Carbyne Ring Activated Using ZnCl2 for Hydrogen Adsorption: DFT Study

We have studied the feasibility of activated carbyne as a good hydrogen storage material. Density functional theory (DFT) simulations through van der Waals interactions have been applied to investigate calcium sorption on activating carbyne with zinc dichloride (ZnCl2) and also interactions of molecular hydrogen with pristine carbyne and Ca functionalized on an activated carbyne C12-ring. The obtained results showed that (i) the chemical activation of the C12-ring with ZnCl2 increases its area by 5.17% with respect to pristine carbyne. (ii) Ca atoms at small concentrations tend to get atomically sparse on carbyne, donating +0.94e and +1.05e to the ring, according to Mulliken population analysis and the electrostatic potential fitting charges, respectively. Furthermore, in the presence of calcium, hydrogen sorption increases by 21.8% in comparison with Ca-decorated pure carbyne. (iii) Seven hydrogen molecules per Ca atom have adsorption energy close to the range of ∼0.3–0.5 eV per H2, which is necessary for effective charge/discharge cycles. (iv) Theoretical uptake (7.11 wt %) with a single Ca atom is higher than the U.S. Department of Energy target (5.5 wt %). Therefore, an activated C12-ring can bind three Ca atoms with its seven H2 molecules reaching 13.8 wt %. (v) Equilibrium pressure for CaC12–7H2 and Ca3C12–21H2 systems (5–15 MPa) by means of adsorption isotherm calculations. The calculated van’t Hoff desorption temperatures exceed considerably the boiling point of liquid nitrogen. In addition, we also performed DFT-based molecular dynamics simulations for the C12, CaC12, CaC12–7H2, and Ca3C12–21H2 systems to study thermal stability. Our results confirm the potential of Ca-decorated carbyne for hydrogen storage.


■ INTRODUCTION
The aim here is to determine hydrogen storage properties on a carbyne C 12 -ring structure through chemical activation with zinc dichloride (ZnCl 2 ) and decorated with calcium atoms, by density function theory (DFT) calculations. In order to know the increasing demands necessary to hold common living standards while at the same time avoiding resource reduction and environmental pollution, there is a necessity for the growth of high-efficiency, low-cost, and eco-friendly energy storage systems. 1 As we all know, hydrogen is an ideal clean energy source that could one day replace fossil fuels, particularly for transportation applications, and combat global warming. One of the principal challenges in the growth of this technology is a compact, safe, and accessible storage system. A desirable system has to be capable of storing hydrogen with upper gravimetric density (HGD) under ambient conditions. 2−4 The U.S. Department of Energy (DOE) establishes a goal for ideal hydrogen storage materials: they ought to reach 4.5−5.5 wt % gravimetric density by the 2025 year. 5 In general, most of the studies have been dedicated to pristine carbon-based nanomaterials, such as activated carbons, 6,7 fullerenes, 8−10 graphene, 8,11 and nanotubes, 12,13 because most candidates for H 2 storage are explored owing to their low density, high thermal and chemical stability, and plainness of production; nevertheless, it has been stablished that the hydrogen storage capacity in these systems considerably diminishes at room temperature and ambient pressure, 14 being attributed to weak interactions between hydrogen molecules and carbon-based materials, due to physical adsorption (∼0.05 eV). 15 Metal doping is one of the effective methods to upgrade the strength of binding between hydrogen molecules and carbon-based nanomaterials. Alkaline-earth metal dopants, especially Ca atoms, show better hydrogen storage performance. 4,16−24 Ca atom is selected as the main dopant because of not only its lower cohesive energy (1.84 eV) compared with the transition metals (∼4 eV) but also its lightness in weight, its lower trend to aggregate on the host material whenever they are deposited, and its ability to retain the hydrogen content after doping. 20−22 Carbyne is composed of sp-hybridized carbon atoms. 25−28 The material has been proposed as nanoelectronic and also is likely to be used for hydrogen storage owing to an effective surface area around 13,000 m 2 g −1 , four times larger than theoretical graphene values. 18,25 The carbyne-ring structure is the base state of small carbon clusters (up to about 20 atoms) and an alternative form of linear chains, which are obtained by laser vaporization of graphite. 29−31 Between carbon clusters that result beginning with this technique in which carbyne has been found, ring structures are comparatively the most stable compared to other configurations and are the principal precursors of fullerenes and nanotubes. 32 Two carbyne structures might be defined as cumulene (equal double bonds) and polyyne (alternative single/triple bonds). 25−32 Previous research has shown theoretical estimation of Ca-decorated pristine carbyne for hydrogen storage on linear chains 18 and rings, 21 which meet the U.S. Department of Energy target requirement of 5.5 wt %. 5 Nevertheless, a single calcium atom can bind with binding energy higher than the cohesive energy, which makes cluster formation energetically favorable in these systems. To increase hydrogen storage properties on pristine carbyne molecule and enhance the binding energy of subsequent Ca atoms on carbyne, the carbyne ring has been activated through chemical activation with ZnCl 2 to upgrade the superficial area, and enhance pore size distribution (PSD).
