Density functional theory study of doped coronene and circumcoronene as anode materials in lithium-ion batteries

Abstract

Density functional theory calculations are carried out to investigate the adsorption properties of Li⁺ and Li on twenty-four adsorbents obtained by replacement of C atoms of coronene (C₂₄H₁₂) and circumcoronene (C₅₄H₁₈) by Si/N/BN/AlN units. The molecular electrostatic potential (MESP) analysis show that such replacements lead to an increase of the electron-rich environments in the molecules. Li⁺ is relatively strongly adsorbed on all adsorbents. The adsorption energy of Li⁺ (E_ads-1) on all adsorbents is in the range of − 42.47 (B₁₂H₁₂N₁₂) to − 66.26 kcal/mol (m-C₂₂H₁₂BN). Our results indicate a stronger interaction between Li⁺ and the nanoflakes as the deepest MESP minimum of the nanoflakes becomes more negative. A stronger interaction between Li⁺ and the nanoflakes pushes more electron density toward Li⁺. Li is weakly adsorbed on all adsorbents when compared to Li⁺. The adsorption energy of Li (E_ads-2) on all adsorbents is in the range of − 3.07 (B₂₇H₁₈N₂₇) to − 47.79 kcal/mol (C₅₃H₁₈Si). Assuming the nanoflakes to be an anode for the lithium-ion batteries, the cell voltage (V_cell) is predicted to be relatively high (> 1.54 V) for C₂₄H₁₂, C₁₂H₁₂Si₁₂, B₁₂H₁₂N₁₂, C₂₇H₁₈Si₂₇, and B₂₇H₁₈N₂₇. The E_ads-1 data show only a small variation compared to E_ads-2, and therefore, E_ads-2 has a strong effect on the changes in V_cell.

Introduction

There is an increasing demand for rechargeable energy storage devices such as lithium ion batteries (LIBs) for their application in portable electronic devices and electric vehicles^1,2,3. Since LIBs were first commercialized by Sony Corporation in the 1990s, they have occupied a dominant position in the portable electronics and automobile markets because of their high energy density and long service life^1,2,3. Carbon materials such as graphene, carbon nanotube, carbon nanofiber, and polycyclic aromatic hydrocarbon (PAH) are widely used to construct anode materials in LIBs^4,5,6,7,8,9. For example, graphene, a two-dimensional sheet of sp²-hybridized carbon atoms, has been proved to be a good electrode material for LIBs owing to its high surface area, high electrical conductivity, and superior mechanical flexibility. Doped carbonaceous materials were also used to construct anode materials in LIBs^{10,11,12,13,14}.

PAHs are composed of two or more fused benzene rings and have many delocalized π electrons. Researchers have designed and synthesized various heteroatom-embedded PAHs to modify the π-electron properties^15,16,17. Planar PAHs such as coronene (C₂₄H₁₂) and circumcoronene (C₅₄H₁₈) consist of seven and nineteen fused benzene rings, respectively. They can be considered as small portions of a graphene sheet with hydrogenated edges. There have been DFT studies on the adsorption properties of coronene, circumcoronene and their doped analogues^{18,19,20,21,22,23,24,25,26,27,28,29,30}. The presence of silicon atoms in coronene favored its interaction with thiophene and similar compounds¹⁸. The hydrophobic ionic liquid adsorption on coronene and circumcoronene was stronger than that for the hydrophilic ionic liquid¹⁹. The free energy of adsorption of ionic liquids on BN-circumcoronene (B₂₇H₁₈N₂₇) was negative, and thus, the adsorption occurred spontaneously²⁰. The adsorption of organic molecules on Cu-doped coronene and circumcoronene was exothermic²¹. The relative positions of nitrogen and boron substitutions in the coronene gave different stabilities and different responses to the CO adsorption²². The interaction energies usually increased with the cluster size of the palladium atoms adsorbed on the coronene²³. The doping of coronene with nitrogen atoms resulted in superior performance for CO₂ and H₂ adsorption²⁴. The DFT studies on the adsorption of Li⁺ and Li on coronene, circumcoronene and BN-circumcoronene have recently attracted increasing interest. It was found that Li⁺/Li binds to the peripheral rings of coronene and circumcoronene^25,26,27. Based on the cell voltage data, coronene was suggested as a good anode material for LIBs²⁷. The adsorption energy of Li atom on B₂₇H₁₈N₂₇ was found to be lower than that of circumcoronene²⁸. However, the adsorption of Li⁺ and Li on adsorbents such as BN doped coronene is yet to be studied.

In this work, DFT calculations are performed to investigate the adsorption properties of Li⁺ and Li on twenty-four adsorbents obtained by replacement of C atoms of C₂₄H₁₂ and C₅₄H₁₈ by Si/N/BN/AlN units. The most-negative valued molecular electrostatic potential (MESP) point of molecules (V_min) indicates the electron-rich regions such as π-region and lone-pair region^31,32. A key observation is that the adsorption energies of Li⁺ on the nanoflakes are linearly correlated with the MESP V_min values of the nanoflakes. The V_cell is predicted to be relatively high (> 1.54 V) for C₂₄H₁₂, C₁₂H₁₂Si₁₂, B₁₂H₁₂N₁₂, C₂₇H₁₈Si₂₇, and B₂₇H₁₈N₂₇ The insights obtained from this work may be useful to design and explore better anode materials for LIBs.

Computational details

All the DFT calculations were performed using the Gaussian 16 code³³. In this work we consider a total of twenty-four adsorbents (C₂₄H₁₂ and its analogues C₂₃H₁₂Si, o-C₂₂H₁₂N₂, m-C₂₂H₁₂N₂, m-C₂₂H₁₂BN, p-C₂₂H₁₂BN, C₂₀H₁₂B₂N₂, C₁₈H₁₂B₃N₃, C₁₆H₁₂Si₈, C₁₂H₁₂Si₁₂, B₁₂H₁₂N₁₂, B₁₁H₁₂N₁₂Al; C₅₄H₁₈ and its analogues C₅₃H₁₈Si, o-C₅₂H₁₈N₂, m-C₅₂H₁₈N₂, m-C₅₂H₁₈BN, p-C₅₂H₁₈BN, C₅₀H₁₈B₂N₂, C₄₈H₁₈B₃N₃, C₃₆H₁₈Si₁₈, C₂₇H₁₈Si₂₇, B₂₇H₁₈N₂₇, B₂₆H₁₈N₂₇Al) and two adsorbates (Li⁺ and Li). The other adsorbents are designed by the replacements of C atoms in coronene and circumcoronene by Si/N/BN/AlN units. Here we also employed structural isomers of, for example, C₂₂H₁₂N₂ (the two N atoms occupy adjacent positions in o-C₂₂H₁₂N₂). Furthermore, C₁₆H₁₂Si₈, C₁₂H₁₂Si₁₂, and B₁₂H₁₂N₁₂ can be considered as small portions of SiC₂, SiC, and BN graphene-like sheets, respectively. The same applies to C₃₆H₁₈Si₁₈, C₂₇H₁₈Si₂₇, and B₂₇H₁₈N₂₇. All structures were optimized at the M062X/6-31G(d,p) level³⁴ and confirmed to be energy minima by frequency analysis. The MESP function V(r)^35,36,37 is computed at the M062X/6-31G(d,p) level of theory using the below equation:

$$V\left(\textbf{r}\right)=\sum_{A=1}^{N}\frac{{Z}_{A}}{|{\textbf{r}-\textbf{R}}_{A}|}-\int \frac{\rho ({\textbf{r}}^{{{\prime}}})}{|{\textbf{r}-\textbf{r}}^{{{\prime}}}|}{\text{d}}^{3}{\textbf{r}}^{{{\prime}}}$$

