Linking Bi-Metal Distribution Patterns in Porous Carbon Nitride Fullerene to Its Catalytic Activity toward Gas Adsorption

Abstract

Immobilization of two single transition metal (TM) atoms on a substrate host opens numerous possibilities for catalyst design. If the substrate contains more than one vacancy site, the combination of TMs along with their distribution patterns becomes a design parameter potentially complementary to the substrate itself and the bi-metal composition. By means of DFT calculations, we modeled three dissimilar bi-metal atoms (Ti, Mn, and Cu) doped into the six porphyrin-like cavities of porous C₂₄N₂₄ fullerene, considering different bi-metal distribution patterns for each binary complex, viz. Ti_xCu_z@C₂₄N₂₄, Ti_xMn_y@C₂₄N₂₄, and Mn_yCu_z@C₂₄N₂₄ (with x, y, z = 0–6). We elucidate whether controlling the distribution of bi-metal atoms into the C₂₄N₂₄ cavities can alter their catalytic activity toward CO₂, NO₂, H₂, and N₂ gas capture. Interestingly, Ti₂Mn₄@C₂₄N₂₄ and Ti₂Cu₄@C₂₄N₂₄ complexes showed the highest activity and selectively toward gas capture. Our findings provide useful information for further design of novel few-atom carbon-nitride-based catalysts.

1. Introduction

Porous carbon-based catalysts are widely used as sorbents and support materials in heterogeneous catalysis [1,2,3]. The archetypical example is C₆₀ fullerene, which has a closed-cage structure and can be synthesized with a highly defective surface and abundant holes [4,5]. It has high thermal stability, unique mechanical properties, high electronegativity, and high electron affinity [6]. Therefore, both pure and metal-doped C₆₀ show promising applications in energy conversion [7,8], fuel cells [9,10], and for biomedical applications [11].

Recently, the adsorption and conversion of gas molecules on doped C₆₀ fullerene by single transition metal (TM) or heteroatoms, especially nitrogen atoms, has gained significant interest [12,13]. Upon N-doping, carbon π electrons are activated by conjugating with the lone-pair electrons from N. Thus, the C atoms neighboring N become active centers for catalytic reactions. For instance, Chen et al. [14] theoretically investigated the oxygen reduction reaction (ORR) mechanisms and catalytic abilities of pure and N-doped fullerenes of various sizes (C₂₀, C₄₀, C₆₀, and C₁₈₀). They found that the two pure and N-doped C₂₀ and C₁₈₀ structures are not active toward the adsorption of common intermediates produced during the ORR process. In contrast, C₃₉N showed the largest decrease in reaction energy of the rate-determining step in the relative energy profile, suggesting its ORR activity is the best among all the different sizes of fullerenes. Experimentally, N-doped carbon materials are prepared using chemical vapor deposition (CVD) or reactive magnetron sputtering [15,16]. For example, Usachov et al. [17] synthesized a N-doped graphene nanosheet from s-triazine molecules. Recently, Zhai et al. [18] for the first time synthesized metal-free N-doped graphene films on glass through plasma-assisted hot filament CVD using N₂ gas as dopant. They found that both the hot filament and plasma source are essential for growing N-doped graphene of high quality. By adjusting the N₂ flow, the authors could easily modulate the N content, transmittance, and electrical properties of the graphene films.

The chemical inertness of pure fullerenes prevents their possible application for gas capture. Single metal doping (M-C₆₀), like C₅₈Pt and C₅₉Pt [19], significantly modifies the electronic structure of C₆₀, rendering it chemically active. However, one of the main challenges in the synthesis of M-C₆₀ is the often-observed aggregation of metal atoms [8,20]. Recently, extensive efforts have been put into developing single-site catalysts such as pyrolyzed TM-modified porphyrin complexes (TM = Fe, Co, Mn, Cr, Ni) [21,22,23,24,25,26,27,28,29,30,31], which can be used in various applications like ORR and batteries [24,32,33,34,35,36]. The single TM atom doped in these porphyrin units was firmly fixed, preventing metal aggregation. Recently, the porphyrin-like porous C₂₄N₂₄ has been of great interest as truncated N-doped C₆₀ nanocage. The C₂₄N₂₄ fullerene has six N₄ cavities with eight s-triazine rings, which are connected via C-C bonds. Each porphyrin-like N₄ cavity of C₂₄N₂₄ can host a single TM atom. Recently, TM-doped C₂₄N₂₄ and C₂₄B₂₄ fullerenes were studied for hydrogen storage [37,38,39], ORR [40], and gas conversion [41].