Chemical activation with KOH, NaOH, H 3 PO 4 , or ZnCl 2 is a process where an activating agent is aggregated into the carbon precursor prior to pyrolysis at a temperature normally in the 450−900°C range. 1,8,33,34 The chemical agents help to develop porosity by means of dehydration (ZnCl 2 or H 3 PO 4 ) and degradation of the biomass structure, especially when the activation agent is highly alkaline (KOH). 1,33 Among the various activation agents, ZnCl 2 activation reacts with lignocellulosic precursor at T < 500°C, producing a template effect and inducing a uniform micropore formation. The surface areas are normally between 1500 and 2000 m 2 g −1 with pore volumes < Figure 1. (a) Geometry optimization of pristine carbyne C 12 -ring (alternating bond angles (α ̅ = (α 1 + α 2 )/2) and alternating bond lengths (triple, 1.24 Å; single, 1.34 Å). (b) Bond strengths of C 12 + H 2 , where the H 2 molecule is adsorbed at the outer surface (single/triple bonds and in front of carbon atom) and at the inner surface (center of the ring). (c) Geometry optimization of C 12 + ZnCl 2 at the center of the molecule at 2.529 and 2.41 Å (input). (d) Activated C 12 -ring (output). (e) H 2 adsorption at the inner surface of the carbyne molecule at 3.06 Å. (f) Bond strengths of activated C 12 -ring + H 2 , where the H 2 molecule is adsorbed at the outer and the inner surfaces. 1.5 cm 3 g −1 , and the broad pore size distribution increases with the concentration of ZnCl 2 . 1,33,35 The highest hydrogen adsorptions at 77 K and 1 bar reported for any natural and synthetic activated carbon material derived are 3.28 wt % from hemp stem, 36 2.85 wt % from petroleum pitch, 37 and 2.96 wt % from NAC-1.5-600 34,38 when the activating agent is KOH. For ZnCl 2 , the storage capacities obtained on CH 4 and CO 2 are 13 cm 3 g −1 from oil palm shell 39 and 1.3 mmol g −1 from rice husk, 40 respectively. Overall, the specific surface area (SSA) is key to not just enhancing H 2 storage but also achieving a higher electrochemical capacitance in terms of power delivery rate and energy storage. 41 So, in this study, we have investigated how functionalization with Ca atoms on activated carbyne with ZnCl 2 could influence the hydrogen storage ability. The results show adsorption energy which corresponds to chemisorption between activated carbyne and dopant agents and agreed with gas adsorption on a solid surface; with clarity we found physical adsorption between Ca atoms and hydrogen molecules. In addition, we have studied hydrogen desorption temperatures with respect to the equilibrium pressure by using the van't Hoff equation, and we determine the equilibrium pressure for the Cadecorated carbyne by means of adsorption isotherms, to thoroughly evaluate the potential of carbyne as a hydrogen storage material.

■ RESULTS
To carry out the analysis of this work, we take the pristine C 12ring 21 previously investigated and then we activate with zinc dichloride (ZnCl 2 ) in order to grow the surface area and enhance pore size distribution, with the aim of improving its hydrogen storage properties. The C 12 -ring corresponds to a C 4N structure with N = 3; with a D (n/2)h symmetry. 31,32 Figure 1a shows geometry optimization of pristine carbyne C 12 -ring with alternating single/triple bonds, called polyyne, where the most general case is linear acetylene (H−CC−H). 25,27,42 First, to estimate the H 2 adsorption capacity on the pristine carbyne without calcium attachment, we use two measures: specific surface area (SSA) 43 and accessible surface area (ASA). 44 The SSA method is based on the geometrical calculation of the area, whereas the ASA method is based on the Monte Carlo integration technique where the probe molecule is "rolled" over the framework surface. The SSA calculations of pristine and activated carbyne C 12 -ring have been carried out by inserting triangles on the ring using the Heron formula, eq 1. 45 where P is the perimeter of a triangle with a, b, and c sides, whereas the PSD is calculated as an approximation to the circle area.
