Electronic Properties and CO2-Selective Adsorption of (NiB)n (n = 1~10) Clusters: A Density Functional Theory Study

In this study, we investigated the electronic properties and selective adsorption for CO2 of nickel boride clusters (NiB)n, (n = 1~10) using the first principles method. We optimized the structures of the clusters and analyzed their stability based on binding energy per atom. It was observed that (NiB)n clusters adopt 3D geometries from n = 4, which were more stable compared to the plane clusters. The vertical electron affinity, vertical ionization energy, chemical potential, and highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap were calculated. Our results revealed that (NiB)6 and (NiB)10, with high chemical potential, exhibit a higher affinity for CO2 adsorption due to a charge delivery channel that forms along the Ni→B→CO2 path. Notably, (NiB)10 demonstrated a more practical CO2 desorption temperature, as well as a broader window for the selective adsorption of CO2 over N2. The density of states analysis showed that the enhanced CO2 adsorption on (NiB)10 can be attributed to the synergistic effect between Ni and B, which provides more active sites for CO2 adsorption and promotes the electron transfer from the surface to the CO2 molecule. Our theoretical results imply that (NiB)10 should be a promising candidate for CO2 capture.


Introduction
The issue of global climate change caused by human activities such as fossil fuel consumption and deforestation has become a major concern in the 21st century. The concentration of greenhouse gases, especially CO 2 [1], has increased dramatically, leading to global warming [2,3]. Although CO 2 has a lower global warming potential (GWP) than other greenhouse gases like N 2 O and CH 4 , it is thought to considerably contribute to the global greenhouse effect owing to its abundance in the atmosphere. As a result, a significant amount of scientific effort, such as energy efficiency improvement, energy demand reduction, use of renewable energy, electrochemical reduction [4,5], direct hydrogenation of CO 2 into formic acid, methane, methanol or other chemicals [6,7], and CO 2 capture and storage [8][9][10], has been concentrated into reducing or controlling the concentration of CO 2 . One of the most important research topics is the separation, storage, and recovery of CO 2 , as it is a reactant in significant industrial processes and a greenhouse gas that contributes to global warming [11]. An ideal CO 2 sorbent should meet several requirements, including high capacity and selectivity, rapid adsorption/desorption kinetics, and good chemical stability [12].
In recent years, Ni-based materials have received a lot of interest due to their low cost and availability for CO 2 capture and activity. Roque-Malherbe et al. [13] synthesized Ni-, Zn-, and Cd-nitroprussides, and studied the interactions with CO 2 molecules. The results showed that Ni-nitroprussides are excellent for CO 2 storage. However, the accumulation of carbonaceous deposits on the surface of Ni-based catalysts can lead to deactivation [14,15], which eventually blocks the active sites. To address this issue, many attempts have been made with various methods and materials to inhibit the accumulation of carbonaceous deposits [16][17][18][19]. One promising approach is the addition of a small amount of boron to enhance the activity of Ni-based catalysts. First-principle studies suggested that the addition of a small amount of boron can enhance the activity of Ni-based catalysts. Xu and Sayes proposed that boron atoms can effectively block carbon diffusion into nickel lattice by preferentially occupying octahedral sites of the first subsurface layer [20,21]. Experimental studies support this hypothesis. Xu et al. [22] investigated the impact of boron addition on the stability and activity of Ni catalysts used for the steam-reforming of methane.
Their results indicate that the catalytic activity of boron-modified catalysts declines with time-on-stream, but less carbon is formed compared to the unpromoted catalyst. Fouskas et al. [17] employed the wet co-impregnation synthesis method to simultaneously deposit Ni and B precursors on the alumina carrier. They demonstrated that B can greatly enhance the resistance to carbon deposition due to its ability to decrease the size of Ni particles. Shakir et al. [23] found that the presence of B facilitated the formation of Ni-B species along with metallic Ni, controlled the particle size and stabilized the metallic state, and influenced the Ni-C interaction, leading to the advancement in catalytic performance and diminution in deactivation.
Ni and B can generate different Ni-B binary compounds. Shein et al. [24] calculated the lattice constant, magnetic properties, and formation energy of Ni 3 B, which indicated that the strong stability of Ni 3 B was due to the strong Ni-B hybridization. Zhou et al. [25] researched the electronic structure and mechanical properties of NiB. However, there is no literature on the structure and electronic property of the NiB cluster and its availability for CO 2 capture and activity.
