Doped hexa-peri-hexabenzocoronene as anode materials for lithium- and magnesium-ion batteries

Abstract

The adsorption processes of Li⁺, Li, Mg²⁺, and Mg on twelve adsorbents (pristine and N/BN/Si-doped hexa-peri-hexabenzocoronene (HBC) molecules) were studied using density functional theory. The molecular electrostatic potential (MESP) analyses show that the replacement of C atoms of HBC by N/BN/Si units can provide a more electron-rich system than the parent HBC molecule. Li⁺ and Mg²⁺ exhibit strong adsorption on pristine and doped HBC molecules. The adsorption energy of cations on these nanoflakes (E_ads-1) was in the range of −247.44 (Mg²⁺/m-C₄₀H₁₈N₂ system) to −47.65 kcal mol⁻¹ (Li⁺/B₂₁H₁₈N₂₁ system). Importantly, our results suggest the weaker interactions of Li⁺ and Mg²⁺ with the nanoflakes as the MESP minimum values of the nanoflakes became less negative. In all studied systems, we observed electron donation from the nanoflakes to Li⁺ and Mg²⁺. For the metal/nanoflake systems, the adsorption energy of metals on the nanoflakes (E_ads-2) was in the range of −33.94 (Li/C₃₈H₁₈B₂N₂ system) to −2.14 kcal mol⁻¹ (Mg/B₂₁H₁₈N₂₁ system). Among the studied anode materials for lithium-ion batteries (LIBs), the highest cell voltage (V_cell) of 1.90 V was obtained for B₂₁H₁₈N₂₁. Among the studied anode materials for magnesium-ion batteries (MIBs), the highest V_cell value of 5.29 V was obtained for m-C₄₀H₁₈N₂. E_ads-2 has a significant effect on the variation of V_cell of LIBs, while E_ads-1 has a significant effect on the variation of V_cell of MIBs.

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1. Introduction

Rechargeable energy storage devices like lithium-ion batteries (LIBs) are in high demand due to their potential applications in electronic devices and electric transportation.^1–3 Since the commercialization by Sony Corporation in 1991,^1–3 LIBs have dominated the markets of portable electronic devices and electric vehicles because of their high energy densities and long cycle lives. LIBs are mainly composed of an anode, a cathode, and an electrolyte. Lithium cobalt oxide, lithium iron phosphate, and lithium manganese oxide are typically used as cathode materials for LIBs. The electrolyte of LIBs is mostly based on a lithium salt dissolved in organic solvents. Carbon materials like graphene, carbon nanofibers, carbon nanotubes, polycyclic aromatic hydrocarbons (PAHs), etc. have been frequently employed for the construction of anode materials for LIBs.^4–9 For instance, the high surface areas, electrical conductivities, and mechanical flexibilities of graphene make it a good candidate for anode materials in LIBs.⁵ Park et al. achieved good rate capabilities and cycling stability for LIBs by employing PAH in the design of anode materials.⁷ Arya et al. also obtained good cycling stability, high specific capacity, and excellent rate capability for LIBs by employing PAHs in the design of anode materials.⁹ Doped carbon materials have also been employed for the construction of anode materials for LIBs.^10–13 Recently, divalent metal-ion batteries such as magnesium-ion batteries (MIBs) have attracted considerable interest.^14,15 Mg could donate two valence electrons and therefore higher storage capacities may be realized in MIBs than in LIBs. Additional features of MIBs such as natural abundance of Mg, lower costs, and good safety make them an excellent alternative to LIBs.¹⁶

PAHs consist of multiple aromatic rings and are rich in delocalized π-electrons. Planar PAHs like coronene, hexa-peri-hexabenzocoronene (HBC), and circumcoronene are formed by fusion of 7, 13, and 19 benzene rings, respectively. These planar PAHs may be considered as finite-size models of graphene. Great progress has been made in the design and synthesis of different heteroatom-doped PAHs.^17–20 For example, the synthesis of HBC with a central borazine core was reported by Krieg et al. in 2015.¹⁷ There have been several studies of molecular adsorption on pristine and doped PAHs using density functional theory (DFT).^21,22 There have also been studies of the application of pristine and doped PAHs as anode materials in metal-ion batteries using DFT.^23–29 Li⁺ and Li were observed to be bound to the peripheral benzene rings of coronene and circumcoronene.²³ On the basis of cell voltage (V_cell), PAHs such as circumbiphenyl and coronene were recommended as good anode materials for LIBs.²⁴ Li has a higher interaction with circumcoronene than with BN-circumcoronene.²³ Li⁺ and Li were found to be bound to the peripheral rings of HBC.²⁵ Li⁺ and Li were also bound to the peripheral rings of BN-doped HBC.²⁶ Mg²⁺ was chemically adsorbed on HBC, while Mg was physically adsorbed on HBC.²⁷ For the sodium-ion batteries, the V_cell value obtained using HBC with a central borazine core was lower than that obtained using the pristine HBC.²⁸ A similar result was obtained for the calcium-ion batteries.²⁹ However, the interactions of Mg²⁺ and Mg with adsorbents like Si-doped HBC have not yet been investigated.

In the present study, DFT calculations were carried out to understand the adsorption process of Li⁺, Li, Mg²⁺, and Mg on twelve nanoflakes (pristine and N/BN/Si-doped HBC molecules). The molecular electrostatic potential (MESP) minimum point (designated as V_min) is often observed at the electron-rich sites like lone pairs and π-regions.^30–32 Importantly, our results suggest the weaker interactions of Li⁺ and Mg²⁺ with the nanoflakes as the MESP V_min values of the nanoflakes become less negative. For LIBs, the highest V_cell value of 1.90 V was obtained for B₂₁H₁₈N₂₁ and for MIBs, the highest V_cell value of 5.29 V was obtained for m-C₄₀H₁₈N₂. This study can provide some new insights into the design and exploration of anode materials suitable for metal ion batteries.

2. Computational details

All DFT computations were conducted through the Gaussian 16 program.³³ In the present study, we use a total of twelve adsorbents (pristine and N/BN/Si-doped HBC molecules C₄₂H₁₈, o-C₄₀H₁₈N₂, m-C₄₀H₁₈N₂, p-C₄₀H₁₈N₂, o-C₄₀H₁₈BN, m-C₄₀H₁₈BN, p-C₄₀H₁₈BN, C₃₈H₁₈B₂N₂, C₃₆H₁₈B₃N₃, C₂₈H₁₈Si₁₄, C₂₁H₁₈Si₂₁, and B₂₁H₁₈N₂₁) and four adsorbates (Li⁺, Li, Mg²⁺, and Mg). The adsorbents were obtained by the replacement of C atoms of HBC by N/BN/Si units. The structural isomers of, for instance, C₄₀H₁₈N₂ (two nitrogen atoms occupied adjacent positions in o-C₄₀H₁₈N₂) were considered in this work. Note that, C₂₈H₁₈Si₁₄, C₂₁H₁₈Si₂₁, and B₂₁H₁₈N₂₁ may be considered as finite-size models of graphene-like SiC₂, SiC, and BN nanosheets, respectively. All structures are optimized at the M062X/6-31G(d,p) level³⁴ and characterized as energy minima by frequency calculations. M06-2X is a hybrid meta functional with 54% of exact Hartree–Fock (HF) exchange. It is a high-nonlocality functional with double the amount of nonlocal exchange (2X) and it also considers the dispersion forces. The M06-2X functional is parameterized for nonmetals and recommended for the study of noncovalent interactions, kinetics, and main-group thermochemistry. The 6-31G(d,p) basis set was used for the geometry optimization calculations. In the geometry optimization process, the geometry is adjusted until a stationary point on the potential surface is found. Vibrational frequency analysis has been carried out to ensure that all the optimized structures correspond to the local minima containing only positive vibrational frequencies.

