Be12O12 Nano-cage as a Promising Catalyst for CO2 Hydrogenation

An efficient conversion of CO2 into valuable fuels and chemicals has been hotly pursued recently. Here, for the first time, we have explored a series of M12x12 nano-cages (M = B, Al, Be, Mg; X = N, P, O) for catalysis of CO2 to HCOOH. Two steps are identified in the hydrogenation process, namely, H2 activation to 2H*, and then 2H* transfer to CO2 forming HCOOH, where the barriers of two H* transfer are lower than that of the H2 activation reaction. Among the studied cages, Be12O12 is found to have the lowest barrier in the whole reaction process, showing two kinds of reaction mechanisms for 2H* (simultaneous transfer and a step-wise transfer with a quite low barrier). Moreover, the H2 activation energy barrier can be further reduced by introducing Al, Ga, Li, and Na to B12N12 cage. This study would provide some new ideas for the design of efficient cluster catalysts for CO2 reduction.

The energy crisis and greenhouse effect caused by the emission of carbon dioxide (CO 2 ) are the two serious global problems at the present day and even remain in the next 50 years 1 , which stimulated the current research interest in efficient conversion of CO 2 into valuable fuels and chemicals [2][3][4] . However, due to the negative adiabatic electron affinity (EA) and large ionization potential (IP), the CO 2 molecule is thermodynamically stable and kinetically inert, thus making the conversion difficult under normal conditions 5 . To overcome these challenges, we need to understand the basic chemical processes of the conversion and seek for highly efficient, cost-effective, and environmentally sound catalysts. Since formic acid (FA) has been widely used as a medium for hydrogen storage and an industrial chemical, catalytic hydrogenation of CO 2 to FA becomes one of the most common and promising way to utilize CO 2 .
Recently, systems containing frustrated Lewis pairs (FLPs) have been found as effective catalysts for H 2 activation 6-8 , CO 2 reduction 9-11 and hydrogenation [12][13][14] for the production of C1 fuels. As we know that a FLP contains both Lewis acid and base centers, and the most common active Lewis pairs are B/N, B/P, Al/N and Al/P. Furthermore, a cationic Lewis acid component has also been extended to silicon 15,16 , carbon 17 , in ref. 9 and even the transition-metal (Zr 18,19 and Ti 20 ) complexes, while the Lewis base component has been extended to O 9 , carbenes 21 , ethers 22 , ketones 23 , and sulfides 24 . The reduction of CO 2 via FLPs usually consists of two major steps: hydrogen activation and hydrogen transfer to CO 2 , where a hydrogen molecule is first split into a proton (H + ) and a hydride (H − ), and then CO 2 is reduced via a concerted or sequential transfer of H + and H − to CO 2 . By theoretical calculations, Liu et al. found a relationship between these two steps, i.e. a stronger FLP results in a lower energy barrier for H 2 activation, but in a higher energy barrier for H transfer 12 .
Inspired by the mechanism of CO 2 hydrogenation by FLPs, here we raise a question: whether the clusters consisting of the active element for FLPs such as B/N, B/P, Al/N and Al/P etc. could act as catalysts for H 2 splitting and CO 2 further hydrogenation?
