**3.1. N***n***@C70 structures and reaction energies**

**N3** . The minimum energy structure corresponds to a linear and centered N3 , which shows the same structure in charged and neutral systems, see **Figure 3**. There is also found a second stable structure that may closely resemble the association between the N2 molecule and an "isolated" nitrogen atom. The difference in the relative energies exceeds 40 kcal/mol, leading us to assume that the linear isomer encapsulated in C70 would predominate, if it was ever produced. Distances between nitrogen atoms (1.20 Å) suggest a weaker bond than that observed for N2 (1.11 Å).

Reaction energies were calculated based on various assumptions. First, it is considering only the stabilization due to the encapsulation of nitrogen atoms as reagents. Second, considering structures that can be found at room temperature as starting materials (**Table 1**).

The 3N + C70 → N3 @C70 reaction was used to evaluate the role of the C70 box for the stabilization (or not) of 3 isolated nitrogen atoms, compared to placing them within the cage in polymer

**Figure 3.** Structure of Nn@C70, where *n* = 3–10, endohedral fullerenes, calculated using the B3LYP/6-311G method.

form as N3 . Apparently reactions are energetically favored. This energy difference is also highest for the cation, followed by the anion and finally the neutral (**Table 1**).

We evaluated energy differences for the reactions presented, while attempting to evaluate the role of the box, when initial material consisted of existing structures (such as N<sup>3</sup> − and N2 , rather than isolated nitrogen atoms). Evidently, as is stated in **Table 1**, the cation has lower ∆E energy. This molecule would be the most viable option at the time of the reaction, as the carbon cage would effectively stabilize the nitrogen polymer. Similarly, fullerene C70 is able to stabilize and cage the anion polynitrogen, as it also has a negative ΔE value. Contrastingly, in the case of the neutral structure, this is not predicted as a favorable reaction. In spite of this, stabilization of N<sup>2</sup> + N in the C70 cage is favorable (∆E = −60.44 kcal/mol).

energetically favored. Similar to that observed in the previous isomer, it is predicted that the interaction with the cationic system would be greater than with the anionic or with the neutral one.

**Table 1.** Reaction energies due to the encapsulation of nitrogen structures for N*n*@C70, where *n* = 3–6, obtained at

charged), evidently the neutral one is not predicted to be energetically favorable. This would lead to a structure which could be very interesting for possible high energy density material (HEDM) applications, a field where metastable compounds and single nitrogen-nitrogen bonds are encouraged. However, the distance between nitrogen atoms (1.11 Å) is characteristic for a triple bond, which discards (at least in principle) this structure as a candidate. For charged systems, the reaction energy is favorable. This gives an idea of the role played by the

, neutral and

Analyzing encapsulation reactions initiating with different materials (such as N<sup>2</sup>

**N***n***@C70 Anion Neutral Cation**

<sup>−</sup> 3N + C70 → N3

<sup>−</sup> 1.5N2 + C70 → N3

<sup>−</sup> 4N + C70 → N4

<sup>−</sup> 2N2 + C70 → N4

<sup>−</sup> 5N + C70 → N5

5 N-a −764.51 −652.59 −814.12 5 N-b −745.26 −646.04 −804.31

<sup>−</sup> 2.5N2 + C70 → N5

−0.13 156.04 −167.21

<sup>−</sup> N2 + N3 + C70 → N5

34.89 73.75 −43.31

−881.66 −807.24 −965.47

<sup>−</sup> 6N + C70 → N6

<sup>−</sup> 3N2 + C70 → N6

<sup>−</sup> N5

50.62 163.12 −23.19

−117.29 −385.00 −131.54 N3 <sup>−</sup> + N3 + + C70 → N6

−255.14

<sup>−</sup> + N+

+ C70 → N6

@C<sup>70</sup>

−495.82 −383.89 −544.51

−39.13 101.29 −106.97

−678.69 −606.42 −764.55

−69.85 40.49 −145.73

@C<sup>70</sup> 2N + N+

@C<sup>70</sup> N3

@C<sup>70</sup> 3N + N+

@C<sup>70</sup> N2 + N2

@C<sup>70</sup> 4N + N+

@C<sup>70</sup> 2N2 + N+

@C<sup>70</sup> N2 + N3

@C<sup>70</sup> 5N + N+

@C<sup>70</sup> 2N2 + N2

@C<sup>70</sup> N3 + N3

+ + C70 → N3

+ C70 → N3

Reactivity Indexes and Structure of Fullerenes http://dx.doi.org/10.5772/intechopen.70642

