-PdBi2 Monolayer: Two-Dimensional Topological Metal with Supe- rior Catalytic Activity for Carbon Dioxide Electroreduction to For- mic Acid

The lack of efficient electrocatalysts has been a main obstacle for the large-scale commercialization of CO2 electroreduction. In this work, we demonstrate that two-dimensional (2D) -PdBi2 monolayer is a promising solution for this issue. PdBi2 monolayer is a stable 2D crystal and the three-dimensional (3D) bulk interlayer energy is similar as for other layered materials that can be exfoliated into 2D crystals. Interestingly, -PdBi2 monolayer has rather intriguing electronic properties: while being metallic, it also has a nontrivial topological point. Remarkably, the extra electronic states at the Fermi level induced by the intrinsic spin−orbit coupling (SOC) effect significantly enhance the adsorption of OCHO* intermediate on -PdBi2 monolayer, resulting in a rather small onset potential of −0.26 V vs. RHE for CO2 electroreduction to HCOOH. These results not only suggest a promising candidate for CO2 electrolysis but also deepen our understanding of the factors dominating the catalytic activity of 2D materials. Formic acid (HCOOH) is an important chemical intermediate and a promising liquid fuel for driving direct formic acid fuel cells. At present, methanol carbonylation remains the most common industrial strategy for the production of HCOOH. However, this method is energy intensive and can cause environmental pollution. In contrast, the utilization of electricity generated from renewable energy sources such as wind and solar energy to produce HCOOH through CO2 electroreduction represents a more efficient and green strategy, which also helps to reduce the amount of CO2 in the atmosphere. CO2 is a stable linear molecule with robust chemical inertness. Therefore, the CO2 electroreduction requires an electrocatalyst to activate the C=O bonds and accelerate the reaction kinetics. In the 1980s, Hori et al. reported that some metals (Pb, Cd, Hg, TI) have good activity for the electroreduction of CO2 to HCOOH. However, these metals are highly toxic and therefore cannot be used in industrial production. The noble metal Pd catalyzes CO2 reduction to HCOOH at a very low overpotential, but it suffers gradual activity decay induced by the formation of a poisoning CO adlayer. Although the preparation of HCOOH from Sn-based electrocatalysts has received much attention recently, it is often accompanied by a large amount of H2 and CO products due to its limited catalytic selectivity. In recent years, the application of two-dimensional (2D) metals in the field of CO2 electroreduction has received widespread attention. The large specific surface area of 2D materials facilitates the diffusion of reactants, and its more exposed active sites are conducive to rapid charge transfer. Xie et al. reported that atomically thin Co layers show significantly improved catalytic activity for CO2 reduction to HCOOH compared to bulk Co. However, the ultrathin transition metal layers are prone to oxidation, causing a rapid decay in cyclability. Recently, group-15 metal elements, including Sb and Bi, were revealed to be highly active and selective for CO2 electroreduction to HCOOH when thinned into 2D few-layer structures. However, the reported current density of 2D Sb and Bi electrocatalysts is generally lower than 30 mA cm, which is far below the technical requirements for large-scale industrial applications (200 mA cm). At present, stable and efficient 2D electrocatalysts for CO2 reduction to HCOOH are highly sought. In this communication, by means of density functional theory (DFT) calculations (using the PBE functional, see supporting information for the computational details), we identified a novel 2D material, namely, -PdBi2 monolayer, as a promising candidate. Bulk -PdBi2 has been known since 1895, while its layered structure was discovered in 1953. According to our results, PdBi2 monolayer is experimentally viable and shows rather good catalytic performance towards CO2 electroreduction to HCOOH. In particular, the intrinsic spin−orbit coupling (SOC) effect plays an important role in governing the catalytic activity of the -PdBi2 monolayer. Figure 1. (a) Side view of the bulk -PdBi2. (b) Top view of the single-layer -PdBi2 structure. Figure 1a displays the optimized geometric structure of bulk PdBi2, which