(1)

where Z_A is the charge on nucleus A located at R_A and ρ(r) is the electronic charge density. The first term on the right-hand side of Eq. (1) stands for the nuclear contribution and the second term stands for the electronic contribution. V(r) is positive if the nuclear effects dominate, while it is negative if the electronic effects dominate.

The adsorption energy (E_ads) is evaluated according to the formula:

$$E_{{{\text{ads}}}} = E_{{{\text{adsorbate }}/{\text{nanoflake}}}} {-} \, \left( {E_{{{\text{nanoflake}}}} + E_{{{\text{adsorbate}}}} } \right) \, + {\text{ E}}_{{{\text{BSSE}}}}$$

(2)

where E_{adsorbate/nanoflake}, E_nanoflake, and E_adsorbate represent the energy of adsorbed system, adsorbent (e.g., coronene), and adsorbate (Li⁺ or Li), respectively. E_BSSE is the basis set superposition error energy determined by the counterpoise approach³⁸. The E_ads of Li⁺ and Li on the nanoflakes is represented as E_ads-1 and E_ads-2, respectively. Our calculated E_ads-1 and E_ads-1 values are consistent with previous results^26,27,28 (Fig. 1).

Figure 1

Comparison of our results for adsorption energies with literature values^26,27,28.

The highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) energy gap (E_g) is calculated as follows:

$${\text{E}}_{{\text{g}}} = {\text{ E}}_{{{\text{LUMO}}}} - {\text{E}}_{{{\text{HOMO}}}}$$

(3)

where E_HOMO and E_LUMO represent the energy of HOMO and LUMO, respectively. The E_g of the pristine nanoflakes, Li⁺-adsorbed nanoflakes, and Li-adsorbed nanoflakes is represented as E_g-1, E_g-2, and E_g-3, respectively.

The percentage change in the HOMO–LUMO energy gap is estimated as:

$$\Delta {\text{E}}_{{{\text{g}} - {1}}} = \, [({\text{E}}_{{{\text{g}} - {2}}} - {\text{E}}_{{{\text{g}} - {1}}} )/{\text{E}}_{{{\text{g}} - {1}}} ] \times {1}00$$

(4)

$$\Delta {\text{E}}_{{{\text{g}} - {2}}} = [({\text{E}}_{{{\text{g}} - {3}}} - {\text{E}}_{{{\text{g}} - {1}}} )/{\text{E}}_{{{\text{g}} - {1}}} ] \times {1}00$$

(5)

Assuming the nanoflake to be an anode for the LIBs, we can write the reaction in the anode and cathode as follows:

$${\text{Anode}}{:}\;\;{\text{ Li}}/{\text{nanoflake}} \leftrightarrow {\text{ Li}}^{ + } /{\text{nanoflake }} + {\text{e}}^{ - }$$

(6)

$${\text{Cathode}}{:}\;\;{\text{ Li}}^{ + } + {\text{ e}}^{ - } \leftrightarrow {\text{ Li}}$$

(7)

Thus, the total cell reaction can be written as follows:

$${\text{Li}}/{\text{nanoflake}} + {\text{ Li}}^{ + } \leftrightarrow {\text{ Li}}^{ + } /{\text{nanoflake }} + {\text{ Li }} + \Delta {\text{G}}_{{{\text{cell}} }}$$

(8)

Here ∆G_cell is the Gibbs free energy change for the total cell reaction, which can be expressed as

$$\Delta {\text{G}}_{{{\text{cell}}}} = \, \Delta {\text{E}}_{{{\text{cell}}}} + {\text{P}}\Delta {\text{V}}{-}{\text{T}}\Delta {\text{S}}$$

(9)

where

$$\Delta {\text{E}}_{{{\text{cell}}}} = {\text{ E}}_{{\text{ads - 1}}} - {\text{ E}}_{{\text{ads - 2}}}$$

(10)

The cell voltage can be calculated using the Nernst equation:

$${\text{V}}_{{{\text{cell}}}} = \, - \Delta {\text{G}}_{{{\text{cell}}}} /{\text{zF}}$$

(11)

where F and z are the Faraday constant (96,485.3 C/mol) and the charge of Li⁺, respectively. It may be assumed that ΔG_cell ≈ ΔE_cell, since the contribution of entropy and volume effects to V_cell is expected to be very small³⁹.

Results and discussion

Coronene and its analogues as anode materials in lithium-ion batteries

Structural properties of coronene and its analogues

The optimized structures of coronene and its analogues are given in Fig. 2, indicating all the important bond length values. The XY (X = C, Si, N, B, Al; Y = C, Si, N, B, Al) bond lengths of coronene and its analogues are in the range of about 1.35 to 1.81 Å. In comparison to the CC bond length in benzene (1.395 Å)⁴⁰, we see that the CC bond lengths in coronene are in the range of about 1.37 to 1.43 Å. The six outermost CC bonds in coronene are noticeably shorter (1.37 Å) than the other ones. Their bond lengths are close to the CC bond length in ethylene (1.330 Å)⁴¹, indicating the significant double bond character of these bonds. Here the CSi (> 1.73 Å) and NAl (> 1.74 Å) bond lengths are found to be significantly longer than all the CC bond lengths in coronene.

Figure 2

Optimized structures of (a) C₂₄H₁₂, (b) C₂₃H₁₂Si, (c) o-C₂₂H₁₂N₂, (d) m-C₂₂H₁₂N₂, (e) m-C₂₂H₁₂BN, (f) p-C₂₂H₁₂BN, (g) C₂₀H₁₂B₂N₂, (h) C₁₈H₁₂B₃N₃, (i) C₁₆H₁₂Si₈, (j) C₁₂H₁₂Si₁₂, (k) B₁₂H₁₂N₁₂, (l) B₁₁H₁₂N₁₂Al. The bond distances are given in Å. Color code: gray-C, green-B, blue-N, purple-Al, yellow-Si.