To summarize, the development of efficient and effective CO 2 sorbents is crucial for reducing the concentration of greenhouse gases and mitigating the effects of global climate change. Ni-based materials, especially those modified with boron, have shown great potential for CO 2 capture and activity. In our research, we conducted a comprehensive investigation on the structures, electronic properties, CO 2 adsorption, and activities of NiB clusters of various sizes using first-principles calculations. The obtained results could provide guidance for the properties of Ni-based material for CO 2 adsorption and activity, which could play a crucial role in mitigating the effects of global climate change.

Geometrical Structures of Clusters
To begin, we constructed and optimized the lowest-energy structures of the most stable (NiB) n (n = 1~10) clusters. The resulting ground states of the (NiB) n (n = 1~10) are visible in Figure 1. For (NiB) 1 , the ground-state structure is linear. The bond length and the binding energy for NiB dimer is 1.68 Å and −7.13 eV/atom, respectively. For (NiB) 2 , a rhombus structure with four bonds of 1.81 Å is obtained as the ground-state structure. In the case of n = 3, it is observed that the planar structure exhibits an inner Ni atom triangle, which is nearly equilateral, with a bond length of 1.80 Å. For n = 4-10, (NiB) n clusters adopt 3D configurations, with a bond of ca. 1.95 Å. Clusters (n = 4, 5, 6, 8) are especially the most symmetric.
Next, we turn to the electronic properties of these (NiB) n clusters. The data reported in Figure 2 show that the binding energy per atom (E b ) exhibits an asymptotic behavior. In this figure, it is observed that beyond the 8-atom cluster (n = 4), the value of Eb increases slowly as the cluster size increases. The exponential fitting for (NiB) n (n = 4~10) gives E b = 0.3557 ln(n) − 1.065, and R 2 value of 0.994. This trend is rationalized by noticing that the average number of nearest neighbors grows with cluster size, thus increasing the number of atomic interactions [26]. Remarkably, this nuclearity represents the size after Next, we turn to the electronic properties of these (NiB)n clusters. The data reported in Figure 2 show that the binding energy per atom (Eb) exhibits an asymptotic behavior In this figure, it is observed that beyond the 8-atom cluster (n = 4), the value of Eb increase slowly as the cluster size increases. The exponential fitting for (NiB)n (n = 4~10) gives = 0.3557 ln( ) − 1.065, and R 2 value of 0.994. This trend is rationalized by noticing that the average number of nearest neighbors grows with cluster size, thus increasing the numbe of atomic interactions [26]. Remarkably, this nuclearity represents the size after which the clusters change from planar to 3D. Therefore, Figure 2 depicts the stabilization toward 3D structures [27]. Binding energy (Eb, in eV) and the highest occupied molecular orbital (HOMO)-lowes unoccupied molecular orbital (LUMO) gap (Eg) of (NiB)n (n = 1-10) clusters.
In addition to the findings discussed in the previous paragraph, the study also calcu lated the VIE and VEA for each size cluster ( Table 1). The results show that the (NiB) cluster has a tendency to donate an electron, as indicated by the positive VIE and VEA [28,29]. The VIE and VEA values were also used to determine the global reactivity de scriptors (GRDs) [30,31], with the most widely used parameter being µ. The µ value re flects the escaping tendency of an electron, with higher values indicating greater reactivity  Next, we turn to the electronic properties of these (NiB)n clusters. The data reported in Figure 2 show that the binding energy per atom (Eb) exhibits an asymptotic behavior In this figure, it is observed that beyond the 8-atom cluster (n = 4), the value of Eb increase slowly as the cluster size increases. The exponential fitting for (NiB)n (n = 4~10) gives = 0.3557 ln( ) − 1.065, and R 2 value of 0.994. This trend is rationalized by noticing that the average number of nearest neighbors grows with cluster size, thus increasing the numbe of atomic interactions [26]. Remarkably, this nuclearity represents the size after which the clusters change from planar to 3D. Therefore, Figure 2 depicts the stabilization toward 3D structures [27]. In addition to the findings discussed in the previous paragraph, the study also calcu lated the VIE and VEA for each size cluster ( Table 1). The results show that the (NiB) cluster has a tendency to donate an electron, as indicated by the positive VIE and VEA [28,29]. The VIE and VEA values were also used to determine the global reactivity de scriptors (GRDs) [30,31], with the most widely used parameter being μ. The μ value re flects the escaping tendency of an electron, with higher values indicating greater