crystallizes in a layered body-centered tetragonal structure (I4/mmm) with an eight-coordinated PdBi8 building motif. The lattice parameters of bulk -PdBi2 were optimized to be a = b = 3.38 Å, c = 12.85 Å, which are in good agreement with experimental data (a = b = 3.36 Å, c = 12.98 Å). The interlayer Bi-Bi distance is 3.76 Å, indicating the absence of covalent bonds between PdBi2 layers. Nevertheless, isolating an -PdBi2 layer from the bulk phase still results in a slight lattice shrinkage (a = b =3.34 Å). In -PdBi2 monolayer, every four Bi atoms are faceshared with the neighbouring PdBi8 motifs to a 2D network (Figure 1b). By intruding a fracture in a five-layer model of -PdBi2, the cleavage energy of -PdBi2 monolayer was estimated to be 0.88 J m (Figure S1), which is comparable to calculations at the same computational level for well-known 2D crystals that have been realized experimentally via various exfoliation techniques, such as MoS2 (0.42 J m) and Ca2N (1.09 J m). High mechanical and chemical stability are prerequisites for any catalyst. The calculated phonon dispersion of -PdBi2 monolayer is shown in Figure S2. No imaginary phonon modes are present, which is indicative for good kinetic stability. Moreover, ab initio molecular dynamics simulations in a 6x6x1 super cell confirm the thermodynamic stability. According to our results (Figure S3), -PdBi2 monolayer remains crystalline throughout a 10 ps simulation at 500 K, suggesting that -PdBi2 monolayer has appreciable thermodynamic stability as its structure is separated from other local minima by an adequate barrier on the potential energy surface. Figure 2. Band structure and DOS of -PdBi2 monolayer. The activity of an electrocatalyst is fundamentally governed by its electronic structure. Therefore, we have calculated the band structure of -PdBi2 monolayer to obtain a preliminary understanding of its catalytic activity. As shown in Figure 2, -PdBi2 monolayer is metallic with several energy levels crossing the Fermi level, which is the same as in bulk -PdBi2 (Figure S4). Interestingly, there is a Dirac-like cone at the M (0.5, 0.5, 0) point below the Fermi level. Since Bi and Pd are both heavy elements that give raise to considerable SOC, we also calculated the SOCcorrected band structure of -PdBi2 monolayer (Figure 2). Remarkably, although the metallic character of -PdBi2 monolayer is still preserved, SOC opens a large gap at the Dirac-like cone at the M point and a flat band emerges at the Fermi level. According to the calculated orbital-resolved band structures (Figure S5), the flat band is mainly contributed by the 6px and 6py orbitals of Bi and partially by the 4dxz and 4dyz orbitals of Pd. Especially, due to the existence of the flat band, the DOS at the Fermi level is very high (an effect that is not reflected without consideration of SOC) (Figure 2). A higher DOS at the Fermi level is likely to promote electron transfer and thus enhances the affinity to adsorbed species, which is beneficial for electrocatalytic activity. To substantiate our results, we also calculated the band structure and DOS of -PdBi2 monolayer using the hybrid HSE06 functional. Both functionals (PBE and HSE06) produce very similar results (Figure S6). The SOC-induced deformation of the Dirac-like point is a strong hint for the existence of topologically nontrivial phase, which we have confirmed by calculation of the Z2 topological invariant () of -PdBi2 monolayer. Due to the existence of structural inversion symmetry, the  of -PdBi2 monolayer can be directly calculated on the basis of the parity of the Bloch wave function for all the filled bands at the four time-reversal-invariant momenta (TRIM) points in the Brillouin zone (, X, M and Y). Especially, the parities at X and Y points are identical for -PdBi2 monolayer owing to the square symmetry, and thus have no effect on the band topology. Therefore, we calculated the parity eigenvalues of the Bloch wave function for the occupied spindegenerate bands of -PdBi2 monolayer at the  and M points. As listed in Table S1, the product of the parity eigenvalues at the  point is +1, whereas it is −1 at the M point, resulting in  = 1 and confirming the topological states for -PdBi2 monolayer. To confirm the non-trivial topological character, we identified the topological edge states of a ~10 nm wide -PdBi2 nanoribbon (Figure S7). The calculated