A First Principle Comparative Study on Chemisorption of H 2 on C 60 , C 80 , and Sc 3 N @ C 80 in Gas Phase and Chemisorption of H 2 on Solid Phase C 60

1 College of Environmental Science and Engineering, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China 2 Key Laboratory of Coal Science and Technology of Shanxi Province and Ministry of Education, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China 3National Supercomputing Center in Shenzhen, Shenzhen 518055, China 4 Shanghai Research Institute of Petrochemical Technology SINOPEC, Shanghai 201208, China


Introduction
From the beginning of the "fullerene area, " hydrogenated fullerenes have attracted wide-spread attention due to their potential application.It may not only be interesting for hydrogen storage [1][2][3][4][5], but also be used as an additive for lithium ion cells to significantly prolong the lifetime of these cells [6].
Experimentally, studies on the interaction between hydrogen and fullerenes have been focused on the chemical process of hydrogenation, with the products C 60 H X and C 70 H X being of fundamental interest as a model for other fullerene derivatives [7,8].A variety of chemical procedures have been devised to produce hydrogen radicals that could adsorb readily on these carbon atoms, using either reducing reagents [1,9,10], or catalysts [11].In addition, direct hydrogenation of C 60 and C 70 has also been achieved without the usage of a catalyst by exposing solid-phase fullerenes to highpressure hydrogen gas (0.5-30 kB) at elevated temperature (500-600 K) [4].
Theoretically, hydrogen storage based on fullerene materials has attracted many attentions.Using first principle calculations based on density functional theory, Sun and coworkers reported that each B 36 C 36 cage can store at most 18 hydrogen molecules at zero temperature [12].They also find that an isolated Li 12 C 60 cluster where Li atoms are capped onto the pentagonal faces of the fullerene not only is very stable but also can store up to 120 hydrogen atoms in molecular form with a binding energy of 0.075 eV/H 2 [13].Zhao and coworkers report that a particular Scandium organometallic buckyballs can bind as many as 11 hydrogen atoms per transition metal, which gives the maximum retrievable H 2 storage density 9 wt% [14].Kang and coworkers reports that Ni-dispersed fullerenes are considered to be capable of storing 6.8 wt% H 2 , with H 2 desorption activation barrier of 11.8 kcal/mol, which is ideal for many practical hydrogen storage [15].
However, the mechanism for direct reactions between H 2 and these fullerenes remains unexplained to the best of our knowledge.Chan et al. proposed the mechanism of H 2 molecule dissociative chemisorption on the close cousin of fullerenes, carbon nanotubes, in solid phase under high pressure [16].The breaking of the H-H bond is concerted with the formation of two C-H bonds on two adjacent carbon nanotubes in solid phase, facilitated by the application of high pressure which shortens the interstitial distance between nanotubes.The adsorption behavior gives some hints on H 2 adsorption on fullerenes.
In this work, we proposed a chain reaction mechanism for H 2 molecules dissociative adsorption on solid C 60 under high pressure.In comparison, we also studied H 2 adsorption on the most stable fullerenes C 60 and C 80 in gas phase as well as endofullerene Sc 3 N@C 80 .

Computational Method
The first principles total energy and electronic structure calculations were carried out within the framework of DFT [17] with a plane wave basis set and pseudopotentials for the atomic cores, as implemented in the Vienna ab initio simulation package (VASP) [18,19].The PW91 gradient correction was added to the local density exchange-correlation functional and projector augmented wave (PAW) pseudopotentials [20,21] were employed, with an energy cutoff of 400 eV for the plane-wave expansion as these approaches have successfully applied to similar systems [16].The supercell is sampled with a 1 × 1 × 1 -points mesh, generated by the Monkhorst-Pack algorithm.The convergence criteria were 1.0 × 10 −4 eV for the SCF energy, 1 × 10 −3 eV for total energy, and 0.05 eV/ Å for atomic force, respectively.
A climbing image nudged elastic band method was used to locate the transition states [22][23][24].The vibrational frequencies and normal modes were calculated by diagonalization of the mass-weighted force constant matrix, which was obtained using the method of finite differences of forces as implemented in VASP.The ions are displaced in the +/directions of each Cartesian coordinate by 0.02 Å.There is only one imaginary frequency for all these structures, indicating that they are indeed the transition states in the potential energy surface.
The adsorption energies ( ads ) for the adsorption of H 2 on fullerenes were calculated by where (fullerene + H 2 ), (fullerene), and (H 2 ) are the total energies of H 2 adsorbed fullerene, total energies of fullerene (fullerene = C 60 , C 80 , Sc 3 N@C 80 ), and the total energies of H 2 , respectively.The larger adsorption energy indicates the stronger adsorption.Addition on adjacent sites such as 5-6 bond and 6-6 bond engenders isomers.Furthermore, addition can take place on nonadjacent sites, which would produce many isomers.For C 60 H 2 , the simplest fullerene dihydride, there are 23 isomers.However, there is only one isomer that has been characterized.Among all kinds of C 60 H 2 isomers, (1,2) addition products are considered as the most stable.To compare the adsorption difference, we investigated H 2 adsorption on both 5-6 and 6-6 bonds.In addition, two adsorption modes are considered.One case is that the H-H bond of incoming H 2 is to be considered to parallel the 6-6 bond (Structure A and Structure E in Figure 1).The other one is that the incoming H-H bond is to be considered to point perpendicularly to the C-C bond (Structure C and Structure G in Figure 1).Energetically, the total exothermic energy for the formation of the two C-H bonds in 6-6 bond addition production is 0.77 eV favorable than that for 5-6 bond addition (Table 1), indicating that 6-6 bond addition gives the most stable structure.The two adsorption modes result in two possible adsorption mechanisms.The parallel adsorption mode gives a concerted mechanism, in which two H atoms bonded to two C atoms (TS 1 in Figure 1), respectively.In contrast, the perpendicular adsorption mode gives a step mechanism (one H atom is adsorbed first, then the second one, TS 2 in Figure 1).The barriers for both concerted mechanism and step mechanism are so high that the reaction is very difficult  to take place, although the barrier for the step mechanism is 0.11 eV favorable than that for the concerted mechanism.