Using eq 1, we calculated the area and pore diameter showing values of 18.37 Å 2 and 4.83 Å, respectively. With these results, we calculated the SSA 43 (2) where N H is the number of hydrogen atoms physisorbed on the inner and outer surfaces of pristine and activated carbyne C 12ring, E C 12 −nH 2 and E C 12 are the total energies of the hydrogenated carbyne ring and corresponding pristine and activated C 12 -ring, respectively, and E H is the energy of an isolated hydrogen atom. As in the cases of graphene, 8 CNTs, 12 and C 60 , 13 hydrogen adsorption on pristine C 12 -ring is due to weak van der Waals (vdW) interactions. The adsorption energy of a single H 2 molecule to the outer and inner surfaces of pristine carbyne only reaches adsorption energies of 0.077 and 0.028 eV, respectively. The next hydrogen molecules added to the host material on the inner and outer surfaces diminish the binding energy until 0.01 eV; this means that the pristine carbyne is not a good candidate for hydrogen storage directly. The interactions are evident through the potential energy surfaces (PESs), which give the minimum E(r) and correlate with the equilibrium point later to geometry optimization of the interacting system (C 12 + H 2 ) on the outer and inner surface of pristine carbyne. Figure 1b shows the bond strengths of C 12 + H 2 , where the H 2 molecule is adsorbed at the outer and at the inner surfaces. The resulting values show the dissociation energy to form C 12 + H 2 corresponding to physisorption, 47 which involves binding hydrogen molecules to the host material and requires very low temperatures and high hydrogen gas pressure. Subsequently, through chemical activation with zinc dichloride (ZnCl 2 ), we activate the pristine carbyne to increase the surface area and enhance PSD. In widespread terms, these characteristics are central to not only enhancing hydrogen storage but also achieving the best work in power distribution rate and energy storage. We place a ZnCl 2 molecule to the center of the pristine C 12 -ring at 2.529 and 2.410 Å distances as shown in Figure 1c. By applying geometry optimization and removing ZnCl 2 , the area and pore size diameter result in 19.32 Å 2 and 4.96 Å, respectively, using eq 1, representing increases of 5.17% and 2.69% with respect to pristine C 12 -ring ( Figure 1d). In addition, we calculate the SSA and ASA of activated carbyne C 12ring as a function of their geometrical characteristics. The obtained values show ∼4844.53 m 2 g −1 (SSA) and 15047.88 m 2 g −1 (ASA), which represents a macroscopic parameter that might be the kind to modify the synthesis condition of carbyne molecules. Even more, from literature, activated carbon shows a surface area of fewer than 2000 m 2 g −137 and cannot be used for hydrogen storage. Activated carbyne ring represents an alternative due to high specific surface area as a hydrogen storage material. Then, we investigate the hydrogen adsorption of a single H 2 molecule as much at the outer as the inner surface of activated C 12 -ring ( Figure 1e). The results show that only in the center of the C 12 -ring the H 2 molecules might be adsorbed; however, only two H 2 molecules may be adsorbed with an adsorption energy higher than ∼0.1 eV. The outer zones of the activated C 12 -ring only reach an adsorption energy of ∼0.030 eV (Figure 1f), which corresponds to lower adsorption energies for hydrogen storage at environmental conditions. These results are compared against toroidal carbon nanostructure C 120 , 46 where hydrogen adsorption energies are lower by 0.1 eV per H 2 ; a full hydrogen storage uptake of 2.05 wt % is for 15 H 2 molecules adsorbed at the inner surface of the toroidal carbon C 120 . The same case is observed for the activated C 12 -ring, where the full hydrogen storage capacity is 2.72 wt % with only two H 2 molecules adsorbed at the inner surface, which do not meet the goals established by the DOE. Although there is an upgrade in hydrogen adsorption on activated carbyne, this makes it impractical for mobile applications, just like a pristine carbyne ring. However, this is a good start for future research to address this.
Subsequently, we studied the behavior of Ca-doped activated carbyne with ZnCl 2 . The modeling of the Ca−carbyne complex considers several starting configurations at the inner and outer surfaces (in front of single and triple bonds and at the center of the activated carbyne ring) separated at 2.48 Å, and we examine the Ca−carbyne stability by determining the binding energy (E b Ca ) using eq 3. 19,20,48 where E C 12 is the total energy of the activated carbyne molecule, E Ca is the total energy per calcium atom, and E Ca x C 12 is the total energy of one carbyne molecule with x Ca atoms. For a single Ca atom, we find three optimal positions around the C 12 -ring to be located in front of either single or triple bonds and also at the center of the ring, with binding energies of 2.79 eV (single and triple bonds) and 3.34 eV (center of the ring), which with respect to the pristine CaC 12 complex 21 represent increases of 25.11% and 49.77%, respectively, which means it is strongly chemisorbed. 47 (Table 1).
