First-Principles Investigation of Phosphorus-Doped Graphitic Carbon Nitride as Anchoring Material for the Lithium-Sulfur Battery

Abstract

The utilization of lithium–sulfur battery is hindered by various challenges, including the “shuttle effect”, limited sulfur utilization, and the sluggish conversion kinetics of lithium polysulfides (LiPSs). In the present work, a theoretical design for the viability of graphitic carbon nitride (g-C₃N₄) and phosphorus-doping graphitic carbon nitride substrates (P-g-C₃N₄) as promising host materials in a Li-S battery was conducted utilizing first-principles calculations. The PDOS shows that when the P atom is introduced, the 2p of the N atom is affected by the 2p orbital of the P atom, which increases the energy band of phosphorus-doping substrates. The energy bands of P_C and P_i are 0.12 eV and 0.20 eV, respectively. When the lithium polysulfides are adsorbed on four substrates, the overall adsorption energy of P_C is 48–77% higher than that of graphitic carbon nitride, in which the charge transfer of long-chain lithium polysulfides increase by more than 1.5-fold. It is found that there are powerful Li-N bonds between lithium polysulfides and P-g-C₃N₄ substrates. Compared with the graphitic carbon nitride monolayer, the anchoring effect of the LiPSs@P-g-C₃N₄ substrate is enhanced, which is beneficial for inhibiting the shuttle of high-order lithium polysulfides. Furthermore, the catalytic performance of the P-g-C₃N₄ substrate is assessed in terms of the S₈ reduction pathway and the decomposition of Li₂S; the decomposition energy barrier of the P-g-C₃N₄ substrate decrease by 10% to 18%. The calculated results show that P-g-C₃N₄ can promote the reduction of S₈ molecules and Li-S bond cleavage within Li₂S, thus improving the utilization of sulfur-active substances and the ability of rapid reaction kinetics. Therefore, the P-g-C₃N₄ substrates are a promising high-performance lithium-sulfur battery anchoring material.

1. Introduction

The burgeoning demand for specific energy conversion and storage devices in contemporary society has spurred extensive exploration and research beyond the conventional lithium-ion battery [1,2,3]. The lithium-sulfur (Li-S) battery has emerged as a promising candidate for commercial lithium-ion batteries on account of its gravimetric energy density and theoretical specific capacity. The benefit of the Li-S battery lies in its low equivalent weight, cost-effectiveness, natural abundance, and minimal environmental impact. The charge/discharge processes of the Li-S battery proceed via a series of polysulfide intermediates (the LiPSs, Li₂S_n (n = 1, 2, 4, 6, and 8)), accompanied by the gradual reduction of the S₈ molecule. However, the high-order intermediates (Li₂S₄, Li₂S₆, and Li₂S₈) exhibit a tendency to dissolve in organic solvents, leading to the undesirable “shuttle effect”. As a consequence, the robust self-discharge, significant capacity loss, and depletion of active sulfur have coexisted in the Li-S battery [4,5].

In recent years, considerable endeavors have been directed towards mitigating the dissolution and diffusion of high-order polysulfides, involving physically confining the high-order LiPSs within the pores or layers of high-surface-area carbon nanostructures, such as carbons featured with micro or mesopores [6,7,8,9,10,11]. Nevertheless, these physical adsorption strategies often fail to efficiently address the “shuttle effect” because of the weak affinity of nonpolar carbon materials for high-order LiPSs. Recently, chemical adsorption has emerged as a viable strategy for LiPSs retention. The polar nanomaterials, including metal oxides [12,13,14], metal nitrides [15], transition metal sulfides [16,17], and metal-organic frameworks [18], have shown promising prospects in this regard. These materials featured with polar surfaces provide chemical anchoring sites for the LiPSs. Nevertheless, the utilization of metallic materials in Li-S batteries tends to reduce the energy density and increase the proportion of inactive materials in the composition of host materials. Very recently, considerable attention has been directed toward identifying compelling host materials for the confinement of S and the anchoring of the LiPSs, with particularly effort focused on the two-dimensional (2D) materials renowned for their high surface areas, active adsorption sites, and porous configurations [19]. Graphitic carbon nitride (g-C₃N₄) [20,21,22,23,24], as a lightweight, polar, highly ordered polymeric material, showcases an excellent prospect for enhancing the capacity and cycling performance of the Li-S battery. Within the crystal structure of the g-C₃N₄ monolayer, the sp² hybridized nitrogen atoms with lone pair electrons are separated by carbon atoms, showcasing some delocalization. Meanwhile, one sp3 hybridized nitrogen atom forms a covalent bond with three adjacent carbon atoms [25,26,27,28]. However, the intrinsically poor electrical conductivity of g-C₃N₄ limits the Li-S battery’s performance. Chemical doping has proven to be an effective strategy for altering semiconductors’ electronic structures and surface characteristics. For instance, Zhang et al. demonstrated a significant enhancement of electrical conductivity through the phosphorus doping polymeric g-C₃N₄ [29,30]. Similarly, Ma et al. significantly improved the electrochemical performance of phosphorus-doping graphitic carbon nitride [31]. These findings indicate that the phosphorus-doping graphitic carbon nitride (P-g-C₃N₄) is a promising anchor host material for Li-S batteries. However, the doping configuration for P-g-C₃N₄ and the anchoring mechanism have not been identified clearly in the theoretical and experimental work on the Li-S battery. Therefore, a comprehensive investigation of the P-g-C₃N₄ configuration of the anchoring mechanism of S₈ and LiPSs interacting with P-g-C₃N₄ substrates is imperative for addressing this issue.