H 2
Adsorption on C 80 in Gas Phase.C 80 has the same I h symmetry as C 60 , so it can also be served as adsorption media, although experimentally no hydrite of C 80 has been characterized.We carried out the same calculations as we did on C 60 as shown in Figure 2. The 6-6 parallel and perpendicular adsorption modes have the same energy barrier of 2.47 eV whereas 5-6 parallel and perpendicular adsorption  modes have the same barrier of 2.27 eV.Comparing to that of C 60 , the calculated energy barrier is about 1 eV lower than that for C 60 due to the less stability of C 80 .

H 2 Adsorption on Sc
3 N@C 80 in Gas Phase.As one of the most stable endofullerene, Sc 3 N@C 80 has become accessible in macroscopic quantities.Since the adsorption barrier for C 80 has decreased more obviously than that for C 60 , its stable derivative Sc 3 N@C 80 is expected to be a promising hydrogenation material.As shown in Figure 3, we considered two different adsorption modes: either adsorption to Sc bonded C or Sc nonbonded C.However, whichever atom H bonds, the calculated energy barriers are more  than 3.5 eV, indicating that Sc 3 N@C 80 can hardly react with H 2 .In addition, the overall exothermic energy is quite low at 0.1 eV, indicating that the reaction is not very favorable thermodynamically.

H 2 Adsorption in Solid
Phase.In contrast, the solid phase, composed of bundles of C 60 , provides a unique chemical environment dependent on the external pressure and makes it much easier for H 2 dissociative chemisorption on C 60 bucky balls.In our calculations, the interactions between hydrogen molecule H 2 and C 60 were modeled in a supercell of size 9.55 Å × 9.55 Å × 13.50 Å, and an external pressure of ∼50 kB was introduced.

Adsorption of the
First H 2 on Solid C 60 .Under the pressure of pressure of ∼50 kB, we explored the reactive trajectory of the first H 2 dissociative chemisorption on C 60 as shown in Figure 4.There are three steps involved: first, the incoming H 2 dissociation and deposition on two adjacent C 60 , from structure U to V, through transition structures (TS 11); second, the rotation of C 60 ; and finally, hydrogen migration through TS 12 to structure W, a 1,2-addition product.Figure 5 gives the plot of the relative energies for the dissociative H 2 chemisorption on solid C 60 .From this figure, we can see that the initial dissociative chemisorption step has a barrier of 1.36 eV, while the barrier for the subsequent H migration is much lower at 0.5 eV.Compared to adsorption barrier on single C 60 in gas phase, the barrier for H 2 molecules adsorption on two adjacent C 60 is quite low at 1.36 eV, which indicates that the reaction can easily take place at room temperature [16].The energy barrier differences are mainly due to the rotation.In high pressure, C 60 does not stand in his own position quietly but rotates around the center of mass randomly.The rotation deforms the H-H bond to help break the H-H bond, which leads to lower reaction barrier.
In addition, we have made some comparison between the first H 2 chemisorption on solid C 60 and solid (6,6) armchair carbon nanotube.The barrier difference for initial chemisorption is 0.14 eV.And the barrier difference for the H atom migration is 0.38 eV.Both the barrier differences are small.From this table, we can conclude that, energetically, there are no significant differences between the chemisorption on solid C 60 and solid carbon nanotube under high pressure.