The E_HOMO, E_LUMO, and E_g-1 values of coronene and its analogues are given in Table 1. The molecular orbital diagrams for some representative nanoflakes are shown in Fig. S1. Our results show that the E_HOMO, E_LUMO, and E_g-1 values of coronene and its analogues are in the ranges of − 8.27 (B₁₂H₁₂N₁₂) to − 3.82 eV (m-C₂₂H₁₂N₂), − 1.43 (p-C₂₂H₁₂BN) to 1.24 eV (B₁₂H₁₂N₁₂), and 2.95 (m-C₂₂H₁₂N₂) to 9.51 eV (B₁₂H₁₂N₁₂), respectively. The E_HOMO, E_LUMO, and E_g-1 values of coronene are − 6.62, − 0.72, and 5.90 eV, respectively. In general, the E_HOMO (E_LUMO) of the doped coronene is higher (lower) than that of the pristine coronene. Also, the E_g-1 of the doped coronene is generally lower than that of the pristine coronene. The opposite trends are observed for the B₁₂H₁₂N₁₂ and B₁₁H₁₂N₁₂Al. Typically, a smaller HOMO–LUMO energy gap indicates a better electronic conductivity. These E_HOMO, E_LUMO, and E_g-1 values reported here are consistent with previous theoretical results²⁹.

Table 1 V_min, E_HOMO, E_LUMO and E_g-1 for doped coronenes^a.

MESP of coronene and its analogues

The MESP features of coronene and its analogues are given in Fig. 3. The MESP analysis suggest that electron-rich regions (e.g., green regions) are present on coronene due to cyclic π-electron delocalization. We see that the replacements of C atoms of coronene by Si/N/BN/AlN units lead to an overall increase of the electron-rich environments (e.g., blue regions) in the molecules. The MESP V_min values of coronene and its analogues (represented as V_min) are provided in Table 1. The locations of V_min in the MESP plots of coronene and its analogues are provided in Fig. S2, electronic Supporting Information (ESI). The MESP V_min points are located near the peripheral rings of coronene. This shows that the peripheral rings of coronene are electron richer than its central ring. This is because the peripheral rings of coronene contain C–H bonds also and the sp² carbon is more electronegative than H. For other adsorbents also, the MESP V_min points are located near the peripheral rings. We find that the MESP V_min values of coronene and its analogues are in the range of − 15.44 (C₁₈H₁₂B₃N₃) to − 31.38 kcal/mol (m-C₂₂H₁₂BN). The MESP V_min value of coronene is − 16.06 kcal/mol. The MESP V_min of the doped coronene is generally higher than that of the pristine coronene. However, the MESP V_min of C₁₈H₁₂B₃N₃ is slightly lower than that of coronene. For the N-doped coronenes, the MESP V_min value of o-C₂₂H₁₂N₂ (− 24.22 kcal/mol) is higher than that of m-C₂₂H₁₂N₂ (− 21.34 kcal/mol). The MESP V_min values of Si-doped coronenes increase in the order C₂₃H₁₂Si < C₁₂H₁₂Si₁₂ < C₁₆H₁₂Si₈. Furthermore, the MESP V_min values of BN/AlN-doped coronenes increase in the order C₁₈H₁₂B₃N₃ < B₁₂H₁₂N₁₂ < B₁₁H₁₂N₁₂Al < C₂₀H₁₂B₂N₂ < p-C₂₂H₁₂BN < m-C₂₂H₁₂BN.

Figure 3

MESP mapped on 0.01 a.u. electron density isosurface of (a) C₂₄H₁₂, (b) C₂₃H₁₂Si, (c) o-C₂₂H₁₂N₂, (d) m-C₂₂H₁₂N₂, (e) m-C₂₂H₁₂BN, (f) p-C₂₂H₁₂BN, (g) C₂₀H₁₂B₂N₂, (h) C₁₈H₁₂B₃N₃, (i) C₁₆H₁₂Si₈, (j) C₁₂H₁₂Si₁₂, (k) B₁₂H₁₂N₁₂, (l) B₁₁H₁₂N₁₂Al. 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.

Li⁺ adsorption on the doped coronenes

The optimized geometries for the adsorption of Li⁺ on coronene and its analogues are provided in Fig. 4. Our results show that Li⁺ binds to the peripheral rings of coronene. This is in line with the fact the peripheral rings of coronene are electron richer than its central ring (see above). The adsorption process here involves the cation–π interaction^27,42. This interaction is basically of electrostatic origin because a positively charged cation interacts with the negatively charged electron cloud of π-systems. For other adsorbents also, Li⁺ binds to the peripheral rings. It can be seen that Li⁺ is relatively strongly adsorbed on coronene and its analogues. For example, the adsorption distance of Li⁺ on these adsorbents is in the range of 2.15 (C₁₆H₁₂Si₈) to 2.34 Å (C₁₂H₁₂Si₁₂). This observation is further supported by the adsorption energy of Li⁺ on coronene and its analogues (Table 2). The E_ads-1 values of Li⁺ on coronene and its analogues are in the range of − 42.47 (B₁₂H₁₂N₁₂) to − 66.26 kcal/mol (m-C₂₂H₁₂BN). These E_ads-1 values are negative, which implies that all of the adsorption processes were exothermic in nature. The more negative the E_ads-1 value, the stronger the adsorption is. The E_ads-1 value of Li⁺ on coronene is − 47.92 kcal/mol. For the N-doped coronenes, the E_ads-1 value of o-C₂₂H₁₂N₂ (− 57.33 kcal/mol) is higher than that of m-C₂₂H₁₂N₂ (− 54.48 kcal/mol). The E_ads-1 values of Si-doped coronenes increase in the order C₁₂H₁₂Si₁₂ < C₂₃H₁₂Si < C₁₆H₁₂Si₈. Furthermore, the E_ads-1 values of BN/AlN-doped coronenes increase in the order B₁₂H₁₂N₁₂ < C₁₈H₁₂B₃N₃ < B₁₁H₁₂N₁₂Al < C₂₀H₁₂B₂N₂ < p-C₂₂H₁₂BN < m-C₂₂H₁₂BN. A key observation is that these adsorption energies are well correlated with the MESP V_min values of coronene and its analogues, with a correlation coefficient of 0.908 (Fig. 5a). These results indicate a stronger interaction between Li⁺ and the nanoflakes as the MESP V_min of the nanoflakes becomes more negative.

Figure 4

Optimized structures of Li⁺ adsorbed on (a) C₂₄H₁₂, (b) C₂₃H₁₂Si, (c) o-C₂₂H₁₂N₂, (d) m-C₂₂H₁₂N₂, (e) m-C₂₂H₁₂BN, (f) p-C₂₂H₁₂BN, (g) C₂₀H₁₂B₂N₂, (h) C₁₈H₁₂B₃N₃, (i) C₁₆H₁₂Si₈, (j) C₁₂H₁₂Si₁₂, (k) B₁₂H₁₂N₁₂, (l) B₁₁H₁₂N₁₂Al. The bond distances are given in Å. The color code is the same as in Fig. 2. In addition, Li is denoted by orange color.

Table 2 E_ads-1, ΔV_MESP-1, E_HOMO E_LUMO, E_g-2 and ∆E_g-1 values for Li⁺ adsorbed coronenes^a.

