Mechanism of the decomposition reaction
The thermal decomposition reaction of a series of 5-nitro-5-R-1,3-dioxane compounds with R= H, CH3 and Br, was computationally modeled to observe the effect of the substituent group on the reaction parameters and mechanism.
The reactions were carried out under conditions simulating the gas phase and also in solution with DMSO as solvent. The mechanisms postulated in Figures 2 and 3 were used as a starting point
Figure 2 represents a reaction mechanism that proceeds through a 5-atom cyclic transition state and involves the breaking of the carbon-nitrogen bond and the migration of a hydrogen from carbon 6 to one of the oxygens of the nitro group, thus leading to the subsequent formation of the alkene: 5-R-4H-1,3-dioxine and a nitrous acid molecule.
Alternatively, when R=H, the two-stage mechanism depicted in Figure 3 was also followed, where the reaction starts with the breaking of the C4-O3 and N9-C5 bonds and the formation of new bonds between C6-O3 and C4-N9. This leads to the formation of the intermediate compound 4-(nitromethyl)-1,3-dioxolane, which in a later stage decomposes through a cyclic transition state of 5 atoms. This involves the migration of hydrogen from carbon 5 and the detachment of the nitro group. The alkene 4-methylene-1,3-dioxolane is also produced by the formation of double bonds at carbons 4 and 5.
Kinetic and thermodynamic parameters
Computational optimization of the molecules was accomplished at M06-2X/6-311+G(d,p) in the temperature range of 503.15 – 563.15 K. Figure 4 depict the optimized geometry of the reactants, transition states (TS1-5-H-M1, TS1-5-methyl-M1 and TS1-5-Br-M1) and products (P1-H, P1-methyl and P1-Br) involved in the decomposition reactions, following the one-stage mechanism.
The vibrational frequency data and the linearization of the Arrhenius equation allowed to calculate the kinetic values shown in Table 1. It is worth noticing that the lowest activation energies (Ea and ΔG≠) for the decomposition reaction are given in their order for the molecules with R = methyl, Br and H.
An important contribution to the decrease of the free energy of activation can be noticed in the activation entropy with the highest value 12.4 J∙mol−1∙K−1 for methyl as a substituent group, which is also evident when looking at the values of the frequency factor (A).
Table 1
Kinetic parameters obtained from computational modeling at 523 K, for thermal decomposition of the studied compounds according to the one-stage mechanism. First inlet gas phase, second inlet solution with DMSO
R
|
k
(s−1)
|
kDMSO/kgas
|
Ea
(kJ mol−1)
|
A
(s−1)
|
ΔG≠
(kJ mol−1)
|
ΔS≠
(J mol−1 K−1)
|
H
|
4.06 x 10−8
(1.82 x 10−7)
|
4.5
|
212.1
(207.0)
|
6.14 x 1013
(8.59 x 1013)
|
204.6
(198.1)
|
5.9
(7.619)
|
Ha
|
2.04 x 10−17
|
|
|
|
297.7
|
13.752
|
Hb
|
1.47 x 10−9
|
|
|
|
219.0
|
-12.401
|
Methyl
|
4.19 x 10−7
(3.39 x 10−5)
|
80.9
|
205.3
(192.8)
|
1.33 x 1014
(6.09 x 1014)
|
194.4
(175.3)
|
12.4
(15.564)
|
Br
|
1.39 x 10−7
(2.21 x 10−7)
|
1.6
|
208.2
(207.2)
|
8.66 x 1013
(1.098 x 1014)
|
199.3
(197.2)
|
8.9
(7.686)
|
aMechanism figure 3, stage 1, gas phase bMechanism figure 3, stage 2, gas phase |
The two-stage mechanism turned out not to be feasible for the decomposition reaction 5-nitro-1,3-dioxane compared to that occurring in a single-stage mechanism. We see that the first stage is the limiting of the speed with a free energy of activation of 297.7 kJ∙mol−1, that is 93 kJ∙mol−1 higher than the activation free energy in the reaction occurring according to the single-stage mechanism.
