Modeling of Si–B–N Sheets and Derivatives as a Potential Sorbent Material for the Adsorption of Li⁺ Ion and CO₂ Gas Molecule

Abstract

In the present exploration, a few Si–B–N derivatives are derived to adsorb Li ions and CO₂ gas molecules for the potential application of metal–air batteries. The newly derived structure’s bond lengths are as follows: Si=Si, 2.2 Å; Si–B, 1.9 Å; Si–N, 1.7 Å; and B–N, 1.4 Å, consistent with the experimental results of relevant structures. The stability of the newly derived structures is examined by the atom-centered density propagation study by varying the temperature from 270 to 400 K, and no structural variations are observed throughout the dynamics. Li adsorption on the Si₄B₂ ring has the maximum binding energy of −3.9 eV, and the result is consistent with the previous results. The rings with the 2:1 silicon–boron ratio provide strong adsorption for Li atoms. The calculated maximum electromotive force of the newly derived sheets is 0.56 V with the maximum theoretical density of 783 Wh/kg. Similarly, the maximum adsorption of CO₂ on the sheet is −0.106 eV, which is considerably higher than that on graphene and its derivatives. CO₂ adsorption has been carried out in the presence of water molecules to investigate the change in CO₂ adsorption with the moisture (water) content, and the results show no significant change in the adsorption of CO₂ with moisture. However, water has a strong interaction with the maximum interaction energy of −0.72 eV. Further, to explore the potential ability of the sheets, each sheet’s edges are examined as hydrogen storage expedient and the surface as an artificial photosynthesis platform. The Si₄B₂ ring is more favorable for the adsorption of H atom with the chemisorption of −7.138 eV. Similarly, all of the major UV-absorption spectral peaks fall between 450 and 800 nm, which shows that the sheet can be used as an artificial photosynthesis platform.

1. Introduction

The need for rechargeable batteries emerged in the early 1970s when the oil crisis exposed the vulnerability of U.S. society, when nonrechargeable batteries of a lithium anode and an organic-liquid electrolyte were known.¹ However, nowadays, life on earth is probably inconceivable without rechargeable batteries; still, plenty of quests and challenges are forbidden in energy storage technology. The major challenges in developing rechargeable batteries are high power and energy capacity with rapid charging/discharging rates for several cycles.² On the other hand, abundance, low cost, safety, and environmental friendliness are the main objectives to be kept in mind while designing a rechargeable battery. Over the last decade, the word “environmental friendly” has attracted increasing attention from the researchers due to the human-forced climate changes by increasing the concentration of greenhouse gases in the atmosphere. Every year, fossil fuel combustion alone produces thousands of tons of CO₂ in the atmosphere.³ Reduction of the CO₂ level in the atmosphere is as important as the social and economic development; however, capturing and converting CO₂ into a fuel is a better idea to reduce fossil fuel consumption and consequently lessen the global warming. This is not the first time that the word “metal–CO₂ battery” is used, lithium and sodium have also been examined in metal–air batteries.⁴ A primary Li–CO₂ battery has high discharge capacity of ∼2500 mAh/g at room temperature,⁵ and the Li–CO₂ battery can be discharged and charged reversibly for seven cycles with a capacity cutoff of 1000 mAh/g at 30 mAh/g.⁶

In recent decades, two-dimensional (2D) graphene has attracted researchers to work on new 2D electrode materials for energy storage applications. The hallmark features of two-dimensional materials are slit-shaped ion diffusion channels that enable fast movements of ions through the membrane.⁷ In addition to that, Li et al.⁶ have used graphene⁸ and carbon nanotubes⁹ as an air electrode, which enhances the discharge capacity above 14 000 mAh/g over 20 cycles. Further results showed that the performance of battery increased with conductivity, large surface area, and high electrochemical stability of graphene and carbon nanotubes. Long Qie et al.¹⁰ have reported that boron- and nitrogen-doped holey graphene electrode exhibits high reversibility, low polarization, excellent rate of performance, and superior long-term stability over 200 cycles at a high current density of 1.0 A/g in a Li–CO₂ battery. These excellent properties shown by two-dimensional graphene encourage the researchers to explore a new class of graphene-like two-dimensional materials.

Besides graphene, several classes of two-dimensional materials have been widely explored and reported with high capacity as an electrode material for lithium-ion batteries (LIBs). The class of two-dimensional materials comprising transition metal dichalcogenides such as MoS₂¹¹¹¹ and VS₂¹¹ has been reported with high capacities of 335 and 466 mAh/g, respectively. Similarly, transition metal dicarbides,¹² metal nitrides,¹³ and metal oxides¹⁴ were also examined as electrode materials. In addition to that, an anisotropic two-dimensional material called phosphorene, which has been successfully isolated from phosphorus, has been proved as a potential electrode material with ultrafast ionic diffusion and low barriers.¹⁵ The two-dimensional counterpart of boron called borophene¹⁶ and the hydrogenated counterpart of borophene known as borophane¹⁷ are investigated as anode materials for LIBs. These kinds of fascinating results are encouraging the researchers to explore a new class of two-dimensional materials toward energy storage applications.

Analogous to graphene, Andriotis et al.¹⁸ designed Si₂BN two-dimensional sheets based on extensive ab initio density functional theory (DFT) simulations. A monolayer Si₂BN sheet has a hexagonal lattice with sp² hybridization and consists of Si, B, and N atoms in plane buckling. The authors have reported that the Si₂BN sheet has high flexibility, high electron mobility, tunable band structure, and high thermal conductivity. Further, the stability of the structure is examined by molecular dynamics simulation, and the results confirmed the structural stability up to 1000 K. Followed by this report, the Si₂BN material has been computationally investigated as a hydrogen storage substrate¹⁹ and high-capacity anode material for Li-ion and Na-ion batteries.² Both authors highlighted the superior structural stability of the Si₂BN material. Similarly, the optical properties of hybrid nanostructures made by Si₂BN have been explored in another study.²⁰

Here, the Si₂BN sheet is terminated with hydrogen on the edges and the structural modifications are carried out by rearranging the structure of the atom in the hexagonal lattice. Symmetrically, the Li-ion and CO₂ gas adsorption behaviors of the Si₂BN sheet and modified sheets are investigated. Further, moisture is taken into account by adding H₂O with CO₂ to mimic real circumstances. The present predictions with the help of density functional theory (DFT) show that the structural rearrangements induce interesting electronic properties and adsorption properties. This piece of work is fundamentally important as there are no known precedents of CO₂ adsorption on a Si₂BN sheet, structural modifications, and hydrogen termination in favor of metal–CO₂ battery applications. To make the work more interesting, the modified sheets are investigated as a hydrogen storage and artificial photosynthesis platform. Interestingly, the obtained results show that the modified sheets have the compatibility to work as a multi-energy-harvesting device.

2. Result and Discussion

2.1. Geometrical Investigation of Electrodes

The optimized structures of different Si–B–N combinations are shown in Figure 1, and the structural stability of each structure is confirmed by frequency results, where no imaginary frequency has been found in the graph, as shown in Figure S1 (Supporting Information). The proposed structures, denoted O (here, the original structure of Andriotis et al.¹⁸ is denoted O and modified structures are denoted M), have lack of in-plane isotropy under threefold rotational symmetry. However, the structures keep considerable amount of stress and distorted hexagonal symmetry due to the particular decoration of lattices with three different types of atoms.^2,18 Both O1 and O2 sheets are those Si₂BN sheets predicted by Andriotis et al.,¹⁸ whereas each Si4–B–N ring in O1 consists of either N–N or B–B alternatively with the sequence of A–B–A and O2 has a reciprocal sequence of B–A–B, as shown in Figure 1. The average bond lengths of O1 and O2 sheets are as follows: Si=Si, 2.20 Å; Si–B, 1.97 Å; B–N, 1.42 Å; and Si–N, 1.77 Å. A quick visual examination of M1 and M2 in Figure 1 can suggest the difference between O1 and O2, where the neighbors across the Si–Si strip are now B–N and N–B instead of B–B and N–N. This alteration in the rings increases the electrostatic interaction between B and N atoms, which would likely increase the stability of the structure by reducing the total energy. Generally, the molecule with the lowest total energy has the highest chemical bond energy.²¹ As expected, the DFT results have shown that the total energy has reduced by 1.25 eV due to swapping of atoms and the stability of the structures M1 and M2 has increased by ∼35 meV/atom. The results are consistent with the reports of Sandoval et al.,²² and the reported higher stability in the structure is 42 meV/atom. The average bond lengths of M1 and M2 sheets are as follows: Si=Si, 2.22 Å; Si–B, 1.96 Å; B–N, 1.44 Å; and Si–N, 1.76 Å. Similar to O1 and O2, M1 and M2 scuffle with two sequences, such as A–B–A and B–A–B. Further, the Si–B–N composition has been edited and named M3 and M4.

