Lithium Decorated Borane Clusters (BnHnLi6, n=5-7) as Promising Materials for Hydrogen Storage: A Computational Study

In this study, we have investigated the hydrogen adsorption potential of lithium decorated borane clusters (B n H n Li 6 , n = 5–7) using density functional theory calculations. The principle of maximum hardness and minimum electrophilicity conrmed the stability of the hydrogen adsorbed complexes. The outcomes of the study reveals that, the hydrogen molecules are adsorbed in a quasi-molecular fashion via Niu-Rao-Jena type of interaction with average adsorption energy falling in the range of 0.10-0.11eV/H 2 and average Li-H 2 bond length is in the range of 2.436–2.550Å. It was found that the hydrogen molecules are physiosorbed at the host clusters at low temperature range 0K- 77K with gravimetric density up to 26.4 wt% which was well above target set by U.S. Department of Energy (US-DOE). ADMP-MD simulations showed that almost all the H 2 molecules are desorbed at higher temperature form 373K-473K without distorting the host clusters which indicates the studied clusters can be promoted as promising reversible hydrogen storage


Introduction
Rapid consumption of fossil fuel and their restricted supply have not only depleted the natural source of energy to a shocking amount but also engendered many environmental problems such as global warming, greenhouse issues, and air-pollution etc [1][2][3][4]. Hence, during the past couple of decades tremendous effort has been devoted to explore clean, e cient and cost-effective alternative energy sources that should be non-polluting and non-hazardous in nature. In this regard, hydrogen being the most abundant element in the earth can be considered as one of the prominent energy carriers that can be projected as the future fuel [5,6]. In addition, the combustion of the hydrogen fuel yields water and non-toxic by-products which insure it to be one of the most environment friendly gas available [7][8][9].
However, the major bottleneck of utilizing it is to nd an e cient storage system that can trap hydrogen in a large speci c area and with high gravimetric and volumetric densities (4.5 wt% and > 30 gH 2 /L by 2020) as proposed by US Department of Energy (US-DOE) [10,11]. In addition, to achieve cost-effective reversible hydrogen storage and to release hydrogen at ambient conditions, hydrogen binding energy should be in the intermediate range of physisorption and chemisorption process [12,13]. Moreover, fast adsorption and desorption kinetics of hydrogen at ambient conditions are also taken into account while considering the storage materials. Therefore, for the practical onboard application, tremendous research efforts have been put for designing materials for effective hydrogen storage.
Nanostructured clusters are of particular interest in hydrogen storage due to their riveting reaction kinetics, thermodynamics and catalytic behavior and which possess high diffusivity and surface to volume ratio as compared to their bulk counterparts [14,15] Li decorated B 24 cluster and who reported that through charge polarization mechanism the cluster could capture 9.24 wt% hydrogen molecules with 0.10 eV/H 2 of average adsorption energy [23]. Recently, our investigation on Sc doped small boron clusters for hydrogen storage capacity using molecular dynamics simulations revealed that these clusters could accommodate maximum of 9.43 wt% with average adsorption energy in the range 0.08-0.10 eV/H 2 and which are desorbable at ambient conditions [24].
Besides, a lot of boron based materials have also been investigated for hydrogen storage by many other authors [25][26][27].
Besides, hydrogen storage in boranes (B m H n ) which are synthetic class of boron hydrides possessing non classical 3-centre-2-electron bonding, were also reported by many authors. For instance, Using rst principle calculation Ghosh et al. studied the hydrogen uptake in lithium doped closo borane and found that the designed material could bind molecular hydrogen through charge-dipole interaction with average binding energy of 2.2 Kcal/mol giving rise to gravimetric density up to 7.3 wt% [28]. The hydrogen adsorption capacity of lithium decorated diborene and diboryne was also explored by Ghosh et al. who reported that these clusters could capture H 2 molecules through ion quadruple and ion induced dipole interaction resulting in a gravimetric density up to 23% and 24% respectively [29]. Chaudhuri et al. investigated the hydrogen capturing ability of Li, Sc, and Be decorated B 6 H 6 using rst princple calculation and found that these complexes could be considered as a promising candidate for hydrogen storage at low temperatures with a gravimetric density up to 12.5 wt% [30]. Similarly, Ali et al. explored the interaction of hydrogen molecules with B 6 H 6 2− complex and reported the adsorption energy close to 3.5 Kcal/mol per H 2 which was the optimal adsorption energy required for reversible hydrogen storage at ambient temperature [31]. A similar study was also reported by Wan and co-workers. [32]. In addition, hydrogen storage in other borane and carborane based clusters are reported by many others [33][34][35][36].
In the present study we have investigated hydrogen storage in inorgano-metallic complexes, (B n H n Li 6 , n = 5-7).

