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

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 PC and Pi are 0.12 eV and 0.20 eV, respectively. When the lithium polysulfides are adsorbed on four substrates, the overall adsorption energy of PC 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.


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, Li 2 S n (n = 1, 2, 4, 6, and 8)), accompanied by the gradual reduction of the S 8 molecule.However, the high-order intermediates (Li 2 S 4 , Li 2 S 6 , and Li 2 S 8 ) 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-C 3 N 4 ) [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-C 3 N 4 monolayer, the sp 2 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-C 3 N 4 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-C 3 N 4 [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-C 3 N 4 ) is a promising anchor host material for Li-S batteries.However, the doping configuration for P-g-C 3 N 4 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-C 3 N 4 configuration of the anchoring mechanism of S 8 and LiPSs interacting with P-g-C 3 N 4 substrates is imperative for addressing this issue.
In the present work, a comprehensive exploration of the interactions between the LiPSs and substrates (the g-C 3 N 4 and P-g-C 3 N 4 ) is undertaken through first-principles calculations.The diverse doping configurations of P-g-C 3 N 4 , involving the substitutional and interstitial doping sites, are considered.S 8 and LiPSs species exhibit favorable adsorption energy for P-g-C 3 N 4 , 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-C 3 N 4 substrates emerge as a promising host material for high-performance Li-S batteries.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 The graphite-like g-C 3 N 4 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-C 3 N 4 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].

Results and Discussion
To obtain an accurate configuration of the g-C 3 N 4 monolayer, a theoretical comparison of the lattice parameters of the g-C 3 N 4 monolayer is conducted, as depicted in Table 1.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-C 3 N 4 monolayer in ref. [36,38].

Formation Energies of P-Doping g-C 3 N 4
The 2 × 2 × 1 supercell with 24 C and 32 N atoms is employed for P-doping g-C 3 N 4 ; p can replace the C/N atoms or form an interstitial atom.To determine the most stable configuration of the P-doping g-C 3 N 4 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-C 3 N 4 monolayer.The following equations, (1) and (2), are adopted to calculate the formation energy of substitutional and interstitial dopants: where the E tot (sub − dopant) and E tot (int − dopant) represents the total energies for the substitutional and interstitial dopants, respectively.The E tot (pure) denotes the total energies of g-C 3 N 4 .The µ A and µ B denote the atomic potentials of the P and C/N atoms, respectively.The µ C and µ N are estimated from the energy of the graphite and a nitrogen molecule (µ N = 1/2µ N 2 ), respectively.The µ 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-C 3 N 4 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-C 3 N 4 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. Lower defect formation energy indicates that impurity ions prefer to be incorpo-rated into the substrate [38,46].Among the doping sites, the defect formation energies of g-C 3 N 4 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-C 3 N 4 monolayer, leading to destabilization [34].Some previous experimental findings suggest that P atoms primarily substitute C1 atoms within the g-C 3 N 4 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 sp 2 hybrid orbitals of P form bonds with two sp 2 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-C 3 N 4 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-C 3 N 4 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-C 3 N 4 monolayer.
Figures S2 and S3 of SI present the electronic band structures and partial density of states (PDOS) of pristine g-C 3 N 4 and P-g-C 3 N 4 (P C , P N , and P i ), respectively, and the corresponding band gaps (E g ) are listed in Table 3.The g-C 3 N 4 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-C 3 N 4 (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-C 3 N 4 monolayer, the Fermi level of P-g-C 3 N 4 (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-C 3 N 4 .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.

Anchoring Structure and Adsorption Energy
To assess the anchor effect of S 8 and the LiPSs on the g-C 3 N 4 and P-doping g-C 3 N 4 substrates (P C , P N , P i ), the adsorption energy [43] (E ad ) between the Li 2 S n species and the substrates is determined by the following equation.
where E S 8 /LiPSs , E sub , and E S 8 /LiPSs@sub denote the total energies of S 8 and the LiPSs, the substrates system (g-C 3 N 4 , P C , P N , P i ), and S 8 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 S 8 or Li 2 S n and monolayer substrates (g-C 3 N 4 , 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 S 8 or Li 2 S n on the surface of the g-C 3 N 4 , P C , P N , and P i substrates, and the corresponding structures are listed in Table S1 of SI.The E ad values for S 8 anchoring on the g-C 3 N 4 , P C , P N , and P i surfaces fall within the 1.82-3.50eV range.As the lithiation process initiates, significant variations are discovered for the adsorption processes of the LiPSs on the surfaces of the g-C 3 N 4 , P C , P N , and P i compounds.Specifically, for the lithiation stages from Li 2 S 8 to Li 2 S 4 , 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-C 3 N 4 (3.77 to 3.81 eV).Meanwhile, the E ad values of P C and P N are significantly higher than those of g-C 3 N 4 (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-C 3 N 4 , 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-C 3 N 4 is more favorable for the adsorption of S 8 and the LiPSs [51][52][53][54].PC, PN, and Pi exhibit similar adsorption intensities, particularly for the PC substrate, which emerges as the most favorable substrate for anchoring the LiPSs.The adsorption energy of the LiPSs@PC increases gradually with the decrease in the proportion of the S element.A similar tendency is also discovered for the PN and Pi situations.Therefore, compared with g-C3N4, the PC, PN, and Pi 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, PC, PN, and Pi 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 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].Table S1 of SI presents the most favorable structures of S 8 and the LiPSs anchoring on the g-C 3 N 4 , 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 S 8 and LiPSs adsorption on substrates are listed in Tables 4, 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-C 3 N 4 .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].