Figure 1.

Optimized structures of H-functionalized Si, B, and N derivatives with different sequences, where M and O stand for modified and original sheets, respectively. (a) Each Si4 ring consists of either two N or two boron alternatively with the sequence Si4BN–Si2B2–Si4BN. (b) Si₂BN sheet with the reciprocal sequence of (a) such as Si2B2–Si4BN–Si2B2. (c) Each Si₄ ring consists of boron and nitrogen with the sequence Si4BN–Si2B2–Si4BN. (d) Reciprocal sequence of (c). (e) New sequence has been introduced in the sheet, which consists of Si2BN–Si2B2N2–Si3B2N1&Si3BN2–Si2BN. (f) Defect has been created in the Si₂BN sheet, which results in two pentagonal and two octagonal rings resembling the Stone–Wales defect on a graphene sheet.

In the M3 sheet, a new sequence is included in the parent sequence, where Si atoms do not direct form bonds with each other. Each included formation consists of three silicon atoms, two boron atoms, and one nitrogen atom;, similarly, the adjoining ring has three silicon atoms, two nitrogen atoms, and one boron atom as shown in the Figure 1 (M3). The inclusion of new rings in the structure did not change the planar nature of the sheet. These kinds of structures are theoretically reported previously.^22,23 To include more variety of Si–B–N combinations, the exotic motif has threefold coordinated atoms, and it is connected to pentagonal and octagonal rings as shown in Figure 1 (M4). The M4 structure is slightly bent (nonplanar) because the nonvalance silicon atoms in the defective rings have a stronger attractive nature that pulls the other atoms strongly toward it and creates the structural stress. The bond lengths of all of the structures are summarized in Table 1, where the bond lengths of Si–Si, Si–B, Si–N, and B–N are consistent with previous results.^2,18,22 Especially, the experimentally reported bond length of B–N is 1.45 Ų⁴ and present investigation reports in Table 1 are exactly the same. The parameters such as the area and perimeter of the rings play a vital role in the adsorption mechanism. In the present investigation, the calculated average area and perimeter of each ring in all six sheets are summarized in Table S1. On the hexagonal rings in O1, O2, M1, M2, M3, and M4 sheets (Si₄BN: area (a), 9.9 Ų; perimeter (p), 11.7 Å; Si₂B₂N₂: a, 7.6 Ų; p, 10.3 Å; Si₃BN₂: a, 8.4 Ų; p, 10.8 Å; Si₃B₂N: a, 8.8 Ų; p, 11.1 Å; Si₄B₂: a, 10.6 Ų; p, 12.2 Å; and Si₄N₂: a, 9.5 Ų; p, 11.5 Å), the rings with more boron atoms and less nitrogen atoms have the larger area and perimeter due to the larger radius of the boron atom. As expected, the Si₄B₂ ring has the largest area and perimeter among the rings and the Si₂B₂N₂ sheet has the smallest area and perimeter. The defective rings in the M4 sheet have Si₂B₃N₃ octagonal rings with the area of 12.8 Ų and perimeter of 13.1 Å; similarly, SiB₂N₂ pentagonal rings have the area of 4.4 Ų and perimeter of 8.1 Å. To use the sheets in real-time applications, the H atom has been terminated on the edges for the prevention of edges from environmental radicals. Hydrogen is the simplest atom in the known world, and capping on graphene has been proven as a potential addition to adsorb other molecules. Thus, this is sufficient to justify the hydrogen termination of edges in the sheets. The formation energy of each ring is calculated by both Perdew–Burke–Ernzerhof (PBE0) and Heyd–Scuseria–Ernzerhof (HSE06) levels of theories, which are summarized in Table S2. The obtained results for Si–B–N rings are consistent with the previous results.^2,22

Table 1. Comparison between Obtained Bond Lengths and Available Literature Bond lengths^a.

bond	O1 (Å)	O2 (Å)	M1 (Å)	M2 (Å)	M3 (Å)	M4 (Å)	ALV (Å)
Si=Si	2.20	2.24	2.21	2.20	2.22	2.22	2.262
Si–B	1.94	1.92	1.94	1.93	1.91	1.92	1.932
Si–N	1.75	1.75	1.74	1.73	1.74	1.75	1.752
B–N	1.42	1.45	1.43	1.45	1.45	1.44	1.4418
Si–H	1.48	1.48	1.48	1.48	1.49	1.48
B–H	1.19	1.20	1.19	1.20	1.19	1.19
N–H	1.01		1.01	1.01	1.01	1.01

^aAVL—available literature value.

The atom-centered density propagation (ADMP) matrix study has been carried out to confirm the dynamical stability of each structure at 270.0, 300.0, 350.0, and 400.0 K temperatures. The total energy versus time trajectories are plotted for 100 fs as shown in Figure 2. The obtained results from the ADMP calculation show that there is no significant change in the bond length of each atom in the different sheets at each temperature. In the present study, an energy versus time graph is plotted for 400.0 K as shown in the Figure 2. The obtained energy versus time graph shows significant energy fluctuations for all of the sheets, but the corresponding energy fluctuations in the graphs are between 0.0001 and 0.00001 hartree, which are well shown in the Y axis of the graph. Corresponding geometrical variations in the sheets are not observed throughout the simulation, and the negligible deviations in the energies as shown in the graphs are due to the small fluctuation in the bonds of edge-hydrogen atoms. These results show that the newly modified sheets are stable within the temperature range of 278–400 K, and they can be examined as an electrode material.

Figure 2.

Total energy (in hartree) vs time of trajectory (in femtoseconds) plotted by the atom-centered dynamic matrix propagation (ADMP) calculations at 400.0 K temperature. No notable structural changes are observed during the course of molecular dynamics, which confirms the stability of the structures at 400 K. The lines and the respective Y axis scales are represented by the same colors.

2.2. Electronic Properties of Monomers

Due to the absence of hexagonal symmetry in the originally reported Si₂BN sheet, π bands near the symmetry points are degenerated.¹⁸ Further, p-orbitals of Si and N atoms are the main contributors of (Fermi energy) E_F states.^18,19 From the previous reports, one can understand the significance of investigation on p-orbitals in the present discussion, and Figure 3 shows the contribution of p-orbitals to the total density of states (TDOS) of each sheet. The band gap energies of the O1 structure of 0.671 eV and of the O2 structure of 0.637 eV show the sequential change as shown in Figure 1. A–B–A (O1) and B–A–B (O2) have two different band gaps. Even though both O1 and O2 have similar number of atoms present in the unit cell, sequential changes imply different band gaps. Both O1 and O2 have the dominant contribution of Si p_z orbitals near the Fermi level, but the difference is accumulated by the presence of B p_y orbital at −0.1 eV in O2, whereas O1 does not have that influence of B p_y orbital, clearly shown in Figure 3. The presence of B p_y orbital shifts the lowest unoccupied molecular orbital (LUMO) by 0.143 eV in the O2 sheet. Similarly, shifting the B and N atoms in M1 and M2 pushes the P states down around the Fermi level by deepening the density-of-state (DOS) valley. Both the M1 and M2 TDOS approach zero near the Fermi level, and this is clearly visible in Figure 3. A similar effect has been observed by Sandoval et al.²² Stability of a structure can be confirmed by the placement of Fermi level near the bottom of DOS, and this confirms that M1 and M2 are more stable than O1 and O2. Results in Section 2.1 are in good agreement with this result. Like O1 and O2, M1 and M2 have different band gaps due to the swapping of sequences. Unlike M1, DOS-M2 in Figure 3 shows the dominant presence of Si p_y, Si p_z, and N p_y orbitals near the Fermi level. The M1 Fermi level is completely dominated by the presence of the N p_y orbital alone. The inclusion of new atomic formations in the structures M3 and M4 results in different kinds of electronic properties. The sheet M3 has four Si atoms with no direct Si–Si bond formation, and these atoms dominate the LUMO level of the sheets, as clearly shown by the frontier molecular diagrams in Figure S2 (Supporting Information). This domination reduces the band gap to 0.557 eV, which is the lowest among all six sheets; thus, it has the highest conductivity among the sheets. Formation of pentagonal and octagonal rings as shown in M4, Figure 1, pushes the highest occupied molecular orbital (HOMO) and LUMO apart from each other to open up the band gap. In the pentagonal rings, B and N are a bit closer than normal, causing strong electrostatic interaction between them, which is sufficient to open up the band gap. In other words, the stability of the structure is increased due to the strong electrostatic interaction of B and N atoms.