MESP V(r)^30–32 is described by the following expression:

where Z_A denotes the charge on nucleus A positioned at R_A and ρ(r) denotes the electron density. The first and second terms in eqn (1) represent the nuclear and electronic contributions to the MESP, respectively. V(r) is positive when the first term in eqn (1) dominates and negative when the second term dominates. The MESP analysis was performed at the M062X/6-31G(d,p) level of theory.

The adsorption energy (E_ads) is described by the following expression:

E_ads = E_{adsorbate/nanoflake} − (E_nanoflake + E_adsorbate) + E_BSSE (2)

where E_{adsorbate/nanoflake}, E_nanoflake, and E_adsorbate denote the energies of the adsorbed system, adsorbent (e.g., HBC), and adsorbate (Li⁺/Li/Mg²⁺/Mg), respectively. E_BSSE denotes the basis set superposition error energy calculated using the counterpoise approach.³⁵ The E_ads of Li⁺/Mg²⁺ and Li/Mg on the nanoflakes was denoted as E_ads-1 and E_ads-2, respectively. The adsorption energies calculated in our study are in line with previous DFT data^25–27 (Fig. 1 and Table S1, ESI†). The adsorption free energy (G_ads) is described by the following expression:

G_ads = G_{adsorbate/nanoflake} − (G_nanoflake + G_adsorbate) (3)

where G_{adsorbate/nanoflake}, G_adsorbate, and G_nanoflake denote the free energies of the adsorbed system, adsorbent, and adsorbate, respectively.

Fig. 1 Comparison of our results for adsorption energies with literature values.^25–27

The highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) energy gap (E_g) can be calculated using the below equation:

E_g = E_LUMO − E_HOMO (4)

where E_HOMO and E_LUMO denote the HOMO and LUMO energies, respectively. The E_g of the pristine nanoflake, the Li⁺/Mg²⁺-adsorbed nanoflake, and the Li/Mg-adsorbed nanoflake is denoted by E_g-1, E_g-2, and E_g-3, respectively.

The percentage change in the HOMO–LUMO energy gap can be calculated using the below equations:

ΔE_g-1 = [(E_g-2 − E_g-1)/E_g-1] × 100 (5)

ΔE_g-2 = [(E_g-3 − E_g-1)/E_g-1] × 100 (6)

For using a nanoflake as an anode material in, for example, MIBs, the reactions in the anode and cathode can be written as:

Anode: Mg/nanoflake ↔ Mg²⁺/nanoflake + 2e⁻ (7)

Cathode: Mg²⁺ + 2e⁻ ↔ Mg (8)

Therefore, the total cell reaction is:

Mg/nanoflake + Mg²⁺ ↔ Mg²⁺/nanoflake + Mg + ΔG_cell (9)

The Gibbs free energy change for the total cell reaction (ΔG_cell) is described by the following expression:

ΔG_cell = ΔE_cell + PΔV − TΔS (10)

where

ΔE_cell = E_ads-1 − E_ads-2 (11)

The cell voltage can be calculated using the Nernst equation:

V_cell = −ΔG_cell/zF (12)

where F is the Faraday constant (96485.3 C mol⁻¹) and z is the valence of Li⁺/Mg²⁺. It might be assumed that ΔG_cell ≈ ΔE_cell, because the contributions of the entropy effect and the volume effect to V_cell are expected to be negligible.³⁶

3. Results and discussion

3.1 Doped HBC molecules as anode materials in lithium-ion batteries

3.1.1. Structural properties of doped HBC molecules. Fig. 2 provides the optimized configurations and the relevant bond lengths for the pristine and doped HBC molecules. The XY (X = C, B; Y = C, N, Si) bond lengths in the pristine and doped HBC molecules span from 1.36 to 1.83 Å. The carbon–carbon bond lengths in HBC span from 1.38 to 1.46 Å. This result is in good agreement with the experimental data.³⁷ Clar's aromatic sextet rule can be applied for HBC³⁸ and thus the carbon–carbon bond length in the central and the six peripheral benzene rings of HBC spans from 1.38 to 1.42 Å. For comparison, the carbon–carbon bond length in benzene is about 1.395 Å.³⁹ In all cases, the carbon–silicon bond lengths (>1.76 Å) are significantly longer than the carbon–carbon bond lengths.

Fig. 2 Optimized structures of (a) C₄₂H₁₈, (b) o-C₄₀H₁₈N₂, (c) m-C₄₀H₁₈N₂ (d) p-C₄₀H₁₈N₂, (e) o-C₄₀H₁₈BN, (f) m-C₄₀H₁₈BN, (g) p-C₄₀H₁₈BN, (h) C₃₈H₁₈B₂N₂, (i) C₃₆H₁₈B₃N₃, (j) C₂₈H₁₈Si₁₄, (k) C₂₁H₁₈Si₂₁, and (l) B₂₁H₁₈N₂₁. The bond distances are given in Å. Color code: green – C, purple – B, blue – N, gray – H, and yellow- – Si.

Table 1 lists the E_HOMO, E_LUMO, and E_g-1 values of the pristine and doped HBC molecules. Here the E_HOMO, E_LUMO, and E_g-1 values are in the ranges of −8.10 (B₂₁H₁₈N₂₁) to −4.01 eV (m-C₄₀H₁₈N₂), −1.74 (C₃₈H₁₈B₂N₂) to 0.89 eV (B₂₁H₁₈N₂₁), and 2.46 (m-C₄₀H₁₈N₂) to 9.00 eV (B₂₁H₁₈N₂₁), respectively. The E_HOMO, E_LUMO, and E_g-1 values of HBC are −6.39, −1.00, and 5.40 eV, respectively. These results are in good agreement with previous theoretical calculations.⁴⁰ Overall, the E_HOMO (E_LUMO) values of the doped HBC molecules are higher (lower) than those of the pristine HBC. Also, in general, the E_g-1 values of the doped HBC molecules are lower than those of the pristine HBC. A smaller E_g-1 value usually indicates a higher electronic conductivity. However, the E_g-1 values of C₃₆H₁₈B₃N₃ and B₂₁H₁₈N₂₁ are higher than those of the pristine HBC.