reactivity [30]. The low μ values of (NiB)n (n = 1-3) clusters indicate their low reactivity. This is con sistent with their low chemical potential. Additionally, these cluster sizes exhibit high band gap energies (Eg), as shown in Figure 2, while for (NiB)n clusters with n > 4, the band gap energies are lower. Consequently, these clusters may exhibit higher reactivity In addition to the findings discussed in the previous paragraph, the study also calculated the VIE and VEA for each size cluster ( Table 1). The results show that the (NiB) n cluster has a tendency to donate an electron, as indicated by the positive VIE and VEA [28,29]. The VIE and VEA values were also used to determine the global reactivity descriptors (GRDs) [30,31], with the most widely used parameter being µ. The µ value reflects the escaping tendency of an electron, with higher values indicating greater reactivity [30]. The low µ values of (NiB) n (n = 1-3) clusters indicate their low reactivity. This is consistent with their low chemical potential. Additionally, these cluster sizes exhibit high band gap energies (E g ), as shown in Figure 2, while for (NiB) n clusters with n > 4, the band gap energies are lower. Consequently, these clusters may exhibit higher reactivity compared to (NiB) n (n = 1-3) clusters. The band gap reflects the possibility of electrons to jump from occupied to unoccupied orbitals. Based on the high E g and low µ value, clusters n = 1-3 are identified as least reactive in the series presented here. Therefore, this paper only focuses on the (NiB) n structures n = 4-10. Table 1. Vertical ionization energy (VIE), vertical electron affinity (VEA), and chemical potential (µ) of (NiB) n (n = 1-10) clusters (units are in eV).  4 3.85 2.56 −3.21 (NiB) 5 3.40 2.49 −2.94 (NiB) 6 3.21 2.41 −2.81 (NiB) 7 3.37 2.67 −3.02 (NiB) 8 4.52 1.77 −3.18 (NiB) 9 5.17 1.29 −3.23 (NiB) 10 2.15 2.07 −2.11

CO 2 Adsorption
This passage focuses on the physisorption of CO 2 molecules on different (NiB) n surfaces. The initial placement of all CO 2 molecules was at a distance of 2.5 Å above the surface, to simulate the physisorption process. As shown in Figure 3, (NiB) 10 has the highest chemical potential and possesses the highest activity for CO 2 adsorption compared to all the structures studied, followed by (NiB) 6 . Furthermore, it is also found that the distance between CO 2 and the surface ( Figure 3) is highly correlated with the adsorption energies. CO 2 tends to adsorb at the top of Ni instead of B (Figure 4), except adsorption on (NiB) 8 , which illustrates that CO 2 should preferably obtain electrons from the Ni atoms rather than B atoms in the cluster. For CO 2 adsorption on (NiB) 8 , CO 2 binds to B instead of Ni due to the spherical-like structure of (NiB) 8 , which creates a more exposed or accessible surface for B atoms at the top. n = 1-3 are identified as least reactive in the series presented here. Therefore, this paper only focuses on the (NiB)n structures n = 4-10. Table 1. Vertical ionization energy (VIE), vertical electron affinity (VEA), and chemical potential (µ) of (NiB)n (n = 1-10) clusters (units are in eV).

CO2 Adsorption
This passage focuses on the physisorption of CO2 molecules on different (NiB)n surfaces. The initial placement of all CO2 molecules was at a distance of 2.5 Å above the surface, to simulate the physisorption process. As shown in Figure 3, (NiB)10 has the highest chemical potential and possesses the highest activity for CO2 adsorption compared to all the structures studied, followed by (NiB)6. Furthermore, it is also found that the distance between CO2 and the surface ( Figure 3) is highly correlated with the adsorption energies. CO2 tends to adsorb at the top of Ni instead of B (Figure 4), except adsorption on (NiB)8, which illustrates that CO2 should preferably obtain electrons from the Ni atoms rather than B atoms in the cluster. For CO2 adsorption on (NiB)8, CO2 binds to B instead of Ni due to the spherical-like structure of (NiB)8, which creates a more exposed or accessible surface for B atoms at the top.  The local structures and charge differences for different adsorption complexes are shown in Figure 5. Compared with other complexes, CO 2 molecules obtain additional electron from the unsaturated Ni atom of (NiB) 6 and (NiB) 10 (Figure 5c,g). Thus, the adsorption enhancement by the two surfaces is reasonable. Most importantly, (NiB) 10 is determined to be the most active for CO 2 adsorption by its largest ∆E ads (−0.24 eV) and with the most charges transferred to CO 2 (∆q = −0.027 e). As per Figure 5g, a charge delivery channel forms along the Ni→B→CO 2 path, which provides more electrons traveling from Molecules 2023, 28, 5386 5 of 13 the surface to CO 2 molecules. The channel is strengthened in the order of (NiB) 