The Surface Reactivity and Electronic Properties of Small Hydrogenation Fullerene Cages

Density functional theory calculations within the G03W package, with B3LYP exchange functional and applying basis set 6 31 G (d,p) are performed. The surface reactivity and electronic properties of endo-hydrogenation and exo-hydrogenation fullerene cages are studied. It is found that the surface reactivity of mono-hydrogenation fullerene cages is larger than the surface reactivity of un-hydrogenation fullerene cages and the later is larger than the fully hydrogenation fullerene cages. In addition, the calculations show that the endo-hydrogenation fullerene cages possess the same band gaps as the un-hydrogenation fullerene cages, however, the exo-hydrogenation is reduced the band gaps of the un-hydrogenated fullerene cages form ~7 eV to ~5 eV.


Introduction
The discovery of fullerenes in 1985 was the beginning of a new field of hydrogen storage research [1].Fullerenes possess a wide range of applications in optical and electronic devices such as solar cells, photovoltaic and electro-optical devices [2], in commercial cosmetic products [3], as well as in biomedicine [4].Hydrogen bond has been one of the most important elements bonded to the fullerene cages both inter-or intra-molecular [5]- [11].Fullerene cages possess an outer and an inner surface available for hydrogen storage.Study the surface reactivity of endo-hydrogenation and exo-hydrogenation fullerene cages becomes an attractive research topic.Several hydrogenation techniques of C 60 are well described.However, the structures and the symmetry of the small hy-drogenation fullerene cages are not understood [12]- [14].Therefore, the present work is investigated the surface reactivity and the electronic properties of endo-hydrogenation and exo-hydrogenations mall fullerene cages.The hydrogenation is applied with different concentrations and on seven different location sites of small fullerene cages.

Methodology
All calculations are performed with the DFT as implemented within G03W package [15]- [21], using B3LYP exchange-functional [22] [23] and applying basis set 6 -31 G (d, p).All obtained structures are fully optimized.In this work, the energy gap is calculated as E g = E LUMO − E HOMO [24], where E LUMO is the energy of the lowest unoccupied molecular orbital and E HOMO is the energy of the highest occupied molecular orbital.The hydrogen atoms are inserted inside (endo-hydrogenation) and outside (exo-hydrogenation) the fullerene cages.The reactivity and electronic properties of mono-hydrogenation (C n H) and fully hydrogenation (C n H n and C n H n+1 ) fullerene cages are investigated and then compared with un-hydrogenation (C n ) fullerene cages.There is only one hydrogenation site for C 60 and C 20 fullerene cages at site and site respectively.However, there are four different hydrogenation sites for C 40 cages at site, site, site and site and there are five different hydrogenation sites for C 58 cages at site, site, site, site and site, see Figure 1.The hydrogenation sites have been previously explained in details [13].
For the site, each angle of the pentagon is about 108˚ and each angle of the heptagon is about 128.57˚, so that the cone angle at the vertex of two pentagons and one heptagon is 344.57˚.In the site, each angle of the hexagon is about 120˚, so that the cone angle at vertex of one heptagon, one hexagon and one pentagon is 356.57˚.In the site, the cone angle at the vertex of two hexagons and one heptagon is about 368.57˚.For the site, the cone angle at the vertex of the three pentagons is about 324˚.In the site, the cone angle at the vertex of two pentagons and one hexagon is 336˚.For the site, the cone angle at vertex of two hexagons and one pentagon is 348˚.For the site, the cone angle at the vertex of three hexagons is equal 360˚, forming plane with zero curvature surface.

Electronic Properties of Un-and Mono-Hydrogenation Fullerene Cages
The band gaps for un-hydrogenation (C n ) and mono hydrogenation (C n H) cages, from n = 20 to n = 60 are calculated and are listed in Table 1 and Table 2.In general, the hydrogenation increases the band gaps of the fullerene cages where E g (C n H cages) > E g (C n cages).For mono hydrogenation, the band gaps of exo-hydrogenationfullerene cages are smaller than the band gaps of endo-hydrogenation fullerene cages.For exo-hydrogenation, the band gaps from C 20 H to C 44 H cages are in the following order: the E g ( site) < E g ( site) < E g ( site) < E g ( site).The band gaps of fullerene cages from the C 46 H to C 60 H cages are in the order E g ( site) < E g ( site) < E g ( site) and for the C 58 H cage, the E g ( site) < E g ( site) < E g ( site) < E g ( site) < E g ( site).The smallest band gap is 0.94 eV for mono exo-hydrogenation C54H fullerene cage at site and is less than 1.36 eV of un-hydrogenation C 54 fullerene cage.

