Introduction

Significant efforts are underway to find suitable renewable and environmentally safe energy sources to address the energy crisis arising from the depletion of fossil fuel resources and their detrimental effects on the environment [1]. Hydrogen has gained major attention as a clean, renewable source of energy that holds promise in addressing the elevated emissions resulting from fossil fuels [2,3]. As hydrogen has a better specific heat capacity as well as lesser toxicity compared to other conventional fuels such as gasoline and methane, it is considered a safer and more efficient fuel [4,5] compared to fossil fuels. While large-scale production of hydrogen can be achieved via methods like water electrolysis, gasification, steam reforming etc [6,7], its utilization is severely limited by the absence of efficient storage technologies to transport or contain it until usage. For industrial usage, hydrogen has been primarily stored in high-pressure cylinders, or as a liquid in cryogenic vessels. However, these methods are not highly scalable owing to the safety concerns stemming from the use of high-pressure containers as well as the high price of storing hydrogen at cryogenic temperatures [8]. Previous methods of storing hydrogen such as storing it in glass microspheres were discontinued after experiencing high losses in the form of escaped H2 from the containers [9]. In recent times, a new approach to chemically store hydrogen in solid state materials using adsorption techniques has gained major attention. Substrates with high specific area, low cost, and chemical stability are thus being extensively studied in this regard [10].
To filter out feasible materials that can be used for storing hydrogen, the United States Department of Energy (DOE) has set a target of 6.5 wt.% for the system gravimetric density for storing hydrogen via adsorption onto solid materials [11]. Materials like metallic hydrides, mixed metal oxides, zeolites, carbon and boron nanotubes, and metal organic frameworks have been previously shown to provide convincing results as adsorbents due to their high surface area to volume ratio and porosity. [12-19]. In systems such as metal hydrides hydrogen is stored via chemisorption which involves the hydrogen molecules chemically bonding to the adsorbents. This leads to high hydrogen desorption energies and hinders the efficiency of the system. For the adsorption process to be practically efficient, the hydrogen molecules must be adsorbed onto the material with binding energies that are sufficiently low to allow for easy desorption. Materials that adsorb hydrogen based on physisorption are thus being seen as a viable choice to store hydrogen.
Recent studies have found two-dimensional (2D) materials or Xenes to be competitive adsorbents for storing hydrogen. Materials such as graphene and phosphorene have been previously used in the batteries and supercapacitors industry mainly due to their band gap and tuneable electronic properties [20-26]. Defect engineering and metal functionalization have been shown to significantly increase the adsorption capabilities of graphene with boron and sulphur doped graphene being able to adsorb unwanted gases in the atmosphere such as NO2 and SO2 [27]. High-defect density systems of graphene were reported to exhibit gravimetric densities up to 5.81 wt.% H2 [28]. Ambrusi et al. investigated hydrogen adsorption onto rhodium decorated graphene in various configurations and reported hydrogen binding energies of up to -1.08 eV/H2 [29]. The high binding energies were a result of the strong binding between the d-orbital of rhodium and the s-orbital of hydrogen due to Kubas interaction. Modifications using other transition metals such as nickel and iron have been carried out on phosphorene to obtain high hydrogen adsorption energies as well [30, 31]. However, the large mass of the transitional metal adatoms used for substrate decoration leads to low gravimetric densities in many of these systems. Transition metals can be replaced with lighter alkali metals such as lithium and sodium which can bind hydrogen to the decorated substrate with viable adsorption energies while simultaneously increasing the gravimetric density of the systems [32]. For instance, blue phosphorene nanosheets decorated with Li were shown to have hydrogen binding energies of -0.25 eV/H2 as reported by John et. al [33]. Liu at el. also found lithium functionalized B2S to adsorb hydrogen with up to 9.1% wt./H2 and average binding energies of -0.14 eV/H2 showing the effectiveness of lithium as a metal adatom for physisorption based hydrogen storage substrates [34]. Many of these alkali metal-based systems however suffer from low binding energies between the alkali metal adatom and the substrate, especially in the case of graphene, which can lead to agglomeration of the metal adatoms on top of the substrate thus reducing its efficiency and stability.
Silicene is another 2-D material that shows a strong structural resemblance to graphene due to its hexagonal repetition of silicon atoms [35]. Unlike graphene however, the atoms in silicene arrange themselves in a buckled fashion [36]. Silicene has found ground-breaking applications in enhancing the performance of lithium-ion batteries due to its high capacity with regards to lithium adsorption [37-39]. Silicene is also being studied for possible applications in spintronics, batteries and superconductors [40, 41]. Owing to its structural and surface properties, applications of silicene have also extended towards hydrogen storage in recent times. Metal functionalized hydrogenated silicene or silicane was studied by Hussain et al. to understand the effectiveness of hydrogen adsorption on its surface [42]. Wang et. al adsorbed hydrogen on metal decorated silicene systems to conclude that hydrogen adsorption in the case of Li and Na was via physisorption whereas Sc and Ti bound to H2 in a chemisorbed fashion [43]. Different structures of silicene such as penta-silicene have also shown promising hydrogen binding energies of -0.35eV/H2 with gravimetric densities of around 6.42 wt.% when decorated with Li [44]. Silicene also shows metal adatom binding energies higher than the metal-metal cohesive energies in most cases thus preventing metal adatom agglomeration. One approach to further increase the hydrogen storage capacity of the substrate has been to increase the number of viable sites via creation of defects onto the surface. These defects, such as vacancies not only lead to an increase in the metal-substrate decoration energies but also increase the gravimetric density of the substrate. While the sole effect of defects and metal decorations on hydrogen storage has been heavily discussed in the case of other 2-D materials such as graphene, such literature is sparse in the case of silicene. The combined effect of both metal decoration as well as defects as a means of improving hydrogen adsorption in silicene has also not been discussed in the literature.
This study aims to use Density Functional Theory (DFT) calculations to understand the effect of lithium decoration and defects on the hydrogen storage capabilities of silicene based systems. The single vacancy defect and Stone-Wales defect were chosen due to their low formation energies and were created by removing a Si atom and rotating a Si-Si bond in the silicene monolayer respectively. The presence of defects not only increases the metal adatom binding energies preventing clustering and is more practical as defects are an inherent part of the material synthesis process. Hydrogen adsorption was subsequently studied onto the lithium decorated defective silicene substrates. It was observed that lithium decoration greatly enhances the hydrogen binding energies in the defective silicene systems. Double side Li decoration of the substrates was further performed to investigate the total number of H2 molecules that can be effectively stored onto these defective substrates. An analysis of the projected density of states (pDOS) plots of the Li decorated systems showed combined interactions of the Li(s) and Li(p) orbitals with the H(s) orbitals which lead to enhanced hydrogen adsorption energies. Charge density diagrams were also plotted to conclude that there is a significant electronic interaction between Li and H2 which leads to an improvement in the hydrogen adsorption energies. Ab-initio molecular dynamics (AIMD) simulations were performed at 300 K and verified that Li decoration and subsequently H2 adsorption is stable on the defective substrates. All the lithium decorated systems were found to show high reversibility with the hydrogen binding energies being favourable even for higher number of H2 molecules showing a maximum gravimetric density of 5.97 wt.% H2.