4 < (NiB) 5 <(NiB) 8 < (NiB) 9 < (NiB) 7 < (NiB) 6 < (NiB) 10 , in accordance with the adsorption energy. This suggests that the charge delivery channel along the Ni→B→CO 2 path is the key factor that contributes to the strong adsorption capacity of (NiB) 10 for CO 2 . The charge delivery channel provides a pathway for the transfer of electrons from the cluster to the CO 2 molecule, which enhances the CO 2 adsorption. The results suggest that the synergistic effect between Ni and B provides more active sites for CO 2 adsorption and promotes the electron transfer from the surface to the CO 2 molecule. The larger cluster size leads to a higher adsorption energy for CO 2 , which is attributed to the formation of the charge delivery channel along the Ni→B→CO 2 path. These findings have important implications for the design of efficient sorbents for CO 2 capture and separation, which is crucial for mitigating the negative impacts of greenhouse gas emissions on the environment.  The local structures and charge differences for different adsorption complexes are shown in Figure 5. Compared with other complexes, CO2 molecules obtain additional electron from the unsaturated Ni atom of (NiB)6 and (NiB)10 ( Figure 5c,g). Thus, the adsorption enhancement by the two surfaces is reasonable. Most importantly, (NiB)10 is determined to be the most active for CO2 adsorption by its largest ΔEads (−0.24 eV) and with the most charges transferred to CO2 (Δq = −0.027 e). As per Figure 5g, a charge delivery channel forms along the Ni→B→CO2 path, which provides more electrons traveling from the surface to CO2 molecules. The channel is strengthened in the order of (NiB)4 < (NiB)5 <(NiB)8 < (NiB)9 < (NiB)7 < (NiB)6 < (NiB)10, in accordance with the adsorption energy. This suggests that the charge delivery channel along the Ni→B→CO2 path is the key factor that contributes to the strong adsorption capacity of (NiB)10 for CO2. The charge delivery channel provides a pathway for the transfer of electrons from the cluster to the CO2 molecule, which enhances the CO2 adsorption. The results suggest that the synergistic effect between Ni and B provides more active sites for CO2 adsorption and promotes the electron transfer from the surface to the CO2 molecule. The larger cluster size leads to a higher adsorption energy for CO2, which is attributed to the formation of the charge delivery channel along the Ni→B→CO2 path. These findings have important implications for the design of efficient sorbents for CO2 capture and separation, which is crucial for mitigating the negative impacts of greenhouse gas emissions on the environment.  The local structures and charge differences for different adsorption comple shown in Figure 5. Compared with other complexes, CO2 molecules obtain add electron from the unsaturated Ni atom of (NiB)6 and (NiB)10 (Figure 5c,g). Thus, sorption enhancement by the two surfaces is reasonable. Most importantly, (NiB)1 termined to be the most active for CO2 adsorption by its largest ΔEads (−0.24 eV) an the most charges transferred to CO2 (Δq = −0.027 e). As per Figure 5g, a charge d channel forms along the Ni→B→CO2 path, which provides more electrons travelin the surface to CO2 molecules. The channel is strengthened in the order of (NiB)4 < <(NiB)8 < (NiB)9 < (NiB)7 < (NiB)6 < (NiB)10, in accordance with the adsorption energ suggests that the charge delivery channel along the Ni→B→CO2 path is the key fac contributes to the strong adsorption capacity of (NiB)10 for CO2. The charge deliver nel provides a pathway for the transfer of electrons from the cluster to the CO2 mo which enhances the CO2 adsorption. The results suggest that the synergistic effect b Ni and B provides more active sites for CO2 adsorption and promotes the electron t from the surface to the CO2 molecule. The larger cluster size leads to a higher adso energy for CO2, which is attributed to the formation of the charge delivery channe the Ni→B→CO2 path. These findings have important implications for the design cient sorbents for CO2 capture and separation, which is crucial for mitigating the n impacts of greenhouse gas emissions on the environment.

Adsorption Selectivity over N 2
In addition to the remarkable CO 2 adsorption activity, an effective adsorbent should control selectivity over other competitive gaseous molecules, especially N 2 . Hence, N 2 adsorption on different (NiB) n surfaces was also studied and the corresponding results are listed in Figure 6. Interestingly, the largest adsorption enhancement of N 2 is still located in the (NiB) 10 slab of −0.066 eV, which has a similar pattern to CO 2 adsorption. listed in Figure 6. Interestingly, the largest adsorption enhancement of N2 is still loc in the (NiB)10 slab of −0.066 eV, which has a similar pattern to CO2 adsorption.