+ C70 → N4

+ C70 → N5

+ C70 → N5

+ C70 → N6

+ + C70 → N4

+ + C70 → N5

+ + C70 → N6

+ + C70 → N6

@C<sup>70</sup> +

@C<sup>70</sup> + 35

@C<sup>70</sup> +

@C<sup>70</sup> +

@C<sup>70</sup> +

> @C<sup>70</sup> +

@C<sup>70</sup> +

@C<sup>70</sup> +

> @C<sup>70</sup> +

@C<sup>70</sup> +

@C<sup>70</sup>

@C<sup>70</sup>

@C<sup>70</sup>

@C<sup>70</sup>

@C<sup>70</sup>

@C<sup>70</sup>

@C<sup>70</sup>

@C<sup>70</sup>

@C<sup>70</sup>

<sup>−</sup> + C70 → N5

<sup>−</sup> + C70 → N6

<sup>−</sup> + N + C70 → N6

@C<sup>70</sup>

<sup>−</sup> + C70 → N4

For *n* = 3 2N + N<sup>−</sup> + C70 → N3

For *n* = 4 3N + N<sup>−</sup> + C70 → N4

N2 + N2

For *n* = 5 4N + N<sup>−</sup> + C70 → N5

For *n* = 6 5N + N<sup>−</sup> + C70 → N6

2N2 + N2

B3LYP/6-311G level of theory.

N5

<sup>−</sup> + C70 → N5

5 N-a N5

5 N-b N2 + N3

<sup>−</sup> + C70 → N3

N3

C70 cage in general, as it stabilizes systems with higher charge density.

**N4** . We analyzed structures consisting of two pairs of N<sup>2</sup> molecules, **Figure 3**, in almost parallel positions (with an approximate distance of 2.67 Å between the two N<sup>2</sup> pairs). An arrangement very similar to the neutral one was observed for the charged systems. Unstable structures for charged systems were also found, as in essence they could almost be considered as 4 atoms with no obvious interacting link.

The stabilization of arrangements of 4 nitrogen atoms in the cage was evaluated in terms of reaction energy, results for which are shown in **Table 1**. Evidently, the encapsulation would be


**Table 1.** Reaction energies due to the encapsulation of nitrogen structures for N*n*@C70, where *n* = 3–6, obtained at B3LYP/6-311G level of theory.

form as N3

**N4**

. Apparently reactions are energetically favored. This energy difference is also high-

− and N2 ,

molecules, **Figure 3**, in almost parallel

pairs). An arrangement

We evaluated energy differences for the reactions presented, while attempting to evaluate

rather than isolated nitrogen atoms). Evidently, as is stated in **Table 1**, the cation has lower ∆E energy. This molecule would be the most viable option at the time of the reaction, as the carbon cage would effectively stabilize the nitrogen polymer. Similarly, fullerene C70 is able to stabilize and cage the anion polynitrogen, as it also has a negative ΔE value. Contrastingly, in the case of the neutral structure, this is not predicted as a favorable reaction. In spite of this,

very similar to the neutral one was observed for the charged systems. Unstable structures for charged systems were also found, as in essence they could almost be considered as 4 atoms

The stabilization of arrangements of 4 nitrogen atoms in the cage was evaluated in terms of reaction energy, results for which are shown in **Table 1**. Evidently, the encapsulation would be

the role of the box, when initial material consisted of existing structures (such as N<sup>3</sup>

**Figure 3.** Structure of Nn@C70, where *n* = 3–10, endohedral fullerenes, calculated using the B3LYP/6-311G method.

est for the cation, followed by the anion and finally the neutral (**Table 1**).

stabilization of N<sup>2</sup> + N in the C70 cage is favorable (∆E = −60.44 kcal/mol).

positions (with an approximate distance of 2.67 Å between the two N<sup>2</sup>

. We analyzed structures consisting of two pairs of N<sup>2</sup>

34 Fullerenes and Relative Materials - Properties and Applications

with no obvious interacting link.

energetically favored. Similar to that observed in the previous isomer, it is predicted that the interaction with the cationic system would be greater than with the anionic or with the neutral one.

Analyzing encapsulation reactions initiating with different materials (such as N<sup>2</sup> , neutral and charged), evidently the neutral one is not predicted to be energetically favorable. This would lead to a structure which could be very interesting for possible high energy density material (HEDM) applications, a field where metastable compounds and single nitrogen-nitrogen bonds are encouraged. However, the distance between nitrogen atoms (1.11 Å) is characteristic for a triple bond, which discards (at least in principle) this structure as a candidate. For charged systems, the reaction energy is favorable. This gives an idea of the role played by the C70 cage in general, as it stabilizes systems with higher charge density.

