Yttrium decorated fullerene C30 as potential hydrogen storage material: Perspectives from DFT simulations

Using the density functional theory method, hydrogen storage capacity for Yttrium doped fullerene has been studied. Bonding of Y atom with that of C30 is due to the charge transfer taking place from the d-orbital of the Y atom to the 2p-orbital of the C atom of C30. It has been predicted that a single Y atom can adsorb 7 hydrogen molecules, whose binding energy falls within the range as suggested by the U.S. Department of Energy (DOE). Interaction of hydrogen on the metal is because of the Kubas interaction where charge donation occurs from the metal d-orbital to the hydrogen 1s-orbital and there is also back donation as a result the hydrogen adsorption energy is more than physisorption. However, H atoms in the H2 molecule is not getting dissociated, only a small elongation of H–H bond in the H2 molecule is observed. The gravimetric weight percentage for 5 Y atoms loaded fullerene C30, with each Y atom adsorbing 7 H2 molecules is recorded to be 8.060%, higher than the limit of 6.5% by DOE. These findings suggest Y doped fullerene C30 may be considered as a potential candidate for hydrogen storage devices.


Introduction
Energy plays a very pivotal role in our everyday life.However larger usage of traditional fossil fuels, acid rain, and the greenhouse effect impose a serious threat for the living beings and the surrounding environment as well [1].There are various renewable sources of energy namely solar energy, wind energy, etc. which have been used as an alternative to these fossil fuels.But these sources are not stable as they fluctuate [2].Therefore, a need arises for developing energy storage systems.Hydrogen is regarded as one of the efficient, renewable and promising sources of energy carrier because of its environment-friendly characteristic and abundant presence [3][4][5][6][7][8].Among other sources of energy, hydrogen is also regarded as one of the cleanest energy sources for numerous applications in fuel cells which includes, portable, stationary and mobile power applications as well as generation of electricity [2,[9][10][11][12].Hence, hydrogen energy may be used to reduce global warming, as it can be considered as a replacement of conventional fossil fuels [13].
Any particular system considered for hydrogen storage must follow the limits that are set by US DOE for an ideal hydrogen storage device, which can store at least 6.5 wt % of hydrogen gravimetric density [14].Additionally, the average energy of hydrogen adsorption should fall in the range given by US DOE [15].The other important requirements for a hydrogen-storage material are that (1) host systems storing hydrogen molecules must possess not only appropriate adsorption kinetics, but also should undergo reasonable desorption, (2) host systems must show structural stability when exposed to various ranges of pressure and temperature, (3) the host systems should be experimentally synthesized using minimum number of synthetic routes for lower costs in their production, and (4) the binding or the adsorption energy of the adsorbed hydrogen molecules must lie in the 94 Page 2 of 11 range between physisorption and chemisorption [16][17][18][19].However, usage of hydrogen faces unique challenges due to its high diffusivity, broad range of flammability and low density relative to hydrocarbons.Developing an appropriate storage media in order to capture and store hydrogen at high density, favourable thermodynamics and fast kinetics has not been an easy job [20].
To realize adsorption and desorption of hydrogen molecules under ambient temperature and pressure, various types of porous systems have been used as hosts.For instance, the metal-organic frameworks (MOFs) and the covalent organic frameworks (COFs) are extensively studied for hydrogen storage as well as other gas storage [21][22][23][24][25][26][27].But they have their own disadvantages since they adsorb hydrogen with lower adsorption values, which does not achieve the requirement needed for applications in automobile industries [28][29][30].Along with large number of hydrogen storage systems like the porous framework materials, metal hydrides, amino boranes, etc. family of carbon nanostructures like zero-dimensional fullerene, one-dimensional carbon nanotube, two-dimensional graphene, B 3 CN 4 monolayer, B 4 CN 3 sheet etc. have been extensively considered for efficiently storing hydrogen [31][32][33][34][35]. Curved carbon nanostructures are found to be more promising as compared to the planar ones as observed from some ab initio studies [36].But for practically storing hydrogen molecules, unfortunately, pristine carbon nanosystems are deemed to be chemically inert [37][38][39][40][41][42].Metal decoration, on the other hand, has produced enhanced hydrogen adsorption enthalpies.By doping the carbon nanosurfaces with various transition metal atoms, hydrogen adsorption energies on them are found to be suitable for hydrogen storage [43][44][45][46][47][48][49][50][51].Pd doped multi-walled carbon nanotubes (MWCNT) have been reportedly used to store hydrogen experimentally using