As a note, unlike the pristine CaC 12 complex, only the single bond C 1 −C 2 , C 5 −C 6 , or C 9 −C 10 was the better zone for calcium atoms; these zones present the blue lobes for HOMO−LUMO spatial distribution. For activated C 12 -ring we found a better HOMO−LUMO distribution (Figure 2a) around the ring, where the Ca atom prefers to bind indistinctly in any zone of carbyne C 12 -ring. Here, the positive value of E b Ca means that the doped complex is thermodynamically stable. In addition, our results of binding energy values were higher than those of fullerenes, 16 carbon nanotubes, 17 carbyne chains, 18,21 graphene, 23 and heterofullerenes. 20 Therefore, this indicates that cluster formation is energetically unfavorable, so this factor will not diminish the possible hydrogen capacity on activated C 12ring. Panels b−d of Figure 2 show the geometry optimization of the activated doped complex. The calcium atom tends to extend the double and single bonds to the activated carbyne to 1.404 and 1.405 Å, respectively, and how the Ca atom is adsorbed at the center of the ring.
In addition, we have also achieved DFT-based molecular dynamics (MD) simulations for both C 12 and CaC 12 systems in their forms pristine and activated with ZnCl 2 . All of the

ACS Omega
http://pubs.acs.org/journal/acsodf Article 6 ps of MD production show better thermal stabilities of all activated structures with Nose−Hoover thermostat at 300 K. Every system was equilibrated for 3−6 ps, and after 5 ps of production, no breaking of bonds was observed, which implied the thermal stability of C 12 and CaC 12 systems. The average temperature of the MD production run for pristine carbyne C 12ring is 327.11 K and 299.11 K for massive GGM and Nose− Hoover thermostat, respectively, along the 6 ps MD production run. For activated C 12 -ring the average temperature was 327.46 K and 300.04 K for massive GGM and Nose−Hoover thermostat, respectively. The mean square displacement (MSD) is shown in Figure 3a−h for all of the systems (C 12ring and Ca-decorated carbyne). To summarize, the run of MD production showed that activated CaC 12 is a good candidate since this structure after 6 ps retains its initial properties without too much variation in bond lengths and considerably lower temperatures, which implied good thermal stability of activated carbyne. In addition, using the Nose−Hoover thermostat we have carried out an MD production run at 200 and 100 K for the carbyne C 12 -ring and doped complex CaC 12 (pure and activated) that is shown in the Supporting Information. Through Mulliken population analysis and electrostatic potential (ESP)-fitted charges, we observe positive charge on the Ca atom toward the carbyne ring, which results in (+0.949e and +1.056e), (+0.944e and +1.052e), and (+0.99e and +1.464e) for a single bond, triple bond, and center of carbyne molecule, respectively. As shown in the Supporting Information, we added the charge-transfer mechanism of carbyne C 12 -ring and doped complex CaC 12 −nH 2 with n = 1−7 H 2 molecules adsorbed around the Ca atom for pristine and activated carbyne with ZnCl 2 .
Once the CaC 12 activated complex reaches equilibrium, the next step is the adsorption analysis of H 2 molecules on the decorated complex. Using eqs 4 and 5, 4,18,20,21 we calculate the average binding energy and adsorption energy of nH 2 molecules adsorbed on the doped complex.
where E (Ca x C 12 ) and E( H 2 ) are the total energies of the Ca x C 12 complex and an isolated H 2 molecule, respectively. The E (Ca x C 12 −nH 2 ) is the total energy of the Ca x C 12 system with nH 2 molecules and E (Ca x C 12 +(n−1)H 2 ) is the total energy of the Ca x C 12 system with (n−1) H 2 molecules adsorbed on the doped complex. The next H 2 molecules were placed one by one around the Ca atom until there were seven H 2 molecules. The average energy and adsorption energy results of the nth H 2 molecule  Table 1. In Figure 4, we legibly illustrated the process of attaching molecules to the CaC 12 , performed by setting one by one until a maximum of seven H 2 molecules. We determine that the first six H 2 molecules tend to be adsorbed around the calcium atom, and the seventh H 2 molecule is physically adsorbed on the upper side of the calcium atom. The optimized systems of CaC 12 −7H 2 are rather similar for single and triple bonds; therefore, we only take the triple bonds and center to properly put each one of the seven H 2 molecules adsorbed on the doped complex. The first H 2 molecule is adsorbed on the doped complex with an average energy and adsorption energies of 0.5362, 0.4515, and 0.3818 eV per H 2 , when the Ca atom is placed in front of single and triple bonds and the center of the activated carbyne molecule, respectively (see Table 1). To determine the relationship between the Ca− H 2 distance and the H 2 adsorption energy, according to the literature 19 if the Ca−H 2 distances are less than 3 Å the adsorption energies are greater than 0.2 eV per H 2 .
