Lithium and phosphorus-functionalized graphitic carbon nitride monolayer for e�cient hydrogen storage: A DFT study

We have explored the consequence of lithium and phosphorous functionalization on the graphitic carbon nitride (g-C 3 N 4 ) monolayer for hydrogen storage using density functional theory. Both pristine and Li and P decorated g-C 3 N 4 show a semiconductor nature. The substantial overlap between the s orbital of Li and the p orbital of nitrogen near the Fermi level shows the binding between Li and the g-C 3 N 4 . The repositioning of HOMO and LUMO is noticed in the Li and P decorated g-C 3 N 4 . The Bader charge analysis indicates the charge allocation from the Li and P atom to the g-C 3 N 4 , which results in the adsorption of H 2 by electrostatic interaction. The hydrogen storage capacity of 5.78 wt% is obtained after functionalizing Li and P into the g-C 3 N 4 . The obtained adsorption energies for the H 2 adsorption con�rm that Li and P functionalized g-C 3 N 4 is a mesmerizing candidate for the reversible loading of H 2 at ambient conditions.


Introduction
Hydrogen is considered a promising candidate to encounter energy necessity since it is a clean, nontoxic, economical, abundant, environment-friendly, and renewable energy source [1][2][3].Numerous hydrogen storage mechanisms have been projected in the last decades via the physisorption and chemisorption processes to discover suitable material [4][5][6].The U.S Department of Energy (DOE) system has xed a target of 5.5 wt% gravimetric hydrogen storage capacity and 0.05 Kg hydrogen/L volumetric capacity for onboard light-duty vehicles, materialshandling equipment, and moveable power applications by the end of 2025 [7].Nevertheless, developing materials that can accumulate hydrogen by that standard and function under ambient conditions is not easy.
The hydrogen bonding is either too feeble when interacting with carbon nanostructure or too robust as inorganic molecules and light metal hydrides [8,9].So, continuous efforts are given to nd the ideal storage system with binding energy intermediate between physisorption and chemisorption.Formerly, LiBH 4 has been considered a suitable material due to its 18.4 wt% hydrogen storage capacity, but this hybrid assembly is comparatively unbalanced at high temperatures (400 o C) [10].Recently, nanostructures based on carbon and graphene have been recommended for hydrogen loading claims as a result of their excellent surface-to-volume ratio, porous structure, and lightweight.Zhang et al. have reported in theory that graphitic carbon nitride (g-C 3 N 4 ) (triazine-based) is an admirable material for the steady and sound-dispersed embellishment of Ti atoms with high hydrogen adsorption capacity and binding strength appropriate for mobile application [11].M.D. Ganji et al. have studied the hydrogen storage capacity of Si-decorated graphene sheets using density functional theory (DFT) and found ~ 15 wt% of hydrogen storage capacity by considering hydrogen on both sides of the Si-decorated graphene sheet [12].Menghao Wu et al. have found that Li-functionalization on g-C 3 N 4 has a large capacity of 10 wt% for hydrogen storage [13].Also, Y. Wang et al. have shown that g-C 3 N 4 nanotubes functionalized with Na and Li atoms have a storage capacity of 9.09 wt% at 0 K for hydrogen [14].Nevertheless, the binding strength of Li on the g-C 3 N 4 has been computed to be just 2.20 eV at 0 K, which would encourage the development of the Li-clusters at advanced process temperature and afterward reduce hydrogen storage capacity.Y. Liu et al. have found that up to 7.8 wt% of H 2 molecules can be stored by Ti-decorated graphene [15].N.  [17].They nd out the effect of different Li decorations on the storage capacity of heptazine-based g-C 3 N 4 for H 2 storage.
Our recent work demonstrated that P doping as distinct and organized with metal outcomes in sturdy delocalization of frontier molecular orbitals (MOs), which slows and opposes the charge recombination rate in the g-C 3 N 4 [18].The P doping in g-C 3 N 4 changes the electronic structure of g-C 3 N 4 with lesser bandgap energy and boosts electric conductivity and dye degradation capacity [19,20].Thus, in this work, we have investigated the synergetic consequence of lithium and phosphorus decoration on the structural, electronic, and optical properties and hydrogen storage capacity of the heptazine-based g-C 3 N 4 monolayer.