**N5** . The geometries for N5 @C70 nitrogen polymers are shown in **Figure 3**. Captions 5 N-a and 5 N-b symbolize the optimized structures, noting that 5 N-a represents a cycle of 5 nitrogen atoms that is quite similar to cyclopentazole; a system found only as an anion [29, 31]. Distances between nitrogen atoms (~1.34 Å) for the cycle suggest a double-like bond. Contrastingly, 5 N-b isomers essentially consist of two systems; N2 and N3 , separated by approximately 2.4 Å. We attempted to optimize a structure similar to N<sup>5</sup> + that was predicted theoretically; however, our efforts were in vain, as all the structures presented fragmentation. Distances between nitrogen atoms are, for bended N3 fragment, 1.19 Å, whereas for N<sup>2</sup> dimer 1.11 Å.

be the case. Again this presents a possible other use (as HEDM) for this type of molecule. We also present alternative reactions with energetically favored schemes, which we essentially

. The most stable isomer for this composition consists of the assembly between a hexagon and a dimer as two separate units. Bond distances for N─N are around 1.33–1.34 Å, more related to a double bond. Likewise, isomers that involve the formation of a distorted—but unstable—octagon are found with considerably higher energies, making it possible to ensure

@C<sup>70</sup> 6N + N+

@C<sup>70</sup> 3N2 + N+

@C<sup>70</sup> 7N + N+

@C<sup>70</sup> 3.5N2 + N+

@C<sup>70</sup> 8N + N+

@C<sup>70</sup> 4N2 + N+

@C<sup>70</sup>

@C<sup>70</sup>

@C<sup>70</sup>

+ C70 → N7

Reactivity Indexes and Structure of Fullerenes http://dx.doi.org/10.5772/intechopen.70642

+ C70 → N7

+ C70 → N8

+C70 → N8

+ C70 → N9

+ C70 → N9

+ C70 → N10@C<sup>70</sup>

+C70 → N10@C<sup>70</sup>

+

@C<sup>70</sup> + 37

@C<sup>70</sup> +

@C<sup>70</sup> +

> @C<sup>70</sup> +

@C<sup>70</sup> +

> @C<sup>70</sup> +

> > +

+

attribute to the stabilization of charges in the fullerene cage (**Table 2**).

**N***n***@C70 Anion (−) Neutral (0) Cation (+)**

<sup>−</sup> N5

<sup>−</sup> N5

<sup>−</sup> 7N + C70 → N7

−979.94 −866.37 −1026.35

<sup>−</sup> 3.5N2 + C70 → N7

107.89 265.72 −55.99

<sup>−</sup> 8N + C70 → N8

<sup>−</sup> 4N2 + C70 → N8

<sup>−</sup> 9N + C70 → N9

187.33 392.54 70.88

<sup>−</sup> + N3 + + C70 → N8

−1046.85 −995.79 −1149.58

<sup>−</sup> 4.5N2 + C70 → N9

364.43 459.75 144.23

<sup>−</sup> + N3 +

+ N3 + C70 → N9

<sup>−</sup> 10N + C70 → N10@C<sup>70</sup> 9N + N+

<sup>−</sup> 5N2 + C70 → N10@C<sup>70</sup> 4N2 + N2

**Table 2.** Reaction energies due to the encapsulation of nitrogen structures for N*n*@C70, where *n* = 7–10, obtained at

<sup>−</sup> N3

b −1143.41 −981.87 −1192.45 a −1150.42 −996.12 −1184.66

a 438.36 621.14 396.74

<sup>−</sup> + N2 + + C70 → N7

−1615.18 −1528.77 −1688.71

@C<sup>70</sup>

@C<sup>70</sup>

@C<sup>70</sup>

123.67 −148.76

@C<sup>70</sup>

@C<sup>70</sup>

171.55 −41.48

@C<sup>70</sup>

@C<sup>70</sup>

@C<sup>70</sup>

−

380.20 −47.35

**N8**

For *n* = 7 6N + N<sup>−</sup> + C70 → N7

N2 + N5

2N2 + N3 − +C70 → N7

For *n* = 8 7N + N<sup>−</sup> + C70 → N8

N3 + N3

N3 + N5 − → N8 @C<sup>70</sup>

For *n* = 9 8N + N<sup>−</sup> + C70 → N9

N5 − + 2N2

3N2 + N3 − + C70 → N9

For *n* = 10 9N + N<sup>−</sup> + C70 → N10@C<sup>70</sup>

N3 −

N5

B3LYP/6-311G level of theory.

