## 2 Results and Discussion
### The Formation of Maleimide and Succinimide Products: Mechanism of Polymerization-Rupture
#### 2.1.4 NBO Analysis  
When the changes in the NBO atom charges--obtained from the respective natural bond orbital (NBO) calculations--were studied from INT12 to INT13 (see Figure 5), it was possible to identify that the larger charge transfers occurred around the transition state (IRC \(\approx\) 0.45), while in the rest of the  
Figure 4: Change in the bond length from INT12 to INT13, between atoms involved in the proton transfer N-H (red) and H–O (yellow), and between atoms involved in the bond breakings N–C (green) and C–C (blue). Segmented lines define the six regions associated with the different works mentioned earlier. Figure 3: Captures of some structures through the first rupture process of the proposed mechanism for the production of maleimide and succinimide during pyrolysis of asparagine. Each capture is associated to a specific intrinsic reaction coordinate of that elementary step. intrinsic coordinate, the NBO atomic charge kept almost constant in the selected atoms. Relatively large changes of charge also occurred around the vertical asymptote of the reaction force plot (IRC \(\approx\) 0.9). In the first section of the plot (associated with work w1), there are no significant changes of charge; therefore, this work can be related to geometrical rearrangements, as mentioned earlier. The second and third sections show substantial charge changes, representing the rupture of the ring: N(2) and C(3) are the atoms that lost more electronic density, while O(9) and C(7) are the ones that gained more negative charge; these four atoms are located in the extremes of the double rupture (bonds C(7)-N(6) and C(4)-C(3) are broken), while atoms C(4) and N(6), located between the two broken bonds, are practically not affected by the rupture (in terms of atomic charge), which means that their charges are immediately compensated, and therefore, it can be assumes that both bond breakings occur practically at the same time. In the fourth and five sections, charge changes are practically negligible except for the small area around the vertical asymptote, which represents the final hydrogen transfer: O(9), that takes the hydrogen and loses electronic density due to the bond formation; and N(2) that drops the hydrogen and gains electronic density due to the rupture of the bond. It is interesting to notice that C(7) and C(3) also relaxed, losing and gaining electronic density, respectively; thus, the evidence suggest that they were sharing the respective positive and negative charge densities before the proton transfer. Theoretical Comparison: Why Does the Pyrolysis of Asparagine Not Produce the 2,5-Diketopiperazine Product? [PERSON] et al. (2012) generalized the formation of 2,5-diketopiperazine (DKP) products based on the pyrolysis reaction of some amino acids, such as proline and glycine, describing a reaction with two  
Figure 5: Change in NBO atomic charge of selected atoms during the first rupture process in the mechanism of polymerization-rupture for asparagine. The grey horizontal band at the center of the plot represents an arbitral selected zone where changes of charge are assumed too small to be considered in the analysis. Vertical, dashed lines separate the plot in six sections associated with the six works previously calculated. main processes: a dimerization and a cyclization [12]. The mechanism involved in this process was evaluated recently in detail by us [16]. The DKP mechanism (DKP mech) consists of a dimerization in the first stage, which is reached after the intermolecular condensation between a carbonyl group and an amino group, and is followed by a dehydration of the glycol group just formed. The cyclization process occurs by similar elementary steps, but the condensation step is intramolecular, and the dehydration from the glycol group created leads to the 2,5-diketopiperazine product (Scheme 2).