Adsorption of the
Second H 2 on Solid C 60 .To explore whether it is possible to chemisorb more H 2 on the solid C 60 under high pressure, we investigate the reaction path for the addition of the second H 2 on C 60 as shown in Figure 6.The reaction mechanism is quite similar to the addition of the first one.In this process, the second H 2 also dissociatively chemisorbs on two adjacent C 60 in the initial step and then rotates slightly; one of the H atom migrates from one C 60 to another and finally forms two 1,2-addition products.The relative energies for the chemisorption of second H 2 on solid C 60 were shown in Figure 7. Compared to the first H 2 chemisorption, the calculated barrier for the second H 2 is 1.21 eV in the dissociation step, which is a littler lower than that for the first H 2 adsorption.In addition, the overall process is also more exothermic, from 0.44 eV to 1.77 eV.This is mainly due to the fact that the first H 2 molecule adsorption has already partially disrupted the conjugated system, so further addition is much easier.
In the first H 2 adsorption process, we have mentioned that one of the H atoms will transfer from one C 60 radical to another.There is another probability that H 2 molecules react with the intermediate radical directly.We also investigate this kind of adsorption modes.For the C 60 H intermediate, there are two active sites: site 2 and site 4.There are three probable adsorption modes: (1,2)-(1,2) adsorption, (1,4)-(1,4) adsorption, and (1,2)-(1,4) adsorption.For (1,2)-(1,2) adsorption, it means one H atom is adsorbed in site 2 and another H atom is also adsorbed in site 2 (Figure 8).The rules also apply for both (1,2)-(1,4) adsorption and (1,4)-(1,4) adsorption.The barriers of three category reactions are listed in Table 2. From this table, we can see that all the barriers are no more than 0.8 eV.They are much lower than the formerly calculated barrier 1.21 eV.The overall exothermic energies are also a little larger than the former calculated exothermic energy 1.77 eV.Based on these data, a conclusion can be drawn that the subsequent H 2 molecules will easily react with C 60 intermediate radicals.Thus the reaction is a chain reaction: once the first H 2 is adsorbed, the H 2 will be adsorbed one by one.There is no extra energy needed because the overall exothermic energy will compensate the energy which is needed to overcome the barrier.Herein the first H 2 molecule adsorption has become the crucial step in the overall adsorption.

Conclusions
Based on the investigation of H

Figure 1 :
Figure 1: Structures and transition states structures for H 2 molecule adsorption on C 60 in gas phase.Selective distances are given in Å.

Figure 2 :
Figure 2: Optimized structures and transition states structures for H 2 molecule adsorption on C 80 in gas phase.Selective distances are given in Å.

Figure 3 :
Figure 3: Optimized structures and transition states structures for H 2 molecule adsorption on Sc 3 N@C 80 in gas phase.Selective distances are given in Å.

Figure 4 :
Figure 4: Optimized structures and transition state (TS) structures for the first H 2 dissociative chemisorption on solid C 60 array.Selective distances are given in Å.

Figure 5 :
Figure 5: Reaction profile for the adsorption of the first H 2 on solid C 60 array.Energies are given in eV.

Figure 6 :
Figure 6: Optimized structures and transition state (TS) structures for the second H 2 dissociative chemisorption on C 60 .Selective distances are given in Å.

Figure 7 :
Figure 7: Reaction profile for the second H 2 , dissociative chemisorption on solid C 60 .Energies are given in eV.

Figure 8 :
Figure 8: Adsorption modes for the second H 2 adsorption.

2
molecules chemisorption on fullerenes C 60 and C 80 and endofullerene Sc 3 C@C 80 , we proposed a mechanism for H 2 molecules adsorption on solid C 60 under high pressure.Due to the rotation of C 60 , the H 2 molecule will easily chemisorb on two adjacent C 60 under high pressure, which is more favorable than the H 2 molecule adsorption on single C 60 .The overall reaction is a chain reaction.The first H 2 molecules adsorption is the crucial step in the overall H 2 molecules adsorption process.Once the first H 2 molecules is adsorbed on the C 60 , the second and subsequent H 2 will easily be adsorbed on the C 60 due to the lower reaction barrier.

Table 1 :
Energy barriers and reaction energies (Δ) for H 2 adsorption on C 60 , C 80 and Sc 3 N@C 80 in gas phase.Energies are given in eV.
3.1.H 2 Adsorption in GasPhase.We firstly consider the H 2 adsorption on fullerenes C 60 and C 80 and endofullerene Sc 3 N@C 80 to explore the possible adsorption media without any catalyst in gas phase.In the calculations, the interactions between H 2 molecule and fullerenes (or endofullerenes) were modeled in a supercell of size 16.0 Å × 16.0 Å × 16.0 Å, with one -point (gamma point).The energy barriers and reaction energies are listed in Table1.3.1.1.H 2Adsorption on C 60 in Gas Phase.The icosahedral C 60 consists of 12 pentagons and 20 hexagons.Hence the bonds can be categorized as two types, pentagon-hexagon bonds (5-6 bond) and hexagon-hexagon bonds (6-6 bond).

Table 2 :
Reaction barriers and reaction energies (Δ) for the second H 2 absorption on solid C 60 with three different absorption modes.