Computational Methods
The density functional theory-based calculations are made in MedeA-VASP (Vienna Ab Initio Simulation Package) with the projector augmented-wave pseudopotential and PBE-GGA functional [21,22].A supercell of the g-C 3 N 4 layer with a 2 × 2 × 1 unit cell size [(g-C 3 N 4 ) 8 ] is used in all the calculations.A vacuum space of 18 Å is kept between headto-head layers to avoid interactions between them, and 3 × 3 × 1 k-points and 500 eV cut-off energy is chosen for the structure optimization.5 × 5 × 1 k-points mesh is considered for the density of states (DOS) and band structure calculations.The cut-off criteria for energy and force convergence are kept at 1 × 10 − 5 eV and 0.05 eV/ Å, respectively.The van der Walls (vdW) interactions are computed with the help of Tkatchenko and Scheffer (T.S.) correction [23].The Monkhorst-Pack arrangement is used to sample the Brillouin zone.The value of Gaussian smearing width is seized to be 0.2.The Bader charge study approaches the allocation of electronic charge among Li, P dopants, adsorbed hydrogen, and the monolayer [24].
The interaction energy of the Li and P dopants on the g-C 3 N 4 monolayer is calculated as [25]: where m and n are the quantity of added Li and P atoms, respectively.E(X) is the energy of the composite, molecule, or atom, X.A favorable interaction is given by the negative interaction energy.
The H 2 adsorption energy E ads (x ) of the Li and P functionalized systems is computed using the: The PBE0 [27] functional and the Lanl2dz [28] basis set are used for the frontier MOs estimation in Gaussian 16 software [29].
To study the optical properties of pristine and metals embedded g-C 3 N 4 systems, optical absorption ( ) and optical conductivity ( ) are calculated using the following formulae [30]: Where is the light frequency, and are the real and imaginary fragments of dielectric function correspondingly.