Subsequently, CO2 adsorption selectivity over N2 is identified in Figure 6. An ig able distinction in the calculated results is discovered between CO2 and N2 absorbe (NiB)4, (NiB)5, and (NiB)8. However, the two widest variations occur in the situatio CO2 adsorption on (NiB)6 and (NiB)10 with the largest increase in adsorption energy. ing CO2@(NiB)10 as an example, the ΔEads (−0.24 eV) is almost four times that for N2 (− eV) on the same surface, which shows that (NiB)10 exhibits the potency of a highly sele adsorbent for CO2 capture.
The results suggest that the larger cluster size leads to a higher adsorption energ both CO2 and N2, but the increase in adsorption energy for CO2 is more significant that for N2. The results indicate that (NiB)n clusters have the potential to be highly sele adsorbents for CO2 capture and separation, which is crucial for the development of tainable energy technologies. Strictly, the adsorption energies calculated for CO2 and N2 on (NiB)n (n = 4-10) s as discussed earlier, have the Helmholtz-free energy of 0 k, without zero-point en correlation. To evaluate the relative adsorption stability for different configuration sp under finite temperature and pressure, we adopted the ab initio thermodynamic appr (Equation (7)) and extended our DFT energy results to plot the temperature and pres Subsequently, CO 2 adsorption selectivity over N 2 is identified in Figure 6. An ignorable distinction in the calculated results is discovered between CO 2 and N 2 absorbed on (NiB) 4 , (NiB) 5 , and (NiB) 8 . However, the two widest variations occur in the situations of CO 2 adsorption on (NiB) 6 and (NiB) 10 with the largest increase in adsorption energy. Taking CO 2 @(NiB) 10 as an example, the ∆E ads (−0.24 eV) is almost four times that for N 2 (−0.066 eV) on the same surface, which shows that (NiB) 10 exhibits the potency of a highly selective adsorbent for CO 2 capture.
The results suggest that the larger cluster size leads to a higher adsorption energy for both CO 2 and N 2 , but the increase in adsorption energy for CO 2 is more significant than that for N 2 . The results indicate that (NiB) n clusters have the potential to be highly selective adsorbents for CO 2 capture and separation, which is crucial for the development of sustainable energy technologies.
Strictly, the adsorption energies calculated for CO 2 and N 2 on (NiB) n (n = 4-10) slabs, as discussed earlier, have the Helmholtz-free energy of 0 k, without zero-point energy correlation. To evaluate the relative adsorption stability for different configuration species under finite temperature and pressure, we adopted the ab initio thermodynamic approach (Equation (7)) and extended our DFT energy results to plot the temperature and pressure (T-P) phase diagram between CO 2 @surfaces and N 2 @surfaces in the temperature and pressure range of our interest (Figures 7 and 8). a superior adsorbent for CO2 capture under mild conditions.
The T-P phase diagram provides a comprehensive understanding of the adsorption behavior of CO2 and N2 on (NiB)n clusters. It shows that the adsorption selectivity of CO2 over N2 is highly dependent on the cluster size and structure, and the larger cluster size leads to a higher desorption temperature for CO2. The results suggest that (NiB)n clusters can be a promising candidate for CO2 capture and separation under mild conditions, which is crucial for the development of sustainable energy technologies.  Figure 8 illustrates the equilibrium states for the adsorption of a single gas species under varying temperature and pressure conditions. The curves in the graph stand for the adsorption isotherms for each gas species. In the upper left part above the curve, the CO2/N2 molecule is inclined to be desorbed as a gaseous species, while the bottom right part indicates an adsorbed state. The interval between two different curves is positively correlated with their selectivity over each other.
For instance, taking the CO2/N2 adsorption on (NiB)6 as an example (Figure 8c), under the partial pressure of 1.0 atm, N2 can be adsorbed below 97.08 K and desorbed above this temperature. However, the desorption temperature of CO2 is 134.91 K. Therefore, in the temperature range of 97.08-134.91 K, (NiB)9 selectively adsorbs CO2 over N2. The temperature range can be defined as the selective window of CO2/N2. Compared with the situation of (NiB)6 and (NiB)10, the selective window for CO2/N2 is distinctly narrowed on five other surfaces. The results suggest that the selectivity of CO2/N2 adsorption on NiB clusters is highly dependent on the cluster size and structure. These findings provide valuable insights into the design of efficient sorbents for CO2 capture and separation.