2. Computational Details

QUANTUM ESPRESSO was used to carry out spin-polarized Density Functional Theory (DFT) calculations [45]. In order to approximate the exchange correlation energy, the Generalized Gradient Approximation using Perdew, Burke and Ernzerhof - PBE-GGA [46] was used. 45 Ry was chosen as the cut-off energy for the plane wave expansion and the Projector Augmented Wave (PAW) was used to describe the interactions between ions and electrons. The Monkhorst-Pack scheme of 9x9x1 and 18x18x1 k-points were used for relaxation and the electronic calculations respectively [47]. To account for the van der Waals interaction between the H2 molecules and the other atomic species, the DFT-D3 approach was used [48]. The structure geometries were relaxed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method [49]. Pristine silicene was modelled using a monolayer of 32 atoms arranged in a 4x4 supercell with a vacuum spacing of 20 Å in the z- direction to avoid the repeating unit cell interactions that occur due to periodic boundary conditions. The unit cell parameter was found to be a = 3.83 Å which matches with previous studies.
The formation energy for the pristine monolayer of silicene was assumed to be 0 eV and the defect formation energy was then calculated using -
Ef = Edef - NpEp (1)
where Ef is the defect formation energy, Edef is the energy of the defective silicene system and Np is the number of silicon atoms in the defective system which was taken to be 31 and 32 for the single vacancy and Stone-Wales defective system respectively. Ep is the energy per silicon atom in the pristine system.
The lithium decoration energy was calculated as:
ELi ads = ELi+system – (Esystem+ELi) (2)
Where ELi ads is the binding energy of a single lithium atom onto the monolayer system surface, E Li+system is the energy of the lithium decorated monolayer and Esystem is the energy of the defective silicene substrate. ELi is taken to be the energy of a single lithium atom.
The hydrogen adsorption energies (EH2 ads) for multiple pairs of H2 molecules on the lithium decorated systems were calculated using:
EH2 ads = EH2+Li+system – ELi+system + (NH2*EH2))/ NH2 (3)
Here, EH2+Li+system and EH2 refers to the total energy of the hydrogen adsorbed lithium decorated structures and the energy of a single H2 molecule respectively. NH2 is the total number of hydrogen molecules adsorbed onto the substrate at any given instance.
Gravimetric densities were also calculated for the substrates using –
Gravimetric Density = (n1WH2)/ (n1WH2 + n2WSi +2WLi) (4)
Where WH2, WC/Si and WLiare the mass of the H2 molecule, silicon atom and lithium atom respectively. The number of H2 molecules and number of atoms in the silicene substrate are represented using n1 and n2 respectively.