Li and P functionalization on g-C 3 N 4
The optimized structure of pristine g-C 3 N 4 monolayer is shown in Fig. 1(a), and a cell constant value of a = 7.134 Å = b is obtained, which is consistent with previously simulated (7.14 Å) as well as experimental (6.810Å) outcomes [31,32].According to the symmetry of the g-C 3 N 4 , there are two distinct carbon atoms (C1 and C2) and three distinct nitrogen atoms (N1, N2, and N3) (Fig. 1a) [33].There are ve substitutional sites (C1, C2, N1, N2, and N3) and two interstitial sites (I1 and I2), as shown in Fig. 1(a), for the loading of metals and non-metals in heptazine-based g-C 3 N 4 [18].The large cavity (I2 site) is the steadiest position for metal loading, and the P atom at I1/I2 site is the most reliable con guration compared to other doping sites [34,35].Therefore, we have considered a large cavity for the Li atom and the I1 site for the P atom.In the case of single Li atom adsorption on the g-C 3 N 4 monolayer, the Li atom is positioned in the center of the membrane plane's pore, with the adsorption energy of − 4.36 eV, very close to the result reported in the literature [36].However, three Li in the large pore orient directly above (2.04Å above the monolayer plane) the cavity with a slight shift of internal nitrogen towards the Li atoms after optimization (Fig. 1(c)) with adsorption energy of -3.61 eV [37].The adsorption energy (E ads = -3.61eV) of Li on the g-C 3 N 4 monolayer is considerably more than the cohesive energy (E coh = -1.63eV) of Li [13].This adsorption energy value shows an even dispersal of Li dopants without cluster formation.As shown in Fig. 1(c), the length between the Li atom and the adjacent N atoms is ~ 1.89 Å, while the distance between two Li atoms is about 3.52 Å.In the case of Li and P functionalized g-C 3 N 4 , we have considered a g-C 3 N 4 monolayer having three Li atoms and one P atom in the empty cavity at a distance of 2 Å from the monolayer plane.After the geometry optimization, the P atom sits 2.37 Å above the monolayer plane, and the space between the P and the neighboring C and N atoms are 1.79 Å and 1.83 Å, respectively, as shown in Fig. 1(d).The high adsorption energy value (-3.94 eV) ensures the stability of the Li and P functionalized g-C 3 N 4 monolayer.This con guration is carefully chosen to guarantee judicious space for the adsorption of H 2 all over the Li and P on the two sides of the monolayer.
The electronic band structure, along with the partial density of states (PDOS), is also used to study the functionalization of Li and P into the g-C 3 N 4 monolayer.The band structure indicates the semiconducting nature of the g-C 3 N 4 monolayer having a bandgap of 1.1 eV (Fig. 2(a)), which is less than the reported experimental value of 2.7 eV due to the well-identi ed fact that GGA-PBE underrates the bandgap energy [38].Nonetheless, while the band gap calculated from GGA-PBE is not close to the experimental value, it gives vital insight into the impacts of element doping on g-C 3 N 4 , particularly on partial DOS, projected DOS, electronic band structure, and optical properties [39,40].Hence, as discussed in the manuscript, we have used GGA-PBE to calculate the properties of all the doped systems.After the Li addition to the g-C 3 N 4 monolayer, the band structure changes signi cantly due to the allocation of extra electrons from the Li to N, causing the Li-doped g-C 3 N 4 monolayer to become metallic [37].After adding Li and P to the g-C 3 N 4 monolayer, its metallic nature diminishes with a feeble bandgap of 0.036 eV, as shown in Fig. 2(c).The partial density of states (PDOS) of valence s orbital of the Li atom and p orbital of P, C, and N atoms (close to the Li and P atoms) are shown in Fig. 2(d)-(f).In a pure g-C 3 N 4 monolayer, the valence band is principally contributed by the 2p orbital of the N atom, while the conduction band is conquered by the 2p orbital of the C atom (Fig. 2(d)).Over the incorporation of Li atoms in the g-C 3 N 4 monolayer, mid-band states appear near the Fermi level due to the transfer of additional electrons from Li to N, as revealed in Fig. 2(e).The binding of Li to the monolayer is indicated by the substantial overlap between the 2s orbital of Li and the 2p orbital of N near the Fermi level.A similar trend can also be observed in the PDOS of Li and P added g-C 3 N 4 monolayer, as visible in Fig. 2(f).
The frontiers MOs of the pristine-(g-C 3 N 4 ) 8 , (g-C 3 N 4 ) 8 Li 3 , and (g-C 3 N 4 ) 8 Li 3 P monolayers are given in Fig. 3 to show the charge localization and delocalization.In the pristine g-C 3 N 4 monolayer, there is a localization of photogenerated couples in a speci c heptazine unit, which results in an extreme recombination proportion of couples.This charge localization explains the poor photocatalytic performance of pristine g-C 3 N 4 .In (g-C 3 N 4 ) 8 Li 3 and (g- As displayed in Fig. 4, we have also calculated the optical properties, for example, refractive index, re ectivity, optical conductivity, and optical absorption of pure, Li functionalized, and Li and P functionalized graphitic carbon nitride. There is a substantial perfection in the re ectivity in the infrared area after adding Li and P atoms to the pure graphitic carbon nitride, as revealed in Fig. 4(b).Optical conductivity is considered a crucial means for studying electronic circumstances in materials.Figure 4(c) shows robust growth in the optical conductivity in the infrared as well as visible area after adding Li and P atoms.Li-functionalized graphitic carbon nitride shows better optical absorption in the infrared region.However, Li and P functionalized graphitic carbon nitride has the best absorption in