Table 1 V _min, E_HOMO, E_LUMO and E_g-1 values of doped HBCs^a

Nanoflake	V min	E HOMO	E LUMO	E g-1
a The values are given in eV and Vmin in kcal mol^−1.
C42H18	−15.56	−6.39	−1.00	5.40
o-C40H18N2	−19.70	−4.89	−1.11	3.78
m-C40H18N2	−24.97	−4.01	−1.55	2.46
p-C40H18N2	−16.44	−4.74	−0.95	3.80
o-C40H18BN	−18.64	−6.09	−1.22	4.87
m-C40H18BN	−23.41	−5.90	−1.41	4.49
p-C40H18BN	−22.53	−6.37	−0.99	5.38
C38H18B2N2	−18.14	−5.45	−1.74	3.71
C36H18B3N3	−16.32	−6.73	−0.69	6.05
C28H18Si14	−31.38	−5.71	−1.71	4.00
C21H18Si21	−28.43	−6.44	−1.14	5.30
B21H18N21	−17.57	−8.10	0.89	9.00

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3.1.2. MESP of doped HBC molecules. Fig. 3 displays the MESP surfaces of the pristine and doped HBC molecules. The MESP plots show the electron-rich region (e.g., green region) on the central and peripheral benzene rings of HBC arising from the cyclic delocalization of π-electrons. Our results show that the replacement of C atoms of HBC by N/BN/Si units can provide a more electron-rich environment (e.g., the blue region). Fig. S1, ESI,† provides the location of the MESP V_min of the pristine and doped HBC molecules. The MESP V_min points were situated near the six peripheral benzene rings of HBC. This indicates the higher electron-richness of the peripheral benzene rings of HBC as compared to the inner rings of HBC. This is due to the fact that the peripheral benzene rings of HBC also have carbon–hydrogen bonds and hydrogen is less electronegative than the sp² carbon. Overall, the MESP V_min points of all doped HBC molecules were also situated near the peripheral rings. However, the MESP V_min points of o-C₄₀H₁₈N₂ are situated near the inner N atoms. The MESP V_min values of the pristine and doped HBC molecules are listed in Table 1. A higher negative value of MESP V_min reflects a more electron rich nature of the nanoflake. These values were in the range of −31.38 (C₂₈H₁₈Si₁₄) to −15.56 kcal mol⁻¹ (C₄₂H₁₈). A higher negative value of MESP V_min reflects a more electron rich nature of the nanoflake. The MESP V_min value of the doped HBC molecules was more negative than that of the pristine HBC. In the case of N-doped HBC molecules, the absolute value of MESP V_min followed the order p-C₄₀H₁₈N₂ < o-C₄₀H₁₈N₂ < m-C₄₀H₁₈N₂. In the case of BN-doped HBC molecules, the absolute value of MESP V_min followed the order C₃₆H₁₈B₃N₃ < B₂₁H₁₈N₂₁ < C₃₈H₁₈B₂N₂ < o-C₄₀H₁₈BN < p-C₄₀H₁₈BN < m-C₄₀H₁₈BN. The MESP V_min value of C₂₁H₁₈Si₂₁ (−28.43 kcal mol⁻¹) was less negative than that of C₂₈H₁₈Si₁₄ (−31.38 kcal mol⁻¹).

Fig. 3 MESP mapped on the 0.01 a.u. electron density isosurface of (a) C₄₂H₁₈, (b) o-C₄₀H₁₈N₂, (c) m-C₄₀H₁₈N₂ (d) p-C₄₀H₁₈N₂, (e) o-C₄₀H₁₈BN, (f) m-C₄₀H₁₈BN, (g) p-C₄₀H₁₈BN, (h) C₃₈H₁₈B₂N₂, (i) C₃₆H₁₈B₃N₃, (j) C₂₈H₁₈Si₁₄, (k) C₂₁H₁₈Si₂₁, and (l) B₂₁H₁₈N₂₁. The colour coding from blue to red indicates MESP values in the range −0.03 to 0.03 a.u. The colours at the blue end of the spectrum indicate the electron-rich regions, while those toward the red indicate the electron-deficient regions.

3.1.3. Li⁺ adsorption on doped HBC molecules. Fig. 4 provides the optimized configurations and the adsorption distances for the adsorption of Li⁺ on pristine and doped HBC molecules. We see that Li⁺ is bound to the peripheral benzene rings of HBC. This is possibly due to the higher electron-richness of the peripheral benzene rings of HBC as compared to the inner rings of HBC (see the above). These adsorption processes involve the cation–π interactions.^24,41 These interactions are predominantly electrostatic in nature, involving the interaction of Li⁺ with the electron cloud of the π-system. Overall, Li⁺ is also bound to the peripheral rings of all doped HBC molecules. However, Li⁺ is bound to the central ring of o-C₄₀H₁₈N₂. We observe that Li⁺ exhibits a relatively strong adsorption on pristine and doped HBC molecules. For instance, the adsorption distances of Li⁺ on these nanoflakes span from 2.20 (Li⁺/m-C₄₀H₁₈N₂ system) to 2.41 Å (Li⁺/C₂₁H₁₈Si₂₁ system). The adsorption energy data (Table 2) also support this possibility. Here the E_ads-1 values were in the range of −67.34 (Li⁺/C₂₈H₁₈Si₁₄ system) to −47.65 kcal mol⁻¹ (Li⁺/B₂₁H₁₈N₂₁ system). A higher negative value of E_ads-1 typically implies a stronger interaction between Li⁺ and the nanoflake. The E_ads-1 value of the Li⁺/HBC system was −51.57 kcal mol⁻¹. This value is more negative than that of the Li⁺/C₃₆H₁₈B₃N₃ and Li⁺/B₂₁H₁₈N₂₁ systems. In the case of Li⁺ adsorption on N-doped HBC molecules, the absolute values of E_ads-1 followed the order o-C₄₀H₁₈N₂ < p-C₄₀H₁₈N₂ < m-C₄₀H₁₈N₂. In the case of Li⁺ adsorption on BN-doped HBC molecules, the absolute values of E_ads-1 followed the order B₂₁H₁₈N₂₁ < C₃₆H₁₈B₃N₃ < o-C₄₀H₁₈BN < C₃₈H₁₈B₂N₂ < p-C₄₀H₁₈BN < m-C₄₀H₁₈BN. The E_ads-1 value of the Li⁺/C₂₁H₁₈Si₂₁ system (−60.82 kcal mol⁻¹) was less negative than that of the Li⁺/C₂₈H₁₈Si₁₄ system. Notably, a linear relationship between E_ads-1 and MESP V_min values of the nanoflakes exists with a correlation coefficient of 0.913 (Fig. 5a). This finding reflects the weaker interactions of Li⁺ with the nanoflakes as the MESP V_min values of the nanoflakes become less negative. For all cases, the adsorption free energies were negative, indicating the spontaneous nature of the adsorption process (see Table 2). Here the G_ads-1 values were in the range of −58.02 (Li⁺/C₂₈H₁₈Si₁₄ system) to −37.15 kcal mol⁻¹ (Li⁺/B₂₁H₁₈N₂₁ system).

Fig. 4 Optimized structures of Li⁺ adsorbed on (a) C₄₂H₁₈, (b) o-C₄₀H₁₈N₂, (c) m-C₄₀H₁₈N₂ (d) p-C₄₀H₁₈N₂, (e) o-C₄₀H₁₈BN, (f) m-C₄₀H₁₈BN, (g) p-C₄₀H₁₈BN, (h) C₃₈H₁₈B₂N₂, (i) C₃₆H₁₈B₃N₃, (j) C₂₈H₁₈Si₁₄, (k) C₂₁H₁₈Si₂₁, and (l) B₂₁H₁₈N₂₁. The bond distances are given in Å. The color code is the same as in Fig. 2. In addition, Li is denoted by the orange color.