chemical reduction and laser ablation methods with around 6 wt % for maximum numbers of Pd atoms [52].Another study predicts that a graphene surface decorated with a single Zr atom can adsorb at most 9 hydrogen molecules with 11 wt % of hydrogen loading [53].Ti atom doped on zigzag graphene nanoribbons are also explored as host materials for hydrogen storage with a gravimetric percentage more than the requirement of US DOE [54].Hydrogen storage on Pd decorated graphene sheet and its B-N co-doped counterpart have been reported where DFT-D3 dispersion corrections are included [55].Hydrogen storage on nickel and titanium doped defective graphene nanoplatelets have also been studied, where adsorption of hydrogen molecules on the nickel doped host favours the Kubas type of interaction [56].Experimentally, Pd 3 Co decorated on boron or nitrogen-doped composites of graphene have been used for storing hydrogen molecules [57].Hydrogen uptake capacity is experimentally obtained to be more than 6.5 wt % with magnesium catalyzed, graphene-Ni nanocomposites [58].Graphyne nanotubes as well as a monolayer of graphyne decorated with Li, Ca, Sc, Ti is also reportedly used to store hydrogen molecules and a comparative study on these has been done by Lu et al. [59,60] Lithium-doped graphyne has reportedly achieved a very high storage capacity with 18.6% weight percentage of hydrogen molecules and can be an emerging hydrogen storage material [61].Yttrium (Y) is a rare earth transition metal atom having the promising capability to be used as hydrogen storage material [62].Yttrium doped on single-walled carbon nanotube (SWCNT) can physisorb up to 6 hydrogen molecules having 100% desorption and 6.1 wt % of hydrogen loading.Y doped graphene and graphyne have also been used for hydrogen storage devices [63,64].
Fullerene is a closed cage carbon nanostructure, possessing fascinating properties and it covers a broad field of research [65][66][67].Both pristine, as well as doped fullerenes, have been used as hydrogen storage material [37,38].Apart from carbon, nitrogen and boron are also used as host materials for storing hydrogen molecules both theoretically and experimentally.Porous fullerene, substituted by 24 B atoms and then doped with Ti, has been found to adsorb up to 8.2 wt % of hydrogen.Metal decorated systems namely, C 48 B 12 M 12 (M = Fe, Co, Ni) and M 32 B 80 (M = Ca and Sc) recorded good hydrogen adsorption capacity [68,69].Sc [70] and Ti doped B 24 C 24 [70,71] are explored for storing hydrogen molecules and Sc doped host gains a storage capacity of 6.80 wt % by adsorbing five molecules of hydrogen [70].Six hydrogen molecules are adsorbed by Ti doped C 24 B 24 and the gravimetric density is recorded as 8.1 wt % [71].In a similar study, where Sc and Ti are doped on C 24 N 24 , the hosts are found to adsorb thirty H 2 molecules and the respective weight percentages are 6.30 wt % and 6.20 wt % [72].Studies with even carbon and boron-nitrogen terminated chains on fullerene C 20 decorated with Ti atom is being used as hosts for hydrogen storage with weight percentage 5.7 wt % and 5.6 wt % respectively [73].
Various works have been reported on metal-doped nanosystems for hydrogen storage using local density approximation (LDA).But LDA generally overestimates the binding energy and weight percentage of hydrogen molecules on the hosts, which is experimentally not feasible.Here in this study, we have adopted generalized gradient approximation (GGA) along with dispersion correction; the computed results of which will be close to experiments.Moreover, in many hydrogen storage systems, stability checking with the help of ab initio molecular dynamics have also not been performed.We have checked the stability of our host system at room temperature and the metal-metal clustering effect is also taken care of.
Although C 60 is the most famous fullerene and is being widely used in various studies, yet search for other smaller and higher fullerenes has been a topic of interest.The existence of smaller fullerenes starting from fullerene C 20 (the smallest one) are found by experiment through photoelectron spectra analysis.Fullerene C 30 is one of them [74].In addition, smaller fullerenes are studied extensively by researchers [75,76].Different properties like cohesive energy, chemical reactivity parameters, nonlinear optical properties, UV-visible absorption spectra of pristine as well as doped fullerene C 30 have been studied [65,77,78].Although hydrogen storage on metal-doped C 60 [37,38,70,79] have been reported, there is no work on hydrogen storage on Y doped C 30 .So it is interesting to investigate the hydrogen storage capability of Y decorated C 30 which is unexplored.
Being motivated by the above studies, we have designed Y doped fullerene C 30 as our host system for hydrogen storage.One Y atom can adsorb 7 molecules of hydrogen on it.The structural stability, as well as practical feasibility of the system, has been checked.Density of states and Bader charge analysis of the host both with and without hydrogen molecules adsorbed has been done, which suggests that the chosen system may evolve as a promising hydrogen storage device.