In the present work, a comprehensive exploration of the interactions between the LiPSs and substrates (the g-C₃N₄ and P-g-C₃N₄) is undertaken through first-principles calculations. The diverse doping configurations of P-g-C₃N₄, involving the substitutional and interstitial doping sites, are considered. S₈ and LiPSs species exhibit favorable adsorption energy for P-g-C₃N₄, underscoring the suitability of phosphorus-doped graphitic carbon nitride as a moderate host material for suppressing the shuttle effect of the high-order LiPS species. Therefore, the P-g-C₃N₄ substrates emerge as a promising host material for high-performance Li-S batteries.

2. Results and Discussion

2.1. Structures for S₈, LiPSs Species, g-C₃N₄ and P-Doping g-C₃N₄

The optimized structures for the LiPSs are shown in Figure 1 and Figure S1 of the Supporting Information (SI). All calculations have been implemented for the heptazine-based graphitic carbon nitride (g-C₃N₄) with the 2 × 2 × 1 supercell. Figure 1a and Figure S1a present the optimized structures of S₈, LiPSs (Li₂S_n, n = 1, 2, 4, 6, and 8) clusters with point groups and lattice parameters. The S₈ molecule adopts a puckering ring configuration with a D_4d point group, with an S–S bond length and an angle of 2.059 Å and 109.2°, respectively. For the LiPSs, the Li₂S and Li₂S₂ display the C_2v point group, while the absence of mirror symmetry results in C₂ symmetry for the Li₂S₄, Li₂S₆, and Li₂S₈ molecules. Within the LiPSs clusters, the shortest Li–S bond length increases as the rising cluster size: 2.108 Å for Li₂S, 2.247 Å for Li₂S₂, and 2.388 (2.425 and 2.414) Å for Li₂S₄ (Li₂S₆ and Li₂S₈), while a reduced tendency is observed for the Li–S–Li bond angle, namely, 126.1° for Li₂S, 96.5° for Li₂S₂, and 72.2° (66.1° and 67.7°) for Li₂S₄ (Li₂S₆ and Li₂S₈). The optimized structures of S₈ and the LiPSs (Li₂S_n, n = 1, 2, 4, 6, and 8) molecules are in line with previous calculations [32,33,34,35].

The graphite-like g-C₃N₄ monolayer, characterized by an N-linked heptazine unit, prefers to crystallize in the hexagonal configuration (Figure 1b), in line with the findings of Thomas et al. [28,36,37,38,39]. In the structure of the g-C₃N₄ monolayer, the bridge and inner N atoms are 3-fold coordinated by three C atoms, whereas the edge N atoms are only 2-fold coordinated by two C atoms. A limitation of DFT-based means is their insufficient resolution on weak vdW interactions, which are essential for compounds resembling graphite [40].

To obtain an accurate configuration of the g-C₃N₄ monolayer, a theoretical comparison of the lattice parameters of the g-C₃N₄ monolayer is conducted, as depicted in

Table 1. Comparison of lattice parameters of g-C₃N₄ with various theoretical methods.