Table 2 E _ads-1, ΔV_MESP-1, E_HOMOE_LUMO, E_g-2 and ΔE_g-1 values of Li⁺ adsorbed HBCs^a

Nanoflake	E ads-1	G ads-1	ΔVMESP-1	E HOMO	E LUMO	E g-2	ΔEg-1
a The values of Eads-1, Gads-1 and ΔVMESP-1 in kcal mol^−1; EHOMO, ELUMO, and Eg-2 in eV; ΔEg-1 in %.
C42H18	−51.57	−46.58	−114.15	−8.98	−4.54	4.44	−17.69
o-C40H18N2	−52.54	−43.76	−122.27	−8.67	−4.41	4.26	12.73
m-C40H18N2	−63.17	−52.97	−133.74	−7.06	−4.25	2.81	14.03
p-C40H18N2	−52.75	−43.65	−119.68	−7.65	−4.20	3.45	−9.10
o-C40H18BN	−55.25	−45.65	−119.46	−8.80	−4.30	4.50	−7.65
m-C40H18BN	−59.30	−49.77	−124.32	−8.67	−4.37	4.31	−4.12
p-C40H18BN	−58.67	−49.26	−123.26	−9.05	−4.07	4.98	−7.53
C38H18B2N2	−55.60	−47.70	−121.48	−8.24	−4.62	3.62	−2.49
C36H18B3N3	−50.81	−45.48	−112.35	−9.05	−4.26	4.79	−20.83
C28H18Si14	−67.34	−58.02	−146.76	−8.30	−4.15	4.15	3.81
C21H18Si21	−60.82	−51.17	−148.34	−8.40	−3.76	4.64	−12.42
B21H18N21	−47.65	−37.15	−114.78	−10.45	−4.11	6.35	−29.45

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Fig. 5 Correlation between (a) V_min and E_ads-1 and (b) ΔV_MESP-1 and E_ads-1 for Li⁺-adsorbed HBCs.

The electron donation from the nanoflakes to Li⁺ can be assessed by determining the MESP at the nucleus of Li⁺ before and after adsorption. Therefore, ΔV_MESP-1 is calculated by subtracting the MESP at the nucleus of free Li⁺ (−5.36 a.u.) from that of Li⁺ in the Li⁺/nanoflake system. For all cases, the ΔV_MESP-1 values were negative, indicating the electron donation from the nanoflakes to Li⁺ (see Table 2). Here the ΔV_MESP-1 values are in the range of −148.34 (Li⁺/C₂₁H₁₈Si₂₁ system) to −112.35 kcal mol⁻¹ (Li⁺/C₃₆H₁₈B₃N₃ system). The ΔV_MESP-1 value of the Li⁺/HBC system is −114.15 kcal mol⁻¹. This value is more negative than that of the Li⁺/C₃₆H₁₈B₃N₃ system. A linear relationship between E_ads-1 and ΔV_MESP-1 values exists with a correlation coefficient of 0.863 (Fig. 5b). This finding reflects that stronger interactions of Li⁺ with the nanoflakes push more electron density toward Li⁺.

Table 2 also lists the E_HOMO, E_LUMO, and E_g-2 values of the Li⁺-adsorbed nanoflakes. Here the E_HOMO, E_LUMO, and E_g-2 values are in the ranges of −10.45 (Li⁺/B₂₁H₁₈N₂₁ system) to −8.24 eV (Li⁺/C₃₈H₁₈B₂N₂ system), −4.62 (Li⁺/C₃₈H₁₈B₂N₂ system) to −3.76 eV (Li⁺/C₂₁H₁₈Si₂₁ system), and 2.81 (Li⁺/m-C₄₀H₁₈N₂ system) to 6.35 eV (Li⁺/B₂₁H₁₈N₂₁ system), respectively. The E_HOMO, E_LUMO, and E_g-2 values of the Li⁺/HBC system are −8.98, −4.54, and 4.44 eV, respectively. The E_HOMO and E_LUMO values of all the Li⁺-adsorbed nanoflakes are lower than those of the corresponding Li⁺-free nanoflakes. In general, a similar trend was obtained for E_g-2. The HOMO–LUMO gap decreased by 17.69% due to Li⁺ adsorption on HBC (see the ΔE_g-1 values in Table 2). The maximum decrease in the HOMO–LUMO gap is obtained for Li⁺ adsorption on B₂₁H₁₈N₂₁ (29.45%). The maximum increase in the HOMO–LUMO gap is obtained for Li⁺ adsorption on m-C₄₀H₁₈N₂ (14.03%).

3.1.4. Li adsorption on doped HBC molecules. Fig. 6 provides the optimized configurations and the adsorption distances for the adsorption of Li on pristine and doped HBC molecules. Li is mostly bound to the peripheral rings of these nanoflakes, as observed in the case of Li⁺. The adsorption distances of Li on these nanoflakes span from 2.15 (Li/p-C₄₀H₁₈N₂ system) to 2.25 Å (Li/C₃₈H₁₈B₂N₂ system). For these nanoflakes, the adsorption distances of Li⁺ (see Fig. 4) are typically larger than those of Li. For instance, the adsorption distances of Li⁺ and Li on HBC are 2.27 and 2.17 Å, respectively. However, Li⁺ was strongly adsorbed on these nanoflakes in comparison with Li. The adsorption energy data (see Tables 2 and 3) support this possibility. Here, the E_ads-2 values are in the range of −33.94 (Li/C₃₈H₁₈B₂N₂ system) to −3.93 kcal mol⁻¹ (Li/B₂₁H₁₈N₂₁ system). The E_ads-2 value of the Li/HBC system is −17.39 kcal mol⁻¹. This value is more negative than those of the Li/C₃₆H₁₈B₃N₃ and Li/B₂₁H₁₈N₂₁ systems. In the case of Li adsorption on N-doped HBC molecules, the absolute values of E_ads-2 followed the order p-C₄₀H₁₈N₂ < o-C₄₀H₁₈N₂ < m-C₄₀H₁₈N₂. In the case of Li adsorption on BN-doped HBC molecules, the absolute values of E_ads-2 followed the order B₂₁H₁₈N₂₁ < C₃₆H₁₈B₃N₃ < p-C₄₀H₁₈BN < o-C₄₀H₁₈BN < m-C₄₀H₁₈BN < C₃₈H₁₈B₂N₂. The E_ads-2 value of the Li/C₂₁H₁₈Si₂₁ system (−30.84 kcal mol⁻¹) was less negative than that of the Li/C₂₈H₁₈Si₁₄ system (−32.42 kcal mol⁻¹). Here, E_ads-2 is not well correlated with the MESP V_min values of the nanoflakes (Fig. S2, ESI†). Overall, the adsorption free energies were negative, indicating the spontaneous nature of the adsorption process (see Table 3). However, the G_ads-2 value of the Li/B₂₁H₁₈N₂₁ system is positive (3.87 kcal mol⁻¹), suggesting that the adsorption of Li on B₂₁H₁₈N₂₁ is not spontaneous. ΔV_MESP-2 is calculated by subtracting the MESP at the nucleus of free Li (−5.72 a.u.) from that of Li in the Li/nanoflake system. Overall, the ΔV_MESP-2 values were positive, indicating the electron density transfer from Li to the nanoflakes (see Table 3). However, the ΔV_MESP-2 values were negative for Li adsorption on C₂₁H₁₈Si₂₁ and B₂₁H₁₈N₂₁. Unlike E_ads-1, E_ads-2 did not display a correlation with ΔV_MESP-2 (see Fig. S2, ESI†).

Fig. 6 Optimized structures of Li adsorbed on (a) C₄₂H₁₈, (b) o-C₄₀H₁₈N₂, (c) m-C₄₀H₁₈N₂ (d) p-C₄₀H₁₈N₂, (e) o-C₄₀H₁₈BN, (f) m-C₄₀H₁₈BN, (g) p-C₄₀H₁₈BN, (h) C₃₈H₁₈B₂N₂, (i) C₃₆H₁₈B₃N₃, (j) C₂₈H₁₈Si₁₄, (k) C₂₁H₁₈Si₂₁, and (l) B₂₁H₁₈N₂₁. The bond distances are given in Å. The color code is the same as in Fig. 2. In addition, Li is denoted by the orange color.