Computational details
The host fullerene, C 30 _Y along with its H 2 molecules adsorbed systems have been optimized using density functional theory (DFT) methodology, with the help of Vienna Ab initio Simulation Package (VASP) software [80][81][82][83] in conjunction with Perdew-Burke-Ernzerhof (PBE) Generalized Gradient Approximation (GGA) exchange-correlation functional.Van der Waal's (vdW) dispersion correction using Grimme's DFT-D2 [84] has been included.In order to describe the electron interactions, Projector Augmented Wave (PAW) pseudopotentials have been used.Energy cutoff for plane-wave basis set has been set to 400 eV and for the Hellman-Feynman forces, convergence criterion is taken as 0.01 eV/Å.To sample the Brillouin zone in gamma space, Monkhorst-pack 1 × 1 × 1 K-point grid is considered.All the systems are relaxed in a 20 Å cubic unit cell.Ab initio Molecular Dynamics (MD) simulations have also been carried out at 300 K using the Nosé thermostat for confirming the structural stability of the relaxed systems.

Results and discussion
Fullerene C 30 consists of five hexagons and twelve pentagons.The optimized structure of fullerene C 30 is shown in Fig. 1a.Among the pentagons of C 30 , there are two oppositely faced pentagons (capped pentagons), isolated from the hexagons.These capped pentagons are surrounded by five other pentagons which are shared by the six hexagons.Therefore naturally different bond lengths are present in C 30 .For clarity, another structure of fullerene C 30 is depicted in Fig. 1b and the bond lengths of the carbon atoms given in green colour are noted and compared with literature at GHF/6-31G(d) level of theory [78].It has been found that the C-C bond length of the capped pentagon (P1-P2) is 1.474 Å, and P3-P4 is 1.475 Å, which matches well with the previous study [78] having respective values of 1.460 Å and 1.470 Å.But a little change is accounted for P4-H1 (1.443 Å) and H2-H3 (1.445 Å) in our case, as these particular bond lengths are estimated to be 1.462 Å and 1.420 Å respectively according to the earlier reported work [78].These two bonds are actually parts of the hexagons and hence they just got alternated.The little mismatches found in the bond lengths in our study are due to the difference in the level of calculation.
The structural integrity of C 30 has been verified with the help of ab initio Molecular Dynamics (MD) simulation.At first, the temperature of the system is slowly raised to 300 K in steps of 1 femtosecond for 5 picoseconds performed in a microcanonical NVE ensemble.The system is then allowed to equilibrate in a canonical NVT ensemble at the same 300 K after 5 picoseconds.Simulation results inferred that the structural integrity of C 30 remains preserved and thus indicating the thermodynamic stability of C 30 .The MD snapshot of C 30 at 300 K is depicted in Fig. 2.

