**2. Methodology**

Initiating with considerable structural diversity, we calculated and modeled endohedral fullerenes; Nn@C70 (*n* = 3–10). For this, we used the C70 structure that corresponds to the isomer from this composition and complies with the isolated pentagon rule, IPR. The Avogadro visualizer was used as an auxiliary [66]. Given the considerable number of possible isomers, we determined the minimum energy structures in two stages. Initially, we obtained the geometry optimizations for all molecules, using the PM6 method [67]. To ensure that the global minimum for each composition has been identified, the use of search algorithms, such as those inspired by genetic algorithms, is essential, but this is currently beyond the scope of this type of system. However, the diversity of proven structures inspires confidence in our determination of the most important and representative species. Subsequently, both the geometry and the electronic structure were refined for the lower energy isomers of each composition. Likewise, the calculation of vibrational frequencies was undertaken in order to corroborate that the stationary points located on the potential energy surface correspond to a minimum (NImag = 0). All this was undertaken using the hybrid functional B3LYP with the base set 6-311G [68, 69]. As the structures of the polynitrogen species in free state may differ according to charge, this factor was also evaluated, determining the structures for the isomers neutral, cation and anion. All calculations were performed using the Gaussian09 program [70].

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:

$$
\mu = -\chi = \left(\frac{\partial E}{\partial \mathbf{N}}\right)\_{\text{v}(\mathbf{r})} \approx -\frac{\text{IE} + \text{EA}}{2} \tag{1}
$$

Chemical hardness was calculated as defined by Parr and Pearson [71], differentiating the chemical potential to the number of electrons, also at constant energy potential:

$$
\eta = \left(\frac{\partial^2 E}{\partial \mathbf{N}^2}\right)\_{\text{v(t)}} \approx \frac{\text{IE} - \text{EA}}{2} \tag{2}
$$

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 *n*N + C70 Nn@C70. In the second scheme, the reagents are substituted with nitrogen as found in standard state (N<sup>2</sup> ) or detected in experiments (N<sup>3</sup> − , N5 − , etc).