Figure 3.

Comparative DOS diagram of the presented 2D materials reveals the contribution of p-orbitals in each atom. Colored lines in the graph show the particular orbital explicitly. The DOS and partial density of states (PDOS) values along the x axis are given in the same scale.

To deeply explore the electronic properties of each structure, frontier molecular orbital analysis is carried out. The HOMO and LUMO values of each structure are summarized in Table 2. The O1 sheet has the HOMO and LUMO values of −4.369 and −3.698 eV, respectively. The p-orbitals of the boron atoms are the main contributors of HOMO (99.9%) and LUMO (99.9%). In both HOMO and LUMO, the contribution of s-orbital is 0.07%. HOMO – 1 and LUMO + 1 states are largely dominated by the p-orbitals of Si atoms. In the case of the O2 structure, the p-orbital of the Si atom contributes 99.8% to LUMO and the p-orbital of the B atom contributes 99.9% to the HOMO. HOMO + 1 and LUMO – 1 states are contributed by B atoms. The major contribution of B atoms in the O2 structure slightly narrows the band gap. In the M1 sheet, the HOMO and LUMO values are −4.881 and −3.517 eV, respectively. The p-orbitals of B atoms are the major contributors in the HOMO and LUMO. Similarly, HOMO + 1 and LUMO – 1 are contributed by the p-orbitals of N and Si atoms. However, in the case of M2 sheet, the p-orbitals of B and Si atoms are the major contributors in the HOMO and LUMO. Similarly, HOMO + 1 and LUMO – 1 are contributed by the p-orbitals of Si and B atoms. The M3 sheet has the HOMO and LUMO values of −4.248 and −3.963 eV, respectively, where the p-orbitals of B and Si are the major contributors of HOMO and LUMO. LUMO – 1 and HOMO + 1 are contributed by p-orbitals of Si atoms. The M4 structure has the HOMO and LUMO values of −4.963 and −3.693 eV, respectively. The p-orbitals of B and N are the major contributors, and LUMO – 1 and HOMO + 1 are dominated by p-orbitals of B atoms. From the obtained results, it can be concluded that the major contributions in the HOMO and LUMO are from p-orbitals, and the results are well correlated with the DOS and partial density of states (PDOS) results. Interestingly, O2 (having a smaller band gap than O1), M2 (having a smaller band gap than M1), and M3 have small band gaps and all O2, M2, and M3 sheets’ HOMO and LUMO contributions are made by p-orbitals of Si and B atoms.

Table 2. Electronic Properties of Sheets Calculated at the HSE06 Level of Theory.

sheet	band gap (eV)	HOMO (eV)	LUMO (eV)	Fermi level (eV)	chemical potential (eV)	hardness (eV)	softness (eV)	electrophilicity (eV)
O1	0.671	–4.369	–3.698	–4.033	4.033	0.335	1.490	24.245
O2	0.637	–4.479	–3.841	–4.160	4.160	0.318	1.568	27.146
M1	1.363	–4.881	–3.517	–4.199	4.199	0.681	0.733	12.934
M2	0.770	–4.235	–3.464	–3.850	3.850	0.385	1.297	19.227
M3	0.557	–4.242	–3.684	–3.963	3.963	0.278	1.794	28.186
M4	1.083	–4.693	–3.610	–4.151	4.151	0.541	0.923	15.912

Chemical reactivity, charge transfer, and partial charge transfer between the materials can be identified by the global indices such as chemical potential, hardness, softness, and electrophilicity. The feasibility of the system to exchange electrons with the environment can be measured by calculating the chemical potential. The chemical potential can be stated as the rate of change in energy with respect to the electron number when the external potential is fixed.²⁵

1

Here, μ is the chemical potential, E_HOMO is the energy of the highest occupied molecular orbital, and E_LUMO is the energy of the lowest unoccupied molecular orbital. Hardness is a measure of stability in the presence of electricity or resistance of a molecule to exchange electrons from the environment, whereas softness is the reciprocal of hardness.²⁶

2

where ņ is the hardness, and it is derived from Koopman’s theorem.²⁷

3

4

S is the softness and ω is the electrophilicity of the materials.

Similarly, electrophilicity is a tool to measure the reactivity of the material. Hardness and softness are the parameters that can explain the change of the chemical system with respect to electron density, where the increase in hardness of a molecular cluster indicates an increase in band gap and the increase in softness of a molecular cluster indicates the decrease in band gap.²⁸ In other words, electrophilicity and electron affinity are the most anticipated parameters that can explain the capability of the material to accept electrons. Specifically, electron affinity shows the capability of the material to accept only one electron from the environment, whereas electrophilicity is the measure of energy when the electron flows between a donor and an acceptor.²⁹ From the calculated parameters, as shown in Table 2, it is easy to conclude that M3 has the highest electrophilicity of 28.1 eV and the smallest hardness of 0.27 eV. Similarly, M1 has the lowest electrophilicity of 12.9 eV and the highest hardness of 4.1 eV. In other words, the material with small band gap has higher electrophilicity and the material with large band gap has smaller electrophilicity.

The two-dimensional structures like graphene and silicene are homogeneous and isotropic materials. Thus, it does not make sense if the sequence of sheets is shuffled because the properties will not change. However, the sheet that is examined has three different atoms buckled together to form a two-dimensional sheet so that the sequential changes will provide different properties, which are confirmed by the results in the above discussion.

2.3. Adsorption of Li Ions on Sheets

The binding character of the Li ion on the surface of six sheets is determined at eight different possible ring sites. In each ring, one Li adatom is placed to check the binding energy and find out the most favorable site of adsorption as shown in Figures 4 and S3. The adsorption energies are calculated using the formula³⁰

5

Here, E_a is the adsorption energy, E_complex is the total energy of the Li-adsorbed complex, E_monomer is the energy of the sheet, and E_Li is the energy of the lithium adatom. Adsorption energies of the Li ion on the sheets are summarized in Tables 3 and 4. The calculated adsorption energies in Tables 3 and 4 are negative (E < 0), showing an exothermic reaction, indicating the attractive nature of each surface toward the Li ion. Tables 3 and 4 show that adsorption of Li adatom on the top of the Si₄B₂ ring is more favorable for Li adsorption with the adsorption energies of −2.9 and −3.9 eV, which is comprehensively shown in Figure 5. The van der Waals radii of boron and silicon atoms are 192 and 210 pm, respectively, which are larger than those of the nitrogen atom (155 pm),³¹ which is the reason behind the strong adsorption of Si–B rings than Si–N rings. These results are consistent with the results of Shukla et al.,² and the reported adsorption energy on the Si₄B₂ site is −3.03 eV.

Figure 4.