Figure 5

Correlation between (a) V_min and E_ads-1 and (b) ∆V_MESP-1 and E_ads-1 for Li⁺-adsorbed coronenes.

The electron donation from coronene and its analogues to Li⁺ could be checked by assessing the changes in the MESP at the nucleus of Li⁺ upon adsorption. Hence, the ΔV_MESP-1 was obtained by taking the difference between the MESP at the nucleus of Li⁺ in the Li⁺-adsorbed nanoflake and the MESP at the free Li⁺ (− 5.36 au). Here the negative values of ΔV_MESP-1 (Table 2) indicate the electron donation from coronene and its analogues to Li⁺. These ΔV_MESP-1 values are in the range of − 105.91 (B₁₂H₁₂N₁₂) to − 138.49 kcal/mol (m-C₂₂H₁₂N₂). The ΔV_MESP-1 value of coronene is − 107.01 kcal/mol. The ΔV_MESP-1 of the doped coronenes is typically higher than that of the pristine coronene. However, the ΔV_MESP-1 of B₁₂H₁₂N₁₂ is lower than that of coronene. The adsorption energies of Li⁺ on coronene and its analogues are correlated with these ΔV_MESP-1 values, with a correlation coefficient of 0.792 (Fig. 5b). These results indicate that a stronger interaction between Li⁺ and the nanoflakes pushes more electron density toward Li⁺.

The E_HOMO, E_LUMO, and E_g-2 values of Li⁺-adsorbed coronene and its analogues are given in Table 2. The E_HOMO, E_LUMO, and E_g-2 values of Li⁺-adsorbed coronene and its analogues are in the ranges of − 11.37 (B₁₂H₁₂N₁₂) to − 8.18 eV (m-C₂₂H₁₂N₂), − 5.06 (C₂₃H₁₂Si) to − 4.20 eV (C₁₂H₁₂Si₁₂), and 3.73 (m-C₂₂H₁₂N₂) to 7.04 eV (B₁₂H₁₂N₁₂), respectively. Here, E_HOMO of the Li⁺-adsorbed nanoflakes is lower than that of the pristine nanoflakes for all cases (see Table 1). A similar result is obtained for E_LUMO. The results here show that E_g-2 is typically lower than E_g-1. For example, the E_HOMO, E_LUMO, and E_g-2 values of Li⁺ adsorbed coronene are − 10.05, − 4.38, and 5.67 eV, respectively. The decrease in the HOMO–LUMO energy gap for the adsorption of Li⁺ on coronene is 3.87% (see ΔE_g-1 values in Table 2). A maximum decrease in the HOMO–LUMO energy gap of 26.0% was observed for the adsorption of Li⁺ on B₁₂H₁₂N₁₂. However, E_g-2 is found to be higher than E_g-1 for the adsorption of Li⁺ on o-C₂₂H₁₂N₂, m-C₂₂H₁₂N₂, m-C₂₂H₁₂BN, p-C₂₂H₁₂BN, and C₁₆H₁₂Si₈. A maximum increase in the HOMO–LUMO energy gap of 26.3% was observed for the adsorption of Li⁺ on m-C₂₂H₁₂N₂.

Li adsorption on the doped coronenes

The optimized geometries for the adsorption of Li on coronene and its analogues are provided in Fig. 6. Our results show that Li mostly binds to the peripheral rings of coronene and its analogues, similar to the results obtained for Li⁺. The adsorption distance of Li on these adsorbents is in the range of 2.01 (o-C₂₂H₁₂N₂) to 2.44 Å (B₁₂H₁₂N₁₂). For these adsorbents, the adsorption distance of Li is generally smaller than that of Li⁺ (see Fig. 4). For example, the adsorption distance of Li and Li⁺ on coronene is 2.15 and 2.28 Å, respectively. However, Li is weakly adsorbed on coronene and its analogues when compared to Li⁺. This observation is supported by the adsorption energy of Li on coronene and its analogues (Table 3). The E_ads-2 values of Li on coronene and its analogues are in the range of − 3.14 (B₁₂H₁₂N₁₂) to − 37.63 kcal/mol (p-C₂₂H₁₂BN). The E_ads-2 value of Li on coronene is − 11.32 kcal/mol. For the N-doped coronenes, the E_ads-2 value of o-C₂₂H₁₂N₂ (− 29.75 kcal/mol) is higher than that of m-C₂₂H₁₂N₂ (− 23.69 kcal/mol). The E_ads-2 values of Si-doped coronenes increase in the order C₁₂H₁₂Si₁₂ < C₁₆H₁₂Si₈ < C₂₃H₁₂Si. Furthermore, the E_ads-2 values of BN/AlN-doped coronenes increase in the order B₁₂H₁₂N₁₂ < C₁₈H₁₂B₃N₃ < B₁₁H₁₂N₁₂Al < C₂₀H₁₂B₂N₂ < m-C₂₂H₁₂BN < p-C₂₂H₁₂BN. These adsorption energies are not well correlated with the MESP V_min values of coronene and its analogues (Fig. S3). The ΔV_MESP-2 was obtained by taking the difference between the MESP at the nucleus of Li in the Li-adsorbed nanoflake and the MESP at the free Li (− 5.72 au). In general, the values of ΔV_MESP-2 are positive for the adsorption of Li on coronene and its analogues (Table 3). The positive value of ΔV_MESP-2 suggests the electron density transfer from Li to nanoflakes. However, the values of ΔV_MESP-2 are negative for the adsorption of Li on o-C₂₂H₁₂N₂, m-C₂₂H₁₂N₂, C₁₆H₁₂Si₈, and B₁₂H₁₂N₁₂. Unlike E_ads-1, E_ads-2 does not show a correlation with ΔV_MESP-2 (see Fig. S3).

Figure 6

Optimized structures of Li adsorbed on (a) C₂₄H₁₂, (b) C₂₃H₁₂Si, (c) o-C₂₂H₁₂N₂, (d) m-C₂₂H₁₂N₂, (e) m-C₂₂H₁₂BN, (f) p-C₂₂H₁₂BN, (g) C₂₀H₁₂B₂N₂, (h) C₁₈H₁₂B₃N₃, (i) C₁₆H₁₂Si₈, (j) C₁₂H₁₂Si₁₂, (k) B₁₂H₁₂N₁₂, (l) B₁₁H₁₂N₁₂Al. The bond distances are given in Å. The color code is the same as in Fig. 4.

Table 3 E_ads-2, ΔV_MESP-2, E_HOMO E_LUMO, E_g-3 and ∆E_g-2 values for Li adsorbed coronenes, along with ∆E_cell and V_cell^a.