edge band structure show the topological edge states, which conclusively confirms the nontrivial band topology for 2D -PdBi2 monolayer. Thus, -PdBi2 monolayer can be interpreted as a 2D nontrivial topological metal. Figure 3. (a) Geometric structures of various states and (b) free energy diagrams of CO2 electroreduction to HCOOH on -PdBi2 monolayer. Next, we investigated the catalytic activity of -PdBi2 monolayer for CO2 electroreduction to HCOOH. The water-solid interface was simulated by explicitly placing one water layer above the surface of -PdBi2 monolayer (Figure S8). As SOC is strongly affecting the electronic properties close to the Fermi level, it has been included in reaction free energy (G) calculations in the manner of single-point correction. Generally, the electroreduction of CO2 to HCOOH initiates with the hydrogenation of C atom through a proton-coupled electron transfer process, resulting in the formation of an OCHO* species (Figure 3a). According to our calculations, this step is endothermic with a G of 0.20 eV for -PdBi2 monolayer (Figure 3b). The formed OCHO* species is stabilized on the top of Bi atom with a Bi-O length of 2.68 Å. Upon the second proton-coupled electron transfer that is also endothermic by 0.11 eV, the OCHO* species transforms to a ph

Formic acid (HCOOH) is an important chemical intermediate and a promising liquid fuel for driving direct formic acid fuel cells. 1 At present, methanol carbonylation remains the most common industrial strategy for the production of HCOOH. However, this method is energy intensive and can cause environmental pollution. In contrast, the utilization of electricity generated from renewable energy sources such as wind and solar energy to produce HCOOH through CO2 electroreduction represents a more efficient and green strategy, 2 which also helps to reduce the amount of CO2 in the atmosphere. CO2 is a stable linear molecule with robust chemical inertness. Therefore, the CO2 electroreduction requires an electrocatalyst to activate the C=O bonds and accelerate the reaction kinetics. In the 1980s, Hori et al. reported that some metals (Pb, Cd, Hg, TI) have good activity for the electroreduction of CO2 to HCOOH. 3 However, these metals are highly toxic and therefore cannot be used in industrial production. The noble metal Pd catalyzes CO2 reduction to HCOOH at a very low overpotential, 4 but it suffers gradual activity decay induced by the formation of a poisoning CO adlayer. Although the preparation of HCOOH from Sn-based electrocatalysts has received much attention recently, 5 it is often accompanied by a large amount of H2 and CO products due to its limited catalytic selectivity.
In recent years, the application of two-dimensional (2D) metals in the field of CO2 electroreduction has received widespread attention. 6 The large specific surface area of 2D materials facilitates the diffusion of reactants, and its more exposed active sites are conducive to rapid charge transfer. Xie et al. reported that atomically thin Co layers show significantly improved catalytic activity for CO2 reduction to HCOOH compared to bulk Co. 7 However, the ultrathin transition metal layers are prone to oxidation, causing a rapid decay in cyclability. Recently, group-15 metal elements, including Sb 8 and Bi, 9 were revealed to be highly active and selective for CO2 electroreduction to HCOOH when thinned into 2D few-layer structures. However, the reported current density of 2D Sb and Bi electrocatalysts is generally lower than 30 mA cm −2 , which is far below the technical requirements for large-scale industrial applications (200 mA cm −2 ). 10 At present, stable and efficient 2D electrocatalysts for CO2 reduction to HCOOH are highly sought.
In this communication, by means of density functional theory (DFT) calculations (using the PBE functional, see supporting information for the computational details), we identified a novel 2D material, namely, -PdBi2 monolayer, as a promising candidate. Bulk -PdBi2 has been known since 1895, 11 while its layered structure was discovered in 1953. 12 According to our results, -PdBi2 monolayer is experimentally viable and shows rather good catalytic performance towards CO2 electroreduction to HCOOH. In particular, the intrinsic spin−orbit coupling (SOC) effect plays an important role in governing the catalytic activity of the -PdBi2 monolayer.