Interaction of Y on fullerene C 30
In the beginning, the Y atom is placed above a six-membered ring, a five-membered ring and on a bridge connecting two C atoms. Figure 3 and Table 1 presents three configuration of Y doped fullerene C 30 and their binding energies respectively.
The binding energy of Y doped fullerene C 30 has been calculated using the formula: where E C 30 _Y is the energy of Y doped fullerene C 30 , E C 30 is the energy of pristine fullerene C 30 and E Y is the energy of an isolated Y atom.
Among them, the Y atom stabilizes itself above a sixmembered ring (C 30 _Y configuration) of the fullerene among all the configurations studied, with the highest value of negative binding energy (− 4.150 eV).It may be emphasized here that the negative magnitude of binding energy confirms the stability of the concerned system.Thereafter we have carried out further calculations using this configuration.From Fig. 3a, we observe that the Y atom shares a similar bond length with C1/C4 (Y-C1/C4 = 2.337 Å), C2/ C3 (Y-C2/C3 = 2.722 Å), and C5/C6 (Y-C5/C6 = 2.699 Å) carbon atoms of the six-membered ring above which it is stabilized.
The otherwise non-magnetic fullerene C 30 becomes magnetic with the exohedral doping by Y atom recording a magnetic moment of 0.999 µ B .This is pictorially presented in Fig. 4, where the density of states (DOS) analysis of pristine fullerene C 30 and Y doped fullerene C 30 has been shown.We may see that the Fermi level of C 30 , comprises no states, whereas, on Y doped C 30 , clear presence of electronic states can be seen on the Fermi level.This confirms that the semiconductor C 30 has become metallic on account of doping by Y atom and as such conductivity of pristine C 30 increases.Also since there is no spin splitting on pristine C 30 , so its up spin density is a mirror image of its down spin density.The spin symmetry is however lost in case of Y doped C 30 , as can be seen from the asymmetry in its DOS between the up and down spin channels, thus pointing towards the initiation of magnetic signature in the system.The magnetism in C 30 _Y arises since the transition metal atom Y possesses d electron in it, responsible for inducing magnetic moment.To mention here, Y doped C 30 possesses a magnetic ground state just like single-walled carbon nanotube [85].Moreover, it is visible from the figure that a number of states have appeared due to the introduction of Y atom on C 30 .
From charge transfer analysis, we have found that, in the host system, C 30 _Y, fullerene C 30 gains a charge of 1.303 e, while naturally, the Y atom loses an equal amount of charge.The host C 30 _Y thus possesses higher rate of charge transfer as compared to Y doped SWCNT (1.14 e) [85].This indicates that the 5s electrons also take part in the charge transfer process because the outermost shell of Y atom contains only one d electron.Here the six C atoms of the hexagon above which the Y atom is attached gain an average charge of 0.265 e.

Interaction of H 2 on Y doped C 30
To understand the hydrogen adsorption and storage capability of Y doped fullerene C 30 , we have considered various positions of one H 2 molecule near to the transition metal atom, Y (both parallel and perpendicular) placed at a distance of around 2 Å above the Y atom.However, in all the cases, H 2 molecule aligns itself almost parallel to Y atom of the host system.The optimized structure of the hydrogen molecule adsorbed Y doped C 30 has been shown in Fig. 5.When H 2 molecule is adsorbed on the host, the H-H bond length gets elongated due to the presence of Kubas interactions.The storage capacity of hydrogen molecules on Y doped C 30 has been determined by attaching H 2 molecules around the metal atom, Y in steps of adding two H 2 molecules.The adsorption energy for the H 2 loaded Y doped fullerene C 30 has been given in Table 2.
The hydrogen adsorption energy ( E ad ) for the adsorption of 1 H 2 molecule is calculated using the formula: where E C 30 _Y_1H 2 is the energy of 1 H 2 adsorbed C 30 _Y fuller- ene, E C 30 _Y is the energy of Y doped C 30 fullerene and E H 2 is the energy of an isolated H 2 molecule.
In case of adsorption of 1 H 2 , the adsorption energy with dispersion correction is recorded to be − 0.424 eV, falling in the middle of the prescribed energy range of US DOE.The process of hydrogen molecule adsorption on Y doped fullerene C 30 is exothermic as indicated from the negative adsorption energy of C 30 _Y_1H 2 .
To calculate the adsorption energies of next successive H 2 molecule adsorbed host, we have used the following formula: where n and m are integers.
The dispersion corrected adsorption energy for 3 H 2 molecules adsorbed on C 30 _Y comes to be − 0.514 eV, while when 5 H 2 molecules get adsorbed on the host, the value is found to be − 0.400 eV.For adsorption of 7 H 2 , the adsorption energy is found to be − 0.202 eV.Fortunately, the value comes within the range as provided by the US DOE.Hydrogen molecules are adsorbed on the host system sequentially, for instance, at first one H 2 molecule is adsorbed, then three H 2 molecules are adsorbed, the number is increased to five and finally, seven H 2 molecules are found to get adsorbed by the Y doped C 30 fullerene.After each stage of H 2 molecule adsorption (in steps (2)  from 1, 3, 5 and 7), the adsorption energy has been checked to make clear that the value falls in the range of US DOE of efficient hydrogen storage.
When the H 2 molecules are adsorbed successively on Y doped C 30 , the magnetic moment in each case hardly changes.For 1 and 3 H 2 adsorption, the magnitude becomes 1 µ B , while for 5 and 7 H 2 adsorption, it slightly comes down to 0.995 µ B .But an appreciable change in bond length of H-H (0.742 Å) in an isolated hydrogen molecule is observed when it is adsorbed on the host.This bond length even varies when the number of adsorbed hydrogen molecules is increased.When 1 H 2 gets adsorbed, the H-H bond length elongates to 0.823 Å.When 3 H 2 is adsorbed, the average H-H bond length lowers down to 0.789 Å, it further shrinks to 0.784 Å for 5 H 2 , making it even smaller to 0.774 Å for 7 H 2 .The bond length of H-H after adsorption is increased from its isolated form in each case of H 2 molecule adsorption on the host; the reason is attributed to the Kubas type of interaction.But in all the cases, it remains as a molecule.This means that the adsorption is molecular and is thus important from the point of recycling concept.