Adsorption of Li atoms on M3 and M4 sheets at two different positions is shown (the other positions are shown in Figure S3, Supporting Information). The smallest distance between the sheet and Li atoms is marked in the figures. It is visible that Li adsorption on the M4 sheet bends the structure.

Table 3. Adsorption Energy of Li on Sheets.

sheets	adsorption distance (Å)	adsorption energy by PBE0 (eV)	adsorption energy by HSE06 (single point) (eV)
O1	2.208	–2.352	–2.562
O2	2.171	–2.933	–2.865
M1	2.619	–1.754	–1.798
M2	2.072	–2.030	–2.049
M3-position 1	2.055	–2.046	–2.055
M3-position 2	2.307	–1.842	–1.838
M3-position 3	2.307	–2.012	–1.998
M4-position 1	2.156	–2.296	–2.310
M4-position 2	2.030	–2.029	–2.058
M4-position 3	2.371	–2.237	–2.268

Table 4. Comparative Summary of Theoretical Specific Capacity, Electromotive Force (e.m.f.), and Theoretical Energy Density of Each Ring as an Electrode Material for LiBs^a.

ring	adsorption energy (eV)	specific capacity (mAh/g)	electromotive force (V)	theoretical energy density (Wh/kg)
Si2B2N2	–2.114	1773.188	0.30	533.005
Si4BN	–2.028	1367.851	0.28	394.261
Si3BN2	–2.465	1524.309	0.35	534.274
Si3B2N	–2.918	1564.959	0.41	649.116
Si4N2	–2.144	1336.694	0.31	407.531
Si4B2	–3.937	1400.495	0.56	783.851
SiB2N2	–2.296	2413.958	0.33	787.948
Si2B3N3	–2.237	1436.297	0.32	456.794

^aEach ring has been separately taken into account to understand the adsorption energy of Li on a particular combination of Si–B–N.

Figure 5.

Comprehensive graph between adsorption energy of Li vs no. of atoms, which exhibits the change in adsorption energy with respect to the particular combination of Si–B–N. The maximum adsorption energy has been found in 4-Si and 2-B atoms in the hexagonal ring.

The adsorption energy of Si₄B₂ is higher than that of the recently reported 2D borophene (with the adsorption energy of −2.58 eV), where the adsorption energy is higher in the presence of four silicon atoms in the ring buckled with two boron atoms because of an increase in the strong electrostatic radius compared to borophene. Similarly, P-doped borophene has −3.42 eV adsorption energy as reported by Chen et al.³² Silicene sheets have adsorption energies of −2.2³³ and −2.41 eV.³⁴ Two-dimensional (2D) sheets like MoS₂ and graphene have adsorption energies of −1.75,³⁵ −2.6,³⁶ −2.5,³⁷ −2.01,³⁸ and 1.41 eV.³⁹ By comparing these previous results, it can be concluded that the Si–B–N derivatives have the potential to be a good electrode material. Typically, the stronger binding leads to a rapid loading process of ions with small barriers. To study the barrier height, a graph has been plotted using a localized molecular orbital locator, and it is shown in Figure 6. The localized orbital locator (LOL) reveals the features of bonding as a function of electron density, and it has the potential ability to distinguish atomic interactions (such as covalent, ionic, and van der Waals) in the solid state.⁴⁰ It is visible from Figure 6 that adsorption of Li on the O2 sheet center (Si₄B₂ ring) has the minimum barrier height of 13.4 eV among the other sheets, and the result is in good agreement with present adsorption energy results. Further, a color-filled map is plotted, using the localized orbital locator (LOL), in Figure 7, showing the delocalization of electrons underneath the Li atom due to adsorption. The blue color shows the presence of charge, and the dark blue color shows the depilation region of charge. Mulliken charge analysis provides a good view on charge transfer between the sheets and Li; from Figure S6, it is easy to conclude that the negative value on the Li ion is due to the transfer of charge from sheets to Li and the positive value on Li shows the transfer of charge from Li to the sheet. The Li atoms on position 1 (P1, adsorption takes place on the pentagonal ring) of O2, M2, and M4 sheets have charges −0.23e, −0.29e, and −0.29e, respectively. Similarly, Li atoms on P4 (on the octagonal ring) of the other O1, M1, M3, and M4 sheets have charges 0.27e, 0.63e, 0.77e, and 0.23e, respectively. When adsorption takes place in the presence of two silicon and two nitrogen rings, charges have been pulled from the Li atom to compensate the electron deficiency in the ring.

Figure 6.

Comparative profile of the localized orbital locator between the nearest atom of the sheets and the Li atom. The sharp peak on the right side indicates the Li atom, and the sharp peak on the left side indicates the nearest atom of the sheet. The in-between wide maxima are due to the physisorption, and the maximum of the wide peak is the barrier height, which is mentioned above each graph.

Figure 7.

Projection of the localized orbital locator (LOL) on the surface of Li-intercalated complexes. The dark blue region shows an electron depletion region, and the red region shows the electron-concentrated regions. The presence of light blue color in-between sheets and the Li atom confirms the week interaction.

The stability of the lithium-intercalated complex sheets is examined with global indices such as chemical potential, hardness, softness, and electrophilicity, which are summarized in Table 5. The electrophilicity of sheets is changed with the intercalation of Li atoms, where except for M3-P1 and M3-P2, the entire sheet’s electrophilicity has increased and hardness has decreased. The decrease in hardness shows that the Li atoms can be easily detached from the sheets by applying an electric field. The changes in electronic properties are due to the presence of Li atom near the Fermi level, confirmed by the PDOS, as shown in Figure 8. This intercalation of Li reduces the band gap, which is well exhibited by Figure 8.

Table 5. Electronic Properties of Li-Adsorbed Complexes.

sheet	band gap (eV)	HOMO (eV)	LUMO (eV)	Fermi level (eV)	chemical potential (eV)	hardness (eV)	softness (eV)	electrophilicity (eV)
O1	0.502	–4.298	–3.796	–4.047	4.047	0.251	1.991	32.623
O2	0.644	–4.531	–3.887	–4.209	4.209	0.322	1.550	27.479
M1	0.637	–4.083	–3.446	–3.765	3.765	0.318	1.569	22.245
M2	0.523	–3.849	–3.325	–3.587	3.587	0.261	1.910	24.591
M3-1	0.424	–3.998	–3.574	–3.786	3.786	0.212	2.358	33.815
M3-2	0.636	–4.177	–3.541	–3.859	3.859	0.318	1.570	23.390
M3-3	0.629	–4.155	–3.525	–3.840	3.840	0.314	1.588	23.426
M4-1	0.792	–4.336	–3.544	–3.940	3.940	0.396	1.262	19.599
M4-2	0.423	–4.083	–3.659	–3.871	3.871	0.211	2.360	35.371
M4-3	0.872	–4.439	–3.567	–4.003	4.003	0.436	1.146	18.374

Figure 8.

Total density of states of Li-adsorbed complexes and partial density of states of the Li atom. In M3 + Li and M4 + Li, the Li atom is placed at three different positions, and TDOS and PDOS have been plotted for each position, with respective colors shown in the graph.

The parameters like specific capacity, electromotive force (e.m.f) or open-circuit voltage, and theoretical energy density of the battery are very important to spell the electrode as a potential electrode material. It is important to stress that the specific capacities of the rings are comparatively higher than those of the recently reported 2D materials. The theoretical specific capacity is calculated from the formula

6

Here, x is the number of electrons involved in the electrochemical relation and F is Faraday’s constant with the value of 96 485.332 C/mol, and the value 3.6 is used to convert C/mol into mAh/mol. The calculated values are summarized in Table 4. The calculated Si₂BN specific capacity is 1158.5 mAh/g,² the considered unit cell has Si₄B₂N₂ and present results in the Table 4 are consistent with that result. These values are higher than the recently reported results of graphite (372 mAh/g),⁴¹ MoS₂ (335 mAh/g),¹¹ Ti₃C₂ (447.8 mAh/g),⁴² VS₂ (466 mAh/g),¹¹ black phosphorus (432 mAh/g),⁴³ borophene (620 mAh/g),⁴⁴ P-doped borophene (1732 mAh/g),³² borophane (504 mAh/g),¹⁷ bco-C16 (558 mAh/g),⁴⁵ TiO₂ (200 mAh/g),⁴⁶ silicene (954 mAh/g),⁴⁷ and MgI₂ (211.2 mAh/g).⁴⁸

The electromotive force and theoretical energy densities are calculated from the formula

7

where V is the open-circuit voltage, E_a is the adsorption energy of the lithium atom, n is the number of electrons involved in the electrochemical process, and F is Faraday’s constant.