In addition, the results suggest that the selectivity of CO2/N2 adsorption on NiB clusters is highly dependent on the cluster size and structure. The (NiB)n cluster with a higher chemical potential can greatly elevate the desorption temperature of various gases, making it more practical for industrial use. These findings provide valuable insights into the

Discussion
For the adsorption of CO2 and N2 on (NiB)10, the PDOS (projected density of states) have been calculated and shown in Figure 9. It was observed that the DOS of CO2 is closer For example, taking 0.9 atm as the CO 2 partial pressure, for example, in Figure 7, the desorption temperature is raised in the order of CO 2 @(NiB) 4 < CO 2 @(NiB) 5 < CO 2 @(NiB) 8 < CO 2 @(NiB) 9 < CO 2 @(NiB) 7 < CO 2 @(NiB) 6 < CO 2 @(NiB) 10 . The desorption temperature is raised from 108.56 K for CO 2 @(NiB) 4 to 191.924 K for CO 2 (NiB) 10 . This means the application range for CO 2 adsorption is extended to about 80 K by larger cluster size, leading to a superior adsorbent for CO 2 capture under mild conditions.
The T-P phase diagram provides a comprehensive understanding of the adsorption behavior of CO 2 and N 2 on (NiB) n clusters. It shows that the adsorption selectivity of CO 2 over N 2 is highly dependent on the cluster size and structure, and the larger cluster size leads to a higher desorption temperature for CO 2 . The results suggest that (NiB) n clusters can be a promising candidate for CO 2 capture and separation under mild conditions, which is crucial for the development of sustainable energy technologies. Figure 8 illustrates the equilibrium states for the adsorption of a single gas species under varying temperature and pressure conditions. The curves in the graph stand for the adsorption isotherms for each gas species. In the upper left part above the curve, the CO 2 /N 2 molecule is inclined to be desorbed as a gaseous species, while the bottom right part indicates an adsorbed state. The interval between two different curves is positively correlated with their selectivity over each other.
For instance, taking the CO 2 /N 2 adsorption on (NiB) 6 as an example (Figure 8c), under the partial pressure of 1.0 atm, N 2 can be adsorbed below 97.08 K and desorbed above this temperature. However, the desorption temperature of CO 2 is 134.91 K. Therefore, in the temperature range of 97.08-134.91 K, (NiB) 9 selectively adsorbs CO 2 over N 2 . The temperature range can be defined as the selective window of CO 2 /N 2 . Compared with the situation of (NiB) 6 and (NiB) 10 , the selective window for CO 2 /N 2 is distinctly narrowed on five other surfaces. The results suggest that the selectivity of CO 2 /N 2 adsorption on NiB clusters is highly dependent on the cluster size and structure. These findings provide valuable insights into the design of efficient sorbents for CO 2 capture and separation.
In addition, the results suggest that the selectivity of CO 2 /N 2 adsorption on NiB clusters is highly dependent on the cluster size and structure. The (NiB) n cluster with a higher chemical potential can greatly elevate the desorption temperature of various gases, making it more practical for industrial use. These findings provide valuable insights into the design of efficient sorbents for CO 2 capture and separation, which is crucial for mitigating the negative impacts of greenhouse gas emissions on the environment.

Discussion
For the adsorption of CO 2 and N 2 on (NiB) 10 , the PDOS (projected density of states) have been calculated and shown in Figure 9. It was observed that the DOS of CO 2 is closer to the Fermi level compared to that of N 2 . In the case of CO 2 , its DOS being closer to the Fermi level suggests a higher availability of energy states for CO 2 molecules to interact with the (NiB) 10 surface. This proximity of energy levels facilitates stronger interactions between CO 2 and the adsorbent, leading to a higher adsorption affinity. On the other hand, N 2 , with its DOS farther away from the Fermi level, has fewer available energy states for interaction, resulting in weaker adsorption.
It has been recognized that the Ni→B→CO 2 path provides more electrons traveling from the surface to the CO 2 molecule, which enhances the CO 2 reduction activity. In this study, we further discuss this point and make some generalizations of our findings.