Table 3 E _ads-2, ΔV_MESP-2, E_HOMOE_LUMO, E_g-3 and ΔE_g-2 values of Li adsorbed HBCs, along with ΔE_cell and V_cell^a

Nanoflake	E ads-2	G ads-2	ΔVMESP-2	E HOMO	E LUMO	E g-3	ΔEg-2	ΔEcell	V cell
a The values of Eads-2, Gads-2, ΔVMESP-2, and ΔEcell in kcal mol^−1; EHOMO, ELUMO, and Eg-3 in eV; ΔEg-2 in %; and Vcell in V.
C42H18	−17.39	−15.32	16.73	−3.59	−0.98	2.62	−51.51	−34.18	1.48
o-C40H18N2	−23.10	−16.24	14.88	−3.90	−0.88	3.02	−20.22	−29.44	1.28
m-C40H18N2	−30.68	−23.05	20.44	−3.82	−1.04	2.79	13.26	−32.49	1.41
p-C40H18N2	−18.02	−11.74	13.71	−3.64	−0.82	2.82	−25.72	−34.72	1.51
o-C40H18BN	−20.81	−13.73	16.42	−3.58	−1.02	2.56	−47.43	−34.44	1.49
m-C40H18BN	−26.64	−19.27	18.51	−3.64	−0.97	2.67	−40.52	−32.66	1.42
p-C40H18BN	−18.95	−12.63	9.50	−3.35	−1.08	2.27	−57.81	−39.73	1.72
C38H18B2N2	−33.94	−28.74	21.50	−4.39	−0.63	3.76	1.39	−21.66	0.94
C36H18B3N3	−16.40	−13.51	13.21	−3.61	−0.84	2.77	−54.25	−34.40	1.49
C28H18Si14	−32.42	−25.10	6.07	−3.73	−1.39	2.34	−41.36	−34.92	1.51
C21H18Si21	−30.84	−22.75	−18.32	−4.71	−1.15	3.56	−32.85	−29.98	1.30
B21H18N21	−3.93	3.87	−25.98	−3.10	0.32	3.42	−61.99	−43.72	1.90

---

Table 3 also lists the E_HOMO, E_LUMO, and E_g-3 values of the Li-adsorbed nanoflakes. Here the E_HOMO, E_LUMO, and E_g-3 values are in the ranges of −4.71 (Li/C₂₁H₁₈Si₂₁ system) to −3.10 eV (Li/B₂₁H₁₈N₂₁ system), −0.63 (Li/C₃₈H₁₈B₂N₂ system) to 0.32 eV (Li/B₂₁H₁₈N₂₁ system), and 2.27 (Li/p-C₄₀H₁₈BN system) to 3.76 eV (Li/C₃₈H₁₈B₂N₂ system), respectively. The E_HOMO, E_LUMO, and E_g-3 values of the Li/HBC system are −3.59, −0.98, and 2.62 eV, respectively. The E_HOMO values of all the Li-adsorbed nanoflakes are higher than those of the corresponding Li-free nanoflakes. In general, a similar trend was obtained for E_g-3. For all nanoflakes, the E_LUMO was not much influenced by the presence of Li. The HOMO–LUMO gap decreased by 51.51% due to Li adsorption on HBC (see ΔE_g-2 values in Table 3). The maximum decrease in the HOMO–LUMO gap is obtained for Li adsorption on B₂₁H₁₈N₂₁ (61.99%). However, E_g-1 was lower than E_g-3 for Li adsorption on m-C₄₀H₁₈N₂ (ΔE_g-2 of 13.26%) and C₃₈H₁₈B₂N₂ (ΔE_g-2 of 1.39%).

3.1.5. Cell voltage. The ΔE_cell and V_cell values of LIBs based on the pristine and doped HBC molecules are provided in Table 3. Here the ΔE_cell and V_cell values were in the ranges of −43.72 (B₂₁H₁₈N₂₁) to −21.66 kcal mol⁻¹ (C₃₈H₁₈B₂N₂) and 0.94 (C₃₈H₁₈B₂N₂) to 1.90 V (B₂₁H₁₈N₂₁), respectively. The less negative the ΔE_cell, the lower the V_cell of the system. Thus, a nanoflake with a strong interaction with Li⁺ and a weak interaction with Li might be regarded as a good candidate for the anode material in metal ion batteries. For instance, in the case of B₂₁H₁₈N₂₁, a high V_cell value of 1.90 V was obtained because of a high E_ads-1 value of −47.65 kcal mol⁻¹ (see Table 2) and a low E_ads-2 value of −3.93 kcal mol⁻¹ (see Table 3). In the case of C₃₈H₁₈B₂N₂, a low V_cell value of 0.94 V was obtained due to the higher contribution from E_ads-2 (E_ads-1 value of −55.60 kcal mol⁻¹ and E_ads-2 value of −33.94 kcal mol⁻¹). The ΔE_cell and V_cell values of HBC were −34.18 kcal mol⁻¹ and 1.48 V, respectively. In the case of N-doped HBC molecules, the V_cell values followed the order o-C₄₀H₁₈N₂ < m-C₄₀H₁₈N₂ < p-C₄₀H₁₈N₂. In the case of BN-doped HBC molecules, the V_cell values followed the order C₃₈H₁₈B₂N₂ < m-C₄₀H₁₈BN < C₃₆H₁₈B₃N₃ < o-C₄₀H₁₈BN < p-C₄₀H₁₈BN < B₂₁H₁₈N₂₁. The V_cell value of C₂₁H₁₈Si₂₁ (1.30 V) was lower than that of C₂₈H₁₈Si₁₄ (1.51 V). When considering all the nanoflakes, unlike E_ads-1, E_ads-2 shows large variations (see Tables 2 and 3). Thus, E_ads-2 can have a significant effect on the variation of V_cell. A linear relationship between E_ads-2 and V_cell with a correlation coefficient of 0.765 further supports the significant effect of E_ads-2 on the variation of V_cell (Fig. S3a, ESI†).