Figure 1a
displays the optimized geometric structure of bulk -PdBi2, which crystallizes in a layered body-centered tetragonal structure (I4/mmm) with an eight-coordinated PdBi8 building motif. The lattice parameters of bulk -PdBi2 were optimized to be a = b = 3.38 Å, c = 12.85 Å, which are in good agreement with experimental data (a = b = 3.36 Å, c = 12.98 Å). 12 The interlayer Bi-Bi distance is 3.76 Å, indicating the absence of covalent bonds between PdBi2 layers. Nevertheless, isolating an -PdBi2 layer from the bulk phase still results in a slight lattice shrinkage (a = b =3.34 Å). In -PdBi2 monolayer, every four Bi atoms are faceshared with the neighbouring PdBi8 motifs to a 2D network (Figure 1b). By intruding a fracture in a five-layer model of -PdBi2, the cleavage energy of -PdBi2 monolayer was estimated to be 0.88 J m -2 ( Figure S1), which is comparable to calculations at the same computational level for well-known 2D crystals that have been realized experimentally via various exfoliation techniques, such as MoS2 (0.42 J m -2 ) 13 and Ca2N (1.09 J m -2 ). 14 High mechanical and chemical stability are prerequisites for any catalyst. The calculated phonon dispersion of -PdBi2 monolayer is shown in Figure S2. No imaginary phonon modes are present, which is indicative for good kinetic stability. Moreover, ab initio molecular dynamics simulations in a 6x6x1 super cell confirm the thermodynamic stability. According to our results ( Figure S3), -PdBi2 monolayer remains crystalline throughout a 10 ps simulation at 500 K, suggesting that -PdBi2 monolayer has appreciable thermodynamic stability as its structure is separated from other local minima by an adequate barrier on the potential energy surface. The activity of an electrocatalyst is fundamentally governed by its electronic structure. 15 Therefore, we have calculated the band structure of -PdBi2 monolayer to obtain a preliminary understanding of its catalytic activity. As shown in Figure 2, -PdBi2 monolayer is metallic with several energy levels crossing the Fermi level, which is the same as in bulk -PdBi2 ( Figure S4). Interestingly, there is a Dirac-like cone at the M (0.5, 0.5, 0) point below the Fermi level. Since Bi and Pd are both heavy elements that give raise to considerable SOC, we also calculated the SOCcorrected band structure of -PdBi2 monolayer (Figure 2). Remarkably, although the metallic character of -PdBi2 monolayer is still preserved, SOC opens a large gap at the Dirac-like cone at the M point and a flat band emerges at the Fermi level. According to the calculated orbital-resolved band structures (Figure S5), the flat band is mainly contributed by the 6px and 6py orbitals of Bi and partially by the 4dxz and 4dyz orbitals of Pd. Especially, due to the existence of the flat band, the DOS at the Fermi level is very high (an effect that is not reflected without consideration of SOC) (Figure 2). A higher DOS at the Fermi level is likely to promote electron transfer and thus enhances the affinity to adsorbed species, which is beneficial for electrocatalytic activity. To substantiate our results, we also calculated the band structure and DOS of -PdBi2 monolayer using the hybrid HSE06 functional. Both functionals (PBE and HSE06) produce very similar results (Figure S6).
The SOC-induced deformation of the Dirac-like point is a strong hint for the existence of topologically nontrivial phase, 16 which we have confirmed by calculation of the Z2 topological invariant () of -PdBi2 monolayer. 17 Due to the existence of structural inversion symmetry, the  of -PdBi2 monolayer can be directly calculated on the basis of the parity of the Bloch wave function for all the filled bands at the four time-reversal-invariant momenta (TRIM) points in the Brillouin zone (, X, M and Y). Especially, the parities at X and Y points are identical for -PdBi2 monolayer owing to the square symmetry, and thus have no effect on the band topology. Therefore, we calculated the parity eigenvalues of the Bloch wave function for the occupied spindegenerate bands of -PdBi2 monolayer at the  and M points. As listed in Table S1, the product of the parity eigenvalues at the  point is +1, whereas it is −1 at the M point, resulting in  = 1 and confirming the topological states for -PdBi2 monolayer. To confirm the non-trivial topological character, we identified the topological edge states of a ~10 nm wide -PdBi2 nanoribbon ( Figure S7). The calculated edge band structure show the topological edge states, which conclusively confirms the nontrivial band topology for 2D -PdBi2 monolayer. Thus, -PdBi2 monolayer can be interpreted as a 2D nontrivial topological metal. Next, we investigated the catalytic activity of -PdBi2 monolayer for CO2 electroreduction to HCOOH. The water-solid interface was simulated by explicitly placing one water layer above the surface of -PdBi2 monolayer ( Figure S8). As SOC is strongly affecting the electronic properties close to the Fermi level, it has been