Computational Details
The geometry optimization of the structures with and without H 2 molecules has been carried out using Minnesota 06 (M06) hybrid functional implemented with 6-311 + + G(d,p) basis set within the framework of Density Functional Theory (DFT). M06 functional has been considered to be an e cient method to successfully investigate the non-covalent interactions. Therefore, it has proven to perform well in hydrogen storage investigations because the process of hydrogen storage involves many kind of noncovalent interactions [37]. No optimizations were accomplished with any imaginary harmonic frequencies. All the calculations were performed using computational chemistry program Gaussian 09 and Chemcraft was used to create 3D molecular complexes [38]. To investigate the stability as well as the reversibility of adsorbed hydrogen molecules on the lithium decorated borane clusters, the optimized structures were subjected to Atom-centered Density Matrix Propagation (ADMP) molecular dynamics simulations at different temperatures. The time step for the ADMP-MD simulations was set at 1fs with maximum 1000 steps were speci ed for each trajectory. Furthermore, to explore the nature of interaction between the hydrogen molecules and sorption centers of the host cluster we have employed the Bader's Quantum Theory of Atoms in Molecules (QTAIM) [39]. The partial density of states (PDOS) were calculated and analyzed using GaussSum program [40].
Similarly, the electrophilicity index can be de ned as 1 where The kinetic stabilities of the complexes were determined by calculating the energy gap (E g ) between their highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs).
The average hydrogen adsorption energy without zero point energy correction (E ads ), are obtained using the following equation: Here E Complex, E H2 and E Host is the total electronic energies without zero point energy correction of hydrogenated complex and hydrogen molecule and host cluster respectively.
The hydrogen storage gravimetric density was determined using following equation: Where Stability of the hydrogenated clusters is an important aspect to focus on while studying hydrogen storage mechanism. We have calculated the global reactivity descriptors such as; hardness (η) and electrophilicity index (ω) which provide a quantitative measure of the stability of the clusters. According to the principle of maximum hardness and minimum electrophilicity index proposed by Parr et al., molecules with a high value of hardness (η) and low value of electrophilicity (ω) gives rise to stable con guration [50,51]. We computed the reactivity parameters at M06/6-311 + + G(d,p) level of theory and the values are provided in Table 2. It has been observed that, the η value increases while ω value decreases with sequential adsorption of H 2 molecules in all studied complexes indicating the stability of the systems. For example, in the case B 7 H 7 Li 6 -18H 2 the hardness is found to increase by 7% being maximum for B 7 H 7 Li 6 -18H 2 whereas ω value decreases by 18% being minimum for the same cluster.
Similar observation is also observed in other studied compounds. Therefore all the hydrogen decorated complexes considered here are considered stable. The above fact can be reassured by analysing their HOMO-LUMO energy gaps (E g ) which is found to consistently increases with the number of hydrogen molecules for all the clusters (Fig. 3). So the kinetic stabilities of the clusters increase up to the adsorption of 18 number of H 2 molecules imparting the whole systems a non-reacting atmosphere for further addition of H 2 .
To study the hydrogen adsorption mechanism of lithium decorated borane clusters, the average adsorption energies (E ads ) are calculated using the Eq. 2↑ and the values are plotted in the Fig. 4. It can be observed from plot that the H 2 decorated clusters display an decreasing E ads with increasing H 2 molecule at a adsorption site (Li) which is obvious due to steric repulsion among the H 2 molecules.
However, if we look into the H 2 adsorption on the cluster as a whole, an almost odd-even effect is observed. This might be due to a non local effect of H 2 interaction on one site on the H 2 binding on the other. The calculated adsorption energy found in the ideal range of 0.10 eV/H 2 to 0.16 eV/H 2 which is the required range of physisorption mechanism.   Hirshfeld charge analysis has been carried out to study the charge distribution mechanism during the hydrogen adsorption in lithium decorated borane clusters. In order to reveal the bonding characteristic and frontier molecular orbital, partial density of state (PDOS) of the host clusters as well as hydrogen adsorbed system has been investigated. We set the value of full width half maxima value at 0.3 eV. The PDOS of B and Li atoms in host and hydrogen adsorbed clusters are shown in Fig. 6. For every studied cluster, a very weak overlap between B and Li atom observed which suggests ionic-like bonding between B and Li which is in good agreement with the QTAIM results. It can be observed that, as compared to the host clusters there exist some new peaks in hydrogenated clusters and near Fermi level, LUMO of H 2 has comparatively less contribution than Li LUMO which suggests that prominent charge transfer between them is unlikely to happen. Therefore the H 2 -Li bonding is most probably due to polarization (Niu-Rao-Jena kind of interaction). Table 3 Electron density in (ρ) a.u., ∇ 2 ρ, Total energy density (H BCP ) in a.u at BCP of (Li,H) and (Li,B).
The nature of the interaction between the adsorbed H 2 molecule and the Li decorated borane clusters have been investigated by performing topological analysis using Bader's Quantum Theory of Atoms in Molecules( (QTAIM) [52]. In order to describe the relative decrease or increase of charge accumulation at the bonding sites, we computed topological parameters such as electron density (ρ), and its Laplacian ∇ 2 ρ at the BCPs along with total energy density (H BCP ) that can give a qualitative knowledge about nature of bonding interaction [53,54]. The negative H BCP is an indicator of shared-kind bonding. In Table 3 we provide the computed topological parameters, which were calculated using QTAIM. From molecules also recon rming their kinetic stability. The analysis of the QTAIM results revealed the the nature of the interaction between Li-H to be weak van der Waals type. The MD simulations shows that the H 2 molecules are physisorbed at 0K and 77K, giving rise to gravimetric density up to 26.2 wt% which was well above the target set by US-DOE. At higher temperature such as 373K and 473Kthe host clusters almost all hydrogen molecules without any structural distortion. The above discussion supports the fact that the studied clusters could be promoted as a potential hydrogen storage medium.
Declarations Figure 1 Optimized geometry of Lithium doped Boranes at M06/6-311++G(d,p) level of theory Stability of the hydrogenated clusters is an important aspect to focus on while studying Figure 2 Optimized geometry of Hydrogen trapped lithium doped boranes at M06/6-311++G(d,p) level of theory. Variation of average adsorption energy with number of adsorbed H2 molecules per cluster.