422.59

<sup>−</sup> + C70 → N7

<sup>−</sup> + N2 → N8

+ C70 → N9

+3.5N2 + C70 → N10@C<sup>70</sup>

<sup>−</sup> + 2.5N2 → N10@C<sup>70</sup>

Geometry acquired by 5 N-a molecule represents the most stable. The energy of neutral 5 N-b is 6.5 kcal/mol greater than 5 N-a, which may be considerable, but would not be as difficult to achieve under experimental conditions. Likewise, the energy difference between the anion and cation systems exceeds 10 kcal/mol, with the cyclic isomers proving the most stable.

The formation energies of the different N<sup>5</sup> @C70 isomers were calculated by assuming that nitrogen atoms were the material at initiation, indicating at all times that this reaction would be favored. The highest value corresponded to cationic species, followed by anionic species and finally neutral species. Changing the reagents for other species reveals interesting dilemmas. Assuming formation with the pentazolate anion would imply a slightly favored reaction, but when substitute for N2 + N3 − , these systems become energetically unfavorable. Although this approach might discourage synthesis, it could also act as a motivator, as it would be considered as metastable and a candidate for high energy material, HEDMs.

**N6** . For N6 @C70, the most favored structure corresponds to the arrangement of three N2 molecules, separated 2.4 Å each of the other (**Figure 3**). For previous reports of N6 @C60 [53, 54], the lower energy structure corresponds to the pot-shaped hexagon, in contrast to that presented here. We suggest that this difference is due to the larger volume of C70 as compared to C60, which allows a bigger dispersion within the cage. Cyclic structure with boat-shaped conformation is found 100 kcal/mol greater in energy than reported here and, therefore, is not considered as a possible candidate.

When the reactants are represented by isolated nitrogen atoms, formation energy shows an energetically favorable reaction. However, by changing the reactants for N2 , the prediction becomes highly unfavorable. We undertook analysis by changing the reagents, finding that when we proposed charged species as reactants, negative formation energies appeared. We attribute this mainly to the stabilization of charges by the cage.

**N7** . Of isomers identified in this system, lowest energy consisted of an N<sup>5</sup> –N2 partnership, similar to that found previously for C60 [53, 54]. Other systems involving N3 with 2N2 or even rings of N7 proved to be stable but considerably higher in energy (**Figure 3**). Bond distances for nitrogen-nitrogen in the pentagon are 1.31–1.33 Å long, which indicate a double bond. The second energy isomer in order (with N<sup>3</sup> and 2N2 fragments) is 28 kcal/mol higher in energy, whereas a distorted heptagon N7 cycle is about 90 kcal/mol higher. This is an indication that the pentagon-N2 association would be the only isomer found in a hypothetical experiment.

Reaction energies show that the stabilization of individual nitrogen atoms is favored, whereas if the reagents are exchanged for others found experimentally such as N<sup>5</sup> <sup>−</sup> <sup>+</sup> N2 , this would not be the case. Again this presents a possible other use (as HEDM) for this type of molecule. We also present alternative reactions with energetically favored schemes, which we essentially attribute to the stabilization of charges in the fullerene cage (**Table 2**).

**N5**

**N6**

**N7**

rings of N7

the pentagon-N2

. For N6

. The geometries for N5

5 N-b isomers essentially consist of two systems; N2

between nitrogen atoms are, for bended N3

36 Fullerenes and Relative Materials - Properties and Applications

The formation energies of the different N<sup>5</sup>

but when substitute for N2 + N3

considered as a possible candidate.

second energy isomer in order (with N<sup>3</sup>

whereas a distorted heptagon N7

2.4 Å. We attempted to optimize a structure similar to N<sup>5</sup>

−

sidered as metastable and a candidate for high energy material, HEDMs.

ecules, separated 2.4 Å each of the other (**Figure 3**). For previous reports of N6

energetically favorable reaction. However, by changing the reactants for N2

. Of isomers identified in this system, lowest energy consisted of an N<sup>5</sup>

similar to that found previously for C60 [53, 54]. Other systems involving N3

if the reagents are exchanged for others found experimentally such as N<sup>5</sup>

attribute this mainly to the stabilization of charges by the cage.