included in reaction free energy (G) calculations in the manner of single-point correction. Generally, the electroreduction of CO2 to HCOOH initiates with the hydrogenation of C atom through a proton-coupled electron transfer process, resulting in the formation of an OCHO* species (Figure 3a). According to our calculations, this step is endothermic with a G of 0.20 eV for -PdBi2 monolayer (Figure 3b). The formed OCHO* species is stabilized on the top of Bi atom with a Bi-O length of 2.68 Å. Upon the second proton-coupled electron transfer that is also endothermic by 0.11 eV, the OCHO* species transforms to a physisorbed HCOOH* species that can be spontaneously released from -PdBi2 monolayer. Therefore, the potential-limiting step for CO2 electroreduction to HCOOH on -PdBi2 monolayer is the formation of OCHO* species. In particular, when the SOC correction is canceled, the G of this step is pronouncedly increased to be 0.37 eV (Figure 3b), indicative of the essential role of SOC, with the consequence of high DOS formation, in boosting the catalytic activity. Since the G for the OCHO* formation is equal to the adsorption free energy of OCHO* (GOCHO*), the SOC effect actually significantly enhances the adsorption of OCHO* species on -PdBi2 monolayer, which is consistent with the above DOS analysis. Here, we should note that recently several studies also demonstrated that the topological surface states can enhance the adsorption of hydrogen on catalytsts. 18 In addition to HCOOH, carbon monoxide (CO) is also a possible product of two-electron (2e) CO2 electroreduction if the first hydrogenation of CO2 occurs on the O atom. However, according to our calculations (Figure S9), the formation of COOH* intermediate on -PdBi2 monolayer through the hydrogenation of O atom is significantly endothermic by 1.04 eV, which is much higher than the formation of OCHO* species (0.20 eV). Therefore, the formation of CO on -PdBi2 monolayer could be effectively overwhelmed, contributing to the high selectivity for the formation of HCOOH. Remarkably, the surface of -PdBi2 monolayer only slightly attracts CO by physisorption (adsorption energy of −0.26 eV) and the chemisorbed species is repulsive. This implies that -PdBi2 monolayer presents a high resistance to CO poisoning, which is a large advantage over Pd catalysts. 4 Moreover, the competing HER can be effectively suppressed due to the rather positive adsorption free energy of H* species (0.81 eV) on -PdBi2 monolayer. Therefore, HCOOH will be the major product for CO2 electroreduction on -PdBi2 monolayer. Finally, on the basis of above obtained SOC-corrected data, we further constructed a microkinetics model for the CO2 conversion to HCOOH to give an intuitive demonstration of the catalytic performance of -PdBi2 monolayer. As presented in Figure 4, the simulated polarization curve of -PdBi2 monolayer shows a current onset at approximately −0.26 V, which is much less than the experimentally measured onset potentials of other Bi-based catalysts. 9 Remarkably, with increasing electrode potential, the current density of -PdBi2 monolayer rapidly increases and reaches 200 mA cm −2 at a potential of −0.63 V vs. RHE, which meets the commercialization requirement of an efficient catalyst for CO2 electroreduction. The above results vividly demonstrate that -PdBi2 monolayer is a promising electrocatalyst for CO2 reduction to HCOOH.
To summarize, the structural, electronic and catalytic properties of a proposed 2D material, namely, -PdBi2 monolayer, have been systematically studied on the basis of DFT. -PdBi2 monolayer is a nontrivial 2D topological metal with high experimental feasibility and good stability. The intrinsic SOC effect enhances the adsorption of the OCHO* intermediate on -PdBi2 monolayer, leading to superior catalytic activity for CO2 electroreduction to HCOOH. In particular, the high current density at low operating potentials provided by -PdBi2 monolayers would make the production of HCOOH via CO2 electroreduction commercially viable. Our work highlights the role of SOC effects in boosting the cata-lytic activity, which would promote more experimental and theoretical efforts on developing topological materials for catalysis application.

ASSOCIATED CONTENT Supporting Information
The Supporting Information is available free of charge via the Internet at http://pubs.acs.org. Computational methods, structure of bulk -PdBi2, phonon spectrum of -PdBi2 monolayer, MD simulations results, band structure of bulk -PdBi2, orbital-resolved band structures of -PdBi2 monolayer, HSE band structure and DOS of -PdBi2 monolayer, parity eigenvalues of the Bloch wave function for the occupied spin-degenerate bands of -PdBi2 monolayer, geometric structure and electronic band structure of -PdBi2 nanoribbon, views of solvent model of water on -PdBi2 monolayer, free energy diagrams of CO2 electroreduction to CO on -PdBi2 monolayer.

Notes
The authors declare no competing financial interests.

