Computational Study of the Kinetics and Mechanism of Gas-Phase Decomposition of N-diacetamides Using Density Functional Theory

3. RESULTS and DISCUSSION

The experimental results given by AL-AWADI entails a six-membered ring transition state, where an α hydrogen is extracted by the carbonyl oxygen, Scheme 1. According to Table 1, if X = H, the activation energy is 151.3 ± 2.7 kJ/mol, it rises significantly when hydrogen is substituted by a phenyl group or substituted. The effect was explained by a delocalization of electrons from nitrogen to the phenyl group. This energy difference is about 40 kJ/mol. This increase in energy can be explained computationally, making use of the functional density theory (DFT). For this purpose, five types of functionals B3PW91, X3LYP, B1LYP, LC-BLYP and CAM-B3LYP and different Pople basis sets, with dispersion functions (gd3bj), were chosen. Additionally, Ahlrichs def2-TZVP basis set was also used.

Three compounds were analysed together with three possible mechanisms, NX(COCH3)₂ X = H, Phenyl, and p-nitro Phenyl, Scheme 2. In the first mechanism, Scheme 1 was adopted, as experimentally proposed by AL-AWADI (direct method). The second mechanism (Scheme 3) involved the formation of dimers. These later were modelled in accordance with the formation of a transition state according to the final products found experimentally. The third mechanism involved an initial four-membered cyclic transition state, an intermediate and six-membered cyclic transition state leading to product formation, Scheme 4.

In the case of the second model or mechanism, Scheme IV, the transition state 1 is modelled by placing two fragments perpendicularly. This would generate an intermediate state (A), prior to the formation of the products, that is, a cetene and an amide. The intermediate compound would involve a transitional state of a seven-members ring, as enclosed below, when products are formed.

Table 2 shows the computational results, for the mechanism proposed for the scheme 4, five functionals and four basis sets with different polarization functions, in addition to the basis set of Ahlrichs Def2-TZVP have been used. The calculated thermodynamic parameters were consistent with the values found experimentally, even with signs of entropy. Among all, the functional B3PW91 showed a better agreement with the activation energy values.

At this point it was decided to apply the direct mechanism for the case, NX(COCH₃)₂ X = H. The Table 3 shows the calculation results for diacetamide (X=H), a basis set of Def2-TZVP. As it can be seen, it was not possible to reconcile the results according to the experimentally obtained activation energy value of about 150 kJ/mol. However, the proposed mechanism was adequate when hydrogen is replaced by the chlorine or methyl atom. In the first case, it is possible that chlorine will donate electron density to the nitrogen, strengthening the N-Cl bond, which can help polarize the C=O and increase the attractive force of methyl alfa hydrogens. The calculated thermodynamic parameters were consistent with the values found experimentally, even with signs of entropy. In the case of methyl, there is an electron donor effect. The excellent results found for the functional X3LYP and basis set of Def2-TZVP, highlighted in black in Table 3, led us to use this model for the case of dimers.

For the N-phenyl diacetamide (X=phenyl). Our computational calculations showed that the phenyl group is oriented perpendicular to the plane C(O)NC(O) This conformation prevents electron de localization with the aromatic ring; regardless of whether the phenyl group is substituted with electron withdrawing or electron donor’s groups, the experimental activation energy (Table 1) is approximately 30% of the value compared to hydrogen. In order to explain these values and demonstrate that nitrogen cannot share its electron pair with the phenyl ring, we proposed different actions. In first place, we found three energetically probable conformers, with three possible methyl orientations (Figure 2), once the most stable structure was obtained (Figure 2C), the phenyl was rotated by 10° intervals from 90 to 180°. We calculated its charge, intrinsic bond strength index (IBSI) and the energy change when the phenyl orientation is modified from perpendicular to in plane orientations. The results are shown in Table 4.

Any attempt to place the aromatic ring in the same plane as C(O)NC(O) rendered impossible. To calculate the energy cost, a redundant coordinate calculation was made in which the torsional barrier (TB) was determined. These calculations were performed at the B3PW91/6-311+G(3df,2p) level of theory.