@C70 nitrogen polymers are shown in **Figure 3**. Captions 5 N-a and

and N3

+

fragment, 1.19 Å, whereas for N<sup>2</sup>

@C70 isomers were calculated by assuming that

, these systems become energetically unfavorable. Although

, separated by approximately

dimer 1.11 Å.

mol-

@C60 [53, 54],

, the prediction

partnership,

, this would not

or even

–N2

fragments) is 28 kcal/mol higher in energy,

<sup>−</sup> <sup>+</sup> N2

cycle is about 90 kcal/mol higher. This is an indication that

with 2N2

that was predicted theoretically;

5 N-b symbolize the optimized structures, noting that 5 N-a represents a cycle of 5 nitrogen atoms that is quite similar to cyclopentazole; a system found only as an anion [29, 31]. Distances between nitrogen atoms (~1.34 Å) for the cycle suggest a double-like bond. Contrastingly,

however, our efforts were in vain, as all the structures presented fragmentation. Distances

Geometry acquired by 5 N-a molecule represents the most stable. The energy of neutral 5 N-b is 6.5 kcal/mol greater than 5 N-a, which may be considerable, but would not be as difficult to achieve under experimental conditions. Likewise, the energy difference between the anion and cation systems exceeds 10 kcal/mol, with the cyclic isomers proving the most stable.

nitrogen atoms were the material at initiation, indicating at all times that this reaction would be favored. The highest value corresponded to cationic species, followed by anionic species and finally neutral species. Changing the reagents for other species reveals interesting dilemmas. Assuming formation with the pentazolate anion would imply a slightly favored reaction,

this approach might discourage synthesis, it could also act as a motivator, as it would be con-

the lower energy structure corresponds to the pot-shaped hexagon, in contrast to that presented here. We suggest that this difference is due to the larger volume of C70 as compared to C60, which allows a bigger dispersion within the cage. Cyclic structure with boat-shaped conformation is found 100 kcal/mol greater in energy than reported here and, therefore, is not

When the reactants are represented by isolated nitrogen atoms, formation energy shows an

becomes highly unfavorable. We undertook analysis by changing the reagents, finding that when we proposed charged species as reactants, negative formation energies appeared. We

for nitrogen-nitrogen in the pentagon are 1.31–1.33 Å long, which indicate a double bond. The

Reaction energies show that the stabilization of individual nitrogen atoms is favored, whereas

and 2N2

proved to be stable but considerably higher in energy (**Figure 3**). Bond distances

association would be the only isomer found in a hypothetical experiment.

@C70, the most favored structure corresponds to the arrangement of three N2

**N8** . The most stable isomer for this composition consists of the assembly between a hexagon and a dimer as two separate units. Bond distances for N─N are around 1.33–1.34 Å, more related to a double bond. Likewise, isomers that involve the formation of a distorted—but unstable—octagon are found with considerably higher energies, making it possible to ensure


**Table 2.** Reaction energies due to the encapsulation of nitrogen structures for N*n*@C70, where *n* = 7–10, obtained at B3LYP/6-311G level of theory.

that this isomer would predominate in an experiment. The nitrogen hexagon shows distances that suggest double bonds, ranging from 1.31 to 1.35 Å, whereas for the unstable octagon they range from 1.26 to 1.39 Å.

Similarly, the reaction energy from the stabilization of nitrogen atoms shows that this would be a favored case, starting with the cation, followed by the anion and finally the neutral. Changing the reactants it is found that metastable species would be formed with molecules present at laboratory conditions, such as N2 and N5 − . This alternate reaction scheme opens up the possibility to produce HEDM candidates.

**N9** . The most favored structure for this encapsulation consists of the assembly formed from an N5 ring and two dimers parallel to this. Nitrogen-nitrogen bonds for the cycle are very similar to the corresponding for similar cycles (1.3–1.33 Å) and the distance to N<sup>2</sup> is about 2.29 Å. Qualitatively, it is similar to that found for C60, although with considerably greater distances [53, 54]. Stable structures involving ensembles formed with N3 and 3N2 species are 18.78 kcal/mol higher in energy. The fact that it is preferred a more complex structure instead simple ones, indicates us to suggest a more determinant role of the C70 cage in the stabilization of the structure. The negative values of the reaction energy reflect the stabilization of the polynitrogenated species and evidently the reaction is more favored when the system is positively charged, after which follows the negative system and finally the neutral system. The energy difference revealing a positive energy reflects an unfavorable and endergonic reaction, although probably with metastable products. Moreover, by exploring other reaction paths to obtain the isomers of 9 nitrogen atoms, favorable reactions are obtained.

fullerene, this energy increases to 7.81 eV, implying that more energy is required in order to remove an electron. Contrastingly, when there are 10 nitrogen atoms within the fullerene network, it is easier to remove an electron because the ionization potential decreases. The even/odd effect observed in the first clusters may be explained by the resistance of systems with closed shell (even number of nitrogens) to be ionized, in contrast to those with an open shell (odd number of nitrogens) that contrarily would present a greater tendency to lose an