Desorption temperature
The desorption temperature (T d ) is one of the important parameters for hydrogen storage systems.For H 2 molecule adsorbed on Y doped fullerene C 30 , desorption temperature has been computed using the Van't Hoff equation [86] given as: (4) where E ad represents the average adsorption energy of the H 2 adsorbed host, k B is the Boltzmann constant, P is the pressure (1 atm), R represents gas constant and ∆S is the change in entropy of H 2 when it goes from gas to liquid phase.Van't Hoff equation is being used to understand the adsorption of hydrogen in different metal hydrides.As we know, that this study considers Y doped fullerene C 30 as the host where the hydrogen molecule interacts with the transition metal atom Y and gets adsorbed through Kubas type of interaction, which is found to match with that of metal hydrides cases.One may note that there is no direct interaction of hydrogen molecules with the fullerene, but with the metal atom.The bonding is also measured to be stronger in comparison to the van der Waals interaction.This is due to the additional Kubas type of bonding which exists between the metal d orbital and the hydrogen molecule.This particular bonding arises since charge donation takes place from the d orbital of the metal atom to the hydrogen molecule, which is again followed with a return donation from the s orbital of H atom to the metal atom's d orbital, thus, resulting in an elongated H-H bond length in the H 2 molecule.
The average desorption temperature (Table 3) for the present case, considering the dispersion corrected average adsorption energy of − 0.385 eV has been estimated to 492 K, which is much higher than the normal room temperature and is suitable for applications in fuel cell.
Loading of metal atoms on the concerned host is a very crucial point to take care of since clustering of metal atoms will take place if they are not properly attached, which in turn will directly affect the optimum uptake of H 2 molecules.Metal atoms cannot be placed on all the rings (both hexagon and pentagon) of fullerene C 30 , since they will come closer and metal-metal clustering will take place.In order to avoid this, we have put the Y atom above the five hexagons of fullerene C 30 , where each Y atom is found to adsorb 7 hydrogen molecules (Fig. 6).The weight percentage is recorded to be 8.060%, which is higher as compared to H 2 weight percent target of DOE (6.5%) for reliable hydrogen storage materials.Table 3 presents H 2 uptake weight percentage, adsorption energy per H 2 and average desorption temperature for some theoretically and experimentally reported systems.A comparison with earlier studies has been made with our current work.One may find that among the Y doped as well as other metal atom doped systems (except Fe doped fullerene C 48 B 12 ), the present host, C 30 _Y excels with a comparatively higher level of H 2 uptake capacity (8.060%) along with appreciable adsorption energy and average desorption temperature.Hence on the basis of these findings, it may be anticipated that Y doped fullerene C 30 can be a good hydrogen adsorber bearing 100% recyclability and higher uptake of H 2 molecules.