To determine the torsional barrier (TB), the conformation scan s started with the phenyl perpendicular ring to the plane C(O)NC(O), with an angle of 90.06° and energy -592.92 Ha and ended with the phenyl ring rotated 180° and energy of -592.90 Ha. The energy change difference is 39.96 kJ/mol. The result is shown in Figure 3, along with the total energy scanned. The atom numbers in structure A of Figure 3 depicts to the atom numbering for the NBO calculation. The IBSI parameter are shown in Table 4.

Figure 4 shows the potential energy surface, which results from the additional movement of the groups of atoms attached to the nitrogen atom, the Figure shows two black arrows, at the top the transition state is observed and the one below, corresponds to the global minimum found. When taking the difference in energies between these points (591.533275 - 591.461992) Ha, it corresponds to 187.15 kJ/mol, very close to the value measured experimentally. The IBSI indexes, Table 4, show that when the benzene ring was coplanar to the C(O)NC(O) plane, an electron density shifts from the aromatic ring towards the carbonyl carbon. That effect is not appreciable when the ring is perpendicular to the C(O)NC(O) plane. A slight displacement of the NBO charges can also be seen at the N1-C14 bond of contribution by the ring when the system is in the C(O)NC(O) plane. Table 5 shows the thermodynamic parameters using the functional B3PW91. The best agreement was found when X=Hydrogen. Close attention was paid to two variables: the sign of entropy and the value of the activation energy.

As can be seen in Table 5, the Pople basis set 6-31G and functional B3Pw91 generates the value of 186.95 kJ/mol, very close to the experimental one. However, it is observed that the entropy has a positive value of 17.61 J/K.mol. When we improve the basis sets and add a polarization function (d), the entropy changes to negative, and the activation energy drops to 178.07 kJ/mol. Nonetheless, considering the experimental error, it was a better value. The entropy value decreases as the basis sets improve. When using the B1LYP functional, we found something interesting; the results converge very well, but they worsen as the basis sets size is increased. We investigated if there was basis set superposition error (BSSE) effect [26], since in the transition state, two molecules are separated. This basis effect was calculated to avoid underestimation of the results.

In the case of 4-nitrophenyl, Scheme V, as has been shown for the case of phenyl group when the ring is perpendicular to the plane of the C(O)NC(O), electron withdrawing, or electron donor groups will have no appreciable effect on the reaction rate. In fact, when phenyl is used, the value of the experimentally calculated activation energy is (185.7 ± 7.5) kJ/mol, and compared to 4-nitrophenyl, this value is 192 kJ/mol, which is the same within the experimental error. To prove this assertion, we calculated the activation energy at the level of theory B3PW91/6-311+G(3df,2p) gd3bj.

Calculation of the thermodynamic properties at the level of theory B3PW91/6-311+G(3df,2p)/ gd3bj yields an activation energy value of 150.69 kJ/mol, a value that is comparable to that calculated for the case of phenyl at 156.52 kJ/mol. Regarding the entropy change of -8.64 J/K mole, its value was consistent with a negative value. All the above results allow us to infer that the reaction mechanism is the same as for N-phenyl, direct mechanism. A better result is even obtained by using the functional LC-BLYP and the Def2-TZVP basis set.

Scheme 5. nitrophenyl diacetyl amine until product formation.

Scheme 5. nitrophenyl diacetyl amine until product formation.

Table 6 shows the thermodynamic results maintaining the base set Def2-TZVP and varying the type of functional. A correspondence between the results is observed, the use of the LC-BLYP/Def2-TZVP level of theory was adequate to describe our system and shows that it does not matter in which position the nitro group is located to characterize the displacement of the electrons towards the aromatic ring.