The E_HOMO, E_LUMO, and E_g-3 values of Li-adsorbed coronene and its analogues are given in Table 3. The E_HOMO, E_LUMO, and E_g-3 values of Li-adsorbed coronene and its analogues are in the ranges of − 5.15 (B₁₁H₁₂N₁₂Al) to − 3.24 eV (B₁₂H₁₂N₁₂), − 0.94 (C₂₄H₁₂) to 0.56 eV (B₁₂H₁₂N₁₂), and 2.37 (C₂₄H₁₂) to 4.69 eV (B₁₁H₁₂N₁₂Al), respectively. For all cases, E_HOMO of the Li-adsorbed nanoflakes is higher than that of the pristine nanoflakes (see Table 1). For example, the E_HOMO value of Li-adsorbed coronene is − 3.30 eV. The E_LUMO of coronene and its analogues is not much affected by the presence of Li. The results here show that E_g-3 is usually lower than E_g-1. The decrease in the HOMO–LUMO energy gap for the adsorption of Li on coronene is 59.9% (see ΔE_g-2 values in Table 3). A maximum decrease in the HOMO–LUMO energy gap of 60.0% was observed for the adsorption of Li on B₁₂H₁₂N₁₂. However, E_g-3 is found to be higher than E_g-1 for the adsorption of Li on m-C₂₂H₁₂N₂ (ΔE_g-2 of 6.3%).

Cell voltage of the doped coronenes

The ΔE_cell and V_cell of LIBs based on coronene and its analogues were calculated using eqs. (10 and 11), respectively, and their values are given in Table 3. Here the ∆E_cell and V_cell values are in the ranges of − 41.62 (C₁₂H₁₂Si₁₂) to − 21.04 kcal/mol (C₂₃H₁₂Si) and 0.91 (C₂₃H₁₂Si) to 1.80 V (C₁₂H₁₂Si₁₂), respectively. The more negative the ∆E_cell value, the higher the V_cell value of the nanoflakes. Therefore, the nanoflakes interacting strongly with Li⁺ and weakly with Li may serve as good candidates for the anode materials in LiBs. For example, the highest V_cell value of 1.80 V is observed for C₁₂H₁₂Si₁₂ due to the high E_ads-1 of − 52.14 kcal/mol (see Table 2) and low E_ads-2 of − 10.51 kcal/mol (see Table 3). The lowest V_cell value of 0.91 V observed for C₂₃H₁₂Si can be attributed to a higher contribution from E_ads-2 (E_ads-1 of − 54.14 kcal/mol and E_ads-2 of − 33.10 kcal/mol). The ∆E_cell and V_cell values of coronene are − 36.60 kcal/mol and 1.59 V, respectively. For the N-doped coronenes, the V_cell value of o-C₂₂H₁₂N₂ (1.20 V) is lower than that of m-C₂₂H₁₂N₂ (1.33 V). The V_cell values of Si-doped coronenes increase in the order C₂₃H₁₂Si < C₁₆H₁₂Si₈ < C₁₂H₁₂Si₁₂. Furthermore, the V_cell values of BN/AlN-doped coronenes increase in the order B₁₁H₁₂N₁₂Al < p-C₂₂H₁₂BN < C₁₈H₁₂B₃N₃ < m-C₂₂H₁₂BN < C₂₀H₁₂B₂N₂ < B₁₂H₁₂N₁₂. It can be observed that the E_ads-1 data exhibit only a small variation compared to E_ads-2, and therefore E_ads-2 has a relatively strong influence on the variation of V_cell. The linear correlation of E_ads-2 with V_cell (R = 0.805) also supports the strong influence of E_ads-2 on V_cell (Fig. S4).

Circumcoronene and its analogues as anode materials in lithium-ion batteries

Structural properties of circumcoronene and its analogues

The optimized structures of circumcoronene and its analogues are given in Fig. 7, indicating all the important bond length values. As in the case of coronene and its analogues, the XY (X = C, Si, N, B, Al; Y = C, Si, N, B, Al) bond lengths of circumcoronene and its analogues are in the range of about 1.35 to 1.81 Å. We see that the CC bond lengths in circumcoronene are in the range of about 1.36 to 1.44 Å, and the six outermost CC bonds are noticeably shorter (1.36 Å) than the other ones. Here, all the CSi (> 1.72 Å) and NAl (≈1.74 Å) bond lengths are found to be significantly longer than all the CC bond lengths.

Figure 7

Optimized structures of (a) C₅₄H₁₈, (b) C₅₃H₁₈Si, (c) o-C₅₂H₁₈N₂, (d) m-C₅₂H₁₈N₂, (e) m-C₅₂H₁₈BN, (f) p-C₅₂H₁₈BN, (g) C₅₀H₁₈B₂N₂, (h) C₄₈H₁₈B₃N₃, (i) C₃₆H₁₈Si₁₈, (j) C₂₇H₁₈Si₂₇, (k) B₂₇H₁₈N₂₇, (l) B₂₆H₁₈N₂₇Al. The bond distances are given in Å. The color code is the same as in Fig. 2.

The E_HOMO, E_LUMO, and E_g-1 values of circumcoronene and its analogues are given in Table 4. Our results show that the E_HOMO, E_LUMO, and E_g-1 values of circumcoronene and its analogues are in the ranges of − 8.05 (B₂₇H₁₈N₂₇) to − 4.03 eV (m-C₅₂H₁₈N₂), − 2.00 (C₅₀H₁₈B₂N₂) to 1.08 eV (B₂₇H₁₈N₂₇), and 2.14 (m-C₅₂H₁₈N₂) to 9.12 eV (B₂₇H₁₈N₂₇), respectively. The E_HOMO, E_LUMO, and E_g-1 values of circumcoronene are − 5.95, − 1.60, and 4.35 eV, respectively. In general, the E_HOMO (E_LUMO) of the doped circumcoronene is higher (lower) than that of the pristine circumcoronene. Also, the E_g-1 of the doped circumcoronene is typically lower than that of the pristine circumcoronene. The opposite trends are observed for p-C₅₂H₁₈BN, C₄₈H₁₈B₃N₃, C₂₇H₁₈Si₂₇, B₁₂H₁₂N₁₂, and B₁₁H₁₂N₁₂Al. These E_HOMO, E_LUMO, and E_g-1 values reported here are consistent with previous theoretical results³⁰.

Table 4 V_min, E_HOMO, E_LUMO and E_g-1 for doped circumcoronenes^a.