In this work, we investigate the catalytic activity of bi-metal atom doping in C₂₄N₂₄, using Ti, Mn, and Cu as metals. In particular, we here focus on the influence of the metal atom distribution in the catalytic activity of the modified structures. We carefully investigated the adsorption characteristics, electronic properties, and charge transfer properties of our novel catalysts. We found that varying the TM ratio indeed has an important effect on the properties and catalytic activities of the catalysts toward adsorption of gas species. Our calculations can provide the fundamental adsorption mechanism of such a novel material, supporting its possible exploitation to be applied as a green catalyst for gas detection.

2. Computational Details

All quantum chemical DFT computations are performed using the Gaussian16 package [42]. We first tested fourteen DFT functional/basis set combinations (including GGA, meta-GGA, and hybrid functionals) for geometry optimization (see Table S1 of Supplementary Materials). As can be seen in Table S1, the obtained E_b values calculated with the B3LYP-D3/6-311G* are in close agreement with the reported E_b for H₂ (−4.52 eV) [43,44], formation energy (E_f) of pristine C₂₄N₂₄ (−7.40 eV), and E_b of Ti₆@C₂₄N₂₄ (−8.14 eV), as well as the geometry values for C-C (1.55 Å) and C-N (1.34 Å) bond length [45].

The cohesive energy (per atom) of C₂₄N₂₄ is defined as:

E_coh = (1/48)(E_C24N24 − 24 E_C − 24 E_N)

(1)

where the E_C24N24, E_C, and E_N are the calculated total energy of the pure nanocage, carbon, and nitrogen atom, respectively. The E_b of each doped TM in C₂₄N₂₄ for a homogeneous TM-doped C₂₄N₂₄ (TM₆@C₂₄N₂₄) and with different metal ratios (x, y, z = 0–6) was calculated using Equations (2) and (3), respectively:

E_{b(TM6@C24N24)} = (1/6)(E_TM6@C24N24 − 6 E_TM − E_C24N24)

(2)

E_{b(TixMnyCuz@C24N24)} = (1/6)(E_{TixMnyCuz-C24N24} − E_C24N24 − xE_Ti − yE_Mn − zE_Cu), (x, y, z = 0–6)

(3)

where, in Equation (2), the E_TM6@C24N24 and E_TM refers to the total energy of one type TM-doped C₂₄N₂₄ (Ti, Mn, or Cu) and the TM atom, respectively. In Equation (3), the E_{TixMnyCuz@C24N24} is the total energy of the doped C₂₄N₂₄ complex and xE_Ti, yE_Mn, and zE_Cu are defined as the total energy of Ti, Mn, and Cu metal atoms times the number of doped Ti atoms (x), Mn atoms (y), and Cu atoms (z) into the six porphyrin cavities of C₂₄N₂₄ nanocage, respectively.

The adsorption energy (E_ads) of each gas moiety over the modified cage is defined as:

E_ads = E_{ads@TixMnyCuz-C24N24} − E_{TixMnyCuz-C24N24} − E_adsorbate

(4)

where E_{ads@TixMnyCuz-C24N24}, E_{TixMnyCuz-C24N24}, and E_adsorbate are the total energy of the adsorbate on the complex, pure complex, and the adsorbate molecule, respectively. The x, y, z values represent the number of each TM atom doped into the porphyrin-like C₂₄N₂₄ cavities and are in the range of 0 to 6.