3.2 HBCs and their analogues as anode materials in magnesium-ion batteries

3.2.1. Mg²⁺ adsorption on doped HBC molecules. Fig. 7 provides the optimized configurations and the adsorption distances for the adsorption of Mg²⁺ on pristine and doped HBC molecules. We see that Mg²⁺ is bound to the peripheral benzene rings of HBC, similar to the case of Li⁺. Mg²⁺ is also bound to the peripheral rings of all doped HBC molecules except o-C₄₀H₁₈N₂, o-C₄₀H₁₈N₂, and p-C₄₀H₁₈N₂. We find that Mg²⁺ is strongly adsorbed on pristine and doped HBC molecules. For instance, the adsorption distances of Mg²⁺ on these nanoflakes span from 3.69 (Mg²⁺/m-C₄₀H₁₈N₂ system) to 2.14 Å (Mg²⁺/B₂₁H₁₈N₂₁ system). The adsorption energy data (Table 4) also support this possibility. Here the E_ads-1 values were in the range of −247.44 (Mg²⁺/m-C₄₀H₁₈N₂ system) to −172.35 kcal mol⁻¹ (Mg²⁺/B₂₁H₁₈N₂₁ system). A higher negative value of E_ads-1 usually implies a stronger interaction between Mg²⁺ and the nanoflake. The E_ads-1 value of the Mg²⁺/HBC system is −178.09 kcal mol⁻¹. This value is more negative than that of the Mg²⁺/C₃₆H₁₈B₃N₃ and Mg²⁺/B₂₁H₁₈N₂₁ systems. In the case of Mg²⁺ adsorption on N-doped HBC molecules, the absolute values of E_ads-1 followed the order o-C₄₀H₁₈N₂ < p-C₄₀H₁₈N₂ < m-C₄₀H₁₈N₂. In the case of Mg²⁺ adsorption on BN-doped HBC molecules, the absolute values of E_ads-1 followed the order B₂₁H₁₈N₂₁ < C₃₆H₁₈B₃N₃ < o-C₄₀H₁₈BN < C₃₈H₁₈B₂N₂ < p-C₄₀H₁₈BN < m-C₄₀H₁₈BN. The E_ads-1 value of the Mg²⁺/C₂₁H₁₈Si₂₁ system (−229.05 kcal mol⁻¹) was less negative than that of the Mg²⁺/C₂₈H₁₈Si₁₄ system (−231.69 kcal mol⁻¹). Here a linear relationship between E_ads-1 and MESP V_min values of the nanoflakes exists with a correlation coefficient of 0.690 (Fig. 8a). This finding reflects the weaker interactions of Mg²⁺ with the nanoflakes as the MESP V_min values of the nanoflakes become less negative. Notably a better correlation was obtained for the adsorption of Li⁺ on pristine and doped HBC molecules (see Fig. 5a). For all cases, the adsorption free energies were negative, indicating the spontaneous nature of the adsorption process (see Table 4). Here the G_ads-1 values were in the range of −238.37 (Mg²⁺/m-C₄₀H₁₈N₂ system) to −161.41 kcal mol⁻¹ (Mg²⁺/B₂₁H₁₈N₂₁ system).

Fig. 7 Optimized structures of Mg²⁺ adsorbed on (a) C₄₂H₁₈, (b) o-C₄₀H₁₈N₂, (c) m-C₄₀H₁₈N₂ (d) p-C₄₀H₁₈N₂, (e) o-C₄₀H₁₈BN, (f) m-C₄₀H₁₈BN, (g) p-C₄₀H₁₈BN, (h) C₃₈H₁₈B₂N₂, (i) C₃₆H₁₈B₃N₃, (j) C₂₈H₁₈Si₁₄, (k) C₂₁H₁₈Si₂₁, and (l) B₂₁H₁₈N₂₁. The bond distances are given in Å. The color code is the same as in Fig. 2. In addition, Mg is denoted by the cyan color.

Table 4 E _ads-1, ΔV_MESP-1, E_HOMO, E_LUMO, E_g-2 and ΔE_g-1 values of Mg²⁺ adsorbed HBCs^a

Nanoflake	E ads-1	G ads-1	ΔVMESP-1	E HOMO	E LUMO	E g-2	ΔEg-1
a The values of Eads-1, Gads-1 and ΔVMESP-1 in kcal mol^−1; EHOMO, ELUMO, and Eg-2 in eV; ΔEg-1 in %.
C42H18	−178.09	−173.45	−232.55	−11.39	−9.74	1.65	−69.35
o-C40H18N2	−220.45	−213.17	−382.29	−11.00	−8.62	2.38	−37.05
m-C40H18N2	−247.44	−238.37	−387.90	−10.86	−8.26	2.60	5.64
p-C40H18N2	−220.61	−213.27	−371.99	−11.30	−8.68	2.62	−31.09
o-C40H18BN	−187.15	−177.46	−254.82	−11.48	−9.64	1.84	−62.28
m-C40H18BN	−196.96	−187.18	−267.51	−11.79	−9.31	2.48	−44.70
p-C40H18BN	−192.08	−182.61	−239.19	−11.60	−9.50	2.09	−61.14
C38H18B2N2	−191.56	−183.82	−282.07	−11.12	−9.29	1.83	−50.62
C36H18B3N3	−174.18	−168.92	−227.43	−11.32	−9.96	1.35	−77.60
C28H18Si14	−231.69	−220.39	−286.89	−10.53	−8.20	2.33	−41.70
C21H18Si21	−229.05	−218.53	−294.22	−10.31	−8.05	2.26	−57.34
B21H18N21	−172.35	−161.41	−225.22	−12.62	−10.02	2.60	−71.06

---

Fig. 8 Correlation between (a) V_min and E_ads-1 (b) ΔV_MESP-1 and E_ads-1 for Mg²⁺-adsorbed HBCs.

ΔV_MESP-1 is calculated here by subtracting the MESP at the nucleus of free Mg²⁺ (−39.11 a.u.) from that of Mg²⁺ in the Mg²⁺/nanoflake system. For all cases, the ΔV_MESP-1 values were negative, indicating the electron donation from the nanoflakes to Mg²⁺ (see Table 4). Here the ΔV_MESP-1 values are in the range of −387.90 (Mg²⁺/m-C₄₀H₁₈N₂ system) to −225.22 kcal mol⁻¹ (Mg²⁺/C₃₆H₁₈B₃N₃ system). The ΔV_MESP-1 value of the Mg²⁺/HBC system was −232.55 kcal mol⁻¹. This value is more negative than those of the Mg²⁺/C₃₆H₁₈B₃N₃ and Mg²⁺/B₂₁H₁₈N₂₁ systems. A linear relationship between E_ads-1 and ΔV_MESP-1 values exists with a correlation coefficient of 0.829 (Fig. 8b). This finding reflects that stronger interactions of Mg²⁺ with the nanoflakes push more electron density toward Mg²⁺.

Table 4 also lists the E_HOMO, E_LUMO, and E_g-2 values of the Mg²⁺-adsorbed nanoflakes. Here the E_HOMO, E_LUMO, and E_g-2 values are in the ranges of −12.62 (Mg²⁺/B₂₁H₁₈N₂₁ system) to −10.31 eV (Mg²⁺/C₂₁H₁₈Si₂₁ system), −10.02 (Mg²⁺/B₂₁H₁₈N₂₁ system) to −8.05 eV (Mg²⁺/C₂₁H₁₈Si₂₁ system), and 1.35 (Mg²⁺/C₃₆H₁₈B₃N₃ system) to 2.62 eV (Mg²⁺/p-C₄₀H₁₈N₂ system), respectively. The E_HOMO, E_LUMO, and E_g-2 values of the Mg²⁺/HBC system are −11.39, −9.74, and 1.65 eV, respectively. The E_HOMO and E_LUMO values of all the Mg²⁺-adsorbed nanoflakes are lower than those of the corresponding Mg²⁺-free nanoflakes. In general, a similar trend was obtained for E_g-2. The HOMO–LUMO gap decreased by 69.35% due to Mg²⁺ adsorption on HBC (see ΔE_g-1 values in Table 4). The maximum decrease in the HOMO–LUMO gap is obtained for Mg²⁺ adsorption on C₃₆H₁₈B₃N₃ (77.60%). However, E_g-1 was lower than E_g-2 for Mg²⁺ adsorption on m-C₄₀H₁₈N₂ (ΔE_g-1 of 5.64%).