MESP of circumcoronene and its analogues

The MESP features of circumcoronene and its analogues are given in Fig. 8. The MESP analysis indicate that as in the case of coronene, electron-rich regions (e.g., green regions) are present on circumcoronene. The replacements of C atoms of circumcoronene by Si/N/BN/AlN units lead to an increase of the electron-rich environments (e.g., blue regions) in the molecules. The MESP V_min values of circumcoronene and its analogues are provided in Table 4. The locations of V_min in the MESP plots of circumcoronene and its analogues are provided in Fig. S5. As in the case of coronene, the MESP V_min points are located near the peripheral rings of circumcoronene. For the doped circumcoronenes, the MESP V_min points are located mainly near the peripheral rings, except for C₅₃H₁₈Si, m-C₅₂H₁₈BN, p-C₅₂H₁₈BN, C₅₀H₁₈B₂N₂, and B₂₆H₁₈N₂₇Al. We find that the MESP V_min values of circumcoronene and its analogues are in the range of − 14.56 (C₅₄H₁₈) to − 33.95 kcal/mol (C₂₇H₁₈Si₂₇). The MESP V_min of the doped circumcoronene is higher than that of the pristine circumcoronene. For the N-doped circumcoronenes, the MESP V_min value of o-C₅₂H₁₈N₂ (− 17.19 kcal/mol) is lower than that of m-C₅₂H₁₈N₂ (-24.03 kcal/mol). The MESP V_min values of Si-doped circumcoronenes increase in the order C₅₃H₁₈Si < C₃₆H₁₈Si₁₈ < C₂₇H₁₈Si₂₇. Furthermore, the MESP V_min values of BN/AlN-doped circumcoronenes increase in the order C₄₈H₁₈B₃N₃ < B₂₇H₁₈N₂₇ < C₅₀H₁₈B₂N₂ < B₂₆H₁₈N₂₇Al < p-C₅₂H₁₈BN < m-C₅₂H₁₈BN.

Figure 8

MESP mapped on 0.01 a.u. electron density isosurface of (a) C₅₄H₁₈, (b) C₅₃H₁₈Si, (c) o-C₅₂H₁₈N₂, (d) m-C₅₂H₁₈N₂, (e) m-C₅₂H₁₈BN, (f) p-C₅₂H₁₈BN, (g) C₅₀H₁₈B₂N₂, (h) C₄₈H₁₈B₃N₃, (i) C₃₆H₁₈Si₁₈, (j) C₂₇H₁₈Si₂₇, (k) B₂₇H₁₈N₂₇, (l) B₂₆H₁₈N₂₇Al. 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.

Li⁺ adsorption on the doped circumcoronenes

The optimized geometries for the adsorption of Li⁺ on circumcoronene and its analogues are provided in Fig. 9. Our results show that as in the case of coronene, Li⁺ binds to the peripheral rings of circumcoronene. For the doped circumcoronenes, Li⁺ binds to the peripheral rings, except for C₅₃H₁₈Si, m-C₅₂H₁₈BN, p-C₅₂H₁₈BN, C₅₀H₁₈B₂N₂, and B₂₆H₁₈N₂₇Al. Our results show that Li⁺ is relatively strongly adsorbed on circumcoronene and its analogues. For example, the adsorption distance of Li⁺ on these adsorbents is in the range of 2.21 (C₃₆H₁₈Si₁₈) to 2.46 Å (C₂₇H₁₈Si₂₇). This observation is further supported by the adsorption energy of Li⁺ on circumcoronene and its analogues (Table 5). The E_ads-1 values of Li⁺ on circumcoronene and its analogues are in the range of − 45.36 (B₂₇H₁₈N₂₇) to − 65.61 kcal/mol (C₃₆H₁₈Si₁₈). The more negative the E_ads-1 value, the stronger the adsorption is. The E_ads-1 value of Li⁺ on circumcoronene is − 51.55 kcal/mol. For the N-doped circumcoronenes, the E_ads-1 value of o-C₅₂H₁₈N₂ (− 55.24 kcal/mol) is higher than that of m-C₅₂H₁₈N₂ (− 63.51 kcal/mol). The E_ads-1 values of Si-doped circumcoronenes increase in the order C₅₃H₁₈Si < C₂₇H₁₈Si₂₇ < C₃₆H₁₈Si₁₈. Furthermore, the E_ads-1 values of BN/AlN-doped circumcoronenes increase in the order B₂₇H₁₈N₂₇ < C₄₈H₁₈B₃N₃ ≈ B₂₆H₁₈N₂₇Al < C₅₀H₁₈B₂N₂ < p-C₅₂H₁₈BN < m-C₅₂H₁₈BN. These adsorption energies are correlated with the MESP V_min values of circumcoronene and its analogues, with a correlation coefficient of 0.726 (Fig. 10a). Note that a better correlation was observed for coronene and its analogues (see Fig. 5a).

Figure 9

Optimized structures of Li⁺ adsorbed on (a) C₅₄H₁₈, (b) C₅₃H₁₈Si, (c) o-C₅₂H₁₈N₂, (d) m-C₅₂H₁₈N₂, (e) m-C₅₂H₁₈BN, (f) p-C₅₂H₁₈BN, (g) C₅₀H₁₈B₂N₂, (h) C₄₈H₁₈B₃N₃, (i) C₃₆H₁₈Si₁₈, (j) C₂₇H₁₈Si₂₇, (k) B₂₇H₁₈N₂₇, (l) B₂₆H₁₈N₂₇Al. The bond distances are given in Å. The color code is the same as in Fig. 4.

Table 5 E_ads-1, ∆V_MESP-1, E_HOMO E_LUMO, E_g-2 and ∆E_g-1 values for Li⁺ adsorbed circumcoronenes^a.

Figure 10

Correlation between (a) V_min and E_ads-1 and (b) ∆V_MESP-1 and E_ads-1 for Li⁺-adsorbed circumcoronenes.

The negative values of ΔV_MESP-1 (Table 5) indicate the electron donation from circumcoronene and its analogues to Li⁺. These ΔV_MESP-1 values are in the range of − 113.38 (B₂₇H₁₈N₂₇) to − 155.49 kcal/mol (C₂₇H₁₈Si₂₇). The ΔV_MESP-1 value of circumcoronene is − 117.95 kcal/mol. The ΔV_MESP-1 of the doped circumcoronenes is typically higher than that of the pristine circumcoronene. However, the ΔV_MESP-1 of C₄₈H₁₈B₃N₃ and B₁₂H₁₂N₁₂ is lower than that of circumcoronene. The adsorption energies of Li⁺ on circumcoronene and its analogues are correlated with these ΔV_MESP-1 values, with a correlation coefficient of 0.898 (Fig. 10b). This behavior is similar to what we observe for coronene and its analogues (see Fig. 5b).

The E_HOMO, E_LUMO, and E_g-2 values of Li⁺-adsorbed circumcoronene and its analogues are given in Table 5. The E_HOMO, E_LUMO, and E_g-2 values of Li⁺-adsorbed circumcoronene and its analogues are in the ranges of − 10.28 (B₂₆H₁₈N₂₇Al) to − 7.03 eV (m-C₅₂H₁₈N₂), − 4.98 (C₅₃H₁₈Si) to − 3.59 eV (C₂₇H₁₈Si₂₇), and 2.66 (m-C₅₂H₁₈N₂) to 6.28 eV (B₂₆H₁₈N₂₇Al), respectively. Here also, E_HOMO of the Li⁺-adsorbed nanoflakes is lower than that of the pristine nanoflakes (see Table 4) for all cases. A similar result is obtained for E_LUMO. Our results here show that E_g-2 is typically lower than E_g-1. For example, the E_HOMO, E_LUMO, and E_g-2 values of Li⁺-adsorbed circumcoronene are − 8.40, − 4.37, and 4.04 eV, respectively. The decrease in the HOMO–LUMO energy gap for the adsorption of Li⁺ on circumcoronene is 7.3% (see ΔE_g-1 values in Table 5). A maximum decrease in the HOMO–LUMO energy gap of 34.1% was observed for the adsorption of Li⁺ on B₂₇H₁₈N₂₇. However, E_g-2 is found to be higher than E_g-1 for the adsorption of Li⁺ on m-C₅₂H₁₈N₂, C₅₀H₁₈B₂N₂, and C₃₆H₁₈Si₁₈. A maximum increase in the HOMO–LUMO energy gap of 24.7% was observed for the adsorption of Li⁺ on m-C₅₂H₁₈N₂.

