## 2 Results and Discussion
### The Formation of Maleimide and Succinimide Products: Mechanism of Polymerization-Rupture
#### 2.1.4 NBO Analysis
According to the steps just mentioned, a Gibbs free energy profile was built by the theoretical determination of thermal properties (DFT optimization and frequency calculations) at 300 \({}^{\circ}\)C for all transition states (TS) and stationary points (reactive, R; intermediates, INT; and products, P) involved in the mechanism; a quasi-harmonic correction was additionally applied using the Goodvibes v 2.0.3 program [14] (an average difference of 9 kJ/mol was obtained when comparing with non-corrected Gibbs free energies). The energy profile is shown in Figure 6.  
Figure 6: Gibbs free energy profile for the formation of 2,5-diketopiperazine product through dimerization and cyclization of asparagine. Differences of energy between each point of the profile are shown beside each corresponding blue dashed line; energies for TS1 (the higher transition state), and Pdkp (the diketopiperazine product) are shown in red. Curved arrows represent formation of by-products, residues, or products that come out of the profile. Since the change in the Gibbs free energy for the global reaction is negative (\(\Delta G_{reaction}=-52\) kJ/mol), it can be stated that the reaction is spontaneous. The dimerization process contains the highest energetic barrier in the entire profile (the barrier from 2R to TS1), and according to the degrees of rate control and thermodynamic rate control calculated (See Table 3), this simple step is stablished as the rate-determinant process of the entire reaction (See the corresponding Mjk matrix in Table S1 in the supporting information). Therefore, the amino acid is required to overcome a barrier of 272 kJ/mol corresponding to the first step of the dimerization (the condensation step), while the subsequent elimination of water is considered a more straightforward step. The first difference between the two profiles described in Figures 1 and 6 is noticed in the cyclization process, especially from INT2 to INT3 in both cases. Looking at the respective mechanisms (Schemes 1 and 2), it is interesting to notice that the first and second steps are the same for both reactions, and the primary difference between them is the formation of a five-membered ring (\(\Delta G^{\ddagger}=171\) kJ/mol) in the mechanism of polymerization-rupture instead of the six-membered ring (\(\Delta G^{\ddagger}=203\) kJ/mol) obtained in the DKP mechanism, being the polymerization process kinetically favored by about 32 kJ/mol (Scheme 3). The difference in the Gibbs free energy activation barriers would constitute an excellent answer to the question about why, during pyrolysis of asparagine, the 2,5-diketopierazine product is actually not obtained, but maleimide and succinimide molecules are obtained instead, as reported in experimental works [8; 9; 10; 12]. Since the atoms involved in each process are not the same, there are evident differences from the mechanistic point of view (see Scheme 3). To obtain the 2,5-diketopierazone product, an amine group reacts with a carboxylic group, while for the mechanism of polymerization-rupture, two amide groups are reacting with each other. Therefore, they are two different reactions. Reaction Force Analysis on the Cyclization Process  
The total electronic energy through the reaction coordinate of these two reactions was obtained by the respective IRC calculations (see Figure 7). The reaction force approach and determinations of the corresponding works were done in order to analyze the differences between these two cyclization \begin{table}
\begin{tabular}{c c c c c} \hline _step i_ & \(Min_{i}\) & \(X_{TRC,i}\) & \(TS_{i}\) & \(X_{RC,i}\) \\ \hline
1 & 2 R & \(1.00\times 10^{0}\) & TS1 & \(1.00\times 10^{0}\) \\
2 & INT1 & \(3.69\times 10^{-5}\) & TS2 & \(1.55\times 10^{-15}\) \\
3 & INT2+H2O & \(6.55\times 10^{-5}\) & TS3 dkp & \(5.75\times 10^{-7}\) \\
4 & INT3 dkp & \(4.16\times 10^{-9}\) & TS4 dkp & \(1.59\times 10^{-12}\) \\ - & Pdkp+H2O & — & — & — \\ \hline \end{tabular}
\end{table}