8

Here, E is the energy density of the battery and M is the mass of the electrodes.⁴⁸ The results are summarized in Table 4, and these results are in good agreement with the previous theoretical result.² The results listed in the table show that the Si₄B₂ ring has the maximum open-circuit voltage of 0.56 V with the theoretical energy density of 783 Wh/kg. The adsorption energy is directly proportional to the electromotive force; hence, there is no surprise that the Si₂B sheet has the maximum electromotive force among others. Similarly, the Si₃B₂N sheet has the theoretical capacity of 0.41 V with the theoretical energy density of 649 Wh/kg. Even though the SiB₂N₂ ring has the maximum theoretical density of 787 Wh/kg, it has 0.33 V due to the low adsorption (adsorption energy, −2.2 eV) of Li atoms. From the results, it can be concluded that stronger adsorption energy leads to higher electromotive force. Further, the rings with boron and silicon provide considerably larger adsorption than silicon with nitrogen rings. The silicon–boron ratio of 2:1 in that ring provides good results, but there is a probability that 1:1 (Si₃–B₃) may be more effective than this one, which is not examined in the present study.

2.4. Adsorption of CO₂

The adsorption of CO₂ has been carried out in two different aspects. First, the CO₂ molecule has been placed on each sheet in perpendicular orientation and vertical orientation. Second, moisture is taken into account by adding H₂O molecules on the sheets for a better understanding of the adsorption mechanism in the environment. The adsorption height is calculated from the minimum distance between the gas molecule and sheets. The adsorption energy is calculated from the formula⁴⁹

9

Here, E_a is the adsorption energy of the molecule, E_sheet+CO2 is the energy of the complex for the first aspect, E_{sheet+CO2+H2O} is the energy of the complex with moisture, E_sheet is the energy of the monomer, E_CO2 is the energy of the CO₂ gas molecule, and E_H2O is the energy of the water molecule (used for the second aspect).

The CO₂-adsorbed sheets are shown in Figures 9a and S7, where all of the CO₂ gas molecules prefer parallel orientation and slightly upward orientation but none of the CO₂ molecules have preferred perpendicular orientation. This shows the attractive nature of sheet toward CO₂. The C=O bond length in the CO₂ gas molecule has changed slightly, and the changes are around 1.55–1.60 Å. The adsorption energy of each sheet and its position are summarized in Table 6. The adsorption height of CO₂ on each sheet varies from 3.0 to 3. 8 Å. The maximum CO₂ adsorption energy has been found at position 2 (P2) of M3, where the oxygen atom is attracted by the silicon atom on the hexagonal ring. The CO₂ atom on that particular ring is attracted with the adsorption energy of −0.106 eV, and the CO₂ molecule is approximately 45° upward from the plane of the M3 sheet. To find weak dispersion interactions between the CO₂ molecule and sheets, DFT-D3 corrections are carried out at the PBE0/6-311+g* level of theory and the corresponding results are summarized in Table 6. Adsorption energies calculated for all sheets increase and corresponding adsorption distances are found to be decreased with the dispersion corrections, but the obtained results in both DFT and DFT + D3 calculations show that the M3 (DFT (−0.106 eV), DFT + D3 (−0.283 eV)) and M4 (DFT (−0.089 eV), DFT + D3 (−0.318 eV)) sheets have higher adsorption energy than the other sheets. The physisorption energies calculated in these studies are approximately equal to the adsorption energy of CO₂ on graphene and its derivatives. For the sake of comparison with the available literature, the adsorption energy of CO₂ on graphene and its derivatives by various researchers are as follows: −0.269 eV (at graphene),⁵⁰ −0.036 to −0.33 eV (on H-functionalized pristine graphene),⁴⁷ −0.04 to −0.05 eV (on H-functionalized Stone–Wales defective graphene sheet),⁵¹ −0.055 eV (on H-functionalized 555–777 graphene sheet),⁵² and −0.064 eV (on the fluorine-functionalized graphene sheet).⁵³ Two-dimensional (2D) materials like germene, silicene, and borophene have the adsorption energies of −0.11⁵⁴ and −2.31 (lithium-functionalized germene),⁵⁴ −0.707,²⁵ −0.11,²⁵ and −0.96 (N-doped germene),²⁹ and −0.15,⁵⁵ −0.19,⁵⁵ −0.59,⁵⁶ and −0.7 eV (armchair silicene), respectively.⁵⁶ The charge transfer between the sheets and gas molecules is calculated from the Mulliken charge analysis, and it provides a clear picture of donation and back-donation of charge between CO₂ and sheets. The positive values of the Mulliken charge on CO₂ as shown in Table 6 indicate that charges are transferred from CO₂ to sheets. The molecular electrostatic potential difference map in Figure 9b shows a red color on CO₂, which confirms the donation of charge from CO₂ to sheets.

Figure 9.

(a) Optimized adsorption structure of O1 with CO₂ and M1 with CO₂. (b) Their respective electrostatic potential difference maps are shown. Here, the red region shows the positive and the blue region shows the negative Mulliken charges. Similarly, (c) shows the optimized geometries of O1 + CO₂ + H₂O and M1 + CO₂ + H₂O and (d) shows the respective electrostatic potential difference maps.

Table 6. Adsorption Properties of CO₂-Intercalated Sheets with DFT and DFT-D3 Calculations.

	PBE0			HSE06		DFT-D3
sheet	adsorption distance (Å)	adsorption energy (eV)	net charge of CO2 (e)	adsorption distance (Å)	adsorption energy (eV)	adsorption distance (Å)	adsorption energy (eV)
O1	3.521	–0.079	0.155	3.547	–0.446	3.218	–0.288
O2	3.796	–0.054	0.133	3.794	–0.058	3.187	–0.239
M1-P1	3.749	–0.062	0.121	3.814	–0.088	3.141	–0.258
M1-P2	3.587	–0.076	0.160
M2-P1	3.748	–0.083	0.156
M2-P2	3.813	–0.085	0.158	3.750	–0.064	3.232	–0.263
M3-P1	3.524	–0.096	0.158	3.039	–0.106	3.150	–0.283
M3-P2	3.029	–0.106	0.348
M4	3.386	–0.089	0.113	3.383	–0.091	2.971	–0.318

The comparative density-of-state diagram in Figure S9 shows the contribution of CO₂ to the total density of the sheets. For a proper understanding of the weak interaction between the sheet and CO₂ molecule, a partial density of states of p-orbitals beneath CO₂ sheets is plotted. Figure S9 shows that the total density-of-state graphs near the Fermi level are broadened due to the intercalation of CO₂. Also, these p-orbitals are the main contributors of the HOMO level. Similarly, very slight overlapping of the energy states of p-orbitals and CO₂ molecules at around −9 eV is visible in the graph. The small overlapping confirms the weak interaction between the sheet and CO₂.

The increase in band gap between monomers and CO₂-adsorbed complexes is confirmed by comparing Tables 2 and 7. The band gaps of CO₂-adsorbed complex sheets O1, O2, M1, M2, and M3 are increased 65, 19, 8, 2, and 10 meV, respectively, but the band gap of the M4 sheet is reduced to 2.6 eV. Logically, an increase in the band gap shows the structural stability of the CO₂-adsorbed complexes. M4 sheet’s stability has decreased when CO₂ adsorbed on the defects and this is because the defective-ring bond length has elongated beneath CO₂ while adsorption has taken place. Band-gap-dependent parameters “softness and electrophilicity” are decreased and “hardness” of the material is increased, and this shows the stability of the structure in the presence of an electric field. From the obtained results, one can strongly conclude that the Si₂BN sheet and its derivatives have the potential to adsorb CO₂ gas molecules in an efficient way like graphene. Further, Si₂BN and its derivatives have the potential capability to be used as an air electrode material for metal–air battery applications and it can be used as a potential CO₂ Sensor too.