Li adsorption on the doped circumcoronenes

The optimized geometries for the adsorption of Li on circumcoronene and its analogues are provided in Fig. 11. Our results show that Li binds to the peripheral rings of circumcoronene, similar to the results obtained for Li⁺. For the doped circumcoronenes, Li binds to the peripheral rings only of m-C₅₂H₁₈N₂, C₄₈H₁₈B₃N₃, C₃₆H₁₈Si₁₈, and C₂₇H₁₈Si₂₇. The adsorption distance of Li on these adsorbents is in the range of 1.96 (B₂₆H₁₈N₂₇Al) to 2.41 Å (B₂₇H₁₈N₂₇). For these adsorbents, the adsorption distance of Li is generally smaller than that of Li⁺ (see Fig. 10). For example, the adsorption distance of Li and Li⁺ on circumcoronene is 2.18 and 2.29 Å, respectively. However, as in the case of coronene and its analogues, Li is weakly adsorbed on circumcoronene and its analogues when compared to Li⁺. This observation is supported by the adsorption energy of Li on circumcoronene and its analogues (Table 6). The E_ads-2 values of Li on circumcoronene and its analogues are in the range of − 3.07 (B₂₇H₁₈N₂₇) to − 47.79 kcal/mol (C₅₃H₁₈Si). The E_ads-2 value of Li on circumcoronene is − 18.73kcal/mol. For the N-doped circumcoronenes, the E_ads-2 value of o-C₅₂H₁₈N₂ (− 22.71 kcal/mol) is lower than that of m-C₅₂H₁₈N₂ (− 32.31 kcal/mol). The E_ads-2 values of Si-doped circumcoronenes increase in the order C₂₇H₁₈Si₂₇ < C₃₆H₁₈Si₁₈ < C₅₃H₁₈Si. Furthermore, the E_ads-2 values of BN/AlN-doped circumcoronenes increase in the order B₂₇H₁₈N₂₇ < C₄₈H₁₈B₃N₃ < B₂₆H₁₈N₂₇Al < p-C₅₂H₁₈BN < m-C₅₂H₁₈BN < C₅₀H₁₈B₂N₂. These adsorption energies are not well correlated with the MESP V_min values of circumcoronene and its analogues (Fig. S6).

Figure 11

Optimized structures of Li adsorbed on (a) C₅₄H₁₈, (b) C₅₃H₁₈Si, (c) o-C₅₂H₁₈N₂, (d) m-C₅₂H₁₈N₂, (e) m-C₅₂H₁₈BN, (f) p-C₅₂H₁₈BN, (g) C₅₀H₁₈B₂N₂, (h) C₄₈H₁₈B₃N₃, (i) C₃₆H₁₈Si₁₈, (j) C₂₇H₁₈Si₂₇, (k) B₂₇H₁₈N₂₇, (l) B₂₆H₁₈N₂₇Al. The bond distances are given in Å. The color code is the same as in Fig. 4.

Table 6 E_ads-2, ∆V_MESP-2, E_HOMO E_LUMO, E_g-3 and ∆E_g-2 values for Li adsorbed circumcoronenes, along with ∆E_cell and V_cell^a.

In general, the values of ΔV_MESP-2 are positive for the adsorption of Li on circumcoronene and its analogues (Table 6). The positive value of ΔV_MESP-2 suggests the electron density transfer from Li to nanoflakes. However, the values of ΔV_MESP-2 are negative for the adsorption of Li on C₂₇H₁₈Si₂₇ and B₂₇H₁₈N₂₇. Here also, E_ads-2 does not show a correlation with ΔV_MESP-2 (see Fig. S6).

The E_HOMO, E_LUMO, and E_g-3 values of Li-adsorbed circumcoronene and its analogues are given in Table 6. The E_HOMO, E_LUMO, and E_g-3 values of Li-adsorbed circumcoronene and its analogues are in the ranges of − 5.22 (B₂₆H₁₈N₂₇Al) to − 3.21 eV (B₂₇H₁₈N₂₇), − 1.69 (C₃₆H₁₈Si₁₈) to 0.53 eV (B₂₇H₁₈N₂₇), and 2.20 (p-C₅₂H₁₈BN) to 4.44 eV (B₂₆H₁₈N₂₇Al), respectively. Here also, E_HOMO of the Li-adsorbed nanoflakes is higher than that of the pristine nanoflakes (see Table 4) for all cases. For example, the E_HOMO value of Li-adsorbed circumcoronene is − 3.63 eV. The E_LUMO of circumcoronene and its analogues is not much affected by the presence of Li. The results here show that E_g-3 is usually lower than E_g-1. The decrease in the HOMO–LUMO energy gap for the adsorption of Li on circumcoronene is 49.3% (see ΔE_g-2 values in Table 3). A maximum decrease in the HOMO–LUMO energy gap of 59.0% was observed for the adsorption of Li on B₂₇H₁₈N₂₇. However, E_g-3 is found to be higher than E_g-1 for the adsorption of Li on m-C₅₂H₁₈N₂ (ΔE_g-2 of 23.8%).

Cell voltage of circumcoronene and its analogues

The ΔE_cell and V_cell of LIBs based on circumcoronene and its analogues are given in Table 6. Here the ∆E_cell and V_cell values are in the ranges of − 42.29 (B₂₇H₁₈N₂₇) to − 11.06 kcal/mol (C₅₃H₁₈Si) and 0.48 (C₅₃H₁₈Si) to 1.83 V (B₂₇H₁₈N₂₇), respectively. As mentioned before, the nanoflakes interacting strongly with Li⁺ and weakly with Li may serve as good candidates for the anode materials in LiBs. For example, the highest V_cell value of 1.83 V is observed for B₂₇H₁₈N₂₇ due to the high E_ads-1 of − 45.36 kcal/mol (see Table 5) and low E_ads-2 of − 3.07 kcal/mol (see Table 6). The lowest V_cell value of 0.48 V observed for C₅₃H₁₈Si can be attributed to a higher contribution from E_ads-2 (E_ads-1 of − 58.84 kcal/mol and E_ads-2 of − 47.79 kcal/mol). The ∆E_cell and V_cell values of circumcoronene are − 32.82 kcal/mol and 1.42 V, respectively. For the N-doped circumcoronenes, the V_cell value of o-C₅₂H₁₈N₂ (1.41 V) is higher than that of o-C₅₂H₁₈N₂ (1.35 V). The V_cell values of Si-doped circumcoronenes increase in the order C₅₃H₁₈Si < C₃₆H₁₈Si₁₈ < C₂₇H₁₈Si₂₇. Furthermore, the V_cell values of BN/AlN-doped circumcoronenes increase in the order C₅₀H₁₈B₂N₂ < B₂₆H₁₈N₂₇Al < m-C₅₂H₁₈BN < C₄₈H₁₈B₃N₃ < p-C₅₂H₁₈BN < B₂₇H₁₈N₂₇. Here also, the linear correlation of E_ads-2 with V_cell (R = 0.840) supports the strong influence of E_ads-2 on V_cell (see Fig. S4).