Computational Details
DFT Calculations. Density functional theory (DFT) calculations were performed using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional 1 and the projector-augmented wave (PAW) approach, 2,3 as implemented in the VASP software. 4,5 A 460 eV cutoff energy for the kinetic energy was adopted after thorough testing. k-space samplings of 12 × 12 × 12 for the unit cell of bulk β-PdBi 2 and 12 × 12 × 1 for the unit cell of β-PdBi 2 monolayer have been employed. The energy convergence threshold was set as 1×10 -5 eV, and all geometric structures were fully optimized until the force on each ion was less than 0.01 eV/Å. For monolayer calculations, the distance of vacuum space was set to be 20 Å to avoid the interaction between periodic images. For thermodynamics calculations of electrochemical reactions, van der Waals interactions were included utilizing Grimme's D3 method. 6 The phonon spectrum was computed using Phonopy code 7 with density functional perturbation theory (DFPT). 8 Molecular dynamics simulations were performed using a 6 × 6 × 1 supercell of β-PdBi 2 monolayer within the NVT ensemble, and were lasted for 10 ps with a time step of 1.0 fs. The Nosé -Hoover thermostat has been employed. 9 Free Energy Calculations. We used a 33×1 supercell to explore the catalytic activity of the -PdBi 2 monolayer with the computational hydrogen electrode (CHE) model. 10 The free energy (G) of each species was calculated as where E tot is the total (internuclear repulsion and electronic energy of the PBE optimized structure with single-point spin-orbit coupling (SOC) corrections included) energy from the DFT calculations, T is system temperature (298.15 K), and E ZPE and S are zero-point energy and entropy, respectively. The E ZPE and S corrections to reaction intermediates were calculated by a harmonic analysis, where contributions from the basic -PdBi 2 slab were neglected, while these of small molecules are taken from the NIST database. The E ZPE and S corrections of HCOOH* and CO 2 are taken as the corresponding molecular values, as HCOOH* and CO 2 are physisorbed on the surface of the -PdBi 2 monolayer. The solvent effect on the intermediates has been taken into account by using an explicit water layer as shown in Figure S7. As revealed by previous works, the effect of one layer of water on adsorbate is essentially equivalent to more water layers. 11 After calculating the G of each species (Table S2), we obtained the free energy changes (∆G n , n= 1, 2, 3) of the elementary reaction steps. Following the computational hydrogen electrode (CHE) model, the effects of electrode potential (U) and pH on CO 2 reduction reaction can be treated as the energy shifts to free energy change in the electrochemical steps: ΔG U = eU and ΔG pH = k B Tln10 × pH. In this work the value of pH was assumed to be zero for acidic medium.
Microkinetics Simulations. Following previous study, 12 we further constructed a micro-kinetics model for the conversion of CO 2 to HCOOH on the -PdBi 2 , of which the reaction process is summarized as: where k i (i = 14) is rate constant, and k -i is rate constant of the reverse reaction. Based on steady-state approximation, the dynamical coverage rate of * (active site), CO 2 *, OCHO* and HCOOH* can be written as: where  is the coverage of the reaction intermediate, t is the time, and 2 ( ) and HCOOH(aq) are the mole fraction of CO 2 (aq) and HCOOH(aq), respectively.
2 ( ) is taken as 5.7910 4 , corresponding to 1 atm CO 2 (g) in equilibrium with CO 2 (aq). Since HCOOH should be relatively lower than 2 ( ) during catalysis, we assume that HCOOH is 110 5 . Besides, these coverages on the -PdBi 2 monolayer satisfy the following condition: * + 2 * + * + * = 1 (S10) According to the transition state theory, for CO 2 adsorption and HCOOH removal steps, their rate constant k i is calculated by, where G a,i is activation free energy and A' is an effective pre-exponential factor deduced by (xk B T)/h. x is the effective coefficient, k B is the Boltzmann constant, and h is Planck constant. As the adsorption-desorption step on the slab surface typically involves an energy barrier of 0.22-0.28 eV due to the solvent reorganization, 13, 14 the A' for HCOOH desorption can be estimated as 1.2010 8 s -1 . In addition, the equilibrium constant (K) of CO 2 adsorption and HCOOH desorption are expressed as: where ∆G is the free energy change of CO 2 adsorption and HCOOH desorption.
The k i of electrochemical step, which depends on the electrode potential (U), is calculated by, where U i is the reversible potential of step i deduced by U i = -ΔG i /e, E a,i is the activation energy at the reversible potential U i of step i, and  i is the symmetric factor taken as 0.5. We assume that is 1.2310 9 s -1 , as solvent reorganization may also bring an energy barrier for direct proton-electron transfer. The E a,i of the direct proton-electron transfer is generally small, and thereby we adopted E a,i = 0.3 eV for OCHO* and HCOOH* formation steps. In addition, the K i of nonelectrochemical step also depends on the U, and is given as: For all reaction steps, the k -i can be calculated from the its rate constant and equilibrium constant; that is: These rate equations are solved at steady state, and then we can get the turn over frequency (TOF). Finally, the current density (j) can be calculated by: where ρ is the surface density of active sites.          Table S2. Zero-point energy correction (E ZPE ), entropy contribution (TS), and the total free energy correction (G-E elec ) of the various states for CO 2 electroreduction.