Method	vdW Correction	a/Å	b/Å
LDA-CAPZ	no	7.072	7.072
GGA-PBE	no	7.144	7.144
GGA-PBE	Grimme	7.144	7.144
GGA-PBE	TS	7.138	7.138
Exp. a	-	7.30	-
Other theory b	OBS	7.16	-
Other theory c	-	7.13	-

^a Bojdys et al. (ref. [32]), ^b Ma et al. (ref. [38]), ^c Gracia et al. (ref. [36]).

. The experimental data is also presented for comparison. The results show that the lattice parameter (a = 7.072 Å) calculated by the LDA-CAPZ method [41,42] without vdW correction and the lattice parameter (a = 7.138 Å) calculated by PBE-TS dispersion correction [34] are smaller than the results of the PBE-Grimme (DFT-D2) dispersion; the latter parameters (a = 7.144 Å) are closer to the experimental value (a = 7.300 Å) [32], and PBE–Grimme’s calculations are in better agreement with the theoretical results of the g-C₃N₄ monolayer in ref. [36,38].

2.2. Formation Energies of P-Doping g-C₃N₄

The $2\times 2\times 1$ supercell with 24 C and 32 N atoms is employed for P-doping g-C₃N₄; p can replace the C/N atoms or form an interstitial atom. To determine the most stable configuration of the P-doping g-C₃N₄ system, nine distinct P-doping configurations are evaluated in terms of formation energy. The designations of N1-N4 and C1-C4 denote four N and four C sites, respectively, while Pi represents the interstitial doping site, as illustrated in Figure S1 of SI. The formation energy is calculated using Equations (1) and (2), which represent substitutional and interstitial doping, respectively [38,43,44]. The lower defect formation energy E_f indicates greater defect concentration. Generally, the defect configuration with low formation energy exhibits great tendency information in the structure of the g-C₃N₄ monolayer. The following equations, (1) and (2), are adopted to calculate the formation energy of substitutional and interstitial dopants:

$$E_f=E_{tot}(sub-dopant)-E_{tot}(pure)-{\mu }_A-{\mu }_B$$

(1)

$$E_f=E_{tot}(\mathrm{int}-dopant)-E_{tot}(pure)-{\mu }_A$$

(2)

where the $E_{tot}(sub-dopant)$ and $E_{tot}(\mathrm{int}-dopant)$ represents the total energies for the substitutional and interstitial dopants, respectively. The $E_{tot}(pure)$ denotes the total energies of g-C₃N₄. The ${\mu }_A$ and ${\mu }_B$ denote the atomic potentials of the P and C/N atoms, respectively. The ${\mu }_C$ and ${\mu }_N$ are estimated from the energy of the graphite and a nitrogen molecule (${\mu }_N=1/2{\mu }_{N_2}$), respectively. The ${\mu }_P$ is determined from white phosphorus [43,44]. In general, thermodynamic factors such as vibration and enthalpy should be considered for the free energy calculations; however, due to the limitation of the workstation, the electronic energies are adopted to evaluate the formation energies without considering the influence of temperature [45]. These results are consistent with the reports in refs. [38].

The g-C₃N₄ structure comprises four N sites, four C sites, and one interstitial site, as shown in Figure S1 of SI. Specifically, both substitution and interstitial doping are accounted for in the mono-doping strategy. Several possible P-doping g-C₃N₄ configurations, including three inequivalent N sites (N1, N3, N4), two inequivalent C sites (C1, C2), and one interstitial site (P_i), are obtained, and the corresponding formation energies are shown in

Table 2. The formation energies (E_f, eV) of the P-doping g-C₃N₄ monolayer at different doping positions with the PBE functional.

P-Doping Positions	C1	C2	C3	C4	N1	N2	N3	N4	Interstitial (Pi)
Ef (eV) (2 × 2 × 1)	1.06	1.81	1.07	1.78	2.31	1.34	1.34	5.03	0.81
Ef (eV) (4 × 4 × 1)	0.77	1.65	0.78	1.62	1.70	1.20	1.20	4.83	0.80
Ef (eV) a	0.73	1.52	-	-	1.93	1.33	-	3.55	0.78

^a Ma et al. (ref. [38]).

. Lower defect formation energy indicates that impurity ions prefer to be incorporated into the substrate [38,46]. Among the doping sites, the defect formation energies of g-C₃N₄ with the interstitial site (P_i) are the lowest, implying that the interstitial site is in the optimal position. Such a phenomenon can be attributed to the isoelectronic nature of P with N, whereas C introduces only one electron into the g-C₃N₄ monolayer, leading to destabilization [34].

