Corrigendum: High-throughput screening of metal-porphyrin-like graphenes for selective capture of carbon dioxide

This corrects the article DOI: 10.1038/srep21788.


Results
To measure the CO 2 capture capabilities of nanomaterials from a mixed gas, we constructed a thermodynamic model of CO 2 adsorption on an adsorbent using the grand-canonical partition function 31 . We assumed a surface containing the number of identical, independent, and distinguishable adsorption sites (N s ) with no mixed adsorption of different molecules per adsorption site, wherein the number of adsorbed i-type gas molecules on the surface is N i . If the adsorbed molecules and gases are in equilibrium, the grand partition function of the system can be written as where superscript i indicates the type of gas, µ (< ) 0 i denotes the chemical potential of the i-type gas, and ε n i i (< 0) and g n i denote the average adsorption energy and degeneracy of configuration (for a given adsorption number n i ) of the i-type gas molecules, respectively. When the thermally average number of i-type CO 2 is calculated from i , the occupation function (i.e., coverage) of CO 2 for an adsorption site can be written as Therefore, the thermodynamic CO 2 capture capacity of nanomaterials from a mixed gas can be computed using where M i and m i denote the atomic mass and number of elements comprising the adsorbent, respectively.
The occupation function of CO 2 would have a positive value, i.e., at the adsorption (capture) conditions as shown in Fig. 1a, i is set and the superscript 'other' denotes molecules other than CO 2 . In this case, selective CO 2 adsorption occurs through competitive adsorption between CO 2 and other molecules; this is attributed to the fact that the Gibbs factor for CO 2 adsorption is much greater than unity and the Gibbs factors of other molecules, i.e., µ ) as shown in Fig. 1b, indicating that CO 2 adsorbed on the metal sites is released. Under a CO 2 pressure of ~10 −3 bar, the ideal conditions for adsorption and desorption are assumed to be 300 and 450 K, respectively, where µ CO 2 is approximately − 0.75 and − 1.20 eV, respectively, at ambient conditions. Thus, the key thermodynamic conditions for reversible and selective CO 2 capture from a mixed gas are as follows: From this we construct a computational approach to efficiently predict selective CO 2 capture materials based on first principles thermodynamics shown in Fig. 1(c). The thermodynamic conditions and capacity requirements 11 for screening are as follows: ε − . < 1 20eV CO 2 < 0.75 eV and ∆ ( , ) C P T > 3 mmol g −1 for CO 2 gas, and ∆ > ∆ CO other 2 and ∆ ( , ) C P T > 3 mmol g −1 for a mixed gas. ∆ ( , ) C P T denotes the difference between ( , ) C P T at 300 K and ( , ) C P T at 450 K under a pressure of 10 −3 bar, which indicates the CO 2 working capacity. These requirements may need to be revised depending on the operational environments.
We performed calculations on the adsorption energy of CO 2 molecules on the M sites of M-porphyrin-like graphene (Fig. 2a). Elements of atomic numbers up to 92 for the M site were considered, and the others were ruled out because of their heavy weight. Sc-, V-, Tc-, Os-, and Th-porphyrin-like graphenes out of many candidates met the reversibility requirements, viz. − 1.2 to − 0.8 eV (Fig. 2a), where a CO 2 molecule adsorbs on a TM atom with the distance of ~2.5 Å between the TM atom and the CO 2 molecule. Therefore they were considered for the next step. We also performed CO 2 adsorption calculations on carbon allotropes such as carbon nanotubes, graphene, and C 60 . The adsorption energy of the CO 2 molecule is ca. − 0.05 eV, and the distance between their surface and the molecules is ~3.5 Å. In this case, since the adsorption energy of CO 2 molecules is much smaller than the required adsorption energy, pristine carbon nanostructures may not be suitable for use as CO 2 capture media under low pressure at room temperature. Notably, our approach significantly reduces the computational load because it is not necessary to calculate ∆ ( , ) C P T for all the candidates in CO 2 gas or a mixed gas. To predict the capture capabilities of the candidates, the CO 2 working capacities, ∆ ( , ) C P T , of the structures were computed using Eq. (3) (Fig. 2b). The experimental values of the chemical potentials of CO 2 gas and calculated adsorption energies (ε n CO 2 ) were used in these calculations. Since the working capacities of Sc-, V-, and Tc-porphyrin-like graphenes satisfied the capacity requirement (> 3 mmol g −1 ), they were considered for the next selectivity screening step.