For each system, the zero-point energy (E_ZPE) is calculated by summing vibrational frequencies over all (real) normal modes. Enthalpy and Gibbs energy changes are calculated at 298.15 K following the standard procedure outlined in the reference [46] To follow the nature of the adsorption process, the Wiberg bond indices (WBIs) were computed using NBO analysis. The WBIs are known as a better measure of bond strength relative to the overlap population, which is basis-set-dependent and often does not correlate well to bond strength. The WBIs are often similar in magnitude to the bond order expected from valence bond theory and have been used to propose trigger bonds in various energetic materials.

The WBI is a measure of the density between two atoms A and B. It determines by the sum of the off-diagonal square of the density matrix P (p#q) [47]:

$${\mathrm{WBI}}_{\mathrm{AB}}={{\displaystyle \sum }}_{{\mathrm{P}}^{\mathrm{A}}}{{\displaystyle \sum }}_{{\mathrm{q}}^{\mathrm{B}}}{\mathrm{P}}^2{}_{\mathrm{pq}}$$

(5)

3. Results

3.1. Geometry of Pristine C₂₄N₂₄

The porous C₂₄N₂₄ is formed by first removing the 12 C atoms in C₆₀ that connect two pentagons, thus creating six di-vacancies, as shown with a red circle in Figure 1, and subsequently substituting four undercoordinated C-atoms with N-atoms, thus creating six porphyrin-like N₄ cavities and eight connected s-triazine rings (see Figure 1). The calculated C-C and C-N bond lengths are 1.55 Å and 1.34 Å, respectively. The calculated cohesive energy per atom in C₂₄N₂₄ is E_coh = −7.81 eV, which is close to that reported by Ghosh et al. (−7.40 eV) [45] but significantly higher than the value of Tang et al. (−5.78 eV) [38].

The HOMO-LUMO gap of C₂₄N₂₄ is calculated to be to be E_g = 2.82 eV, which is similar to the value reported by Ma et al. [39] and Song et al. [48] and is higher than the value reported in other investigations [40,45].

3.2. Metal Distribution Patterns

3.2.1. Geometry and Electronic Properties of Bi-Metal Complexes

The agglomeration of catalytically active TMs into clusters is a major challenge. This can be prevented by the strong interaction between TMs and support. C₂₄N₂₄ fullerene possesses natural N₄ rings that can host TM atoms (see Figure 1). We considered a combination of two metal atoms for the selected Ti, Mn, and Cu TMs with 3d²4s², 3d⁵4s², and 3d¹⁰4s¹ valence electrons, respectively, i.e., TiCu, TiMn, and MnCu. Then, various distribution patterns of these dissimilar bi-metal atoms into the six porphyrin-like C₂₄N₂₄ cavities were studied. Due to the presence of six cavities, the TM ratios will vary between zero to six. Therefore, we have Ti_xCu_z, Ti_xMn_y, and Mn_yCu_z doped C₂₄N₂₄ fullerene (Ti_xCu_z@C₂₄N₂₄, Ti_xMn_y@C₂₄N₂₄, Mn_yCu_z@C₂₄N₂₄) with x, y, z = 0–6. Figure 2a–j shows a schematic presentation of possible bi-metal distribution patterns in the N₄ cavities of C₂₄N₂₄ cage. There are two main doping sites available in the C₂₄N₂₄ cavities: equatorial and axial. As can be seen in Figure 2, equatorial and axial positions are placed in x, y (red and black dashed lines), and z (green dashed line) axis directions, respectively. Two metal atoms in a complex can be distributed into the C₂₄N₂₄ cavities through seven different distribution patterns, as listed in

Table 1. Distribution patterns of bi-metal atoms in C₂₄N₂₄ cavities.

Complex/Metal-Ratio	6:0	5:1	4:2	3:3	2:4	1:5	0:6
	a	b	c, d	e, f	g, h	i	j
TixCuz@C24N24	Ti6	Ti5Cu	Ti4Cu2	Ti3Cu3	Ti2Cu4	TiCu5	Cu6
TixMny@C24N24	Ti6	Ti5Mn	Ti4Mn2	Ti3Mn3	Ti2Mn4	TiMn5	Mn6
MnyCuz@C24N24	Mn6	Mn5Cu	Mn4Cu2	Mn3Cu3	Mn2Cu4	MnCu5	Cu6

.