Some previous experimental findings suggest that P atoms primarily substitute C1 atoms within the g-C₃N₄ monolayer before replacing other positions [30], which indicates that a portion of P atoms should be adsorbed within the ample space of the planar structure. Upon P_i doping, one lone pair electron localizes around the P atom, while another electron delocalizes around the N–P–N chain. Two sp² hybrid orbitals of P form bonds with two sp² hybrid orbitals of adjacent N atoms. The configuration of the C–N=C chain results from the interplay between the energy gained from extending the π electron and the repulsive force exerted by the lone pair electrons on the N-side atoms in the heptazine unit [39,40]. The formation energy of P-g-C₃N₄ is consistent with previous theoretical studies [37,38]. Due to the slight difference in formation energies for the replacement P atom on the N and C sites, three distinct doping configurations are also considered, as depicted in Table 2. The (2 × 2 × 1) and (4 × 4 × 1) defect formation energies of the supercells are calculated in Table 2, and the results show that the substitution formation energies at the C/N position are the same as those at the interstitial position. Considering that the focus of our present work is to study the interaction between g-C₃N₄ and polysulfides from the beginning of the monolayer and to study the possibility of doped P elements as a base-anchoring material, and considering factors such as the number of atoms, the amount of work, and the ability to calculate, we choose (2 × 2 × 1) supercells for the subsequent calculations. In Table 2, the highest formation energy is found at the N4 position, and the comparison reveals that Ma et al. use a bilayer AB stacked structure different from the two-dimensional monolayer material in this paper, and the computational functions, parameter settings, and vacuum layers are the difference. The substitution and interstitial position pattern after doping with P elements is consistent with refs. [38,39]. The results show the possibilities of positions including the interstitial site (P_i) (E_f = 0.81 eV), and substituting sites which involved the C1 position (P_C) (E_f =1.06 eV) and N3 position (P_N) (E_f =1.34 eV). Figure 1b–e presents the different configurations of the P-doping g-C₃N₄ monolayer.

Figures S2 and S3 of SI present the electronic band structures and partial density of states (PDOS) of pristine g-C₃N₄ and P-g-C₃N₄ (P_C, P_N, and P_i), respectively, and the corresponding band gaps (E_g) are listed in

Table 3. Band gaps of the g-C₃N₄ monolayer and P-g-C₃N₄ (P_C, P_N, and P_i) with the HSE06 functional.

Eg Gap (eV)	g-C3N4	P Substitute N Site (PN)	P Substitute C Site (PC)	P-Doping Interstitial Site (Pi)
GGA-PBE	1.13	0.89	0.04	0.14
HSE06	2.67	2.14	0.12	0.20
Exp a	2.70	-	-	-

^a Wang et al. (ref. [46]).

. The g-C₃N₄ is a direct band gap semiconductor with an E_g of 2.67 eV, comparable to the experimental value of 2.70 eV [46]. However, within the P-g-C₃N₄ (P_C, P_N, and P_i), the electronic band structures vary significantly on account of the incorporation of the P atom. Compared with the g-C₃N₄ monolayer, the Fermi level of P-g-C₃N₄ (P_C, P_N, and P_i) shifts downward toward the conduction band, resulting in reduced band gaps of 2.14 eV, 0.12 eV, and 0.20 eV for the P_N, P_C, and P_i configurations, respectively. These results align well with the experimental results of Zhang et al. [29], indicating a noticeable improvement in the electrical conductivity of P-g-C₃N₄. Introducing P elements in place of C/N is beneficial for generating lone pair electrons, thereby increasing the carrier concentration and potentially reducing the mobility gap [47]. This shift could facilitate movement towards the conjugated ring, affecting the electronic properties through quantum vibrational effects [48,49], which influences the electrical conductivity. These outcomes are consistent with prior research [50,51].

The DOS and PDOS in Figure S3 of SI reveal that the reduced band gaps are primarily attributed to the P-doping, particularly for the replacement of the C position, leading to a small band gap of 0.12 eV. Further PDOS analysis shows that the P 2s and 2p orbitals provide a dominant contribution near the Fermi level, accompanied by the 2p orbitals of N. A similar trend is observed for the situation of P_i, where P 2p orbitals play a significant role in reducing the band gap. Therefore, replacing the N position with P results in a decreased band gap. Meanwhile, the small gap (E_g = 0.12 eV) of the P_C substrate is beneficial for enhancing the electrical conductivities of the LiPSs@P_C system.