In addition to the case of the phenyl, the case of 4-nitrophenyl offered an opportunity for exploring some of the features of the natural bond analysis (NBO) for studying both inter- and intramolecular interactions, as well as interactions between bonds, charge transfer, or conjugative interactions in molecular systems. In fact, the NBO method gives very useful information about the interactions between full and empty orbitals, which is equally important in the reactivity of interacting systems. This last feature is accomplished by considering all possible interactions between natural bond orbitals (NBOs), donors, and acceptors and then estimating their involved energies using second-order perturbation theory. [27] For each donor orbital (i), there will be an acceptor orbital (j) and the associated stabilization energy $E\left(2\right)$, due to the electronic delocalization would be given by:

$$E\left(2\right)=∆E_{i,j}={\displaystyle \frac{q^{i}F(i,j)}{(E_j-E_i)}},$$

(1)

where $q^i$ is the occupation of the orbital, i.e. the number of electrons, $E_j$ y $E_i$ are the energies involved and $F(i,j)$ are the elements outside the diagonal of the Fock matrix. In this sense, a great value of $E\left(2\right)$ is an indicative of the intensity of the interaction between the electron donor and electron acceptor species, meaning that there will be a greater tendency for electrons to be donated and therefore a greater conjugation of the studied system.

For our case, natural bond orbital analysis was performed using the B3PW91/6-311+G(3df,2p) gd3bj method. For the specific case of the 4-nitrophenyl diacetamide, Figure 5, several points of the IRC graph of Figure S6, were studied passing the structure from a reactant to the products. Here, we selected the bonds: N1-C14, N1-C7, C7-O13, C21-N24. Such bonds would show the path of the electrons or the conjugation that could be present. Figure S6 is formed by 34 points before the transition state and 40 points from then, up to the formation of the products. There, we selected some optimized structure and constructed Table 7. It shows the strong interaction of N1 electrons towards the C7-O13 bond; this electron migration favors the extraction of hydrogen β. During this process, it is also observed that before reaching the transition state, no involvement of the lone electron pairs of nitrogen is observed. After the transition state, the IBSI value for the N1-C2 bond is not displayed, as it is less than 0.05. Within the nitro group there is a strong conjugation above 170 a.u. for the value of the perturbation energy. A total of 8 structures or points were studied, including the transition state. IBSI values for the N1-C14 and N24-C21 bonds remained constant during the mechanistic process. These results reinforce the non-conjugate participation of the benzene ring, and therefore the reaction rate would not be affected by the presence of the nitro group in the phenyl. The NBO was included in the Gaussian16 package and the IBSI indexes were calculated by the IGMPLOT program.

Bond orders can be also used as descriptors of covalent bonding involving two atoms and they are used very widely in chemistry. Indeed, notions of single, double, and triple bonds (with bond orders of 1, 2, and 3, respectively), are very common. In this work, attention was paid to the binding between the group (X=H, Phenyl, or Cl) and nitrogen, in search of any modification of the electron density. In special, the Mayer bond order is a natural extension of the Wiberg bond order, which has proved extremely useful in bonding analysis using semi-empirical computational methods, and the Mulliken population analysis to ab initio theories. Figure 6 shows a Mayer Bond Order analysis for the case of NX(COCH3)2 X = H, Phenyl, and Cl. Most details can be visualized in the supplementary files. The mayor contribution for the bond strength is the Chloro followed by the Phenyl group. In the case when X, it is replaced by hydrogen, there is not much of a change noticed, only during the transition state.

4. Conclusions

The calculations carried out during this work allowed us to identify and study different types of reaction mechanisms from the one proposed in the experimental study by AL-AWADI involving a six-membered ring. In that proposal, the participation of the lone electron pair of nitrogen played an important role, assuming delocalization effects by aromatic substituents at the nitrogen atom. However, it was not possible to use the same mechanism for all molecules studied. Several mechanisms were suggested depending on the substituents present. When at NX(COCH₃)₂X, we substitute X=H, the calculated activation energies suggested a two-stage mechanism, different from the case of X= phenyl, where the best agreement between experimental and calculated parameters led to one direct mechanism, at which the phenyl was almost perpendicular to the C(O)NC(O) plane. A small rotational energy barrier of 39.96 kJ/mol was sufficient to prevent the electron deslocalization between the nitrogen and the aromatic ring, explaining the negligible effect of the ring substituent in the reaction rates.