3.2.2. Binding Energy (E_b)

To assess the stability of the modified complexes, the binding energy of each configuration was calculated (see Tables S2–S4). The computed E_b for each complex changes in the range of −3.55 eV to −8.11 eV. The lowest and highest E_b values correspond to the homogeneous doping with Cu (Cu₆@C₂₄N₂₄) and Ti (Ti₆@C₂₄N₂₄), respectively. The calculated E_b for Ti₆@C₂₄N₂₄ is in good agreement with previous studies (−8.61 eV and −8.14 eV) [39,45]. The binding energy of Ti_xCu_z@C₂₄N₂₄, Ti_xMn_y@C₂₄N₂₄, and Mn_yCu_z@C₂₄N₂₄ (x, y, z = 0–6) configurations is plotted and compared in Figure 3.

The high E_b values indicate a strong chemisorption of two dissimilar TMs at six N₄ cavities of C₂₄N₂₄, which inhibits the diffusion of TMs into the C₂₄N₂₄ fullerene, increasing the stability of nanocages by metal doping. Due to the higher binding energy of Ti₆@C₂₄N₂₄ and Mn₆@C₂₄N₂₄ than the cohesive energy of bulk Ti (4.85 eV/atom) and Mn (2.92 eV/atom) [49], TM aggregation is not expected, and these materials are likely to be stable enough to be used in catalytic processes. In contrast, Cu₆@C₂₄N₂₄ shows an E_b of −3.55 eV, slightly higher than the cohesive energy of bulk Cu (3.49 eV/atom) [50], such that homogeneously Cu-doped C₂₄N₂₄ is much less stable against TM agglomeration.

One can see from Figure 3 and Tables S2–S4 that by increasing the ratio of Cu-to-Ti, Mn-to-Ti, and Cu-to-Mn atoms in Ti_xCu_z@C₂₄N₂₄, Ti_xMn_y@C₂₄N₂₄, and Mn_yCu_z@C₂₄N₂₄, the E_b decreases (i.e., becomes less negative).

3.2.3. NBO Charge Analysis

Figure 4 shows the NBO charge accumulation on individual TMs in different configurations (a–j) for each complex. The precise values are reported in Tables S2–S4. Ti and Cu atoms in Ti_xCu_z@C₂₄N₂₄ and Mn_yCu_z@C₂₄N₂₄ complexes have the highest charge transfer values from the metal atom to the nanocage, in the range of 1.34 to 1.44 |e| and 0.67 to 0.69 |e|, respectively. The high charge on the metal atoms corresponds to the high electron donation induced by the four surrounding N atoms in each porphyrin-like cavity where the d orbitals of Ti, Mn, and Cu atoms overlap with the neighboring nitrogen sp² orbitals of the cavity to form a sp²d hybridization. The charge transfer leads to the elongation of the average C-C bond (≈1.55 Å) compared to that of pristine C₆₀ (1.45 Å), indicating the activation of C₂₄N₂₄ fullerene upon bi-metal doping.

3.2.4. Thermodynamic Properties and Energy Gap (E_g)

Figure 5 shows the changes in Gibbs free energy for each doped configuration, showing that bi-metallic doping is exothermic and exergonic at room temperature. The values are reported in Tables S2–S4.

Doping C₂₄N₂₄ with various Ti, Mn, or Cu distributions significantly narrows the HOMO-LUMO gap of the C₂₄N₂₄, leading to a noticeable energy gap (E_g) reduction. The highest E_g reduction occurs in Ti₂Mn₄@C₂₄N₂₄, where the calculated E_g is reduced from 2.82 eV in pure C₂₄N₂₄ to 0.13 eV, making the complex act as a semi-conductor (see Figure 5b, complex g, purple line). The calculated HOMO−LUMO gap for doped configurations does not follow any particular order but in general is less than <1.58 eV, and thus all configurations can be classified as semiconductors. Since the electrical conductivity is exponentially related to E_g, we expect that Ti₂Mn₄@C₂₄N₂₄ may show good electrical conductivity.