Adsorption of H 2 on the Li and P decorated g-C 3 N 4 monolayer
After con rming the stability of Li and P functionalized graphitic carbon nitride monolayer, we have explored the interaction of the H 2 molecule with Li and P decorated g-C 3 N 4 monolayer by placing H 2 molecules over Li and P atoms in the supercell.The optimized structures of different con gurations of Li and P functionalized graphitic carbon nitride with the maximum quantity of H 2 adsorbed only on one side of the monolayer are given in Fig. 5.After geometry optimization, the adsorption energy, bond length, average Li-H 2 distance, and average P-H 2 distance are noted in Table 1.At rst, a single H 2 molecule is placed near the individual Li and P atoms, and the structure is optimized.We progressively increase the quantity of H 2 molecules, and the structure is re-optimized after each H 2 molecule addition (Fig. 5(d), Fig. 5(e), and Fig. 5(f)).It is found that the highest number of H 2 adsorbed per Li and P atoms in the instance of (g-C 3 N 4 ) 8 Li 3 P is three, as shown in Fig. 5(f); the fourth H 2 is kept away from the monolayers.
A reasonable fraction of the distance is preserved between the H 2 molecules to bypass annoying repulsions.
The adsorption energy of the rst H 2 molecule is evaluated using Eq. 2 and is come up with − 0.131 eV considering GGA-vdW for (g-C 3 N 4 ) 8 Li 3 P (Fig. 5(d)).For the second and the third H 2 molecule, the adsorption energies are − 0.093 and − 0.089 eV, respectively, for (g-C 3 N 4 ) 8 Li 3 P.Even more importantly, according to Table I, the adsorption energies are doubled upon, including dispersion corrections.Hence van der Waals forces play a signi cant role in the binding.Also, as given in Table 1, the adsorption energies reduce thru the rise of H 2 , suggesting that the system can adsorb an inadequate amount of H 2 .It has been noticed that the distance between two hydrogen atoms (H-H) is elongated than the isolated H 2 (0.75 Å).This elongation is due to the polarization between the Li, P, and H 2, as shown in Table 1.
Further, it is observed that the average Li-H 2 and P-H 2 distances increase with the intensi cation of adsorbed H 2 ; however, the H-H bond length shrinkages.This decrease in the H-H bond span implies that the adsorption strength decreases with the intensi cation of the adsorbed H 2 .This is con rmed by the adsorption energies of different con gurations, as given in Table 1.It is observed that the computed adsorption energy is diminished from − 0.131 eV for single adsorbed H 2 to -0.065 eV per H 2 for the six adsorbed H 2 on the Li and P functionalized g-C 3 N 4 , which may be attributable to the steric repulsion between the adsorbed H 2 molecules [14].Even though the typical adsorption energy for each H 2 decreases as the quantity of H 2 increases, the adsorption energy for each H 2 is typical for solid physisorption in the six H 2 adsorbed Li and P functionalized g-C 3 N 4 [12].The graph of volumetric capacity vs. gravimetric capacity is shown in Fig. 7.The ultimate H 2 storage capacity of (g-C 3 N 4 ) 8 Li 3 (Fig. 5(c)) and (g-C 3 N 4 ) 8 Li 3 P (Fig. 5(f)) are found 2.34 (9H 2 ) and 2.98 wt % (12H 2 ) respectively, with the adsorption of H 2 to just a single side of the monolayer.Finally, we have allowed the adsorption of H 2 on both sides of the monolayers (Fig. 6).By the adsorption of H 2 on both sides, we have obtained a gravimetric and volumetric capacity of 5.78 wt% hydrogen and 0.0275 Kg hydrogen/L, respectively, for the (g-C 3 N 4 ) 8 Li 3 P con guration (Fig. 7).
These values are pretty close to the U.S. Department of Energy (DOE) [7].