2.3. Anchoring Structure and Adsorption Energy

To assess the anchor effect of S₈ and the LiPSs on the g-C₃N₄ and P-doping g-C₃N₄ substrates (P_C, P_N, P_i), the adsorption energy [43] (E_ad) between the Li₂S_n species and the substrates is determined by the following equation.

$$E_{ad}=E_{S_8/LiPSs}+E_{sub}-E_{S_8/LiPSs@sub}$$

(3)

where $E_{S_8/LiPSs}$, E_sub, and $E_{S_8/LiPSs@sub}$ denote the total energies of S₈ and the LiPSs, the substrates system (g-C₃N₄, P_C, P_N, P_i), and S₈ and the LiPSs on the substrates, respectively. Obviously, a significant positive value suggests a high adsorption capability. The E_ad values for the most stable adsorption configurations of S₈ or Li₂S_n and monolayer substrates (g-C₃N₄, P_C, P_N, and P_i) [44] are discussed in detail in the following section. The radar chart (Figure 2) depicts the adsorption energies for the anchoring of S₈ or Li₂S_n on the surface of the g-C₃N₄, P_C, P_N, and P_i substrates, and the corresponding structures are listed in Table S1 of SI. The E_ad values for S₈ anchoring on the g-C₃N₄, P_C, P_N, and P_i surfaces fall within the 1.82–3.50 eV range. As the lithiation process initiates, significant variations are discovered for the adsorption processes of the LiPSs on the surfaces of the g-C₃N₄, P_C, P_N, and P_i compounds. Specifically, for the lithiation stages from Li₂S₈ to Li₂S₄, P_i exhibits robust adsorption energies (2.79 to 3.07 eV). However, as the lithiation further occurs, substantially higher E_ad values are observed for the P_i situation (4.48 to 5.75 eV) as compared to the counterparts of g-C₃N₄ (3.77 to 3.81 eV). Meanwhile, the E_ad values of P_C and P_N are significantly higher than those of g-C₃N₄ (Table S2 of SI).

P_C, P_N, and P_i exhibit similar adsorption intensities, particularly for the P_C substrate, which emerges as the most favorable substrate for anchoring the LiPSs. The adsorption energy of the LiPSs@P_C increases gradually with the decrease in the proportion of the S element. A similar tendency is also discovered for the P_N and Pi situations. Therefore, compared with g-C₃N₄, the P_C, P_N, and P_i exhibit superior anchor interactions with the LiPSs, which are beneficial for reducing the shuttle effect during the charging and discharging processes. Compared with the carbon-based matrix, the polar pore structure of P-doping g-C₃N₄ is more favorable for the adsorption of S₈ and the LiPSs [51,52,53,54].

Table S1 of SI presents the most favorable structures of S₈ and the LiPSs anchoring on the g-C₃N₄, P_C, P_N, and P_i substrates. The corresponding adsorption energies and the average S-S, Li-S, and Li-N distance within the S₈ and LiPSs adsorption on substrates are listed in

Table 4. The average S-S, Li-S, and Li-N distances (Å) and adsorption energy (eV) of the S₈ and LiPSs anchoring on the g-C₃N₄ and P_C substrates.

Molecules	LiPSs		g-C3N4			PC
	S-S	Li-S	Li-S	Li-N	Ead	Li-S	Li-N	Ead
Li2S	-	2.108	2.264	2.400	3.809	2.342	1.992	6.760
Li2S2	2.186	2.240	2.593	2.397	3.773	2.515	1.965	6.525
Li2S4	2.093	2.386	3.040	2.351	3.350	2.336	2.250	5.225
Li2S6	2.078	2.428	2.531	2.069	3.198	2.411	2.280	5.245
Li2S8	2.075	2.419	2.781	2.065	3.392	2.473	2.299	5.026
S8	2.060	-	-	-	2.021	-	-	3.502

and Tables S2 and S3 of SI. The average Li-S bond length increases to about 0.2 Å due to the LiPSs adsorbed on the four substrates. However, the Li-N bond length decreases with the increasing adsorption energy, especially the Li-N bond length decreases to 1.9 Å in the short-chain LiPSs@P-g-C₃N₄. It can be seen that in the same concentration of elemental P-doping substrates, P, in addition to increasing the electrical conductivity of the substrate, is also more able to enhance the Li-N bond and the formation of chemical adsorption [42].