**I A μ η**

Reactivity Indexes and Structure of Fullerenes http://dx.doi.org/10.5772/intechopen.70642 39

@C<sup>70</sup> 7.51 4.49 −6 1.51

@C<sup>70</sup> 7.61 2.77 −5.19 2.42

@C<sup>70</sup> 7.47 4.49 −5.98 1.49

@C<sup>70</sup> 7.61 2.87 −5.24 2.37

@C<sup>70</sup> 7.54 4.56 −6.05 1.49

@C<sup>70</sup> 7.54 3.39 −5.46 2.08

@C<sup>70</sup> 7.81 1.85 −4.83 2.98 N10@C<sup>70</sup> 6.3 6.33 −6.31 −0.02

**Table 3.** Global reactivity indexes for N*n*@C70, where *n* = 7–10, obtained at B3LYP/6-311G level of theory.

The odd/even behavior of endohedral fullerenes, on gaining an electron and forming a negative ion, is also reflected in electron affinity; as apparently when C70 fullerenes encapsulate 3, 5 and 7 nitrogen atoms, the energy released is greater than when 4, 6 and 8 nitrogen atoms are caged. Notably, the energy of 8 nitrogen atoms increases to a lesser degree than 4 and 6 atoms of nitrogen. When encapsulating 9 and 10 nitrogen atoms, the sequence tends to change, because higher energy release corresponds to the 10 nitrogen structure and the lower

In terms of electronic chemical potential, endohedral fullerenes: of 4, 6 and 8 N atoms present the highest values for chemical potential, so they tend to accept electrons. Fullerenes of 3, 5 and 7 atoms have the lowest value, so they can donate electrons more easily. However, on reaching 9 and 10 atoms, the sequence changes because the isomer with 9 nitrogen atoms is the one that has the highest value of chemical potential than all other values, whereas the one

With respect to overall hardness, there is a sequence ranging from 3 to 7 nitrogen atoms where the highest hardness values are the even numbers. These, therefore, have the greatest resistance for modifying their electronic density. The lowest hardness values correspond to the odd numbers of nitrogen atoms. At 8 nitrogen atoms, the sequence changes direction: now the odd number of nitrogen atoms is the one that presents the greatest value for global hardness, besides being the molecule that is least reactive in terms of hardness. Considering the case of N10, this structure has the lowest hardness value. Consequently, it can modify

electron, resulting in a closed shell.

N3

N4

N5

N6

N7

N8

N9

energy release corresponds to the 9 nitrogen structure.

with 10 nitrogen atoms has the lowest value of all.

**N10**. As the amount of nitrogen atoms in the fullerene cage increases, a greater variety of nitrogen polymer structures can be perceived. For this system, the neutral minimum corresponds to a distorted cycle of 10 atoms, which contrasts with that reported previously for C60 [53, 54]. However, the second energy structure for charged systems (with an energy difference not exceeding 8 kcal/mol compared to the most stable) corresponds to that reported for C60. Bonding distances between nitrogen atoms are 1.23–1.43 Å for the lowest energy isomer and 1.24–1.48 Å for the second. The formation energy starting from isolated nitrogen atoms shows negative values, suggesting stabilization on the part of the box for N10, which is highest for the cation, followed by the anion and finally the neutral. The formation reaction that initiates from a variety of reagents, such as N3 − , N5 − and N2 , shows positive values, which suggest metastable structures.

#### **3.2. Global reactivity indexes**

We obtained the following chemical reactivity indexes: ionization potential, electron affinity, as well as electronic hardness and chemical potential and the results are summarized in **Table 3**. For ionization potentials, apparently fullerenes encapsulating 3–8 nitrogen atoms fall within a range of 7.4–7.6 eV. Notably, when the fullerenes contain 4 and 6 nitrogen atoms, the force with which the nitrogen endohedral fullerenes retain the electrons is slightly greater than when encapsulating between 3 and 5 nitrogen atoms. When encapsulating between 7 and 8 nitrogen atoms, this force tends to be the same, but with 9 nitrogen atoms within the


**Table 3.** Global reactivity indexes for N*n*@C70, where *n* = 7–10, obtained at B3LYP/6-311G level of theory.

that this isomer would predominate in an experiment. The nitrogen hexagon shows distances that suggest double bonds, ranging from 1.31 to 1.35 Å, whereas for the unstable octagon they

Similarly, the reaction energy from the stabilization of nitrogen atoms shows that this would be a favored case, starting with the cation, followed by the anion and finally the neutral. Changing the reactants it is found that metastable species would be formed with molecules