Table 7. Electronic Properties of CO₂-Adsorbed Complexes.

sheets	band gap (eV)	HOMO (eV)	LUMO (eV)	Fermi level (eV)	chemical potential (eV)	hardness (eV)	softness (eV)	electrophilicity (eV)
O1	0.736	–4.431	–3.694	–4.062	4.062	0.368	1.357	22.401
O2	0.656	–4.489	–3.832	–4.160	4.160	0.328	1.523	26.378
M1-P1	1.371	–4.883	–3.511	–4.197	4.197	0.685	0.729	12.847
M2-P1	0.772	–4.240	–3.469	–3.854	3.854	0.385	1.296	19.257
M2-P2	0.771	–4.440	–3.468	–3.854	3.854	0.385	1.296	19.259
M3-P1	0.560	–4.234	–3.673	–3.953	3.953	0.280	1.784	27.894
M3-P2	0.567	–4.244	–3.677	–3.960	3.960	0.283	1.763	27.663
M4	1.057	–4.668	–3.610	–4.139	4.139	0.528	0.945	16.208

2.5. Adsorption of CO₂ in the Presence of H₂O

The H₂O molecule is placed next to the CO₂ molecule, and both are placed parallel to the sheets as shown in Figures 9c and S8. The presence of H₂O with CO₂ does not influence the adsorption of CO₂ considerably, and the H atom of the water molecule forms a weak interaction with the oxygen atom in CO₂. However, compared to CO₂, H₂O is slightly deeper toward sheet the, and this shows that H₂O has a stronger attraction toward the sheets. The adsorption energy, distance, and net charge of H₂O and CO₂ are summarized in Table 8, and the table shows the positive net charge transfer of both molecules, which confirms the electron-accepting character of sheets. The calculated adsorption energies of CO₂ and H₂O together are summarized in Table 8. To analyze the exact interaction energy of CO₂ in the presence of H₂O, two-body counterpoise calculations are performed, and the results are summarized in Table 9. The calculated interaction energies of CO₂ with the O1 and O2 sheets are −0.032 and −0.033 eV, respectively. When adsorption takes place, the adsorption distances between the O1 or O2 sheet and the CO₂ gas molecule are 3.62 and 3.60 Å, respectively. Similarly, the interaction energies of CO₂ on the M1 and M2 sheets are −0.030 and −0.028 eV, respectively. Among the six sheets, the M3 and M4 sheets have slightly higher interaction energies of −0.040 and −0.046 eV, respectively. Further, the adsorption heights of CO₂ on M3 and M4 sheets are 3.01 and 3.72 Å, respectively. The obtained results show that the sheets have higher interaction energy of −0.7 eV for H₂O molecules. The molecular electrostatic difference map in Figure 9d confirms the charge transfer between the sheets and gas molecules. The comparative density-of-state diagram in Figure S10 shows the strong interaction of H₂O molecule delocalize the p-orbitals, especially, the closest approach of H₂O with O1 and M1 sheets (with the bond distance of 1.998 and 2.004 Å) enlarge the beneath rings that compress the band gap. The interactions are enforced by the Si₄BN ring, where the p-orbitals of silicon attract the oxygen of the H₂O molecule strongly than other rings. It has been confirmed by Figure S10, where the band gap is narrowed due to the major contribution of p-orbitals near the Fermi level. Except for O1 and M1, the band gaps are widened with the adsorption. At the same time, hardness increases with the reduction of electrophilicity and softness.

Table 8. Adsorption Properties of CO₂ in the Presence of H₂O^a.

sheet	adsorption distance of CO2 (Å)	adsorption distance of H2O (Å)	adsorption energy (eV)	net charge of CO2 (e)	net charge of H2O (e)	distance between CO2–H2O (Å)
O1	3.629	1.998	–1.101	0.167	0.527	1.903
O2	3.601	2.713	–0.778	0.156	0.116	2.670
M1	3.679	2.004	–1.073	0.136	0.514	1.909
M2	3.583	3.030	–0.805	0.227	0.110	2.702
M3	3.012	2.679	–0.872	0.209	0.169	2.653
M4	3.721	1.688	–0.929	0.185	0.429	1.908

^aThe adsorption energy combines the adsorption of CO₂ + H₂O together.

Table 9. Exact Interaction Energy of CO₂ and H₂O^a.

sheets	interaction energy between sheet and CO2 (eV)	interaction energy between sheet and H2O (eV)	interaction energy between CO2 and H2O (eV)
O1	–0.032	–0.438	–0.046
O2	–0.033	–0.060	–0.133
M1	–0.030	–0.371	–0.032
M2	–0.028	–0.079	–0.126
M3	–0.040	–0.178	–0.135
M4	–0.046	–0.720	–0.039

^aCalculated from the counterpoise two-body correction with the formula E_I = E_{corrected energy} + E_A + E_B, where E_I is the interaction energy, E_{corrected energy} is the counterpoise corrected energy, E_A is the corrected energy of the first element, and E_B is the corrected energy of the second element.

From the obtained results, it can be observed that the presence of H₂O did not influence the adsorption of CO₂ molecule. One cannot compare CO₂ adsorption energies given in Tables 6 and 9 because Table 6 consists of basis set superposition error corrections, but it is fair to compare CO₂ adsorption distances between both tables. Comparing Tables 6 and 8, it is easy to conclude that the adsorption height of CO₂ remains the same with and without H₂O. This highlights the adsorption capability of Si₂BN and its derivatives. Another conclusion from these results is that Si₂BN and its derivatives can adsorb H₂O very strongly and that this material can also be used as a potential H₂O adsorbent.

2.6. UV-Absorption Spectra: A Possible Artificial Photosynthesis Medium

Mother nature has shown a way to devise a system that has the capability of producing energy through the Sun. Plants generate O₂ and carbohydrates using sunlight, water, and CO₂,⁵⁷ and the process of splitting is shown in the equation below

10

In the plant’s photosynthesis system, a pair of chlorophyll molecules excite and transfer an electron to the acceptor, which reduces CO₂.⁵⁸ This type of mechanism can be used to produce two kinds of artificial splitting. The first one is to split CO₂ into O₂ and carbohydrates (such as HCOOH, HCHO, and CH₃OH) using visible photons, which is performed by Inoue and co-workers.⁶⁶ The second one is to split H₂O into molecular oxygen and hydrogen for renewable hydrogen energy, as shown in the below equation

11

12

13

The first conversion of water into molecular H₂ has been done by Yanagida and his co-workers in 1985.⁶⁰ The primary goal of the artificial photosynthesis system is to convert CO₂ and H₂O into solar fuel within a single integrated system by the principle of photoconversion.⁶¹ Plenty of nanomaterials such as silicon nanowires,⁶² CdS nanodots,⁶³ peptide nanotubes,⁶⁴ and graphene⁶⁵ have been used as a photocatalyst system, but an efficient photosynthesis system is still a concern. The electronic and optical properties of the material can be tailored by reducing the dimensionality, and it will induce the quantum confinement effect. Further, nanosheets and nanoparticles have a high surface-to-volume ratio that provides more chemically activated⁵⁹ sites and more light absorption through the separation of electron–hole pairs as compared to their bulk counterparts.⁶⁷ Another important character of an artificial photosynthesis device is that the device should absorb visible photon from the Sun⁵⁸ to produce induced-electron transfer.⁵² Thus, in the present study, CO₂- and H₂O-adsorbed Si–B–N derivative’s light absorption properties have been investigated by the time-dependent (TD) DFT study.