3.2.2. Mg adsorption on doped HBC molecules. Fig. 9 provides the optimized configurations and the adsorption distances for the adsorption of Mg on pristine and doped HBC molecules. Mg is mostly bound to the peripheral rings of these nanoflakes, as observed in the case of Mg²⁺. The adsorption distances of Mg on these nanoflakes span from 3.10 (Mg/C₂₈H₁₈Si₁₄ system) to 3.88 Å (Mg/C₂₁H₁₈Si₂₁ system). For these nanoflakes, the adsorption distances of Mg²⁺ (see Fig. 7) are typically smaller than those of Mg. For instance, the adsorption distances of Mg²⁺ and Mg on HBC are 2.30 and 3.61 Å, respectively. Mg²⁺ was strongly adsorbed on these nanoflakes in comparison with Mg. The adsorption energy data (see Tables 4 and 5) support this possibility. Here the E_ads-2 values were in the range of −5.11 (Mg/C₂₈H₁₈Si₁₄ system) to −2.14 kcal mol⁻¹ (Mg/B₂₁H₁₈N₂₁ system). The E_ads-2 value of the Mg/HBC system was −3.17 kcal mol⁻¹. This value is more negative than that of the Mg/C₃₆H₁₈B₃N₃ and Mg/B₂₁H₁₈N₂₁ systems. In the case of Mg adsorption on N-doped HBC molecules, the absolute values of E_ads-2 followed the order p-C₄₀H₁₈N₂ < o-C₄₀H₁₈N₂ < m-C₄₀H₁₈N₂. In the case of Mg adsorption on BN-doped HBC molecules, the absolute values of E_ads-2 followed the order B₂₁H₁₈N₂₁ < C₃₆H₁₈B₃N₃ < o-C₄₀H₁₈BN < p-C₄₀H₁₈BN < m-C₄₀H₁₈BN < C₃₈H₁₈B₂N₂. The E_ads-2 value of the Mg/C₂₁H₁₈Si₂₁ system (−3.58 kcal mol⁻¹) was less negative than that of the Mg/C₂₈H₁₈Si₁₄ system. Here E_ads-2 is not well correlated with the MESP V_min values of the nanoflakes (Fig. S4, ESI†). Overall, the adsorption free energies were positive, suggesting that the adsorption of Mg on nanoflakes is not spontaneous (see Table 5). However, the G_ads-2 values of the Mg/C₄₂H₁₈ and Mg/C₃₆H₁₈B₃N₃ systems are negative, indicating the spontaneous nature of the adsorption process. ΔV_MESP-2 is calculated by subtracting the MESP at the nucleus of free Mg (−39.91 a.u.) from that of Mg in the Mg/nanoflake system. The ΔV_MESP-2 values were negative, indicating the electron donation from the nanoflakes to Mg (see Table 5). Unlike E_ads-1, E_ads-2 did not display a correlation with ΔV_MESP-2 (see Fig. S4, ESI†).

Fig. 9 Optimized structures of Mg adsorbed on (a) C₄₂H₁₈, (b) o-C₄₀H₁₈N₂, (c) m-C₄₀H₁₈N₂ (d) p-C₄₀H₁₈N₂, (e) o-C₄₀H₁₈BN, (f) m-C₄₀H₁₈BN, (g) p-C₄₀H₁₈BN, (h) C₃₈H₁₈B₂N₂, (i) C₃₆H₁₈B₃N₃, (j) C₂₈H₁₈Si₁₄, (k) C₂₁H₁₈Si₂₁, and (l) B₂₁H₁₈N₂₁. The bond distances are given in Å. The color code is the same as in Fig. 2. In addition, Mg is denoted by the cyan color.

Table 5 E _ads-2, ΔV_MESP-2, E_HOMOE_LUMO, E_g-3 and ΔE_g-2 values of Mg adsorbed HBCs, along with ΔE_cell and V_cell^a

Nanoflake	E ads-2	G ads-2	ΔVMESP-2	E HOMO	E LUMO	E g-3	ΔEg-2	ΔEcell	V cell
a The values of Eads-2, Gads-2, ΔVMESP-2, and ΔEcell in kcal mol^−1; EHOMO, ELUMO, and Eg-3 in eV; ΔEg-2 in %; and Vcell in V.
C42H18	−3.17	−0.65	−12.38	−5.57	−1.08	4.49	−16.73	−174.91	3.79
o-C40H18N2	−3.37	2.21	−12.13	−4.95	−1.18	3.77	−0.29	−217.08	4.71
m-C40H18N2	−3.50	2.56	−18.73	−4.10	−1.62	2.48	0.66	−243.95	5.29
p-C40H18N2	−3.34	2.94	−11.96	−4.83	−1.03	3.80	0.07	−217.27	4.71
o-C40H18BN	−3.20	3.03	−14.90	−5.45	−1.31	4.14	−15.01	−183.95	3.99
m-C40H18BN	−3.61	2.58	−17.56	−5.30	−1.50	3.80	−15.38	−193.36	4.19
p-C40H18BN	−3.48	2.93	−17.12	−5.33	−1.09	4.24	−21.27	−188.60	4.09
C38H18B2N2	−4.73	0.07	−9.53	−5.54	−1.80	3.74	0.81	−186.83	4.05
C36H18B3N3	−2.57	−2.06	−7.58	−5.74	−0.71	5.03	−16.82	−171.62	3.72
C28H18Si14	−5.11	1.81	−10.95	−5.00	−1.76	3.24	−18.98	−226.58	4.91
C21H18Si21	−3.58	1.95	−3.77	−5.80	−1.15	4.65	−12.27	−225.46	4.89
B21H18N21	−2.14	3.89	−7.07	−5.76	0.12	5.88	−34.65	−170.21	3.69

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Table 5 also lists the E_HOMO, E_LUMO, and E_g-3 values of the Mg-adsorbed nanoflakes. Here the E_HOMO, E_LUMO, and E_g-3 values are in the ranges of −5.80 (Mg/C₂₁H₁₈Si₂₁ system) to −4.10 eV (Mg/m-C₄₀H₁₈N₂ system), −1.80 (Mg/C₃₈H₁₈B₂N₂ system) to 0.12 eV (Mg/B₂₁H₁₈N₂₁ system), and 2.48 (Mg/m-C₄₀H₁₈N₂ system) to 5.88 eV (Mg/B₂₁H₁₈N₂₁ system), respectively. The E_HOMO, E_LUMO, and E_g-3 values of the Mg/HBC system are −5.57, −1.08, and 4.49 eV, respectively. Overall, the E_HUMO, E_LUMO and E_g values of all the nanoflakes are not much influenced by the presence of Mg. The HOMO–LUMO gap decreased by 16.73% due to Mg adsorption on HBC (see ΔE_g-2 values in Table 5). The maximum decrease in the HOMO–LUMO gap is obtained for Mg adsorption on B₂₁H₁₈N₂₁ (34.65%).

3.2.3. Cell voltage. The ΔE_cell and V_cell values of MIBs based on the pristine and doped HBC molecules are provided in Table 5. Here the ΔE_cell and V_cell values were in the ranges of −243.95 (m-C₄₀H₁₈N₂) to −170.21 kcal mol⁻¹ (B₂₁H₁₈N₂₁) and 3.69 (B₂₁H₁₈N₂₁) to 5.29 V (m-C₄₀H₁₈N₂), respectively. As previously noted, a nanoflake with a strong interaction with Mg²⁺ and a weak interaction with Mg might be regarded as a good candidate for the anode material in metal ion batteries. For instance, in the case of m-C₄₀H₁₈N₂, a high V_cell value of 5.29 V was obtained because of a high E_ads-1 value of −247.44 kcal mol⁻¹ (see Table 4) and a low E_ads-2 value of −3.50 kcal mol⁻¹ (see Table 5). The ΔE_cell and V_cell values of HBC were −174.91 kcal mol⁻¹ and 3.79 V, respectively. In the case of N-doped HBC molecules, the V_cell values followed the order o-C₄₀H₁₈N₂ < p-C₄₀H₁₈N₂ < m-C₄₀H₁₈N₂. In the case of BN-doped HBC molecules, the V_cell values followed the order B₂₁H₁₈N₂₁ < C₃₆H₁₈B₃N₃ < o-C₄₀H₁₈BN < C₃₈H₁₈B₂N₂ < p-C₄₀H₁₈BN < m-C₄₀H₁₈BN. The V_cell value of C₂₁H₁₈Si₂₁ (4.89 V) was slightly lower than that of C₂₈H₁₈Si₁₄ (4.91 V). When considering all the nanoflakes, unlike E_ads-2, E_ads-1 shows large variations (see Tables 4 and 5). Thus, here, E_ads-1 can have a significant effect on the variation of V_cell. A strong linear relationship between E_ads-1 and V_cell further supports the significant effect of E_ads-1 on the variation of V_cell (see Fig. S3b, ESI†).