2.4. Charge Transfer and Electronic Properties

To obtain a comprehensive understanding of the interaction between the LiPSs species and substrates (g-C₃N₄, P_C, P_N, and P_i), the charge density differences after adsorption are evaluated using the following equation:

$$\Delta \rho ={\rho }_{{(S}_8/\mathit{LiPSs}\text{@}\mathit{sub})}-{\rho }_{\mathit{sub}}-{\rho }_{S_8/\mathit{LiPSs}}$$

(4)

where ${\rho }_{{(S}_8/\mathit{LiPSs}\text{@}\mathit{sub})}$, ${\rho }_{\mathit{sub}}$, and ${\rho }_{S_8/\mathit{LiPSs}}$ represent the electron density of S₈ or the LiPSs anchoring on the substrates (g-C₃N₄, P_C, P_N, and P_i), pristine substrates, and the S₈ or LiPSs molecules, respectively.

As presented in Figure 3 and Figure S4 of SI, minimal charge transfer occurs between the substrate and S₈, indicating the absence of a chemical bond formation. However, upon the LiPSs anchoring on the substrates, a significant charge transfer occurs within and between the LiPSs. Specifically, there is an increase in the charge transfer between Li atoms and N, P, or C atoms. At the same time, a decrease is observed in the S atoms adjacent to Li atoms, leading to the formation of Li-N, C-S, or Li-P chemical bonds. This behavior is scrutinized across g-C₃N₄ and P-doping substrates (P_C, P_N, P_i), as Figure S4 of SI depicts. A reinforcement of the Li-N bond and a weakening of the Li-S bond is discovered because of the strong electrostatic interaction between the positively charged Li atoms and negatively charged N atoms. Moreover, as the Li atom is introduced, the charge density between the LiPSs and the substrates increases inversely with the S content, particularly for the P_C substrate. This finding aligns well with the adsorption energy analysis. As shown in Figure 3, the distortion of the LiPSs species indicates that there is competition between the Li-N and Li-S chemical bonds, which is affected by charge transfer and changes in electronic structure, indicating a strong chemical adsorption between the LiPSs and the substrate [52,53,54].

To quantify the charge transfer between the g-C₃N₄, P_C, P_N, and P_i substrates and the S₈ or LiPSs, the Mulliken charge analysis [55,56,57] is conducted, as depicted in Figure 4. The electron density transfers from the LiPSs to the substrates, which increases the positive charge of the LiPSs. However, due to the weak interaction between S₈ and the four kinds of substrates, the charge transfer values for S₈ molecules are comparatively small. Concurrently, enhancing the chemical interaction between the substrate and the LiPSs contributes to the elongation of the Li-S bond. For g-C₃N₄, the charge transfer for the adsorbed Li₂S, Li₂S₂, Li₂S₄, Li₂S₆, and Li₂S₈ molecules are 0.84 e, 0.96 e, 0.30 e, 0.23 e, and 0.28 e, respectively, which correlates positively with the adsorption energy analysis as abovementioned. A similar trend is observed in P-doping situations, particularly for P_C substrates. The corresponding charge transfers are 1.06 e, 1.11 e, 0.87 e, 0.81 e, and 0.76 e for Li₂S, Li₂S₂, Li₂S₄, Li₂S₆, and Li₂S₈, respectively. The Mulliken charge is known to be sensitive to the choice of basis set. To provide a more robust analysis, we also calculate the Hirshfield charge [56,58] (Table S4 of SI). The results corroborate the charge transfer analysis presented in Figure 3 and the Mulliken charge shown in Figure 4.

In general, adsorption strength directly correlates with the magnitude of charge transfer in host materials for Li-S batteries. Consequently, the anchoring capability of P-g-C₃N₄ substrates surpasses that of g-C₃N₄. Moreover, the LiPSs molecules gain electrons during the discharging process, leading to the transformation of long-chain intermediates of the LiPSs into short-chain counterparts and vice versa.

However, the S₈ molecule retains the puckered ring because of the negligible charge transfer between the S₈ molecule and the substrate. Conversely, as illustrated in Figure 3 and Figure 4, and Figure S4 of SI, stronger Li-N bonds are discovered between the LiPSs and three P-doped substrates (P_C, P_N, and P_i) in comparison with the counterpart of the g-C₃N₄ substrate. The strength of the Li-N bond within the LiPSs and the g-C₃N₄, P_C, P_N, and P_i substrates is further assessed by the electron localization function (ELF) [57,59], as depicted in Figure 5 and Figure 6 (P_N and P_i substrates). In general, ELF values of 0 and 1 denote the total electron localization and depletion, respectively. In contrast, the ELF values in the ranges of 0–0.5, 0.5–0.75, and 0.75–1 correspond to the ionic bond, metal bond, and covalent bond, respectively. The ELF values surrounding Li and N atoms are located within the range of 0.75–1, representing a covalent bond between the LiPSs cluster and the substrates. Compared with g-C₃N₄, the P_C substrate exhibits stronger Li-N bonds, which are beneficial for suppressing the shuttling of high-order Li₂S_n (n = 4, 6, and 8) molecules.

