Reaction energies due to the encapsulation of nitrogen structures for N
The discovery of fullerenes and their production in measurable quantities launched many studies about their reactivity and possible applications. Their peculiar structure opened possibilities for their study, initially replacing carbon atoms with alternative atoms. The surface also offers the possibility of attaching several species and the interior of their hollow structure represents a challenge because of the possibility of confining elements or molecules that may become less stable when attached to the exterior of the cage. These modifications may considerably affect both chemical and physical properties. In this chapter, we propose the encapsulation of 3–10 nitrogen atoms as aggregates inside the C70 cage. We also study the structures and reactivity indexes and the stabilization conferred as a result of being part of the fullerene. These aggregates are mainly of interest because of their possible application as energetic materials.
- endohedral fullerenes
- Density Functional Theory
- reactivity indexes
- energetic materials
Over the course of time, carbon materials have become important components not only everyday aspects of life, but also vanguard research. The enormous diversity concerning their uses and applications is constantly increasing, representing an area of constant development. Whether as part of a compound or in pure form, carbon has always attracted attention. At least in its purest forms, its structural diversity is extremely attractive (Figure 1).
Research on the formation and arrangement of carbon compounds that included long chains of this element in interstellar space lead to the discovery of fullerenes in 1985. Subsequently, they were produced in measurable quantities for use in experiments [1, 2, 3]. Even though their study may have evolved accidentally, insufficient effort has been dedicated to understanding their structure, properties and applications. The best known examples of fullerenes are C60 and C70, both of which consist of 12 pentagons, and only differ concerning the number of hexagons in their structure: 20 in the case of the first and 25 in the second. These differences result in the C60 structure, which is more like a soccer ball and C70, which is more like a rugby ball (Figure 2). While C60 is more often known as a buckyball, the rest of the hollow structures are inscribed to the general fullerene group.
1.1. Types of fullerenes
Research into fullerenes has been extremely diverse, but can be categorized according to the structural aspect to be studied. Correspondingly, we have the following: exohedral fullerenes (with external ligands or molecules), endohedrals (with internal atoms or molecules) and heterofullerenes (with one or more carbon atoms in the cage replaced by heteroatoms).
Exohedral fullerenes have essentially resulted from efforts to “decorate” the surface of the fullerenes; mainly achieved by means of chemical functionalization. These types of fullerenes have proved to be extremely interesting, both for medical applications and for their possible applications in material sciences [4, 5, 6, 7, 8]. With respect to heterofullerenes, the substitution of carbon atoms by boron, nitrogen and silicon has been proposed; in the case of the first two, these have regularly been as -BN- pairs, thus ensuring that isoelectronic species are obtained, although this has not necessarily been the only purpose; in the case of silicon, the main motive has been to search for useful applications in electronics [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. Last but not least, endohedral fullerenes exist because of the fact that they are hollow; so they have the potential application of confining or protecting molecules, thus acting as carriers or stabilizers. Particularly, those with metallic atoms inside them—endohedral metallofullerenes—have been attractive for chemistry, physics and interdisciplinary areas, such as materials and biological sciences [22, 23, 24, 25].
1.2. Polynitrogenated materials
Considerable interest in nitrogen compounds has emerged, especially those with a high content of this element, because of their particular properties and forms. Apart from the previously known molecular nitrogen (N2), little was known of species with higher nitrogen content, until the synthesis of the azide anion (N3−) . However, over time, new polynitrogenated species such as N3, N4, N5− and N5+ have been discovered or posited, whose synthesis has either represented a challenge or turned out to be surprisingly simple [27, 28, 29, 30]. In spite of this, until now, the species with the highest content of nitrogen produced in measurable quantities has contained 5 nitrogen atoms, meaning that in particular the cyclopentazole anion could be considered as a motivator for theoretical studies on its formation, as well as representing a building block towards more complex structures [31, 32, 33, 34, 35]. As species with higher nitrogen content have proved to be very unstable with respect to decomposition to N2, theoretical studies have outnumbered experimental ones. Of these, it has been determined that the preferred forms of N4 and N6 are acyclic, N8 must be formed from an azide-pentazole (N3–N5) and that more complex polynitrogens may exist such as N7, N12, N18, N20 and a great etcetera [36, 37, 38, 39, 40, 41, 42]. Considering larger structures, there is no doubt that polyhedral or fullerene-type structures have provided inspiration, as they are considered as alternative polynitrogenous arrangements with a greater number of nitrogen atoms [18, 19, 21, 41, 43, 44, 45, 46, 47]. In this sense, a hollow structure could in principle be useful for storing internal molecules, which is why it is common to find hollow carbon structures as candidates for confining polynitrogenous species. Currently, the most notable examples have been studies of N@C60, N@C70 or even N2@C60 [48, 49, 50, 51, 52], which have extended the use of the C60 cage as a way of confining up to 16 nitrogen atoms [53, 54]. Also recently, the encapsulation of a polymer nitrogen chain in a carbon nanotube was conceived, as in principle this could be stable up to room temperature . This contrasts with other proposed polynitrogenated phases of nitrogen that have been inspired by the analogy to phosphorus and arsenic, all superior in energy to the “cubic gauche” (CG). These have been proposed for extreme conditions and some experimental evidence has even been found for them [56, 57, 58, 59, 60, 61]. Therefore, confinement represents an alternative for the stabilization of polynitrogenated species that are not necessarily related to high temperatures and pressure.