The UV-absorption spectra are calculated for ten states, whose dominant absorption wavelengths, oscillator strengths, and excitation energies are summarized in Table 10. All of the absorbed wavelengths fall within the visible regions, which shows that the sheets are capable of absorbing the sunlight. The M1 sheet in the presence of CO₂ has shown the highest absorption peak at 562 nm with the maximum absorption energy of 2.2 eV, and this shows that the sheet has a larger band gap, which is confirmed from Tables 7 and 11. When the M1 sheet adsorbs CO₂ and H₂O together, the absorption wavelength further reduced to 550 nm with the absorption energy of 2.2 eV. This shift toward the blue region shows that the sheet shows the hypochromic effect when it adsorbs CO₂ and H₂O together. Except for O2 and M2 sheets, all other sheets show the hypochromic effect when they adsorb CO₂ and H₂O together, whereas M2 and O2 sheets show the bathochromic effect when they adsorb CO₂ and H₂O together. Figure 10a,b shows the shift toward the blue and red regions when the sheets adsorb CO₂ with and without H₂O. The Thomas–Reiche–Kuhn rules relate the integrated oscillator strength of a material to the sum of electrons in the structure. Further, the chromophores operate with the theoretical oscillator strength limit of 1%.⁶⁸ In other words, stronger oscillator strengths show stronger absorption of UV–visible light and the magnitude of oscillator strength approaches unity. The oscillator strengths of M4 sheets are 0.44 (presence of CO₂) and 0.524 (presence of CO₂ and H₂O), and nearly more than 50% of electrons are transferred due to the impact of photons, which indicates that the sheet with defects shows stronger absorption of photons. Obtained UV-absorption results show that the Si–B–N and its derivatives can be used as an artificial photosynthesis platform. Further, small sequential changes between O1 and O2, and M1 and M2 show different kinds of absorption mechanisms with the presence of CO₂ as well as CO₂ and H₂O together. To understand the electron transition dynamics, the transition density matrix (TDM) been has plotted in Figures 10c,d and S11 for the CO₂- and H₂O-adsorbed sheets. TDM images with higher diagonal values show the charge variance and with higher off-diagonal values show the strong coherence of the electron–hole pair. More spreading in the charges is due to the delocalization of π electrons in Si, B, and N.

Table 10. UV-Dominant Absorption of CO₂-Adsorbed Sheets Calculated from the Time-Dependent Density Functional Theory (TD-DFT) Using the PBE0 Level of Theory.

	sheets with CO2			sheets with CO2 and H2O
sheets	wavelength (nm)	oscillator strength	energy (eV)	wavelength (nm)	oscillator strength	energy (eV)
O1	860.54	0.160	1.440	667.94	0.126	1.856
O2	767.50	0.221	1.615	776.90	0.177	1.595
M1	562.29	0.290	2.202	550.09	0.162	2.253
M2	698.49	0.228	1.775	703.67	0.207	1.762
M3	658.85	0.411	1.881	654.70	0.407	1.893
M4	776.20	0.443	1.567	689.73	0.524	1.797

Table 11. Electronic Properties of CO₂ + H₂O-Adsorbed Complexes.

sheets	band gap (eV)	HOMO (eV)	LUMO (eV)	Fermi level (eV)	chemical potential (eV)	hardness (eV)	softness (eV)	electrophilicity (eV)
O1	0.663	–4.142	–3.478	–3.810	3.810	0.331	1.506	21.872
O2	0.660	–4.576	–3.916	–4.246	4.246	0.330	1.514	27.304
M1	1.347	–4.551	–3.203	–3.877	3.877	0.673	0.742	11.157
M2	0.786	–4.352	–3.566	–3.959	3.959	0.393	1.271	19.932
M3	0.560	–4.236	–3.675	–3.955	3.955	0.280	1.783	27.901
M4	1.197	–4.655	–3.457	–4.056	4.056	0.598	0.835	13.744

Figure 10.

(a) UV-absorption graph of CO₂-adsorbed sheets. (b) UV-absorption graph of CO₂- and H₂O-adsorbed sheets. (c) Transition density matrix of the O2 sheet in presence of CO₂. (d) Transition density matrix map of the M4 sheet in presence of CO₂.

2.7. Possible Hydrogen Storage Expedient

Hydrogen fuel cells are the most efficient energy carriers with 3 times more energy than that in liquid hydrocarbons.^55,56 This significant character of hydrogen fuel cells to produce hazard-free energy in a consistent manner enforces us to investigate them. In the process of hydrogen fuel cells, hydrogen storage is the important phenomena and it has plenty of quests in it. The United States Department of Energy (USDE) has set a target of 6.0 wt % gravimetric densities,^69,70 and it is set to achieve the targets in light-duty vehicles with 0.040 kg H₂/L with the volumetric capacity and the net useful energy per system mass of 1.8 kWh/kg.⁷¹ Hydrogen can be adsorbed and stored on the surface of solid materials such as graphene nano, nanotubes and etc. Physisorption of hydrogen on nanoporous solid materials is advantageous because of reversibility of the process and desorption kinetics. However, the major disadvantage of physisorption is that it requires extreme conditions such as low temperature (around −196 °C) and high pressure for high quantity of storage. On the other hand, chemisorption is a formation of strong bonds between the hydrogen atom and the adsorbent, which is more suitable for hydrogen storage and transport for longer distances.⁷² Thus, in the present study, Si–B–N and its derivatives are examined as hydrogen storage materials. The nonhomogeneous structures of O1, O2, M1, M2, and M3 sheets have six types of rings as shown in Table 12 and each ring’s edges are investigated as a hydrogen binding site as shown in the Figure 11. The average bond lengths between each atom and hydrogen atoms are as follows: Si–H, 1.5 Å; B–H, 1.19 Å; and N–H, 1.01 Å, respectively. Normal bond distances of Si–H (1.48 Å),⁷³ B–H (1.19 Å),⁷⁴ and N–H (1.01 Å) show that the bond distance of Si–H is slightly enlarged when the silicon atom is bounded in the aromatic ring in the presence of B and N. Logically, an increase in the bond length shows the weak interaction of H atoms on the Si atoms. The binding energy of hydrogen on each ring is calculated from the equation⁴⁹

14

Here, B_E is the binding energy per hydrogen atom, E_complex is the energy of the complex, n denotes the number of particular atoms, E_B is the energy of the boron atom, E_Si is the energy of the silicon atom, E_N is the energy of the nitrogen atom, E_H is the energy of the hydrogen atom, and nH is the number of hydrogen atoms present in the system. The calculated binding energies are summarized in Table 12, and it shows that the Si₂B₂N₂ ring has the largest binding energy of −8.7 eV and the Si₄B₂ ring has the lowest binding energy of −7.1 eV. Further, a comprehensive probability graph is plotted between the binding energy of H and the number of atoms, shown in Figure 12, to exactly know the combination of Si–B–N that produces minimum as well as maximum binding energy. From the relation between recovery time and adsorption as shown in the below equation

15

(where τ is the recovery time), one can conclude that the Si₄B₂ ring is more favorable for the adsorption of H atom. Deobrat sing et al.¹⁹ show the physisorption of H₂ molecules, with the binding energy of 1.8 eV, on the surface of Si₂BN. In the previous work,⁴⁹ graphene edges are examined as hydrogen binding sites and the average binding energies are higher than −25 eV. This shows that the edges of Si–B–N derivatives are more suitable for hydrogen binding and storage than graphene.

Table 12. Binding Energy of Hydrogen Atom on the Edges of Each Ring.

ring	binding energy (eV)
Si2B2N2	–8.760
Si4BN	–7.825
Si3BN2	–8.513
Si3B2N	–7.939
Si4N2	–8.288
Si4B2	–7.138

Figure 11.

Each different ring edge is taken as a possible hydrogen chemisorption expedient.

Figure 12.

Comprehensive graph between the binding energy of H and the no. of atoms that exhibit the change in adsorption energy with respect to the particular combinations of Si–B–N. The maximum adsorption energy has been found in 2-Si, 2-B, and 2-N atoms in the hexagonal ring.