Excellent conductivity is a crucial requirement for the host material of a Li-S battery with high performance. Consequently, the density of states (DOS) of S₈ and Li₂S_n (n = 1, 2, 4, 6, 8) molecules anchored on g-C₃N₄, P_C, P_N, and P_i substrates are evaluated, as plotted in Figure 7, Figure 8, Figure 9 and Figure 10. The pristine substrates exhibit semi-metallic properties. When the LiPSs molecule is anchored on the P-doping g-C₃N₄ monolayer, significant electronic states are observed near the Fermi level, rendering the metallic characteristics of the Li₂S_n@P_C system. The LiPSs molecules significantly contribute to the overall DOS, as revealed by the comprehensive PDOS investigation in the vicinity of the Fermi level. Consequently, P-g-C₃N₄ substrates are good candidates for host materials with high conductivity in Li-S batteries.

As depicted in Figure 7, Figure 8, Figure 9 and Figure 10, the band gap of S₈ and the LiPSs upon anchoring on the surfaces of g-C₃N₄ and P-g-C₃N₄ are considerably smaller than the counterparts of pristine substrates. For the LiPSs@g-C₃N₄ or LiPSs@P-g-C₃N₄ systems, particularly for Li₂S₄ and Li₂S₆, electron distribution is observed near the Fermi level, indicating an increase in electrical conductivity. Further DOS analysis highlights the P_C substrate’s strong electrical conductivity, facilitating the Li-S battery’s electrochemical performance.

2.5. Energy Profiles and Decomposition of Li₂S on the Surface of the Monolayer Substrates

To evaluate the catalytic behavior of P-g-C₃N₄ substrates, we focus on the energy profile distribution along the S₈ reduction pathway and the decomposition of the Li₂S molecule, as depicted in Figure 11 and Figure 12. These calculations are performed using the same parameter settings as in the structural optimization: PBE–Grimme generalized-ultrasoft pseudopotentials, K-points 3 × 3 × 1, and a cutoff energy of 550 eV. It is crucial to note that the choice of substrate plays a significant role in these processes. We observe similar reversible production processes of the S₈ molecules for the g-C₃N₄, P_C, P_N, and P_i substrates. This involves the sequential reduction of the first two Li atoms and S₈ to form Li₂S₈, followed by subsequent reduction and oxidation yielding Li₂S₆, Li₂S₄, and Li₂S₂ molecules, ultimately resulting in the final product Li₂S. The S₈ undergoes spontaneous exothermic conversion to Li₂S₈ and Li₂S₆. However, with the further decrease in S content, the energy changes of the subsequent formation of Li₂S₄ exhibit slightly different trends, and the transfer process becomes endothermic. Notably, endothermic reactions occur on g-C₃N₄ and P_C substrates, resulting in the Li₂S formation. Meanwhile, the transfer processes of generating Li₂S on the P_N and P_i substrates become exothermic. Li₂S undergoes conversion to S₈ through the Li-S bond cleavage during the charging process.

To evaluate the catalytic performance of the g-C₃N₄, P_C, P_N, and P_i substrates for the conversion of S active material, the decomposition of Li₂S is assessed as a representative example. Li₂S is selected because of the poor kinetic performance associated with the solid phase and the low utilization rate of S active material. The kinetics of Li₂S oxidation is profoundly influenced by the initial stages of the charging process in Li-S batteries, namely, the decomposition of Li₂S → LiS⁻ + Li⁺. To evaluate the decomposition barrier, the linear simultaneous transit/quadratic simultaneous-transit (LST/QST) approach is used [60] with the PBE functional, and a 2 × 2 × 1 Monkhorst–Pack k-point to identify the transition states. As shown in Figure 12a, the energy barrier for Li-S bond cleavage within Li₂S along the X₁ route of the g-C₃N₄ monolayer is 3.11 eV. The decomposition barrier for the X₂ path on the Pc monolayer is 2.74 eV. Besides, the initial state (IS) energy is lower than the final state (FS) energy, demonstrating an exothermic reaction. At the same time, the IS energy is higher than the FS energy, showing an endothermic response in Figure 12b. However, the decomposition along other substrates (P_i and P_N) reveals distinct features. Specifically, the favorable decomposition barrier for the P_i is 2.86 eV, whereas that of P_N substrates is 2.55 eV (Figure 12b). The barrier height is responsible for the reaction rate. Therefore, the decomposition barriers of the P-g-C₃N₄ substrates are considerably lower than the counterparts of the g-C₃N₄, suggesting that P-g-C₃N₄ substrates can effectively facilitate the decomposition of Li₂S with decreasing decomposition barriers, which is beneficial for enhancing the utilization of sulfur-active material in the Li-S battery.