To investigate the CO 2 adsorption on the (NiB) n cluster, we calculated the projected density of states (PDOS) for the adsorption of CO 2 on (NiB) 4 and (NiB) 10 , which exhibited the lowest and largest adsorption energies, respectively. Figure 10 displays the results of this analysis. Compared with CO 2 on (NiB) 4 (Figure 10a), the localized CO 2 2p peak A was enhanced and shifted to a higher energy level. This indicates that the CO 2 molecule is strongly adsorbed on the (NiB) 10 surface, which is consistent with the high adsorption energy. Furthermore, Ni atoms in clusters hybridized with CO 2 (peak B in Figure 10c) and should be polarized with the approach of positively charged species (e.g., C atom in CO 2 molecule), which is consistent with the formation of the charge delivery channel along the Ni→B→CO 2 path. It has been recognized that the Ni→B→CO2 path provides more electrons traveling from the surface to the CO2 molecule, which enhances the CO2 reduction activity. In this study, we further discuss this point and make some generalizations of our findings.
To investigate the CO2 adsorption on the (NiB)n cluster, we calculated the projected density of states (PDOS) for the adsorption of CO2 on (NiB)4 and (NiB)10, which exhibited the lowest and largest adsorption energies, respectively. Figure 10 displays the results of this analysis. Compared with CO2 on (NiB)4 (Figure 10a), the localized CO2 2p peak A was enhanced and shifted to a higher energy level. This indicates that the CO2 molecule is strongly adsorbed on the (NiB)10 surface, which is consistent with the high adsorption energy. Furthermore, Ni atoms in clusters hybridized with CO2 (peak B in Figure 10c) and should be polarized with the approach of positively charged species (e.g., C atom in CO2 molecule), which is consistent with the formation of the charge delivery channel along the Ni→B→CO2 path.
This suggested that the charge delivery channel and the hybridization of Ni atoms with CO2 are the key factors that contribute to the strong CO2 adsorption capacity of (NiB)10. The charge delivery channel provides a pathway for the transfer of electrons from the cluster to the CO2 molecule, while the hybridization of Ni atoms with CO2 enhanced the interaction between the cluster and the CO2 molecule. The polarization of Ni atoms in a positively charged manner further strengthens the interaction between the cluster and the CO2 molecule, which increases the adsorption capacity of CO2 on the cluster surface. This suggests that the CO2 adsorption promotion by (NiB)10 should be predictable. The enhanced CO2 adsorption on (NiB)10 can be attributed to the synergistic effect between Ni and B, which provides more active sites for CO2 adsorption and promotes electron transfer from the surface to the CO2 molecule. In conclusion, our study provides a deeper understanding of the CO2 adsorption on NiB and sheds light on the design of efficient sorbents for CO2 capture. The results suggest that NiB is a promising sorbent for CO2 molecules due to its high activity and selectivity, and the Ni→B→CO2 path provides a promising strategy to enhance the CO2 adsorption This suggested that the charge delivery channel and the hybridization of Ni atoms with CO 2 are the key factors that contribute to the strong CO 2 adsorption capacity of (NiB) 10 . The charge delivery channel provides a pathway for the transfer of electrons from the cluster to the CO 2 molecule, while the hybridization of Ni atoms with CO 2 enhanced the interaction between the cluster and the CO 2 molecule. The polarization of Ni atoms in a positively charged manner further strengthens the interaction between the cluster and the CO 2 molecule, which increases the adsorption capacity of CO 2 on the cluster surface. This suggests that the CO 2 adsorption promotion by (NiB) 10 should be predictable. The enhanced CO 2 adsorption on (NiB) 10 can be attributed to the synergistic effect between Ni and B, which provides more active sites for CO 2 adsorption and promotes electron transfer from the surface to the CO 2 molecule.
In conclusion, our study provides a deeper understanding of the CO 2 adsorption on NiB and sheds light on the design of efficient sorbents for CO 2 capture. The results suggest that NiB is a promising sorbent for CO 2 molecules due to its high activity and selectivity, and the Ni→B→CO 2 path provides a promising strategy to enhance the CO 2 adsorption performance.