Bonding mechanism
From the above discussions, one may observe that the Y atom doped on fullerene C 30 can adsorb upto 7 H 2 molecules.Population of various electronic states as well as a qualitative idea on the charge transfer taking place among the concerned atoms can be realized through the density of states (DOS) and partial DOS (PDOS) analysis.Hence in order to know in detail about the bonding mechanism, we have performed PDOS analysis in addition to the Bader charge analysis of both Y doping on C 30 and of course the H 2 adsorbed cases.Now we move on to the discussion of orbital analysis.Figure 7a shows the up and down spins of C-2p orbital of pristine and Y doped C 30 .The valance band (VB) for the case of C 30 has a very small and a large peak, while the conduction band (CB) comprises two intermediate peaks.
On the other hand, the VB for the Y doped one contains one large peak along with some smaller peaks in the CB as well.On comparison, it is observed that there are appearances of many peaks in C 30 _Y.However, no higher electronic states can be found in the CB of C 30 _Y as compared to its pristine counterpart.On analysis of the 4d orbital of Y atom in C 30 _Y and 1 H 2 molecule adsorbed C 30 _Y (Fig. 7b), it is clear that adsorption of hydrogen molecule produces appreciable changes in the electronic states in the CB of the host, but the VB is hardly affected, only a slight enhancement is visible for the peak near to the Fermi level.But at many points, an overall depletion of states can be minutely observed for C 30 _Y_1H 2 compared to C 30 _Y.This indicates that a loss of charge from 4d orbital of Y atom to the 1s orbital of H atom occurs.Moreover, as the host adsorbs more numbers of hydrogen molecules, the 4d orbital of Y continues with the charge transfer to the 1s orbital of H, which is required for the Kubas type of interaction.
The PDOS for 4d orbital of an isolated Y atom and on its attachment on C 30 is depicted in Fig. 8a.The electronic states of the isolated Y atom have one peak on the Fermi level and two more peaks on the CB region.But when it is attached to C 30 , though there is suppression of the peaks, yet the states can be seen spread over the considered energy region, with the CB leading as compared to the VB in numbers.The isolated Y atom is magnetic in nature because of the presence of an unpaired electron in its d orbital and so when it gets binded to fullerene C 30 , makes it a spinpolarized one.The reason is attributed to the charge transfer occurring from the Y atom to the fullerene, which results in the redistribution of charge among the participating orbitals.The 1s orbital of H atom in isolated H 2 molecule and when adsorbed on C 30 _Y has also been analysed (Fig. 8b).In isolated H 2 , no states except a very small peak around − 0.2 eV on the VB is found, while three peaks emerge when the H 2 molecule gets adsorbed on C 30 _Y.
Charge transfer analysis on 1 H 2 molecule adsorbed C 30 _Y reveals that overall the host loses a charge of magnitude 0.225 e to the H 2 molecule.The Y atom alone loses 0.281 e charge and an H atom of the H 2 molecule gains 0.132 e amount of charge.Figure 9 and 10 represent the charge density difference.

Diffusion energy barrier
Another crucial point that is to be taken care of for storing hydrogen in metal atom doped carbon nanosystems is to avoid metal-metal clustering for more than one metal-loaded host.If an easy movement of the metal atom is observed from its site, then a higher possibility of metal-metal cluster formation arises, thereby reducing the uptake level of H 2 , thus making the concerned host inappropriate for being a hydrogen storage device.Computationally, one may obtain   9 Charge density difference between C 30 _Y and C 30 for an isovalue 0.28 Å −3 with charge gaining C 30 in green and charge losing Y in red color respectively a higher value of hydrogen uptake, if two or more metal atoms are put closer to each other.However, in reality, this may not be achieved due to the origination of clustering among the metal atoms, which are the hydrogen adsorbers.
Here we have computed and plotted the diffusion energy barrier for the migration of Y atom through the hollow site of one hexagon to another in fullerene C 30 .Single point energy calculation is performed as the Y atom diffuses by small distances through the hexagonal holes and the difference in energy with respect to the initial energy has been pictorized in Fig. 11.Fortunately, the diffusion energy barrier is found to be 1.33 eV.This energy barrier definitely puts restrictions on the movement of the Y atom from one hexagon to another.Hence one may come to a conclusion that the diffusion of the metal atom is restricted and the system is practically viable for hydrogen storage.