In the past few years, experiment and theoretical research efforts have been devoted to (XY) n (M = B, Al, Be, Mg; X = N, P, O) nanostructures such as nanocages, nanohorns, nanotubes, and nanowires [25][26][27][28][29] . Theoretical studies found that the fullerene-like cages (XY) 12 with Th symmetry were the most stable geometry 30,31 . Moreover, B 12 N 12 has been synthesized and detected by laser desorption time-of-flight mass spectrometry 32 . Al-, Gadoped 33 and Li-, Na-decorated 34 stable B 12 N 12 clusters have been also theoretically studied. In addition, previous studies indicated that BN 35 , AlN 36,37 and BeO 38,39 clusters can absorb H 2 molecularly due to the polar bond between B and N, Al and N, Be and O with different electron affinities. Moreover BN clusters can also capture CO 2 40-42 . In fact, the most special point for cluster catalysis is that the addition or removal of a single atom can have a substantial influence on the activity and selectivity of reaction, which provides us the basis for converting H 2 and CO 2 Activation. In order to determine the configuration with the lowest energy for H 2 and CO 2 adsorption on the surface of the cluster, a number of different initial structures have been used for optimization. The results of stable H 2 /M 12 x 12 , CO 2 /M 12 x 12 complexes as well as their corresponding transition state (TS) structures are shown in Fig. 2. For the convenience of discussions, we distinguish the physisorption (P) from the chemical functionalization (C) for the molecules on the cages. As seen from Fig. 2, in the process of physisorption, H 2 and CO 2 molecules are weakly adsorbed on the clusters with minor changes in geometry. While in the chemical adsorption, H 2 is dissociated forming 2H* and CO 2 is chemically activated forming CO 2 *. The corresponding geometry parameters as well as their TSs are shown in Tables S2 and S3, and the interaction energies of H 2 and CO 2 physisorption and chemical absorption are given in Table S4 of Supporting Information.
The activation energies of H 2 on MX-64 and MX-66 are labeled as ∆G H 1 and ∆G H 2 , respectively, while the activation energies of CO 2 on MX-64 and MX-66 are labeled as ∆G C 1 and ∆G C 2 respectively. The energy barriers  for H 2 activation (∆G H ) are calculated as the Gibbs energy difference between the TS H (the TS for H 2 activation) and the initial state of H 2 adsorption: Similarly, the energy barriers for the CO 2 activation (∆G C ) are calculated as the Gibbs energy difference between the TS C (the TS for CO 2 activation) and the initial state of CO 2 adsorption: The calculated results are listed in Table 1, and typical structures with H 2 and CO 2 either in physisorption, or chemisorption as well as their transition states are given in the Fig. 2. All the Gibbs energy barrier for H 2 activation on MX-64 are all lower than which of the MX-66. When the activation barrier is overcome, H 2 can be dissociated generating hydridic (Ha) and protic (Hb) hydrogens.
Instead for CO 2 activation, the Gibbs energy barrier on MX-64 are all higher than that of the MX-66 except for Al 12 P 12 and Be 12 O 12 clusters. The activation barriers of CO 2 are lower than that of H 2 for the studied systems except for B 12 P 12 . The Al, Ga doped and Li, Na decorated B 12 N 12 cages have lower activation energy barriers for H 2 and CO 2 than those of the pristine B 12 N 12 . This illustrates that the doping with Al and Ga as well as decoration with Li and Na can increase the activity of B 12 N 12 cluster.
To clarify the effect of H 2 and CO 2 adsorptions on the electronic structures of nano-cages, natural bond orbital (NBO) analyses are performed and the results are listed in Table S5, from which one can see that upon the adsorption, charges on the cages are redistributed due to the geometry change and charge transfer. For example, in all the cases CO 2 received electrons from cages resulting in the activation. The charges on M sites in all clusters are decreased upon the H 2 adsorption, while increased upon the CO 2 adsorption.
The different behaviors in H 2 activation on MX-64 and MX-66 are due to the different activities between them. As seen from Table S5, more charges are on M and X sites in MX-64 than those in MX-66, which makes the former more active with a lower H 2 activation barrier as compared with the latter one. 2H* transfer mechanism. Two reaction pathways for CO 2 hydrogenation on Lewis pair moiety have been identified, one involves the physisorped CO 2 reacting with the chemisorbed 2H*, and the other one involves the physisorped H 2 reacting with CO 2 *. For the latter, the reaction barrier for hydrogenation of the activated CO 2 * is usually very high as found by Ye 12 (2.65 eV in UiO-66-P-BF 2 catalyst) and by us (2.84 eV for MX-64 and 2.97 eV for MX-66 of B 12 N 12 ), and this pathway leads to the formation of chemisorbed HCO and OH ([HCO + OH]*) instead of HCOOH as shown in Supporting Information (Fig. S1). Consequently, in the following discussions, we only focused on the first path way for HCOOH formation.