The changes in E_g could influence the electrical conductivity (σ) of the material. The relationship between σ and E_g is given as:⁴²

σ ∝ exp(−E_g/2kT)

where k is the Boltzmann constant and T is the temperature. Our results show that the E_g-1 values of the doped HBC molecules are lower than those of the pristine HBC. A smaller E_g-1 value indicates a higher electronic conductivity. Furthermore, the E_g values of the cation/metal-adsorbed nanoflakes were usually lower than those of the cation/metal-free nanoflakes.

The MESP is a real physical property which can be determined using X-ray diffraction techniques or computational methods. The MESP analyses showed that the replacement of the C atoms of HBC by N/BN/Si units provides a more electron-rich system than the parent HBC molecule. Importantly, we observed stronger interactions of Li⁺ and Mg²⁺ with the nanoflakes as the MESP minimum values of the nanoflakes became more negative. We observed weaker interactions of Li⁺ and Mg²⁺ with the nanoflakes as the MESP minimum values of the nanoflakes become less negative. The adsorption energy of Li has a significant effect on the variation of V_cell of LIBs, while the adsorption energy of Mg²⁺ has a significant effect on the variation of V_cell of MIBs. Furthermore, the storage capacity (C = (n × z × F × 10³)/M, where n is the maximum number of adsorbed metal atoms and M is the molecular mass of the electrode) is an important factor for the performance of metal-ion batteries.²³ Such nanoflakes are promising anode materials for high-capacity metal-ion batteries. For example, the lithium storage capacity of coronene was 536.2 mA h g⁻¹ and the magnesium storage capacity of HBC was 923.1 mA h g⁻¹.^23,27 For a comparison, the lithium storage capacity of graphite is 372 mA h g⁻¹, that of Sc₂C MXene is 462 mA h g⁻¹, that of graphene-like C₂N is 671.7 mA h g⁻¹, and that of pentagraphyne is 687 mA h g⁻¹.²³ This work could provide insights into the design and exploration of anode materials suitable for metal ion batteries.

The doping process and/or the adsorption process could affect the planar structure of the HBC molecule. The formation of non-planar structures is more evident in o-C₄₀H₁₈N₂, m-C₄₀H₁₈N₂, and p-C₄₀H₁₈N₂ (see Fig. 2) and Mg²⁺-adsorbed nanoflakes (see Fig. 7). The diffusion of Li⁺/Li/Mg²⁺/Mg on the nanoflake surface could be an important factor for battery applications.⁴³ For example, the lower diffusion barrier of Li⁺ accelerates the charging and discharging process of the battery.⁴³ We plan to study the diffusion processes in a future publication.

4. Conclusions

DFT studies were carried out to understand the adsorption process of Li⁺, Li, Mg²⁺, and Mg on twelve adsorbents (pristine and N/BN/Si-doped HBC molecules C₄₂H₁₈, o-C₄₀H₁₈N₂, m-C₄₀H₁₈N₂, p-C₄₀H₁₈N₂, o-C₄₀H₁₈BN, m-C₄₀H₁₈BN, p-C₄₀H₁₈BN, C₃₈H₁₈B₂N₂, C₃₆H₁₈B₃N₃, C₂₈H₁₈Si₁₄, C₂₁H₁₈Si₂₁, and B₂₁H₁₈N₂₁). The XY (X = C, B; Y = C, N, Si) bond lengths in the pristine and doped HBC molecules span from 1.36 to 1.83 Å. In all cases, the carbon–silicon bond lengths (>1.76 Å) are significantly longer than the carbon–carbon bond lengths. The MESP analyses show that the replacement of C atoms of HBC by N/BN/Si units can provide a more electron-rich system than the parent HBC molecule.

Li⁺ exhibits a relatively strong adsorption on pristine and doped HBC molecules. The adsorption distances of Li⁺ on these nanoflakes span from 2.20 (m-C₄₀H₁₈N₂) to 2.41 Å (C₂₁H₁₈Si₂₁). Here the E_ads-1 values were in the range of −67.34 (Li⁺/C₂₈H₁₈Si₁₄ system) to −47.65 kcal mol⁻¹ (Li⁺/B₂₁H₁₈N₂₁ system). For the Li/nanoflake system, the E_ads-2 values were in the range of −33.94 (Li/C₃₈H₁₈B₂N₂ system) to −3.93 kcal mol⁻¹ (Li/B₂₁H₁₈N₂₁ system). Mg²⁺ also exhibits a relatively strong adsorption on the pristine and doped HBC molecules. Here the E_ads-1 values were in the range of −247.44 (Mg²⁺/m-C₄₀H₁₈N₂ system) to −172.35 kcal mol⁻¹ (Mg²⁺/B₂₁H₁₈N₂₁ system). Our results suggest the weaker interactions of Li⁺ and Mg²⁺ with the nanoflakes as the MESP V_min values of the nanoflakes become less negative. In all studied systems, we found electron donation from the nanoflakes to Li⁺ and Mg²⁺. For the Mg/nanoflake system, the E_ads-2 values were in the range of −5.11 (Mg/C₂₈H₁₈Si₁₄ system) to −2.14 kcal mol⁻¹ (Mg/B₂₁H₁₈N₂₁ system). The HOMO–LUMO gap of the cation/metal-adsorbed nanoflakes was usually lower than that of the cation/metal-free nanoflakes.

A nanoflake with a strong interaction with Li⁺/Mg²⁺ and a weak interaction with Li/Mg might be regarded as a good candidate for the anode material in metal ion batteries. Among the studied anode materials for LIBs, the highest V_cell value of 1.90 V was obtained for B₂₁H₁₈N₂₁ because of the high E_ads-1 value of −47.65 kcal mol⁻¹ and the low E_ads-2 value of −3.93 kcal mol⁻¹. Among the studied anode materials for MIBs, the highest V_cell value of 5.29 V was obtained for m-C₄₀H₁₈N₂ because of the high E_ads-1 value of −247.44 kcal mol⁻¹ and the low E_ads-2 value of −3.50 kcal mol⁻¹. For LIBs, E_ads-2 has a significant effect on the variation of V_cell, while for MIBs, E_ads-1 has a significant effect on the variation of V_cell.

Data availability

The data that support the findings of this study are available upon request from the corresponding author.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. ORFS-2022-CRG11-5028. R. G. S. N. and A. K. N. N. would like to thank KAUST for providing computational resources of the Shaheen II supercomputer.

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Footnote

† Electronic supplementary information (ESI) available: Additional details of DFT analysis. See DOI: https://doi.org/10.1039/d4cp04101a

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