Besides the effects of doping on the geometric, thermodynamic, and electronic properties of the complexes as described above, we find that the location of the second introduced TM atom in axial or equatorial positions has little effect. Therefore, we expect that the complexes c and d, e and f, and g and h exhibit similar catalytic activities.

4. Catalytic Behavior of Bi-Metal Complexes toward Adsorption of Gas Species

4.1. Geometric Properties

To explore the effect of bi-metal-doping on the catalytic behavior of each complex, we investigated the individual adsorption of four gas molecules (CO₂, NO₂, H₂, and N₂) on each complex and their subgroup configurations. As shown in previous investigations, the existence of two dissimilar TM atoms in a catalyst induces various active sites [51,52,53,54]. Thus, it is important to first determine the available active sites in each substrate (see Figure S1). Considering each complex as a sphere, TM atoms are placed in x, y, and z directions. In homogeneous doping with one TM atom, one active site will be available (Figure S1a–j). By adding the second TM atom to the complex, it can be doped into one of the porphyrin vacancies along the x, y, or z direction, forming the complexes that are shown in Figure S1b. With two different TM atoms present in the complex, one would expect to have two different active sites available. However, for the adsorbent, there are not only two sites. We have labeled the TM atoms in Figure S1 (denoted as i, j, and k) to show different possible positions for the adsorbents to adsorb on the TM sites of each catalyst. It is clear that i, k/j sites are located on the axial (perpendicular to the plane of the ring)/equatorial (in the plane of the ring) axis of the catalyst, respectively. Depending on the TM ratio, the adsorbent can adsorb on either i, j, or k positions. One can see that for each configuration, two active sites are available except in configurations b and i, in which, depending on the adsorption position of the adsorbent in the equatorial (j) or axial (i and k) axis, three possible active sites are available. In addition, each adsorbent adopts mainly three adsorption modes on each active site of the substrates: parallel (side-on) or vertical (end-on) to the surface, and bridge positions.

Our results reveal that CO₂, H₂, and N₂ adsorb strongly on Ti_xCu_z@C₂₄N₂₄ and Ti_xMn_y@C₂₄N₂₄ and weakly on Mn_yCu_z@C₂₄N₂₄, while NO₂ adsorbs quite strongly with |E_ads| > 6 eV on all three complexes (see Figure 6 and Table S5). The adsorption behavior of each set of configurations is discussed below.

4.2. Adsorption of CO₂ and H₂

Ti₂Cu₄@C₂₄N₂₄ and Ti₂Mn₄@C₂₄N₂₄ tend to chemisorb CO₂ and H₂ species with high adsorption energies (see Figure 7). The covalent nature of the adsorbed species is confirmed by the calculated WBIs. As a result, the structure of CO₂ is drastically distorted upon its adsorption on these complexes. It is bent over the Ti atom binding via its C and O and forms a triangular ring above the nanocage. The O-C-O angle is bent to 131.12° in its adsorbed form and the C = O bond length is elongated to 1.35 Å, which we attribute to the significant charge transfer of 0.49 |e| from the complex to the 2π* orbitals of the CO₂ molecule. The obtained adsorption energies for CO₂ are lower than those reported on B₈₀ fullerene (−3.49 eV) [55] and higher than those of N-S dual doped graphene (−0.25 eV) [56] and Ti-doped C₂N (E_ads = −0.95 eV) [57]. The WBIs of both Ti-C and Ti-O bonds in Ti₂Cu₄@C₂₄N₂₄ and Ti₂Mn₄@C₂₄N₂₄ are 0.84, confirming the covalent bond between TM and CO₂ atoms and therefore its chemisorption over these substrates. H₂ adsorbs dissociatively in a barrier-less reaction, forming two covalent Ti-H bonds above the Ti atom with H-H bond length of >2.0 Å (see Figure 7). The NBO charge analysis (see Table S5) along with the calculated WBIs for both Ti-H bond lengths (0.89) confirms the covalent binding between Ti and H atoms and consequently the H₂ chemisorption. Interestingly, we find that the adsorption energy of one hydrogen molecule on these complexes is higher than the adsorption of six H₂ molecules on Ti₆@C₂₄N₂₄ (E_ads = −0.48 eV) [39] [39], Fe-B₃₈ (E_ads = −0.42 eV), Co-B₃₈ (E_ads = −0.72 eV), Ni-B₃₈ (E_ads = −0.89 eV) [58], and 2D carbon allotrope $\mathsf{\Psi }$ graphene (E_ads = −0.34 eV) [59].