As our work group has studied fullerenes and their reactivity [7, 16, 62, 63, 64, 65] and it has been proposed that C60 might be an ideal candidate for trapping nitrogen by a polymer [53, 54], the intention now is to show that C70 might also be an alternative way of storing polynitrogenous species, contributing to the development of new materials in the future.
Initiating with considerable structural diversity, we calculated and modeled endohedral fullerenes; N
We also calculated ionization energies (IE) and electron affinities (EA). These were therefore calculated to reveal the following energy differences: IE = Ecation − Eneutral, EA = Eneutral − Eanion.
Chemical potential was computed by conceptual Density Functional Theory approximation. For an N electron system with an external potential v(r) and total energy E, electronegativity is defined as the partial energy derivative to the number of electrons at constant potential and then by the definition of Mulliken as the mean of IE and EA and the negative of electronegativity is the molecular chemical potential, μ:
Chemical hardness was calculated as defined by Parr and Pearson , differentiating the chemical potential to the number of electrons, also at constant energy potential:
Energies were also obtained for the stabilization reactions for polymer species within the C70 structure, applying the formula: ∆E = ΣE(products) − ΣE(reagents) for two possible schemes. In the first, the stabilization of isolated nitrogen atoms could be analyzed through the reaction
It was previously reported that the methodology consisted of an optimization at the PM6 level. As the refinement and electronic structure were performed at the B3LYP/6-311G level, they are presented exclusively in the following.
For the majority of the structures obtained, neutral and charged species correspond to the same arrangement. In cases where it is not observed, it will be mentioned in due course.
n@C70 structures and reaction energies
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).
|For ||2N + N− + C70 → N3@C70−||3N + C70 → N3@C70||2N + N+ + C70 → N3@C70+|
|N3− + C70 → N3@C70−||1.5N2 + C70 → N3@C70||N3+ + C70 → N3@C70+|
|For ||3N + N− + C70 → N4@C70−||4N + C70 → N4@C70||3N + N+ + C70 → N4@C70+|
|N2 + N2− + C70 → N4@C70−||2N2 + C70 → N4@C70||N2 + N2+ + C70 → N4@C70+|
|For ||4N + N− + C70 → N5@C70−||5N + C70 → N5@C70||4N + N+ + C70 → N5@C70+|
|5 N-a||N5− + C70 → N5@C70−||2.5N2 + C70 → N5@C70||2N2 + N+ + C70 → N5@C70+|
|5 N-b||N2 + N3− + C70 → N5@C70−||N2 + N3 + C70 → N5@C70||N2 + N3+ + C70 → N5@C70+|
|For ||5N + N− + C70 → N6@C70−||6N + C70 → N6@C70||5N + N+ + C70 → N6@C70+|
|2N2 + N2− + C70 → N6@C70−||3N2 + C70 → N6@C70||2N2 + N2+ + C70 → N6@C70+|
|N5− + N + C70 → N6@C70−||N5− + N+ + C70 → N6@C70||N3 + N3+ + C70 → N6@C70+|
|N3− + N3+ + C70 → N6@C70|
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 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 N3− 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 N2 + N in the C70 cage is favorable (∆E = −60.44 kcal/mol).
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 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 N2, 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.
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 N5@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.
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.
Reaction energies show that the stabilization of individual nitrogen atoms is favored, whereas if the reagents are exchanged for others found experimentally such as N5− + 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).
|N||Anion (−)||Neutral (0)||Cation (+)|
|For ||6N + N− + C70 → N7@C70−||7N + C70 → N7@C70||6N + N+ + C70 → N7@C70+|
|N2 + N5− + C70 → N7@C70−||3.5N2 + C70 → N7@C70||3N2 + N+ + C70 → N7@C70+|
|2N2 + N3−+C70 → N7@C70−||N5− + N2+ + C70 → N7@C70|
|For ||7N + N− + C70 → N8@C70−||8N + C70 → N8@C70||7N + N+ + C70 → N8@C70+|
|N3 + N3− + N2 → N8@C70−||4N2 + C70 → N8@C70||3.5N2 + N++C70 → N8@C70+|
|N3 + N5−→ N8@C70−||N5− + N3+ + C70 → N8@C70|
|For ||8N + N− + C70 → N9@C70−||9N + C70 → N9@C70||8N + N+ + C70 → N9@C70+|
|N5− + 2N2 + C70 → N9@C70−||4.5N2 + C70 → N9@C70||4N2 + N+ + C70 → N9@C70+|
|3N2 + N3−+ C70 → N9@C70−||N3− + N3++ N3 + C70 → N9@C70|
|For ||9N + N− + C70 → N10@C70−||10N + C70 → N10@C70||9N + N+ + C70 → N10@C70+|
|N3−+3.5N2 + C70 → N10@C70−||5N2 + C70 → N10@C70||4N2 + N2++C70 → N10@C70+|
|N5− + 2.5N2 → N10@C70−|
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.
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 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 its electronic density more easily, so that it represents the most reactive molecule. Previous results for C60 encapsulation  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 . 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 Nitrogen-centered orbitals for LUMO is even greater. Particularly, in the case of N8 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 N
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 from N3 to N8 there is a progressive increase, indicating the role of the cage as an encapsulator 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 the part of frontier orbitals as potential charge stabilizers.
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 polymers (in the form of rings).
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 are ongoing.
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 is also acknowledged.