Therefore, in our case, we observed that each of the Ca−H 2 distances is in the range of 2.3−2.6 Å, and the H−H average bond length is 0.774 Å for all orientations. The next added molecules to the CaC 12 are maintained with an average energy E av = (0.4145, 0.4291, and 0.3554 eV) per H 2 and adsorption energy E ad = (0.3983, 0.3937, and 0.3369 eV) for single and triple bonds and the center of the carbyne molecule, respectively. Therefore, in this study with correction of Grimme calculations, we determine that the CaC 12 complex might adsorb until seven H 2 molecules per Ca atom with enough energy and quantity of hydrogen for using it as a storage material. The weight percent (wt %) of H 2 molecules in a carbyne Ca x C 12 are also calculated with eq 6.
2ads 12 (6) where m H 2ads is the mass of H 2 molecules adsorbed on the decorated complex, and the mass of Ca x C 12 decorated complex is m CaC 12 . The hydrogen storage capacity obtained in this study is 7.11 wt % (Table 1). Thus, the maximum hydrogen storage capacity is greater than the capacity ∼6 wt % of the Ca-decorated carbyne (polyyne), 18 Table 2). Subsequently, we saturate the doped complex by placing up to three Ca atoms on the mentioned positions (single and triple bonds and the center of the ring) and we observe binding energies above 2.8 eV for the second and third Ca atoms, which show stability in the system, indicating that the cluster formation is energetically unfavorable as an increase the calcium atoms concentration in the system. We repeat the same methodology of adding H 2 molecules to the Ca atoms, even to which 7H 2 molecules per Ca atom might bind, with an average binding energy of ∼0.36 eV per H 2 , obtaining a Ca 3 C 12 −21H 2 system. This study reaches 13.8 wt % for the gravimetric density, fulfilling DOE requirements. However, this gravimetric density requires experimental investigation to be validated and makes it very feasible that the system can only absorb up to one Ca atom.
As the next step, we built potential energy surfaces for doped complex CaC 12 −nH 2 with n = 1−7 hydrogen molecules adsorbed on it. The methodology to accomplish potential energy curves for the hydrogen molecules adsorbed by Ca atom is to perform a geometry optimization for each H 2 molecule added to the doped complex as a first step, which provides the minimum energy and distance corresponding to the equilibrium point of each system. Then, single-point calculations by oscillating ±4 Å around the minimum energy with steps of 0.02 Å to calculate energies at each point and build potential energy surfaces, E(r). Figure 5 shows PES for the seven H 2 molecules adsorbed on activated doped complex when the Ca atom is placed in front of a single bond of carbyne molecule. All of the minimum energies obtained and calculated by eq 4 are equivalents and provide information about the 7H 2 molecules that were physically adsorbed by calcium atoms (see Table 1 and Figure 5).
We carry out HOMO−LUMO calculations for the CaC 12 − 7H 2 , which is observed in Table 3. We clearly observed that values of energy difference for the doped complex are about 0.926−0.960 eV for the single bond, 0.925−0.965 eV for the double bond, and 0.13−0.6 eV for the center of the carbyne molecule, indicating that the doped complex is stable enough.
We determine the isothermal curves at three temperatures (274, 298, and 322 K) for the CaC 12 −7H 2 and Ca 3 C 12 −21H 2 systems using the Sorption program as described in Computational Methods. The equilibrium pressure with the fitting curve when we have 7.11 wt % for the CaC 12 −7H 2 system and 13.8 wt % for the Ca 3 C 12 −21H 2 system, since they present energies in the desirable range of 0.2−0.6 eV, for hydrogen storage. Therefore, the equilibrium pressure lies in the range of 5−15 MPa as shown in Figure 6.