3. Computational Methods

First-principles calculations were performed with the CASTEP module implemented in the Materials Studio [61,62]. The Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) and Vanderbilt ultrasoft pseudopotentials were adopted [63,64]. Considering the van der Waals interaction between the substrates (g-C₃N₄ and P-g-C₃N₄) and the LiPSs, Grimme’s (DFT-D2) semi-empirical dispersion energy correction was incorporated into the first-principles calculations [65]. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm was employed to facilitate structure optimization. Pseudo-atomic calculations were conducted for C, N, and Li with electron configurations of 2s²2p², 2s²2p³, and 1s²2s¹, respectively [66]. A cutoff energy of 550 eV and Monkhorst–Pack k-points of 3 × 3 × 1 were utilized. For the electronic structure calculations, a 6 × 6 × 1 mesh was adopted for k-point sampling. Considering the drawback of the GGA method in evaluating the electronic band structure of P-g-C₃N₄, the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional was employed [67,68]. A vacuum layer of 15 Å was incorporated along the z-axis to prevent interactions between adjacent g-C₃N₄ layers. The convergence criteria for energy, maximum force, and maximum displacement were 5.0 × 10⁻⁶ eV/atom, 0.01 eV/Å, and 5.0 × 10⁻⁴ Å, respectively. For the electronic structure calculations, the convergence criterion for energy was 1.0 × 10⁻⁶ eV/atom.

4. Conclusions

In this paper, the feasibility of using graphitic nitrogen carbide (g-C₃N₄) and phosphorus-doping substrate (P-g-C₃N₄) as anchoring materials for the Li-S battery was systematically investigated using first-principles calculations. Three moderately doped configurations were identified by calculating the formation energy of P-doping g-C3N4, considering the substitutional and interstitial sites: P_C, P_N, and P_i. The PDOS results showed that the 2p of N was affected by introducing the P atom, and a synergistic effect occurred to enhance the energy bands of the P-g-C₃N₄ substrates. The energy band of P_C was elevated to 0.12 eV, that of P_i was 0.20 eV, and that of P_N was 2.14 eV; the P-g-C₃N₄ substrate showed metallicity, and the P-doping strategy enhanced the conductivity of the g-C₃N₄ monolayers. In addition, the substrate adsorption energy of P-g-C₃N₄ was enhanced by more than 40% compared to g-C₃N₄ due to the formation of robust Li-N bonds and the higher adsorption energies of S₈ and Li₂S_n (n = 1, 2, 4, 6, and 8). The Mulliken charge analysis showed that the electrons from the LiPSs molecules to the P-doped g-C₃N₄ substrate, especially the charge transfer of the long-chain LiPSs on the P_C substrate, increased by more than 1.5-fold. This means that the strong chemical interactions between them are formed and suppress the shuttling effect of higher-order LiPSs. Further density of states analyses showed that a transition from semi-metallic to metallic occurred in the P-doping g-C₃N₄ monolayers, which is favorable for electrochemical performance. Furthermore, the energy distribution and decomposition barriers of Li₂S and P-doping on the g-C₃N₄ monolayers had similar reaction mechanisms and catalytic properties. In addition, the decomposition barriers of the Li₂S molecules on P-doping g-C₃N₄ were in the range of 2.55–2.86 eV, which was lower than that on g-C₃N₄ (3.11 eV). Therefore, the P-g-C₃N₄ substrates significantly improve Li₂S formation and decomposition, thus increasing the utilization and fast reaction kinetics of the sulfur in the Li-S battery. This work provides detailed theoretical guidance for the experimental synthesis of doped elements as catalysts, and the application of P-g-C₃N₄ can be used as a promising anchoring material for a high-performance Li-S battery.