Due to the lower activity of the Cu₆@C₂₄N₂₄ complex, CO₂ and H₂ physisorb on this structure in their gas-phase form. The calculated E_ads of H₂ on Cu₆@C₂₄N₂₄ is lower than that reported on Ti₂C- and Ti₂CN-Mxenes (E_ads in the range of −0.99 to −1.4 eV) [60]. A negligible charge transfer from CO₂ (H₂) to Cu₆@C₂₄N₂₄, the large Cu-C (Cu-H) bond length, and the low WBIs value of 0.12 (0.2) confirm physisorption of these CO₂ (H₂) species on Cu₆@C₂₄N₂₄.

4.3. Adsorption of N₂ and NO₂

Two different orientations were considered for N₂ adsorption on each structure: side-on or end-on. The ideal catalyst would provide strong binding sites for the N₂ molecule and thus weaken the N−N bond. Our results indicate that the ideal orientation for N₂ adsorption on Ti₂Cu₄@C₂₄N₂₄ and Ti₂Mn₄@C₂₄N₂₄ and Mn₃Cu₃@C₂₄N₂₄ is the end-on (see Figure 8). Upon N₂ adsorption, the N-N bond length increases from 1.09 Å in the gas phase to 1.11 and 1.12 Å in its adsorbed form on Ti₂Cu₄@C₂₄N₂₄ and Ti₂Mn₄@C₂₄N₂₄ complexes, respectively. These values are in between the double and triple bond lengths, indicating the activation of N₂ upon adsorption on Ti sites. The empty d orbitals of the Ti atom can accept the lone-pair electrons of N₂. In turn, the Ti’s capacity to donate electrons to the antibonding π* orbital of N₂ is also significant for N₂ binding to Ti. Therefore, this electron acceptance/donation process between the nanocage and N₂ plays an important role in N₂ activation (see Table S5). Ti₂Mn₄@C₂₄N₂₄ has a greater tendency for N₂ activation with higher adsorption energy than that reported on Co-doped graphitic carbon nitride (−1.63 eV) [61] and Fe doped phosphorene (−0.81 eV) [62].

Although the Mn₃Cu₃@C₂₄N₂₄ complex adsorbs N₂ molecule with lower E_ads, due to its lower catalytic activity toward gas adsorption, this value is still higher than that on Mn-Fe bi-metal atoms anchored pyridinic nitrogen-doped graphene (E_ads = −0.53 eV) [63]. The calculated WBIs (≈0.0001) and charge transfer confirm the N₂ physisorption on Mn₃Cu₃@C₂₄N₂₄.

Regardless of all possible bi-metal distributions into the porphyrin C₂₄N₂₄ cavities, the three Ti_xCu_z@C₂₄N₂₄, Ti_zMn_y@C₂₄N₂₄, and Mn_yCu_z@C₂₄N₂₄ (x, z, y = 0–6) complexes with all the metal ratios exhibit an outstanding activity toward NO₂ adsorption and activation. However, the more stable configurations are shown in Figure 8. One can see that the NO₂ molecule binds via two O atoms with the Ti atom in Ti₆@C₂₄N₂₄ and Ti₂Mn₄@C₂₄N₂₄ and with the Mn atom in the Mn₅Cu@C₂₄N₂₄ complex, respectively. Owing to the great NBO charge transfer from the nanocage to the NO₂ molecule (0.46 |e|) reported in Table S5, the N-O bond length increases compared to that of the gas phase (1.19 Å).