Together with the gravimetric densities, the thermal stability of adsorbed H 2 on activated complex should be investigated as it plays an indispensable role in predicting the effectiveness of hydrogen charge/discharge cycles. The thermal stability correlates with the binding energy of hydrogen to the storage   (7) where E ad is the hydrogen adsorption energy, k B is the Boltzmann constant, ΔS is the change in the hydrogen entropy from molecular gas to dissolved solid hydrogen (standard hydrogen entropy, 130 J K −1 mol −1 ), 14 R is the gas constant, and p is the equilibrium pressure (in our calculations we used the range of 0.1−1 MPa with respect to the standard atmospheric pressure). The activated carbyne complex (shown in Figure 3) is considered as the highest gravimetric density to estimate the hydrogen desorption temperatures. Panels a−c of Figure 7 show van't Hoff desorption temperatures in the range of equilibrium pressures (0.1−1 MPa) corresponding to hydrogen gravimetric densities for the chosen structure. So, all T D (p) dependencies were obtained by employing hydrogen adsorption energies (in the case of CaC 12 −7H 2 activated complex) in eq 6.
Average T D is calculated by using E av (average binding energy of seventh H 2 molecule adsorbed per Ca atom). The onset desorption temperature (min T D ) is obtained to describe adsorption energy (E ad ) of the seventh hydrogen molecule per Ca atom, and it corresponds to the minimal temperature, which is necessary to start hydrogen release. By using the adsorption energy of the first H 2 molecule adsorbed by Ca atom on a doped complex, we calculate the highest desorption temperature, max T D , which is necessary to fully discharge the considered system. At normal atmospheric pressure (p = 0.1 MPa), the average T D is 292 and 295 K (Figure 7a,b) when the Ca atom is placed in front of triple and single bonds and can adsorb until seven H 2 molecules, in the case of the center of the ring the maximum desorption temperature at 0.1 MPa is 275 K (Figure 7c), which is much higher than the critical point of hydrogen (33 K) and more than triple the boiling point to liquid nitrogen (77 K). As a note, desorption temperatures could be further increased by the increase of equilibrium pressure. On the basis of this, we take the equilibrium pressure obtained with the isothermal curves in the range (5−15 MPa) for CaC 12 −7H 2 , Ca 2 C 12 −14H 2 , and Ca 3 C 12 −21H 2 activated complexes, and we compare the thermal stability using eq 7. Here we used the average adsorption energy of all hydrogen molecules adsorbed by the doped complex, and we give an estimate of desorption temperatures (Figure 7d). At pressures of 50, 100, and 150 MPa, the average T D is 384, 407, and 423 K for the CaC 12 −7H 2 , Ca 2 C 12 −14H 2 , and Ca 3 C 12 −21H 2 doped complex, respectively. The highest gravimetric densities for each of the systems are 7.11 wt % (CaC 12 −7H 2 ), 11.17 wt % (Ca 2 C 12 −14H 2 ), and 13.8 wt % (Ca 3 C 12 −21H 2 ). In addition, we also performed DFT-based molecular dynamics for CaC 12 −7H 2 (pristine and activated carbyne) and Ca 3 C 12 −21H 2 systems with massive GGM and Nose−Hoover thermostats at 300 K. We observed unified thermal stability after 6 ps at 300 K for all molecular dynamic's simulations when the Nose−Hoover thermostat was used. The average temperature was 300.94 K, and 300.23 K along the MD-production run for pristine and activated structures (Figure 8a−f). For doped complex Ca 3 C 12 −21H 2 , the average temperature was 301.44 K with the Nose−Hoover thermostat. Every system was equilibrated for 3−6 ps, and after 6 ps of production, no breaking of bonds was observed, which implied the thermal stability of the systems. In addition, using the Nose−Hoover thermostat, we have carried out an MD production run at 200 and 100 K for the CaC 12 −7H 2 , and Ca 3 C 12 −21H 2 -doped complex (pure and activated), which is shown in the Supporting Information.
Along with the previous studies in this work, we can determine that activated carbyne C 12 -ring with zinc dichloride and decorated with Ca atoms can adsorb seven H 2 molecules with a single Ca atom with an average energy of ∼0.39 eV per H 2 molecule corresponding to 7.11 wt %. It is expected that activated C 12 -ring might bind three Ca atoms around the inner/ outer surface with their H 2 molecules, respectively, which represents an increase up to 13.8 wt % with respect to the pristine C 12 -ring 21 previously investigated. This storage capacity satisfies the requirements established by the U.S. Department of Energy by the end of the year 2025. Therefore, the considered material might be a promising choice for efficient hydrogen storage media, so this material certainly requires further experimental investigation.