> and N5 −

. The most favored structure for this encapsulation consists of the assembly formed from

2.29 Å. Qualitatively, it is similar to that found for C60, although with considerably greater

18.78 kcal/mol higher in energy. The fact that it is preferred a more complex structure instead simple ones, indicates us to suggest a more determinant role of the C70 cage in the stabilization of the structure. The negative values of the reaction energy reflect the stabilization of the polynitrogenated species and evidently the reaction is more favored when the system is positively charged, after which follows the negative system and finally the neutral system. The energy difference revealing a positive energy reflects an unfavorable and endergonic reaction, although probably with metastable products. Moreover, by exploring other reaction paths to

**N10**. As the amount of nitrogen atoms in the fullerene cage increases, a greater variety of nitrogen polymer structures can be perceived. For this system, the neutral minimum corresponds to a distorted cycle of 10 atoms, which contrasts with that reported previously for C60 [53, 54]. However, the second energy structure for charged systems (with an energy difference not exceeding 8 kcal/mol compared to the most stable) corresponds to that reported for C60. Bonding distances between nitrogen atoms are 1.23–1.43 Å for the lowest energy isomer and 1.24–1.48 Å for the second. The formation energy starting from isolated nitrogen atoms shows negative values, suggesting stabilization on the part of the box for N10, which is highest for the cation, followed by the anion and finally the neutral. The formation reaction that initi-

> − , N5 − and N2

We obtained the following chemical reactivity indexes: ionization potential, electron affinity, as well as electronic hardness and chemical potential and the results are summarized in **Table 3**. For ionization potentials, apparently fullerenes encapsulating 3–8 nitrogen atoms fall within a range of 7.4–7.6 eV. Notably, when the fullerenes contain 4 and 6 nitrogen atoms, the force with which the nitrogen endohedral fullerenes retain the electrons is slightly greater than when encapsulating between 3 and 5 nitrogen atoms. When encapsulating between 7 and 8 nitrogen atoms, this force tends to be the same, but with 9 nitrogen atoms within the

similar to the corresponding for similar cycles (1.3–1.33 Å) and the distance to N<sup>2</sup>

distances [53, 54]. Stable structures involving ensembles formed with N3

obtain the isomers of 9 nitrogen atoms, favorable reactions are obtained.

ring and two dimers parallel to this. Nitrogen-nitrogen bonds for the cycle are very

. This alternate reaction scheme opens up

and 3N2

, shows positive values, which suggest

is about

species are

range from 1.26 to 1.39 Å.

**N9**

an N5

present at laboratory conditions, such as N2

38 Fullerenes and Relative Materials - Properties and Applications

ates from a variety of reagents, such as N3

metastable structures.

**3.2. Global reactivity indexes**

the possibility to produce HEDM candidates.

fullerene, this energy increases to 7.81 eV, implying that more energy is required in order to remove an electron. Contrastingly, when there are 10 nitrogen atoms within the fullerene network, it is easier to remove an electron because the ionization potential decreases. The even/odd effect observed in the first clusters may be explained by the resistance of systems with closed shell (even number of nitrogens) to be ionized, in contrast to those with an open shell (odd number of nitrogens) that contrarily would present a greater tendency to lose an electron, resulting in a closed shell.

The odd/even behavior of endohedral fullerenes, on gaining an electron and forming a negative ion, is also reflected in electron affinity; as apparently when C70 fullerenes encapsulate 3, 5 and 7 nitrogen atoms, the energy released is greater than when 4, 6 and 8 nitrogen atoms are caged. Notably, the energy of 8 nitrogen atoms increases to a lesser degree than 4 and 6 atoms of nitrogen. When encapsulating 9 and 10 nitrogen atoms, the sequence tends to change, because higher energy release corresponds to the 10 nitrogen structure and the lower energy release corresponds to the 9 nitrogen structure.

In terms of electronic chemical potential, endohedral fullerenes: of 4, 6 and 8 N atoms present the highest values for chemical potential, so they tend to accept electrons. Fullerenes of 3, 5 and 7 atoms have the lowest value, so they can donate electrons more easily. However, on reaching 9 and 10 atoms, the sequence changes because the isomer with 9 nitrogen atoms is the one that has the highest value of chemical potential than all other values, whereas the one with 10 nitrogen atoms has the lowest value of all.

With respect to overall hardness, there is a sequence ranging from 3 to 7 nitrogen atoms where the highest hardness values are the even numbers. These, therefore, have the greatest resistance for modifying their electronic density. The lowest hardness values correspond to the odd numbers of nitrogen atoms. At 8 nitrogen atoms, the sequence changes direction: now the odd number of nitrogen atoms is the one that presents the greatest value for global hardness, besides being the molecule that is least reactive in terms of hardness. Considering the case of N10, this structure has the lowest hardness value. Consequently, it can modify

**4. Conclusions**

to N8

polymers (in the form of rings).

are ongoing.