Charge Transfer and Electronic Properties
To obtain a comprehensive understanding of the interaction between the LiPSs species and substrates (g-C 3 N 4 , P C , P N , and P i ), the charge density differences after adsorption are evaluated using the following equation: where ρ (S 8 /LiPSs@sub) , ρ sub , and ρ S 8 /LiPSs represent the electron density of S 8 or the LiPSs anchoring on the substrates (g-C 3 N 4 , P C , P N , and P i ), pristine substrates, and the S 8 or LiPSs molecules, respectively.
As presented in Figures 3 and S4 of SI, minimal charge transfer occurs between the substrate and S 8 , 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-C 3 N 4 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].In general, adsorption strength directly correlates with the magnitude of charge transfer in host materials for Li-S batteries.Consequently, the anchoring capability of Pg-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 Figures 3  and 4, and Figure S4 of SI, stronger Li-N bonds are discovered between the LiPSs and three P-doped substrates (PC, PN, and Pi) in comparison with the counterpart of the g-C3N4 substrate.The strength of the Li-N bond within the LiPSs and the g-C3N4, PC, PN, and Pi To quantify the charge transfer between the g-C 3 N 4 , P C , P N , and P i substrates and the S 8 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 S 8 and the four kinds of substrates, the charge transfer values for S 8 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-C 3 N 4 , the charge transfer for the adsorbed Li 2 S, Li 2 S 2 , Li 2 S 4 , Li 2 S 6 , and Li 2 S 8 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 Li 2 S, Li 2 S 2 , Li 2 S 4 , Li 2 S 6 , and Li 2 S 8 , 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-C 3 N 4 substrates surpasses that of g-C 3 N 4 .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 S 8 molecule retains the puckered ring because of the negligible charge transfer between the S 8 molecule and the substrate.Conversely, as illustrated in Figures 3, 4 and 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-C 3 N 4 substrate.The strength of the Li-N bond within the LiPSs and the g-C 3 N 4 , P C , P N , and P i substrates is further assessed by the electron localization function (ELF) [57,59], as depicted in Figures 5 and 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-C 3 N 4 , the P C substrate exhibits stronger Li-N bonds, which are beneficial for suppressing the shuttling of high-order Li 2 S 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 Li2Sn (n = 1, 2, 4, 6, 8) molecules anchored on g-C3N4, PC, PN, and Pi substrates are evaluated, as plotted in Figures 7-10.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 Li2Sn@PC sys- 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 S 8 and Li 2 S n (n = 1, 2, 4, 6, 8) molecules anchored on g-C 3 N 4 , P C , P N , and P i substrates are evaluated, as plotted in Figures 7-10.The pristine substrates exhibit semi-metallic properties.When the LiPSs molecule is anchored on the P-doping g-C 3 N 4 monolayer, significant electronic states are observed near the Fermi level, rendering the metallic characteristics of the Li 2 S 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-C 3 N 4 substrates are good candidates for host materials with high conductivity in Li-S batteries.As depicted in Figures 7-10, the band gap of S 8 and the LiPSs upon anchoring on the surfaces of g-C 3 N 4 and P-g-C 3 N 4 are considerably smaller than the counterparts of pristine substrates.For the LiPSs@g-C 3 N 4 or LiPSs@P-g-C 3 N 4 systems, particularly for Li 2 S 4 and Li 2 S 6 , 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.