2.8. Gravimetric Density

The gravimetric density of each ring is explored to estimate the maximum storage capacity of CO₂, Li, and H adsorbed on the surface and edges. Nonhomogeneous Si–B–N sheets have six different rings, and each ring has a different combination of Si–B–N. Thus, each ring is considered to examine the gravimetric density for CO₂, Li, and H atoms. The gravimetric density is calculated from the equation

16

Here, W is the gravimetric density, M_CO2/H/Li is the mass of CO₂/H/Li gas molecules, and M_complex is the mass of CO₂/H/Li-intercalated structures. The calculated results are summarized in Table 13, which shows that the ring consisting of two silicon, two boron, and two nitrogen (Si₂B₂N₂) atoms has the maximum gravimetric densities for CO₂ (22.705 wt %), Li (5.798 wt %), and H (5.407 wt %) atoms. For the adsorption of CO₂, metal–organic frameworks have been regarded as the best candidates with the weight of 48 wt % at 298 K and 14 bar pressure.⁷⁵ Similarly, graphene derivatives have the maximum gravimetric uptake of 37.9 wt % at 195 K and pressure of 1 atm.⁷⁶ Other graphene-like materials such as MoS₂ have the CO₂ uptake of 42 wt %,⁷⁷ and Ca-embedded C₂N has the CO₂ uptake of 50 wt % at 30 bar and 23 wt % at 1 bar.⁷⁸ In comparison, Si–B–N derivatives show a good amount of CO₂ uptake at room temperature and 1 atm pressure. The highest gravimetric density of H atoms on the edges of defective and boron-doped graphene is 3.145 wt %⁴⁹ and Si–B–N derivatives are far better than graphene defects. Other experimental results of H uptake on the graphene sheets are 0.4 and 0.2 wt % at 77 K and 1 bar pressure⁷⁹ and graphite oxide and reduced graphite oxides show 3.1 and 2.7 wt %, respectively.^76,80 Further, results in this investigation are approaching the USDE’s minimum criteria for the hydrogen storage.^69,70 The overall results of gravimetric density calculations show that the derivatives of Si–B–N have the potential to store CO₂, Li, and H efficiently.

Table 13. Gravimetric Density of Each Ring for the Adsorption of CO₂, Li, and H Atoms Calculated in Weight %.

rings	CO2	Li	H
Si2B2N2	22.705	5.798	5.407
Si4BN	19.544	4.594	4.193
Si3BN2	20.830	5.060	4.641
Si3B2N	21.116	5.188	4.764
Si4N2	19.270	4.449	4.102
Si4B2	19.825	4.694	4.288

3. Conclusions

The Si₂BN sheet predicted by Andriotis et al.¹⁸ is modeled into four different types. A slight rearrangement of B and N in the sheets increases the stability of the sheet. To understand the temperature-dependent structural stability of the sheets, ADMP calculations are carried out at 270.0, 300.0, 350.0, and 400.0 K temperatures, respectively. The geometrical variations in the sheets are not observed throughout the simulation, and the results confirm the stability of the structure at 400 K. The electronic properties of the sheets suggest the semiconducting nature of the sheets, and the obtained results are consistent with the Andriotis et al.’s result.¹⁸ To understand the potential of the derived sheets to be used as an electrode material, the adsorption properties of Li ion, CO₂, H₂O, and H are studied. From the obtained results, rings containing B–Si are strongly attracting, especially, the Si₄B₂ ring attracts Li atoms with the adsorption energies of 2.9 and 3.9 eV, respectively, and the results are in agreement with the results of Shukla et al.² The Si₄B₂ ring has the maximum electromotive force of 0.56 V with the theoretical energy density of 783 Wh/kg. Further, the adsorption of CO₂ molecule is studied using PBE0, HSE06, and PBE0-D3 levels of functionals, and the results show that both PBE0 and HSE06 results are similar. From the obtained results, it can be concluded that, like graphene sheets, Si–B–N and its derivatives have shown strong attraction toward CO₂ with the maximum adsorption energy of −0.106 eV in PBE0 and HSE0, but −0.381 eV in DFT + D3 calculations. From the results, it is very clear that the PBE0-D3 results are considerably higher than in the other two cases, and it seems that the D3 corrections slightly overestimate the results. When CO₂ is adsorbed by the sheets, the C–O bond length slightly increases, and they can be used as an artificial photosynthesis platform. Thus, UV-absorption studies are carried out to understand the photon absorption properties of the sheet, and the results show that the major absorption peaks fall within the visible region (450–800 nm). Further, it is very essential to understand the CO₂ adsorption in the presence of moisture for real-time applications, so the H₂O molecule is added to the system. The addition of H₂O does not influence the adsorption of CO₂, and interestingly, H₂O adsorbed well by the sheets with the adsorption energy of −0.72 eV. Since H₂O is a polarized molecule, it is well adsorbed by the sheets, and the sheets could be used in water purification and water splitting applications like graphene. Finally, the H adsorption properties of the sheets are examined by introducing H atoms in the edges of the sheets, and the edges are highly reactive to chemisorb H atoms. From the interesting results in this work, it can be concluded that there are plenty of probabilities to rearrange Si–B–N on the rings, but in the present study, very few fragments are chosen for the investigations. Up to this point, this Si–B–N has the potential to work as a sorbent material for both Li ions and CO₂ gas molecules. With tunable geometrical and electrical properties, the Si–B–N has plenty of quests and exciting features to be examined in the future.

4. Computational Methods

Phenomenal upsurge on the experimental frontier, on a parallel track, computational predictions of materials has provided valuables guideline for the experimentalist. The experimental verification has preceded computational predictions of two-dimensional borophene,⁸¹ hexagonal-BCN,²¹ and blue phosphorous,⁸² which can be regarded as an illustrative example, which shows the importance of the first principle predictions. In recent times, computational methods in terms of formulating admirable predictions of energy materials have been firmly established due to their consistency.⁸³ Galvanized by the above results, all of the geometrical optimization and electronic structure calculations performed in the present work have employed the density functional theory approach with PBE0⁸⁴ and HSE06⁸⁵ levels of theory with the 6-311+G* basis set. The basis function Perdew–Burke–Ernzerhof (PBE0) possesses 25% of exchange correlation and 75% of weighting correlation, which are well suited for physisorption and weak and nonbonded interactions.⁸⁶ The Heyd–Scuseria–Ernzerhof (HSE06) function includes a short-range exchange correlation, which makes the system efficient for a larger molecular system with diffusion function.⁸⁵ Further, with PBE0, overestimation of the band gap has been reported by many authors,⁸⁷ whereas HSE06 has good agreement with the experimental values. Thus, in the present investigation, all of the monomers are optimized with both PBE0 and HSE06 levels of theories. To understand the stability of each structure, atom-centered density matrix propagation (ADMP)⁸⁸ has been performed at the 6-31g level of theory at four different temperatures (270.0, 300.0, 350.0 K, and 400.0 K). The adsorption simulations of Li and CO₂ are optimized at the PBE0 level of theory. To find weak dispersion interactions between the CO₂ molecule and sheets, DFT-D3⁸⁹ corrections are carried out at the PBE0/6-311+g* level of theory. The density functional theory (DFT and DFT + D3) calculations in the present work are carried out by the GAUSSIAN software package.⁹⁰ Charge transfer calculations are carried out by Mulliken charge⁹¹ analysis, and a recent study⁹² revealed that Mulliken charge analysis is as consistent as Bader charge analysis.⁸¹ A multiwave function source code is used to calculate the density of states, partial density of states, and local orbital locator diagrams.⁸⁰

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.9b01354.

• IR frequency graph; frontier molecular orbital diagram; optimized figures of Li-adsorbed sheets; projection of the localized orbital locator; frontier molecular orbital diagram of Li-adsorbed sheets; Mulliken charge of Li-adsorbed rings; optimized figures of CO₂-adsorbed sheets; density of states of CO₂-adsorbed sheets; optimized figures and density of states of CO₂- and H₂O-adsorbed sheets; transition density matrix of CO₂-adsorbed sheets; area and perimeter of each ring; formation energy table; and Cartesian coordinates of Si–B–N derivatives (PDF)

The authors declare no competing financial interest.