom (Ti4c), (b) CO2 adsorption on 2-fold coordinated O atom (O2c), (c) CO2 adsorption on 1-fold coordinated O atom in terminal Ti-O (O1c). The red and grey colors represent O and Ti atoms of the clusters, respectively; black and blue colors represent O and C atoms of the CO2, respectively.
 FIG. 6 CO adsorption geometry and configuration calculated with DFT computational method. (a) CO adsorption on 4-fold coordinated Ti atom (Ti4c), (b) CO adsorption on 2- fold coordinated O atom (O2c), (c) CO adsorption on 1-fold coordinated O atom in terminal Ti-O (O1c). The red and grey colors represent O and Ti atoms of the clusters, respectively; black and blue colors represent O and C atoms of the CO, respectively.

Optimized Cartesian coordinates and total energies of clusters

Table S4 Optimized Cartesian coordinates and total energies of cluster n = 3
Table S5 Optimized Cartesian coordinates and total energies of cluster n = 4
Table 6 Optimized Cartesian coordinates and total energies of cluster n = 5
Table S7 Optimized Cartesian coordinates and total energies of cluster n = 6
Table S8 Optimized Cartesian coordinates and total energies of cluster n = 7
Table S9 Optimized Cartesian coordinates and total energies of cluster n = 8
Table S10 Optimized Cartesian coordinates and total energies of cluster n = 9
Table S11 Optimized Cartesian coordinates and total energies of cluster n = 10
Table S12 Binding energy (B.E/eV), ionization potential (IP/eV), and charge transfer
Table S13 Bond length (dc-o) and bond angle (C-Ti-O) of the reactants, transition states, and product geometries used for theoretical calculation of dissociation barrier of clusters
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a. 中国科学院纳米系统与多级次制造重点实验室，纳米科学卓越创新中心，国家纳米科学中心，北京 100190;
b. 中国科学院大学，北京 100049