According to the first pathway, CO 2 is firstly physiosorbed on MX-2H*(P), and then forms HCOOH (C) via the transition state (TS) (Fig. 3)  In other words, the H transfer step is essentially the donation of a hydride and a proton from the ion-pair products to CO 2 via a concerted mechanism. Tables S6 and S7 list the corresponding geometry parameters, transition states, and interaction energies for CO 2 and HCOOH. When attempting to bind CO 2 with Mg 12 O 12 −2H* in a way shown in Fig. 3(P), we cannot find any stable structures from our calculations. While CO 2 can directly bonds at Mg and O sites (as shown in Fig. 4a) with a stronger binding energy of − 0.5 eV (Table S4). Similarly, when introducing HCOOH to Mg 12 O 12 shown in Fig. 3(C), one H atom of HCOOH was taken away by the O atom in Mg 12 O 12 nano-cage (Fig. 4b). This suggests that Mg 12 O 12 is not competent to be the catalyst for CO 2 hydrogenation to HCOOH.
The activation energies of H 2 transfer on MX-64 and MX-66 are labeled as ∆G HT 1 and ∆G HT 2 and respectively. The energy barriers for H 2 activation (∆G HT ) are calculated as the Gibbs energy difference between the TS HT (the TS for H 2 transfer) and the initial state of CO 2 the physisorbed on MX-2H*:

HT TS HT p HT
The corresponding activation energies for H 2 transfer are listed in Table 2, where one can see that the activation energies of H transfer are all higher than 1.0 eV, except for Be 12 O 12 cage. Just the opposite to the H 2 activation process in Table 1, all the Gibbs energy barriers for 2H* transfer on MX-64 are all higher than that of MX-66.
Based on the overall consideration of H 2 activation and 2 H* transfer barriers as listed in Tables 1 and 2, one can find that introducing Al, Ga, Li, and Na to B 12 N 12 cage has definitely decreased the H 2 activation energy barrier but increased the 2H transfer energy as compared to the pristine B 12 N 12 .
In order to be more intuitive, a potential energy surfaces of the reaction pathway are shown in Fig. 5 showing a balance between H 2 activation and H transfer. Thus, the interaction between the cluster and H 2 is extremely important, the stronger catalyst with more strength to activate the hydrogen molecule would promote a faster hydrogen activation process. On the other hand, a stronger catalyst has more strength to keep the hydrogen, thus would slow down the hydrogen transfer process. This is in accordance with the general Sabatier principle 43 .
To understand the trend of protonation activation barriers for the studied nanocages, we analyze the charges on C site of CO 2. In the free standing state, C carries 1.069 e. When CO 2 is adsorbed with MX-66 configuration on B 12 N 12 -2H*, NaB 12 N 12 -2H* and LiB 12 N 12 -2H*, the charges increase to 1.086, 1.084, and 1.087 e, respectively. The increased charges on C site make it more active to easily bind H with smaller barriers. The similar mechanism can also be applied to other cages. 2H* transfer one by one with stepwise mechanism. When checking the overall the activation energy barrier of H 2 activation and transfer (seen from Tables 1 and 2), one can find that many clusters such as Al 12 N 12 , NaB 12 N 12 and AlB 11 N 12 etc. have lower H 2 activation but higher 2 H* transfer barriers. To search for a lower barrier of H transfer, the other mechanism needs to be investigated further. We find that a new stepwise mechanism exists for CO 2 hydrogenation only on Be 12 O 12 cage as shown in Fig. 6.