Electronic Properties of Fully Hydrogenation Fullerene Cages
The band gaps of the C n H n and C n H n+1 fullerene cages, from n = 20 to n = 60, are calculated and are listed in Table 3 and Table 4.The calculated band gaps of C n H n fullerene cages are higher than the band gap of C n fullerene cages.The endo-hydrogenation C n H n+1 fullerene cages possess the same band gaps as C n fullerene cages, however exo-hydrogenation C n H n+1 fullerene cages is reduced the band gaps of C n fullerene cages form ~7 eV to ~5 eV.
Figure 2 shows the Mulliken charge populations for C 54 , C 54 H, C 54 H 54 and C 54 H 55 fullerene cages.For C 54 cage the atomic population is almost uniform, about six electrons for carbon atom and one electron for hydrogen atom with small charge transfer about 0.024e, see Figure 2(a).For mono exo-hydrogenation C 54 H cage the charge transfer from hydrogen atom to carbon atom is increased to ~0.4e, see Figures 2(b)-(d).For the fully exo-hydrogenation C 54 H 54 fullerene cage, the charge transfer from hydrogen atom to carbon atom is about 0.244e, see Figure 2(e), and for exo-hydrogenation C 54 H 55 fullerene cages is ~0.2 eV, see Figures 2(f)-(h).

Surface Reactivity of Mono Hydrogenated Fullerene Cages
Going down from C 60 cage to C 20 cage by removing the C 2 units, the number of hexagon rings is reduced and more pentagon rings are created.In other words, the number of hexagon rings is gradually reduced until is reached zero in case of C 20 cage.To study the influence of hydrogenation on the surface reactivity of the fullerene cages C n , the dipole moments are calculated for C n and C n H cages, from n = 20 to n = 60 and are listed in Table 5 and Table 6.The Dipole moment is the measure of surface reactivity, where the high value of dipole    moment reflecting the high surface reactivity [25] [26].First, it is found that the surface reactivity of mono hydrogenation fullerene cages (C n H) is higher than the surface reactivity of un-hydrogenation fullerene cage (C n ).Second, the surface reactivity for mono exo-hydrogenation fullerene cages is always higher than the surface reactivity of mono endo-hydrogenation fullerene cages.Third, the highest surface reactivity value is 4.11 Debye for the mono exo-hydrogenation C 54 H cage, comparing with 0.15 eV for un-hydrogenation C 54 cage.Finally, the site is found to be the most reactive site.One can conclude that the surface reactivity of the mono hydrogenation fullerene cages is increased with increasing the number of pentagon-pentagon fusion, agrees with the previous observation [27].Therefore, the less the cone angle, the larger the curvature and the highest reactive site.Result in the localized carbon atom at three pentagons has the highest reactive site, while the localized carbon atom at three hexagons has the lowest reactive site.

Surface Reactivity of Fully Hydrogenation Fullerene Cages
The surface reactivity for the C n H n and C n H n+1 fullerene cages is studied.The dipole moments for C n H n and C n H n+1 fullerene cages from n = 20 to n = 60 are calculated and are listed in Table 7 and Table 8.It is noticed that the surface reactivity for (C n H n+1 ) fullerene cage is higher than the surface reactivity for (C n H n ) fullerene cage.Also, the surface reactivity of exo-hydrogenation fullerene cages is always higher than the surface reactivity of endo-hydrogenation fullerene cages.The order of the surface reactivity of endo-hydrogenation C 58 H 59 cage is at site > site > site > site > site and for the rest of the C n H n+1 fullerene cages is at site > site > site > site.Finally, the highest surface reactivity value is found to be 0.34 Debye for the exo-hydrogenation C 54 H 55 cage, comparing with 0.04 eV for C 54 H 54 cage.From Tables 5-8 the dipole moments for C n , C n H, C n H n and C n H n+1 cages, from n = 20 to n = 60, are calculated.One can sum-

Figure 1 .
Figure 1.Schematic representations of hydrogenation sites on small fullerene cages.The white circle refers to the location of hydrogenation carbon atom.

Table 1 .
The calculated energy gaps (E g ) for un-hydrogenation (C n ) and mono-hydrogenation (C n H) cages, from n = 20 to n = 60.Energy is given by eV.

Table 2 .
The calculated energy gaps (E g ) for un-hydrogenation C 58 and mono-hydrogenation C 58 H fullerene cages.Energy is given by eV.Eg(C58)/eV Eg(C58H)/eV

Table 3 .
The calculated energy gaps (E g ) of C n H n and C n H n+1 fullerene cages, n = 20 to n = 60.Energy is given by eV.Eg(CnHn)/eV Eg(CnHn+1)/eV

Table 4 .
The calculated energy gaps (E g ) of C 58 H 58 and C 58 H 59 fullerene cages.Energy is given by eV.

Table 5 .
The calculated dipole moments for un-hydrogenation fullerene C n and mono hydrogenation C n H cages, from n = 20 to n = 60.The dipole moment is given by Debye.

Table 6 .
The calculated dipole moments for un-hydrogenation fullerene C 58 and mono hydrogenation C 58 H cages.The dipole moment is given by Debye.