Calculation Methods
All the clusters were optimized with the Vienna Ab initio Simulation Package (VASP5.4) [32,33], which uses a plane wave basis set to solve the Kohn-Sham equation of the density functional theory (DFT). The Perdew-Burke-Ernzerhof (PBE) exchange correlation function [34] was used, and the cut-off energy was set to 450 eV for all the calculations within the framework of the projector-augmented wave (PAW) method [35,36]. The (NiB) n clusters were placed in a 30 × 30 × 30 Å cubic super-cell, which makes the interaction between the two neighboring cluster images negligible. The Brillouin zone was sampled with 5 × 5 × 1 k-points sampled using the Monkhorst-Pack method. The cluster structures were converged when the force components were less than a threshold value of 0.02 eV Å −1 , and the change of total energy less than 10 −5 eV. The frequency calculations were performed to confirm that the reported clusters are geometrically stable, and at the same time, to get the zero-point vibration energies (ZPE) of the clusters. If not mentioned, the ZPE correction was included in the total energy. The binding energy per atom (E b ) for the most stable structures of (NiB) n clusters are calculated in order to predict the relative stability of the clusters. The binding energy per atom (E b ) was estimated through Equation (1): where N = 2n is the total number of atoms in the cluster. The total energy, E cluster , corresponds to the lowest energy obtained for a set of same-sized clusters, while E Ni and E B stand for the total ground state energy of Ni and B atoms, respectively. Next, we calculated the vertical electron affinity (VEA), vertical ionization energy (VIE), chemical potential (µ), and highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap (E g ) values according to the formulae below: The adsorption energy (∆E ads ) of (NiB) n toward CO 2 and N 2 is defined as: where E tot , E mol , and E sheet are the total energies of the adsorption complex, the isolated molecule, and the (NiB) n , respectively. The ab initio thermodynamic method [37] is used to calculate the Gibbs free energy G(T, P) of the adsorption processes by taking environmental effects into account. Due to the variation in solid-phase adsorbents under different temperatures and pressures being negligible [38,39], the adsorption of CO 2 gas is regarded as the main contributor leading to the Gibbs free energy change. The formula for calculation is given below: where F vib,ads (T) means the zero-point energy (ZPE) correction, which is considered in all adsorption processes of gases. The contribution of gas enthalpy and entropy under atmospheric pressure (P 0 = 1 × 10 5 Pa) can be obtained in the thermodynamic database. For the adsorbed product CO 2 @(NiB) n and the corresponding free molecule in the gaseous phase, the vibrational contributions from n prominent vibrational modes within the harmonic approximation to the Gibbs free energy (comprising vibrational energy and entropy) are defined as: where β = 1/kT and vi are the vibration frequency. In our cases, the total vibrational correction can be expressed as: F vib,ads (T) = F vib ads (T) − F vib g (T) (9) where F vib ads (T), F vib g (T), and F vib,ads (T) are vibrational Gibbs free energies of the adsorbed molecule, the free gas molecule, and their change arising from the adsorbate-surface interaction, respectively.
The charge density difference for the gas-interacted (NiB) n is plotted to understand the nature of bonding between the gases and the (NiB) n sheet. The charge density difference plot is calculated as follows: where ρ complex is the density of the complex, and ρ f ragments i is the density of the fragments forming the whole system, where fragments consist of (NiB) n and gas molecules. The electronic properties of density of states (DOS) was also evaluated to better understand the nature of chemical bonding.

Conclusions
The adsorption of carbon dioxide (CO 2 ) has become a crucial research topic in recent years due to the increasing concerns about global warming and climate change. The capture and storage of CO 2 is a promising method, which has sparked a lot of scientific interest. The development of efficient sorbents for CO 2 capture and storage is crucial to enhance the performance of the electrochemical process.
In this study, we employed first-principles calculations to investigate the stable structures of (NiB) n clusters (n = 1-10) and their interaction with CO 2 . We first located the structures of (NiB) n clusters and found that they adopt 3D geometries from n = 4. The calculation of binding energy per atom (E b ) revealed that 3D geometries were more stable than plane clusters. We discussed the chemical reactivity of each atom in the clusters based on the calculated vertical electron affinity, vertical ionization energy, chemical potential, and highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap. Our analysis showed that (NiB) 6 and (NiB) 10 with high chemical potential may be more favorable for CO 2 adsorption.
We further investigated the adsorption of CO 2 on various clusters and the selective adsorption of N 2 among these clusters. Our results substantiated that (NiB) 6 and (NiB) 10 exhibited the strongest adsorption of CO 2 due to a charge delivery channel that forms along the Ni→B→CO 2 path, which allows for more electrons traveling from the surface to CO 2 molecules. The results of the density of states analysis show that Ni atoms in clusters hybridized with CO 2 and should be polarized with the approach of positively charged species. In particular, (NiB) 10 showed the highest adsorption selectivity of CO 2 over N 2 , followed by (NiB) 6 . Notably, we found that (NiB) 10 had a more practical CO 2 desorption temperature and a broader window for the selective adsorption of CO 2 over N 2 .
Our theoretical results suggest that (NiB) 10 could be a promising candidate for CO 2 capture. Moreover, the (NiB) n cluster with a higher chemical potential can significantly increase the desorption temperature of various gases, making it more practical for industrial use.