## 2 Results and Discussion
### The Formation of Maleimide and Succinimide Products: Mechanism of Polymerization-Rupture
#### 2.1.3 Reaction Force Analysis  
Following the electronic energy over the reaction coordinate from INT12 to INT13 (step 13) by IRC calculations, an interesting behavior was obtained (see Figure 2), whereby the relaxation of the molecule after achieving TS13 showed a kind of plateau in the middle of the curve, which caused the existence of additional inflection points. The reaction force approach was applied, and six different works (w\({}_{\text{j}}\) \begin{table}
\begin{tabular}{c c c c c} \hline _step i_ & \(\boldsymbol{Min_{i}}\) & \(\boldsymbol{X_{TRC,i}}\) & \(\boldsymbol{TS_{i}}\) & \(\boldsymbol{X_{RC,i}}\) \\ \hline
3 & INT2 + H\({}_{2}\)O & \(2.12\times 10^{-5}\) & TS3 & \(6.77\times 10^{-9}\) \\
4 & INT3 & \(4.66\times 10^{-10}\) & TS4 & \(2.41\times 10^{-6}\) \\
5 & INT4 + NH\({}_{3}\) & \(2.42\times 10^{-4}\) & TS5 & \(2.15\times 10^{-4}\) \\
6 & INT5 & \(5.83\times 10^{-10}\) & TS6 & \(4.49\times 10^{-6}\) \\
7 & INT6 + H\({}_{2}\)O\({}^{\prime}\) & \(5.77\times 10^{-4}\) & TS7 & \(1.93\times 10^{-9}\) \\
8 & INT7 & \(6.86\times 10^{-9}\) & TS8 & \(3.54\times 10^{-7}\) \\
9 & INT8 + NH\({}_{3}\) & \(2.56\times 10^{-2}\) & TS9 & \(1.52\times 10^{-4}\) \\
10 & INT9 & \(1.22\times 10^{-8}\) & TS10 & \(3.82\times 10^{-5}\) \\
11 & INT10 + H\({}_{2}\)O\({}^{\prime\prime}\) & \(2.35\times 10^{-3}\) & TS11 & \(7.64\times 10^{-11}\) \\
12 & INT11 & \(4.27\times 10^{-6}\) & TS12 & \(9.70\times 10^{-7}\) \\
**13 \({}^{\ast}\)** & **INT12 + NH\({}_{3}\)\({}^{\ast}\)** & **9.71 \(\boldsymbol{\times\ 10^{-1}}\)** & **TS13** & **9.99 \(\boldsymbol{\times\ 10^{-1}}\)** \\
14 & INT13 + Res1 & \(7.72\times 10^{-8}\) & TS14 & \(8.41\times 10^{-6}\) \\
15 & INT14 & \(3.41\times 10^{-7}\) & TS15 & \(3.41\times 10^{-7}\) \\
16 & INT15 + Res2 & \(2.29\times 10^{-10}\) & TS16 & \(9.50\times 10^{-12}\) \\
17 & INT16 & \(5.88\times 10^{-6}\) & TS17 & \(5.85\times 10^{-6}\) \\
18 & INT17 + P1 & \(1.67\times 10^{-8}\) & TS18 & \(2.12\times 10^{-11}\) \\ - & P2 & — & — & — \\ \hline \end{tabular} \({}^{\ast}\) Bold text represents the step that contains the maximum degree of rate-control and the degree of thermodynamic-rate control.  
\end{table} 
Table 2: Degrees of rate control (X\({}_{\text{RC}}\)), and degrees of thermodynamic rate control (X\({}_{\text{TRC}}\)) for elementary steps on the polymerization-rupture mechanism during pyrolysis of asparaginewere identified in the reaction force plot. Works w\({}_{1}\) and w\({}_{2}\) are located before TS13; they represent the 66% and 34% of the energy needed to achieve the transition state, and can be easily related to geometrical and electronic rearrangements, respectively. Works w\({}_{3}\) and w\({}_{4}\), located after TS13, are also related to the electronic and geometrical reorganization in the product formation, respectively. Finally, works w\({}_{5}\) and w\({}_{6}\) located around the part corresponding to the last inflection point can be associated with a barrierless process where the proton transfer occurs from nitrogen to the oxygen. As mentioned earlier, the first rupture process represents a difficult step from the mechanistic point of view. Looking at the structures involved during the rupture process through the reaction coordinate (see Figure 3), one can see that the proposed two bond breakings occur before the transition state, breaking the ring and separating the residue from the molecular matrix, while the proton transfer apparently happens on the final stage, just in the part of the reaction force plot where there is a vertical asymptote (around IRC = 0.9). To get more insight into this rupture, the geometrical changes through the intrinsic coordinate of this elementary step were studied (see Figure 4). The bonds that break (blue and green lines) start to lengthen at almost the same time, just before entering to the second region of the plot (associated to work w\({}_{2}\)); then, at the beginning of the fourth region, the bonds are totally broken, although the distance between those atoms slightly increases.