We observed three different geometries for the adsorbed CO 2 molecules on the TM atoms, which were designated as η 1 -CO 2 , η 2 -CO 2 , and η 3 -CO 2 , corresponding to the coordination numbers of the TM atom, i.e., 1, 2, and 3, respectively (Fig. 3a). The adsorption energies of the CO 2 molecules were calculated to be − 0.54, − 0.79, and − 0.78 eV per CO 2 for the Sc-η 1 -CO 2 , Sc-η 2 -CO 2 , and Sc-η 3 -CO 2 geometries, respectively. The preferred CO 2 geometry depends on the metal type. The distance between the CO 2 molecule and TM atoms is 2.2-2.5 Å, which Scientific RepoRts | 6:21788 | DOI: 10.1038/srep21788 is much smaller than the equilibrium van der Waals distance (~3.4 Å), and the bond lengths of CO 2 are elongated by ~5%. Thus, the bonding between the TM atoms and CO 2 molecules must be chemical in nature.
To understand the enhanced interaction between early d orbital-containing elements and CO 2 molecules, we focused on a binding mechanism that appears between TM atoms and olefin molecules and is well known in organometallic chemistry 32 . The Dewar-Chatt-Duncanson model explains the type of chemical bonding between a π -orbital acid alkene and d-orbital metal atom by electron donation (i.e., hybridization of the empty d states with filled π states) and back-donation (i.e., hybridization of the filled d states with empty π states) 32 . The interaction (c) Flow chart for predicting reversible and selective CO 2 capture materials based on first principles thermodynamics: this consists of reversibility screening for pure CO 2 gas and selectivity screening for a mixed gas.
between the TM d orbitals and the olefin π orbitals is called the "Dewar interaction". Therefore, empty d-orbital metals are expected to attract CO 2 molecules. The Dewar interaction is based on chemical bonding between the TM and CO 2 and can enhance the strength of the M-CO 2 bond beyond that of the van der Waals interaction. It is noteworthy that Ca 2+ also has empty 3d orbitals near the Fermi level that could participate in the Dewar interaction.
Next, we investigated whether the enhanced adsorption observed with early TM atoms is caused by the Dewar interaction. We observed the hybridization of the Sc 3d states with the CO 2 states at around − 2.5, − 2.0, and − 2.0 eV for the η 1 -CO 2 , η 2 -CO 2 , and η 3 -CO 2 geometries, respectively (Fig. 3b). The difference in charge density between the Sc atom and CO 2 molecule (Fig. 3c) indicates chemical bonding between CO 2 and the metal atoms. From this, we concluded that the enhanced binding of CO 2 to the metal atom originates from the Dewar interaction. The distinct adsorption geometries of CO 2 can be explained by the different hybridization states of the TM d orbitals with the CO 2 π orbitals (Fig. 3d).
To examine the selectivity of CO 2 adsorption on Sc, V, and Tc sites in the presence of a mixed gas, we also carried out calculations on the adsorption of multiple CO 2 molecules or ambient gas molecules such as N 2 , CH 4 , and H 2 onto the metal atoms. Several CO 2 , H 2 , N 2 , and CH 4 molecules bound to Sc, V, and Tc atoms (Figs 4a,b and 5). The difference between the chemical potential at 300 K and 10 −3 bar and the adsorption energy of CO 2 (or other gas molecules) was calculated (Fig. 4c)  denotes the chemical potential of an ideal monatomic i-type gas for a given the pressure P and the temperature T, and A i and B i are fitted coefficients of i-type gas. The fitted coefficients are presented in Table 1. Since Sc and V, but not Tc, were found to satisfy the conditions for selective CO 2 adsorption (∆ > ∆ CO other 2 ), they were considered for the next screening step.
We also considered the zero-point vibrational energy of the gas molecules adsorbed onto the TM atoms. This energy was calculated to be in the order of a few meV regardless of the metal. Since the zero-point vibrational energy is negligible compared to the (static) adsorption energy (Fig. 4a), we ignored the influence of the zero-point vibrational energy on adsorption in all cases except for H 2 . Since the zero-point energy of the H 2 molecules adsorbed on TM atoms was not negligible (25% of the calculated values), we corrected the H 2 adsorption energies to determine the true adsorption energy.