■ DISCUSSION
The research for hydrogen storage materials is very attractive for fuel cell applications among others. Nevertheless, it is a great challenge to find hydrogen storage materials with great hydrogen gravimetric density under ambient thermodynamic conditions. Previous studies have explored that pristine nanomaterials 6−13 cannot efficiently store hydrogen, mainly due to weak van der Waals interaction between the hydrogen molecules and host material. Pristine carbyne is not an exception; for example, in the C 12 -ring structure only a single H 2 molecule can adsorb with adsorption energies of 0.077 and 0.028 eV at the outer and inner surfaces, respectively, by DFT calculations presented in this analysis, making unsuitable its use as a hydrogen storage material. Previous research has shown that the pristine carbyne C 12 -ring 21 structure is the ground state. We take this structure for new experimentation, activating with ZnCl 2 . Before chemical activation, we calculated the area of pristine carbyne and pore diameter (18.37 Å 2 and 4.83 Å) presented in this work. Even more, we determined the specific surface area shows a value of 4606.31 m 2 g −1 , and accessible surface area shows a value of 13,000 m 2 g −1 . The chemical activation helps to develop the porosity by means of dehydration with ZnCl 2 or H 3 PO 4 of the biomass structure. In this work, we take the pure C 12 -ring and then we activate it with ZnCl 2 as shown in the methodology in this work. By applying geometry optimization and removing the ZnCl 2 , the area and pore diameter result in 19.32 Å 2 and 4.96 Å, respectively, representing  In addition, to improve the hydrogen storage properties, metal doping is one effective method to enhance the adsorption energies between H 2 molecules and host material. Previous research has shown that pristine carbyne C 12 -ring decorated with Ca atoms might bind up to six H 2 molecules with average binding energies of 0.18 eV per H 2 (PW91) and 0.32 eV per H 2 with the empirical correction scheme of Grimme (DFT-D). 21 Nevertheless, only a single Ca atom might be bound to the carbyne molecule with binding energy (E b Ca ) higher than 2 eV, reaching 6.16 wt % for the gravimetric hydrogen storage. Even for cluster C 10 -rings 24 in polyyne and cumulenic forms, only a single Ca atom might be chemisorbed with binding energies greater than 2.5 and 2.33 eV for GGA-PW91 and GGA-PBE functionals, respectively. Up to either six or seven H 2 molecules are physisorbed by Ca atom, with average energies of 0.22 eV per H 2 (PW91) and 0.263 eV per H 2 (DFT-D) for cumulene and polyyne molecules, respectively. The hydrogen storage capacity obtained corresponds to 7.02−8.09 wt %. Thus, hydrogen storage capacities using only one Ca atom in carbyne rings reach H 2 storage capacities, which are much higher than other carbonand boron-based materials (see Table 2), where other investigations saturate the system with more dopant atoms until reaching the goal of DOE requirements. In this work, we demonstrate that activated carbyne can bind up to three calcium atoms around this surface, with binding energy greater than 2.7 eV per Ca atom, which represents up to an increase of 49.77% with respect to the pristine CaC 12 complex, indicating that the system is strongly chemisorbed and up to seven H 2 molecules can be physisorbed with an average energy of 0.39 eV per H 2 . Reaching 13.8 wt % for gravimetric storage capacity, fulfilling the requirements by the DOE. In addition, we also performed DFTbased molecular dynamics for the C 12 and CaC 12 systems in their forms pristine and activated with ZnCl 2 to study the structural stability of the molecules. We determine the equilibrium pressure by means of adsorption isotherms and the van't Hoff equation, which suggests that Ca-decorated carbyne could operate as hydrogen storage media at temperatures above the boiling temperature of liquid nitrogen presented in this work.