**Acknowledgements**

is also acknowledged.

from N3

The C70 fullerene is viable for storage and stabilization of nitrogen aggregates of at least 3–10 atoms, without presenting any concurrent structural deformation in the carbon network or obvious interaction (bond-like) between the nitrogen atoms and the carbon of the fullerene.

Evidently, the formation energy from the isolated nitrogen atoms is favored in all cases and

and stabilizer of polynitrogenous structures. When we propose the formation of endohedral fullerenes, initiating with materials that can be found under laboratory conditions, we predict that metastable structures will form, a fact that may be of interest in the potential use of these materials as HEDMs. The stabilizing contribution of the cage becomes more evident, as the number of nitrogen atoms within it increases, manifested in a considerable contribution on

As C70 fullerene is a large molecule of approximately 1 nm diameter, nitrogen, polymers of 3–7 nitrogen atoms prefer to remain as nitrogen molecules or as azides. However, from 8 atoms onwards, the fullerene cage begins to have greater interaction with the nitrogen polymers, reflected in the fact that these begin to compact and create more complex nitrogen

According to indexes of global chemical reactivity, endohedral fullerenes present an odd/ even behavior that corresponds to that expected for open layer species (odd number of electrons: lower ionization potential and hardness, greater electronic affinity and chemical potential) and closed layer (even number of electrons: greater ionization potential and hardness, lower electronic affinity and chemical potential). However, for 8, 9 and 10 encapsulated nitrogen atoms, there is a change in behavior. This coincides with the change in formation energies and the analysis of frontier orbitals, reflecting greater participation of the cage in fullerene behavior. The fact that smaller fullerenes have been able to encapsulate more atoms is an indication that the point of saturation in this structure has not yet been reached, providing an incentive to find new structures with greater complexity, as the degree of encapsulation progresses. These would thus constitute candidates for energetic materials and studies

The authors like to thank PRODEP (formerly PROMEP) for support provided through the 103.5/13/6900 office. FJTR like to thank the University of Guadalajara for authorizing sabbatical leave. DAHV like to thank CONACYT for support provided by the program "Apoyos para la Incorporación de Investigadores Vinculada a la Consolidación Institucional de Grupos de Investigación y/o Fortalecimiento del Posgrado Nacional." CONACYT through Project 52,827

the part of frontier orbitals as potential charge stabilizers.

there is a progressive increase, indicating the role of the cage as an encapsulator

Reactivity Indexes and Structure of Fullerenes http://dx.doi.org/10.5772/intechopen.70642 41

**Figure 4.** Frontier orbitals for Nn@C70, where *n* = 3–10, endohedral fullerenes, calculated using the B3LYP/6-311G method.

its electronic density more easily, so that it represents the most reactive molecule. Previous results for C60 encapsulation [53] showed a reduced HOMO-LUMO gap, as the number of nitrogens increased: 2, 4, 6, 8, 10. This is somewhat similar to the results for hardness, as one of the approximations to this parameter is precisely the HOMO-LUMO gap (**Figure 4**).

#### **3.3. Analysis of frontier orbitals**

Previous studies have mentioned that from 2 to 10 nitrogen atoms, there would be a charge transfer from the C60 cage to the nitrogen polymer, explained as resulting from the greater ionization and electronegativity potential of N compared to C. For more than 10 nitrogen atoms, there would be a reverse transfer from the nitrogen to the carbon atoms. This was attributed to reduced space availability and overlapping of orbitals [53]. In this work, the frontier orbitals of the most stable structures were analyzed, showing that there is an appreciable contribution from frontier orbitals to the nitrogen atoms. This implies that there must be areas susceptible to receiving charge density. It is especially interesting that when the number of N atoms within the fullerene increases, the contribution of Nitrogencentered orbitals for LUMO is even greater. Particularly, in the case of N<sup>8</sup> and higher systems, a very considerable contribution of HOMO is observed, and a sure indication that possible interactions with the cage are initiating. This may also relate to the suggestion that greater interaction between the cage and the Nn takes place, as the amount of nitrogen atoms increases. The reaction energy may also result from this, particularly as it is apparent that from N3 to N7 there is a more or less constant increase of 150 kcal/mol in stabilization energy. This reaction energy changes with N8 and higher, suggesting greater participation on the part of the cage and its interaction with Nn.