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 p file distribution along the S8 reduction pathway and the decomposition of the Li2S mo cule, as depicted in Figures 11 and 12.These calculations are performed using the sa parameter settings as in the structural optimization: PBE-Grimme generalized-ultras pseudopotentials, K-points 3 × 3 × 1, and a cutoff energy of 550 eV.It is crucial to note t the choice of substrate plays a significant role in these processes.We observe similar versible production processes of the S8 molecules for the g-C3N4, PC, PN, and Pi substra

Energy Profiles and Decomposition of Li 2 S on the Surface of the Monolayer Substrates
To evaluate the catalytic behavior of P-g-C 3 N 4 substrates, we focus on the energy profile distribution along the S 8 reduction pathway and the decomposition of the Li 2 S molecule, as depicted in Figures 11 and 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 S 8 molecules for the g-C 3 N 4 , P C , P N , and P i substrates.This involves the sequential reduction of the first two Li atoms and S 8 to form Li 2 S 8 , followed by subsequent reduction and oxidation yielding Li 2 S 6 , Li 2 S 4 , and Li 2 S 2 molecules, ultimately resulting in the final product Li 2 S. The S 8 undergoes spontaneous exothermic conversion to Li 2 S 8 and Li 2 S 6 .However, with the further decrease in S content, the energy changes of the subsequent formation of Li 2 S 4 exhibit slightly different trends, and the transfer process becomes endothermic.Notably, endothermic reactions occur on g-C 3 N 4 and P C substrates, resulting in the Li 2 S formation.Meanwhile, the transfer processes of generating Li 2 S on the P N and P i substrates become exothermic.Li 2 S undergoes conversion to S 8 through the Li-S bond cleavage during the charging process.
To evaluate the catalytic performance of the g-C3N4, PC, PN, and Pi 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 (Pi and PN) reveals distinct features.Specifically, the favorable decomposition barrier for the Pi is 2.86 eV, whereas that of PN 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.To evaluate the catalytic performance of the g-C 3 N 4 , P C , P N , and P i substrates for the conversion of S active material, the decomposition of Li 2 S is assessed as a representative example.Li 2 S 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 Li 2 S oxidation is profoundly influenced by the initial stages of the charging process in Li-S batteries, namely, the decomposition of Li 2 S → 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 Li 2 S along the X 1 route of the g-C 3 N 4 monolayer is 3.11 eV.The decomposition barrier for the X 2 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-C 3 N 4 substrates are considerably lower than the counterparts of the g-C 3 N 4 , suggesting that P-g-C 3 N 4 substrates can effectively facilitate the decomposition of Li 2 S with decreasing decomposition barriers, which is beneficial for enhancing the utilization of sulfur-active material in the Li-S battery.

Conclusions
In this paper, the feasibility of using graphitic nitrogen carbide (g-C 3 N 4 ) and phosphorusdoping substrate (P-g-C 3 N 4 ) 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-C 3 N 4 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-C 3 N 4 substrate showed metallicity, and the P-doping strategy enhanced the conductivity of the g-C 3 N 4 monolayers.In addition, the substrate adsorption energy of P-g-C 3 N 4 was enhanced by more than 40% compared to g-C 3 N 4 due to the formation of robust Li-N bonds and the higher adsorption energies of S 8 and Li 2 S 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-C 3 N 4 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-C 3 N 4 monolayers, which is favorable for electrochemical performance.Furthermore, the energy distribution and decomposition barriers of Li 2 S and P-doping on the g-C 3 N 4 monolayers had similar reaction mechanisms and catalytic properties.In addition, the decomposition barriers of the Li 2 S molecules on P-doping g-C 3 N 4 were in the range of 2.55-2.86eV, which was lower than that on g-C 3 N 4 (3.11 eV).Therefore, the P-g-C 3 N 4 substrates significantly improve Li 2 S 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-C 3 N 4 can be used as a promising anchoring material for a high-performance Li-S battery.

2 . 1 .
Structures for S 8 , LiPSs Species, g-C 3 N 4 and P-Doping g-C 3 N 4 The optimized structures for the LiPSs are shown in Figures 1 and S1 of the Supporting Information (SI).All calculations have been implemented for the heptazine-based graphitic carbon nitride (g-C 3 N 4 ) with the 2 × 2 × 1 supercell.Figures 1a and S1a present the optimized structures of S 8 , LiPSs (Li 2 S n , n = 1, 2, 4, 6, and 8) clusters with point groups and lattice parameters.The S 8 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.

Figure 2 .
Figure 2. Adsorption energies (Ead) for the most stable S8 and Li2Sn molecules on the surface of g-C3N4, PC, PN, and Pi with the PBE functional.

Figure 2 .
Figure 2. Adsorption energies (E ad ) for the most stable S 8 and Li 2 S n molecules on the surface of g-C 3 N 4 , P C , P N , and P i with the PBE functional.