The statistical model obtained here can correctly describe the adsorption of CO 2 onto TM-porphyrin-like graphene in the presence of a mixed gas because the mixed adsorption of different molecules onto a TM atom is not energetically favorable. For instance, the adsorption energy at which both a CO 2 and N 2 molecule adsorb onto a Sc atom was calculated to be − 0.9 eV, which is much higher than that (− 1.3 eV) at which single CO 2 or N 2 molecules adsorb on different sites.
The CO 2 capture capacities, C(P, T), from mixed gases with different compositions were calculated for Sc-and V-porphyrin-like graphenes (Fig. 6a,b). The ratios of the mixed gases were based on experimental measurements 4,33 from pre-combustion, post-combustion, and oxyfuel-combustion CO 2 capture. These results show high CO 2 selectivity of Sc-and V-porphyrin-like graphene in mixed gases, which is consistent with the prediction of the selectivity requirement of ∆ > ∆ CO other 2 . The CO 2 working capacities, ∆ ( , ) C P T , of Sc-and V-porphyrin-like graphenes can reach ~4 mmol g −1 (Fig. 6c,d), which meets the capacity requirement of 3 mmol g −1 in a mixed gas. Therefore, Sc-and V-porphyrin-like graphene were found to be suitable for highly selective CO 2 capture from flue gases at ambient conditions. Furthermore, the CO 2 pressure range covers the pressure (~0.4 × 10 −3 bar) of CO 2 in the atmosphere because the concentration of CO 2 in the atmosphere is ~400 ppm.

Discussion
We performed first-principles total energy calculations regarding CO 2 adsorption onto metal-porphyrin-like structures to explore the feasibility of achieving room-temperature CO 2 capture under low pressures. We found that transition metal-porphyrin-like structures adsorb CO 2 molecules with the desirable binding energy range  and the practical (usable) capacity under ambient conditions can reach ~3 mmol/g. Equilibrium thermodynamics studies showed that Sc-or V-porphyrin-like graphene structures were found to be suitable for use as room-temperature CO 2 capture media. These results indicate that nanostructures containing empty d orbitals may be applied for selective adsorption of CO 2 from flue gases. We believe our results provide a new approach to achieving CO 2 capture at room temperature.
We address the evidence of CO 2 binding to TM atoms for CO 2 capture. TM-η 1 -CO 2 or TM-η 2 -CO 2 complexes were observed in experiments 34,35 . The capture of CO 2 involved in the first step of carbon capture/storage (CCS) technology requires high energy consumption 36,37 . Thus, the development of media such as TM-porphyrin-like graphene nanostructures, which can selectively adsorb CO 2 at room temperature under low CO 2 partial pressure, is expected to lower the cost of CO 2 adsorption and make CCS more viable.

Methods
We performed first-principles calculations based on the density functional theory (DFT) 38 as implemented in the Vienna Ab-initio Simulation Package (VASP) with the projector augmented wave (PAW) method 39   The following different compositions of gases were considered: Pure CO 2 (100%), CO 2 (89%)-N 2 (11%), CO 2 (40%)-H 2 (57%)-N 2 (3%), CO 2 (20%)-H 2 (75%)-CH 4 (5%), and CO 2 (17%)-N 2 (83%). The partial pressure of gases is given by = P xP i i , where x i is the composition of the gas. Calculated working capacities of CO 2 in the TM-porphyrin-like graphene as a function of the total pressure, P, of the gases from ∆ ( , ) C P T , the difference between ( , ) C P T at 300 K and ( , ) C P T at 450 K: (c) Sc-porphyrin-like graphene and (d) V-porphyrin-like graphene. generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof scheme 40 was used for the exchange correlation energy functional, and the kinetic energy cutoff was taken to be 800 eV. For calculations of gas molecule adsorption, our model for the graphene-based system comprised a 3 × 3 hexagonal supercell, and the composition of the supercell was C 12 N 4 M 1 . Geometrical optimization of the graphene-based system was carried out until the Hellmann-Feynman force acting on each atom was less than 0.01 eV/Å. The first Brillouin zone integration was performed using the Monkhorst-Pack scheme 41 . 4 × 4 k-point sampling was used for the 3 × 3 graphene supercells. The chemical potential of gases, µ = ( − )/ H TS N, where H, S, and N denote the enthalpy, the entropy, and the number of particles was calculated from the data of the enthalpy (H) and entropy (S) in the reference: http://webbook.nist.gov/chemistry/fluid/.