Nature of interaction between H 2 and Li and P functionalized g-C 3 N 4 monolayer
To determine the nature of the Li and P functionalization binding on the g-C 3 N 4 monolayer and the adsorption of hydrogen molecules on the Li and P functionalized g-C 3 N 4 monolayer qualitatively, we have plotted the total electron density.Here is no electron density at the interface area between the Li atom and g-C 3 N 4 monolayer and amid H 2 and the Li atom (Fig. 8 (a) and (b)).These electron density plots specify that the Li functionalization on the g-C 3 N 4 and the H 2 adsorption on the Li functionalized g-C 3 N 4 do not form a covalent bond along the g-C 3 N 4 , indicating the physical nature of the adsorption.The same type of bonding nature is also observed in the case of Li and P functionalization on the g-C 3 N 4 monolayer, as shown in Fig. 8 (c) and (d), which is also con rmed previously by the adsorption energy calculation as given in Table 1.
The CDD plots of the systems, as mentioned earlier, are shown in Fig. 9.As can be seen from Fig. 9 (a) and Fig. 9 (c), few charges exit on the topmost of Li and P atoms, while most of the charges are mainly concentrated near the g-C 3 N 4 monolayer, which indicates some charges transfer from Li and P atoms to the g-C 3 N 4 monolayer.These partially charged Li (P) ions and the g-C 3 N 4 monolayer would yield a local electric eld.These local electric elds polarized the hydrogen molecules and bound them thru the polarization phenomenon [41].Hence the H 2 gets polarized with the electron density gathering on the side adjacent to the g-C 3 N 4 monolayer and the depletion on the side, aside from the g-C 3 N 4 monolayer, as shown in Fig. 9 (b) and Fig. 9 (d).This polarization is the reason behind the elongation of the H-H bond in the H 2 adsorbed on the Li and P functionalized g-C 3 N 4 compared to the H-H bond in the isolated H 2 .Hence, we can say that the H 2 adsorption on the Li and P functionalized g-C 3 N 4 features dipoledipole interactions [14].
We have calculated the charge transfer by Bader charge analysis as given in Table 2 [42].Individual Li drops nearly 0.90 e ¯ to the monolayer in Li atoms added g-C 3 N 4 monolayer, while each Li atom loses almost 0.90 e ¯ and the P atom loses approximately 0.80 e ¯ in case of Li and P atoms added g-C 3 N 4 monolayer.This charge transfer suggests that the bonding between Li and g-C 3 N 4 monolayer and between P and g-C 3 N 4 monolayer is ionic, proved previously by the ELF plots as shown in Fig. S2.These + ve charged Li and P ions yield local electric elds that polarize H 2 molecules and thus enhance the adsorption [43,44].Hence, nding a system in which the metal ion is remained positively charged is the key to molecular hydrogen adsorption [45].Since no charge transfer takes place in the case of the physisorption mechanism, the amount of hydrogen that can be stored on the Li and P functionalized g-C 3 N 4 monolayer is limited mainly by steric hindrance.

C 3 N
photogeneratedpairs.This delocalization of pairs in the Li and P functionalized g-C 3 N 4 monolayers result in the high photocatalytic performance related to the pristine g-C 3 N 4 monolayer.

Figure 1 Top
Figure 1

Figure 5 Different
Figure 5

Figure 8
Figure 8 Song et al. have stated that up to 7.6 wt% of H 2 molecules can be stored with Ti-decorated boron-carbon-nitride [16].Most theoretical studies on hydrogen storage are in triazine-based carbon nitride, even though the allotrope heptazine-based g-C 3 N 4 is more stable and readily available for experimental studies.Wu et al. have found that Lifunctionalized heptazine-based g-C 3 N 4 is a hopeful material for H 2 storage [13].Hussain et al. have extended the work done by Wu et al. by using dispersion corrections and considering large supercells in the DFT calculations

Table 1
The adsorption energy for each H 2 (GGA, GGA + vdW), average Li-H 2 distances, average P-H 2 distances, and typical H-H bond lengths on Li and P decorated carbon nitride monolayers.

Table 2
Bader charges of C and N atoms before and after Li and P functionalization and H 2 adsorption.
4. The Fermi level is xed to zero in these plots.As shown in Fig.6(d), there is no apparent hybridization between the Li and P functionalized g-C 3 N 4 monolayer and the adsorbed hydrogen molecule.Therefore, the hydrogen adsorption mechanism in Li and P functionalized g-C 3 N 4 monolayer is reasonably different from the Kubas interaction, which generally occurs in transition metal-doped materials[46].In Kubas interaction, stronger hybridization exists between the d orbital of the functionalized transition metal and the adsorbed hydrogen σ orbital.