By following this reaction mechanism, the first H transfer is a rate-limiting step-with an activation energy of 0.22 eV on MX-64 bond (red line on Fig. 6) and 0.36 eV on the MX-66 bond (blue line on Fig. 6), In contrast, the 2H* transfer activation on MX-64 and MX-66 bonds is 0.45 eV and 0.24 eV, respectively. Then, we can conclude  that 2H* simultaneously transfer to CO 2 on MX-66 bond has lower activation energy than that of the one H transfer stepwise, but on MX-64 bond the situation is opposite. For practical applications of an efficient catalyst, both the H 2 activation and transfer barriers should be comparable or lower than 1 eV 44 . Among all systems studied here, Be 12 O 12 is the most promising catalyst, where the H 2 activation barrier is close to 1 eV (1.04 eV) on MX-64 bond, and the following H* transfer barriers are all lower than 1 eV, (0.45 eV by the 2H* simultaneously transfer mechanism, while 0.22 eV by the H* stepwise transfer mechanism). Therefore, the reaction pathway on Be 12 O 12 MX-64 bond has the lowest barrier based on the overall consideration of the H 2 activation (1.04 eV) and H* stepwise transfer (0.22 eV).

Conclusions
In summary, based on the DFT and MP2 calculations, a series M 12 X 12 nano-cages have been studied for activating H 2 and CO 2 to form HCOOH. The hydrogenation process mainly consists of H 2 activation to 2H*, and then 2H* further transfer to CO 2 forming a HCOOH molecule. Two kinds of H* transfer mechanisms are found: one involves 2H* simultaneous transfer, and the other is a stepwise H* transfer to CO 2 . The two mechanisms result  in the same product HCOOH. Moreover, Al, Ga doped and Li, Na decorated B 12 N 12 cages have lower H 2 activation energy barriers, but higher 2H* transfer activation barriers than that of the pristine B 12 N 12 . For practical applications, in order to have an efficient catalyst to reduce CO 2 , we should search for a catalyst that has a balance between the energy barriers for H 2 activation and the H transferring. Among all the systems studied here, Be 12 O 12 is found to be the most promising catalyst, its reaction pathway on MX-64 bond has the lowest barriers (1.04 eV for H 2 activation and 0.22 eV for H* transferring). This conclusion would motivate experimental work in the future.

Methods
Since many theoretical calculations have demonstrated that different DFT functions (e.g. B97D, ω -B97X-D, and M06-2X) and basis sets (e.g. 6-31 G*, 6-31 + G**) led to very similar results for the systems only containing main group elements for H 2 activations 7,8,11 . In this work, all the geometry optimizations are performed at the M06-2X/6-31 + G** level as implemented in Gaussian 09 package 45 . Solvent effects are taken into account by using the polarizable continuum model (PCM) with toluene as a solvent. The highly parameterized, empirical exchange correlation functional, M06-2X, developed by Zhao and Truhlar, was shown to better describe the main-group thermochemistry and kinetics than other density functionals such as B3LYP 46 . Moreover, this hybrid density M06-2X functional has been previously proved to have a good reliability in computing molecular binding energies of H 2 and CO 2 on FLPs 47 . Frequency calculations are carried out at the same level to characterize the nature of the stationary points along the reaction coordinates. No imaginary frequencies were found for the local minima, and one and only one imaginary frequency was found for the transition state. The Natural Bond Orbital (NBO 3.1) program 48 , was used to calculate the natural charges at the M06-2X/6-31 + G** level of theory. The thermal contributions at room temperature (298.15 K) including the specific free energies were obtained from a harmonic analysis, and accurate electronic energies were obtained from frequency calculations using Møller-Plesset second-order perturbation theory (MP2) 49,50 with the cc-pVTZ triple-ζ quality basis 51,52 . Using the optimized geometries and starting from the TS, intrinsic reaction coordinate (IRC) calculations are performed to verify the true connection of the reactants, the transition states and the products for both H 2 , CO 2 activation and H transfer processes.