4.4. Electronic and Thermodynamic Properties

To see if the adsorption of CO₂, NO₂, H₂, and N₂ gas species on the selected twelve more energetically stable complexes affects their electronic properties, we also investigated the LUMO-HOMO energy gap of each structure and compared our results with those of pristine bi-metal doped nanocages reported in Figure 5. The obtained E_g values for adsorption structures are listed in Table S5, showing that E_g indeed increases upon gas adsorption. This confirms the tunable electronic properties of C₂₄N₂₄ nanocage induced by hosting six dissimilar bi-metals doping into its N₄ cavities with various distribution patterns. All adsorption reactions are exothermic and exergonic, except for H₂ adsorbed on the Cu₆@C₂₄N₂₄ complex, which is slightly endergonic (see Table S5).

4.5. Lifetime of the Adsorbed Gas Species on Bi-Metal Complexes

The retention time of a molecule on a surface can be calculated with the Frenkel equation [64]:

$$\tau ={\tau }_0{e}^{\raisebox{1ex}{$Q$}\!\left/ \!\raisebox{-1ex}{$RT$}\right.}$$

(6)

where ${\tau }_0$ is 10⁻¹² to 10⁻¹³ s and Q is the adsorption energy. We calculated the lifetime of each adsorbent over each configuration from which the energetically more favorable structures were chosen and plotted versus temperature. Figure 9 shows the computed lifetime vs. temperature for adsorbed CO₂, NO₂, H₂, and N₂ on the twelve nanocages discussed above. As can be seen in Figure 9, the lifetime of gas species on Ti_xCu_z@C₂₄N₂₄ and Ti_xMn_y@C₂₄N₂₄ at 400 K is higher than that on Mn_yCu_z@C₂₄N₂₄ (x, y, z = 0–6), indicating that Ti_xCu_z@C₂₄N₂₄ and Ti_xMn_y@C₂₄N₂₄ are likely to be more efficient for gas capture. Obviously, increasing the temperature reduces the lifetime leading. However, Ti_xCu_z@C₂₄N₂₄, Ti_xMn_y@C₂₄N₂₄, and Mn_yCu_z@C₂₄N₂₄ catalysts capture NO₂ so actively that it will not desorb from the catalyst even at high temperatures. Therefore, we can conclude that, except for NO₂, which effectively adsorbs and is retained on the catalysts, the gas species adsorb and remain on the Ti active site of Ti_xCu_z@C₂₄N₂₄ and Ti_xMn_y@C₂₄N₂₄ fullerene at room temperature, whereas they are not retained on Mn_yCu_z@C₂₄N₂₄ sufficiently for gas capture.

5. Conclusions

In this work, the effect of dissimilar bi-metal doping into the six porphyrin-like cavities of a C₂₄N₂₄ nanocage on the catalytic activity and adsorption characteristic of a number of greenhouse gases are investigated by means of DFT calculations. The binding energy and bulk cohesive energy calculations reveal that the selected TM atoms are stably trapped in the C₂₄N₂₄ cavities, especially Ti/Cu atoms in Ti_xCu_z@C₂₄N₂₄ and Ti/Mn atoms in Ti_xMn_y@C₂₄N₂₄ (x, y, z = 0–6) complexes, suggesting the durability of the catalysts. Studying the adsorption behavior of these catalysts toward H₂, CO₂, NO₂, and N₂ sensing show that the Ti₂Mn₄@C₂₄N₂₄ is more active for adsorption of all species. Furthermore, the lifetime of each gas species on Ti_xCu_z@C₂₄N₂₄ and Ti_xMn_y@C₂₄N₂₄ at 400 K is higher than that on Mn_yCu_z@C₂₄N₂₄ (x, y, z = 0–6)_, indicating that Ti_xMn_y@C₂₄N₂₄ and Ti_xCu_z@C₂₄N₂₄ are likely to be more efficient for gas capture. Overall, this work systematically provides the unique fundamental understanding of catalytic properties of two dissimilar bi-metal atom catalysts that could open a way for the future design and development of novel few-atom catalysts.