Ab-initio MD simulations of Y doped C 30
A system must be stable at room temperature for its practical implementation as a hydrogen storage device.The metal atoms on the metal-loaded host should not get displaced for avoiding cluster formation with each other.The loading pattern of the metal atoms is very important for determining the weight percentage of hydrogen molecules since they are responsible for adsorbing the hydrogen molecules.These atoms should get loaded in a way so that they adsorb a maximum number of hydrogen molecules, without forming clusters among themselves.They should also not get dislodged from the system on which they are doped (here C 30 _Y).Hence, ab initio Molecular Dynamics (MD) simulation have been performed to verify the structural integrity of Y doped C 30 .It may be interpreted from the simulation results that the Y atom does not get dislodged and the host, i.e., C 30 _Y remains stable, which means that the present system can be considered for practical application as a hydrogen storage device.The MD snapshot at 300 K of C 30 _Y and C 30 _2Y systems is represented in Fig. 12.
We have also estimated the bond length fluctuation of Y atom with its two nearest C atoms in Y doped C 30 fullerene (Fig. 13).With an increase in time at a given temperature, we want to see that whether the metal atom Y is stable when placed above the fullerene and is not coming out.For this, we have plotted the nearest Y-C bond lengths at 300 K during the equilibration of the molecular dynamics simulation and the bond length variation is detected to be less than 10%.This small percentage of fluctuation in bond length is may be due to the little bit of movement of Y atom.However to be emphasized that although there are vibrations due to thermal energy, but still the metal atom above C 30 fullerene is intact and is not going out of the site.So this also says that the metal-metal clustering can be avoided as the Y atom is not leaving the particular site and the structure is stable and maintaining its integrity.

Conclusions
An investigation on the hydrogen adsorption capability of transition metal (Y) decorated fullerene has been done with the help of density functional theory.Starting from one, upto seven numbers of hydrogen molecules are adsorbed to a single Y atom.The estimated adsorption energies of all the hydrogen molecules, on the host system fall in the range prescribed by DOE, suitable for hydrogen storage within ambient conditions.Apart from having the average adsorption energy per H 2 (− 0.385 eV), Y doped C 30 , also possesses an average desorption temperature (492 K) optimum for being used in fuel cell technologies.Moreover, the adsorption energies of hydrogen molecules fall in between physisorption and chemisorption energy range, which is attributed to the presence of Kubas type of interaction with the metal atom losing net charge to the hydrogen's 1s orbital.The weight percentage is recorded to be 8.06 (higher than the limit of 6.5% by DOE) with the loading of 5 Y atoms on the fullerene, and a total of 35 H 2 molecules gets adsorbed on this host system.The host system is found to be stable and a higher diffusion energy barrier of Y atom prevents the metal-metal clustering.Hence, Y doped C 30 may serve as a promising hydrogen storage material having high hydrogen uptake capacity and structural stability.

Fig. 1
Fig. 1 Optimized structures of a Fullerene C 30 , b Highlighted bonds of fullerene C 30 .Gray colour: Carbon.Green colour in 1 (b) also represents Carbon atoms and is used for highlighting only

Fig. 8
Fig. 8 PDOS of a Y-4d orbital of isolated Y atom and C 30 _Y and b H-1s orbital of isolated H atom and C 30 _Y_1H 2 .The Fermi level is set to zero

Fig.
Fig. 9 Charge density difference between C 30 _Y and C 30 for an isovalue 0.28 Å −3 with charge gaining C 30 in green and charge losing Y in red color respectively

Fig. 10
Fig. 10 Charge density difference between C 30 _Y_1H 2 and C 30 _Y for an isovalue 0.28 Å −3 with charge gaining H 2 in blue and charge losing Y in red color respectively

Fig. 12
Fig. 12 Molecular dynamics snapshots of a C 30 _Y and b C 30 _2Y systems at 300 K after 5 picoseconds.Gray colour: Carbon, Purple colour: Yttrium

Fig. 13
Fig. 13 Bond length fluctuation of Y atom with two C atoms of C 30 _Y at 300 K. Gray colour: Carbon, Purple colour: Yttrium

Table 2
Adsorption energies (Y and H 2 ) and magnetic moment of adsorption of Y on C 30 and H 2 on Y doped C 30 − 0.330 eV − 0.385 eV Average Desorption temperature 94 Page 6 of 11

Table 3
Hydrogen storage performance of some transition metal doped carbon nanostructures