The adsorption free energies (ΔG_ads = G_{adsorbate/nanoflake} – (G_nanoflake + G_adsorbate)) show that the adsorption of Li⁺ on the nanoflakes is exergonic (Table S1). The ΔG_ads values for the adsorption of Li⁺ on the nanoflakes are in the range of − 33.69 (B₁₂H₁₂N₁₂) to − 56.84 kcal/mol (C₃₆H₁₈Si₁₈). The adsorption of Li on the nanoflakes is generally exergonic. However, the adsorption of Li on B₁₂H₁₂N₁₂ and B₂₇H₁₈N₂₇ is endergonic, indicating weak interactions.

The storage capacity (C = (n x F × 10³)/M, where n is the maximum number of adsorbed Li atoms and M is the molecular mass of the electrode)⁴³ is an important factor for the performance of LIBs. To obtain the lithium storage capacity, we examined the interactions of Li atoms with, for example, C₂₄H₁₂. The resulting 6Li@C₂₄H₁₂ (Fig. S7) is found to be a true local minimum with no imaginary frequency. Therefore, the lithium storage capacity of C₂₄H₁₂ is 536.2 mAh/g, indicating that such nanoflakes are promising for high-capacity LIBs. For a comparison, the lithium storage capacity of graphite⁴⁴ is 372 mAh/g, Sc₂C MXene⁴⁵ is 462 mAh/g, graphene-like C₂N⁴⁶ is 671.7 mAh/g, and pentagraphyne⁴⁷ is 687 mAh/g.

There have been experimental studies on the use of PAHs in LIBs. For example, Park et al. obtained excellent rate capability and cycle endurance for LIBs using PAHs as anode materials⁹. There have also been DFT studies on the potential use of PAHs in LIBs. For example, based on the cell voltage data, Remya and Suresh suggested coronene as a good anode material for LIBs²⁷. Based on our V_cell data, C₂₄H₁₂, C₁₂H₁₂Si₁₂, B₁₂H₁₂N₁₂, C₂₇H₁₈Si₂₇, and B₂₇H₁₈N₂₇ are suggested as good anode materials for the LIBs and B₂₇H₁₈N₂₇ is the best among all tested nanoflakes. The V_cell of B₂₇H₁₈N₂₇ is found to be 1.83 V. For a comparison, the V_cell of circumbiphenyl is 1.51 V²⁷, sumanene is 1.68 V⁴⁸, and hexa-peri-hexabenzocoronene is 1.70 V⁴⁹. The insights on the adsorption mechanism from this study could help design an efficient electrode which could be useful for the further development efficient LIBs.

Conclusions

We performed DFT calculations to investigate the adsorption mechanisms of Li⁺ and Li on a total of twenty-four adsorbents (C₂₄H₁₂ and its analogues C₂₃H₁₂Si, o-C₂₂H₁₂N₂, m-C₂₂H₁₂N₂, m-C₂₂H₁₂BN, p-C₂₂H₁₂BN, C₂₀H₁₂B₂N₂, C₁₈H₁₂B₃N₃, C₁₆H₁₂Si₈, C₁₂H₁₂Si₁₂, B₁₂H₁₂N₁₂, B₁₁H₁₂N₁₂Al; C₅₄H₁₈ and its analogues C₅₃H₁₈Si, o-C₅₂H₁₈N₂, m-C₅₂H₁₈N₂, m-C₅₂H₁₈BN, p-C₅₂H₁₈BN, C₅₀H₁₈B₂N₂, C₄₈H₁₈B₃N₃, C₃₆H₁₈Si₁₈, C₂₇H₁₈Si₂₇, B₂₇H₁₈N₂₇, B₂₆H₁₈N₂₇Al). The XY (X = C, Si, N, B, Al; Y = C, Si, N, B, Al) bond lengths were in the range of about 1.35 to 1.81 Å for all adsorbents. Here all the CSi and NAl bond lengths were found to be significantly longer than all the CC bond lengths. The MESP analysis show that the replacements of C atoms of coronene and circumcoronene by Si/N/BN/AlN units lead to an increase of the electron-rich environments in the molecules.

Li⁺ is relatively strongly adsorbed on all adsorbents. For example, the adsorption distance of Li⁺ on all adsorbents is in the range of 2.15 (C₁₆H₁₂Si₈) to 2.46 Å (C₂₇H₁₈Si₂₇). This observation is further supported by the adsorption energy of Li⁺ on the nanoflakes. The E_ads-1 values of Li⁺ on all adsorbents are in the range of − 42.47 (B₁₂H₁₂N₁₂) to − 66.26 kcal/mol (m-C₂₂H₁₂BN). Our results indicate a stronger interaction between Li⁺ and the nanoflakes as the MESP V_min of the nanoflakes becomes more negative. The electron donation from the nanoflakes to Li⁺ could be checked by assessing the changes in the MESP at the nucleus of Li⁺ upon adsorption. Our results show that a stronger interaction between Li⁺ and the nanoflakes pushes more electron density toward Li⁺. The HOMO–LUMO gap of Li⁺-adsorbed nanoflakes is typically lower than that of pristine ones.

The adsorption distance of Li on the nanoflakes is generally smaller than that of Li⁺. For example, the adsorption distance of Li and Li⁺ on circumcoronene is 2.18 and 2.29 Å, respectively. However, Li is weakly adsorbed on circumcoronene and its analogues when compared to Li⁺. This observation is supported by the adsorption energy of Li on the nanoflakes. The E_ads-2 values of Li on all adsorbents are in the range of − 3.07 (B₂₇H₁₈N₂₇) to − 47.79 kcal/mol (C₅₃H₁₈Si). The HOMO–LUMO gap of Li-adsorbed nanoflakes is typically lower than that of pristine ones. The nanoflakes interacting strongly with Li⁺ and weakly with Li may serve as good candidates for the anode materials in LiBs. Among all adsorbents, the highest V_cell value of 1.83 V is observed for B₂₇H₁₈N₂₇ due to the high E_ads-1 of − 45.36 kcal/mol and low E_ads-2 of − 3.07 kcal/mol. The E_ads-1 data of studied systems show only a small variation compared to E_ads-2, and as a result, E_ads-2 has a relatively strong influence on the variation of V_cell.