■ CONCLUSIONS
We performed the analysis of activated carbyne C 12 -ring with zinc dichloride (ZnCl 2 ) and decorated it with Ca atoms by DFT calculations. First, the pristine carbyne C 12 -ring used in this work corresponds to the C 4N structure with N = 3, with a D (n/2)h symmetry. The pristine C 12 -ring exhibits area and pore diameter of 18.37 Å 2 and 4.83 Å, respectively. According to this, our results using activated carbyne C 12 -ring show an increase in area and pore diameter of 5.17% and 2.69%, respectively. In the case of several carbon-based nanomaterials, the hydrogen adsorption on pristine carbyne is impractical due to weak interactions of H 2 molecules on the host material, since the adsorption energies of a single H 2 molecule at the outer and inner surfaces of pristine carbyne are only 0.077 eV per H 2 and 0.028 eV per H 2 , respectively. In order, to increase the hydrogen storage properties on pristine C 12 -ring, we activate the ring through chemical activation with zinc dichloride (ZnCl 2 ) to increase the surface area and enhance pore size distribution. These theoretical specific surface area on activated carbyne results in an increase from ∼4606.31 m 2 g −1 (pristine C 12 -ring) to ∼4844.33 m 2 g −1 . The accessible surface area shows a value of 13000 m 2 g −1 for pristine carbyne, whereas activated carbyne shows a value of 15045.88 m 2 g −1 , which shows an increase of 15.76% with respect to that of the pure carbyne. These values represent a macroscopic parameter that can be helpful to adjust the synthesis condition of the carbyne molecule. Unlike pristine C 12 -ring, the activated ring can adsorb two H 2 molecules at the center of the molecule with a desirable binding energy of ∼0.1 eV per H 2 . However, the hydrogen storage capacity obtained is only 2.72 wt % which does not fulfill objectives established by the DOE. Subsequently, we studied the case of a single Ca atom adsorbed on a carbyne surface (outer and inner), and we calculate the binding energy of the CaC 12 system, showing values of 2.79 eV for single and triple bond zones, where Ca atom was placed, and of 3.34 eV for the center of the activated ring, which represents an increase of 49.77% with respect to the pristine carbyne. In addition, we determine the zones that Ca atoms prefer to bind on the carbyne molecule (in front of single and triple bonds and the center of the ring), which makes it more attractive in comparison with pristine C 12 -ring, which only has an area for placement of the calcium atom in front of single bonds of the ring. The activation of the carbyne ring produces higher stability on the ring, causing more Ca atoms that can bind to the host material. We showed that Ca adatoms at small concentrations stay atomically dispersed on carbyne, donating +0.94e and +1.05e to the ring, for Mulliken population analysis and ESP-fitted charges, respectively. Furthermore, in the presence of Ca, hydrogen adsorption increases 21.8% in comparison with Ca-decorated pristine carbyne. We determine that up to seven H 2 molecules can be physically adsorbed with an average energy of ∼0.39 eV per H 2 molecule. The first six H 2 molecules tend to adsorb around the Ca atom and the seventh H 2 molecule is adsorbed on the top of the Ca atom. The hydrogen storage capacity obtained in this study is 7.11 wt % and therefore represents an increase of 15% with respect to the pristine carbyne. However, it is expected to reach 13.8 wt % with three Ca atoms, which represents an increase of 124% with respect to pristine carbyne, and satisfactorily meets the target set by the DOE for the year 2025. We determine the equilibrium pressure for CaC 12 −7H 2 and Ca 3 C 12 −21H 2 systems (5−15 MPa), by isotherm calculations. Furthermore, the T D , which is calculated using the van't Hoff equation, suggests that Cadecorated carbyne could operate as hydrogen storage media at temperatures above the boiling temperature of liquid nitrogen. The molecular dynamics after 6 ps at 300 K show unified thermal stability when the Nose−Hoover thermostat was used. The average temperatures were 300.94 and 300.23 K for CaC 12 −7H 2 (pristine and activated carbyne). For doped complex Ca 3 C 12 −21H 2 , the average temperature was 301.44 K with the Nose−Hoover thermostat. Every system was equilibrated for 3−6 ps, and after 6 ps of production, no breaking of bonds was observed, which implied the thermal stability of the systems. Therefore, the activated carbyne decorated with Ca atoms attains H 2 storage capacity which is much higher than other carbon and carbon-based materials reported in the literature (see Table 2), fulfilling DOE requirements, so this material certainly requires further experimental investigation.  59 and spin unrestricted was used. The interaction energies between hydrogen molecules with one C 12 -ring are calculated by means of a set of double numerical plus polarization basis (DNP). For occupied orbital, we consider two atomic orbitals in the basis set. For C and H atoms, d-and p-polarization functions are respectively used. The employed basis set has the advantage of being equivalent to the analytical basis set 6-31G**. All presented geometry optimizations are obtained for a tolerance on which the maximum forces are lower than 0.002 Ha/Å. Here the effect of van der Waals interactions is included explicitly by using the empirical correction scheme of Grimme (DFT-D) for periodic systems. 60 Standard values of the dispersion coefficients C 6 (0.14, 1.75, and 10.80 J nm 6