Figure 3 .
Figure 3. Charge transfer of S8 and LiPSs molecules adsorbed on (a) g-C3N4 and favorable (b) PC substrates with the PBE functional.The green and red isosurfaces represent electron density loss and gain regions.The charge isosurfaces are 0.02 e/Å 3 of S8 and Li2Sn.(n = 1, 2,4, 6, and 8).

Figure 3 .
Figure 3. Charge transfer of S 8 and LiPSs molecules adsorbed on (a) g-C 3 N 4 and favorable (b) P C substrates with the PBE functional.The green and red isosurfaces represent electron density loss and gain regions.The charge isosurfaces are 0.02 e/Å 3 of S 8 and Li 2 S n .(n = 1, 2,4, 6, and 8).

Molecules 2024 , 22 Figure 7 .
Figure 7.The calculated density of states (DOS) of (a-f) S8@g-C3N4 and LiPSs@g-C3N4 molecules.The dashed line indicates the Fermi level with the PBE functional.

Figure 7 .
Figure 7.The calculated density of states (DOS) of (a-f) S 8 @g-C 3 N 4 and LiPSs@g-C 3 N 4 molecules.The dashed line indicates the Fermi level with the PBE functional.

2 Figure 8 .
Figure 8.The calculated density of states (DOS) of (a-f) S8@PC and LiPSs@PC molecules.The dashed line indicates the Fermi level with the PBE functional.

Figure 8 .Figure 9 .
Figure 8.The calculated density of states (DOS) of (a-f) S 8 @P C and LiPSs@P C molecules.The dashed line indicates the Fermi level with the PBE functional.

Figure 9 .
Figure 9.The calculated density of states (DOS) of (a-f)S 8 @P N and LiPSs@P N molecules.The dashed line indicates the Fermi level with the PBE functional.

Figure 10 .
Figure 10.The calculated density of states (DOS) of (a-f) S8@Pi and LiPSs@Pi molecules.The das line indicates the Fermi level with the PBE functional.

Figure 10 .
Figure 10.The calculated density of states (DOS) of (a-f) S 8 @P i and LiPSs@P i molecules.The dashed line indicates the Fermi level with the PBE functional.

Figure 12 .
Figure 12.The energy barriers for the decomposition of Li2S on the g-C3N4 (a), PC (a), PN (b), and Pi (b) substrates with the PBE functional.Li2S undergoes three stages in the decomposition pathway: the initial state (IS), the transition state (TS), and the final state (FS).The top view depicts the decomposition path of the Li-ion from the IS to the FS.

Figure 12 .
Figure 12.The energy barriers for the decomposition of Li 2 S on the g-C 3 N 4 (a), P C (a), P N (b), and P i (b) substrates with the PBE functional.Li 2 S undergoes three stages in the decomposition pathway: the initial state (IS), the transition state (TS), and the final state (FS).The top view depicts the decomposition path of the Li-ion from the IS to the FS.
• , respectively.For the LiPSs, the Li 2 S and Li 2 S 2 display the C 2v point group, while the absence of mirror symmetry results in C 2 symmetry for the Li 2 S 4 , Li 2 S 6 , and Li 2 S 8 molecules.Within the LiPSs clusters, the shortest Li-S bond length increases as the rising cluster size: 2.108 Å for Li 2 S, 2.247 Å for Li 2 S 2 , and 2.388 (2.425 and 2.414) Å for Li 2 S 4 (Li 2 S 6 and Li 2 S 8 ), while a reduced tendency is observed for the Li-S-Li bond angle, namely, 126.1 • for Li 2 S, 96.5 • for Li 2 S 2 , and 72.2 • (66.1 • and 67.7 • ) for Li 2 S 4 (Li 2 S 6 and Li 2 S 8 ).The optimized structures of S 8 and the LiPSs (Li 2 S n , n = 1, 2, 4, 6, and 8) molecules are in line with previous calculations [32-35].

Table 1 .
Comparison of lattice parameters of g-C 3 N 4 with various theoretical methods.

Table 2 .
The formation energies (E f , eV) of the P-doping g-C 3 N 4 monolayer at different doping positions with the PBE functional.

Table 3 .
Band gaps of the g-C 3 N 4 monolayer and P-g-C 3 N 4 (P C , P N , and P i ) with the HSE06 functional.

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 PC substrates.

Table 4 .
The average S-S, Li-S, and Li-N distances (Å) and adsorption energy (eV) of the S 8 and LiPSs anchoring on the g-C 3 N 4 and P C substrates.