When the reactions are carried out in solution with DMSO, the energy barrier in each of them is lowered and as a result the decomposition rate increases. The most important solvent effect occurs in the decomposition reaction of 5-methyl-5-nitro-1,3-dioxane, where the reaction rate is increased by more than 80 times.
It is also observed that when the substituent is a bromine atom, solvent stabilization is practically nonexistent.
Figure 5 features the optimized structures involved in the reaction by the proposed two-stage mechanism. Table 2 summarizes the experimental values reported for the modeled decomposition reactions.
The computational findings obtained, present a great discordance with the experimental findings reported by Stepanov. et.al, 2011 [10]. On the one hand, the reaction rates obtained computationally in this work are lower than the rates reported experimentally and on the other hand, the results reported by the authors indicate that the greatest favorability for the decomposition reactions occurs with the bromine atom in position 5. Our results indicate greater favorability of the decomposition reaction with the methyl group as a substituent.
The free energy profile for the reaction in gas phase and in DMSO is shown in Figure 6.
Table 2
Experimental kinetic parameters reported [1] in gas phase for the decomposition reactions of the 5-R-5-nitro-1,3-dioxane compounds studied at 523 K
R
|
K (s−1) x 10−4
|
Ea (kJ mol−1)
|
Log A
|
ΔS≠(J mol−1 K−1)
|
H
|
0.33
|
173.1
|
12.81
|
-12.7
|
Methyl
|
2.59
|
170.1
|
13.40
|
-1.4
|
Br
|
5.56
|
167.7
|
13.42
|
-1.0
|
From the graphical representation it can be observed that the decomposition reaction of 5-bromo-5-nitro-1,3-dioxane compounds generates the most stable products even though kinetically it is not the most favored reaction among the reactions observed. The reactions in DMSO solution occur with a lower activation free energy value, however, the thermodynamics of the reaction are not significantly favored.
The substituent group on carbon 5 favors the elimination reaction and this occurs more rapidly with the methyl group.
Population analysis (NBO)
The natural bond orbital (NBO) population partitioning technique was used to obtain the Wiberg bond index values and by means of them to follow in depth the processes of bond breaking and bond formation throughout the chemical reaction.
The findings obtained from the NBO analysis and the other indicators that were calculated with equations 1, 2, 3 and 4 are depicted in Table 3.
Table 3
Wiberg bond indices for reactants, transition states and products (BiR, BiTS and BiP) for gas-phase decomposition reactions using the one-stage mechanism. (1) R=H, (2) R=Me, (3) R=Br. %EV: percentage of evolution; δβav: average relative variation; Sy: absolute synchronicity of the reaction
|
C5-C6
|
C6-H7
|
H7-O8
|
O8-N9
|
N9-C5
|
BiR (1)
|
0.9793
|
0.9217
|
0.0022
|
1.5178
|
0.8763
|
(2)
|
0.9633
|
0.9203
|
0.0025
|
1.5147
|
0.8451
|
(3)
|
0.9862
|
0.9083
|
0.0008
|
1.5339
|
0.8408
|
BiTS (1)
|
1.3882
|
0.4261
|
0.3176
|
1.372
|
0.278
|
(2)
|
1.3524
|
0.4393
|
0.3006
|
1.3743
|
0.1187
|
(3)
|
1.3527
|
0.4249
|
0.3183
|
1.371
|
0.2694
|
BiP (1)
|
1.8559
|
0.0000
|
0.752
|
1.0947
|
0.0000
|
(2)
|
1.8092
|
0.0000
|
0.752
|
1.0947
|
0.0000
|
(3)
|
1.795
|
0.0000
|
0.752
|
1.0947
|
0.0000
|
%EV (1)
|
46.65
|
53.77
|
42.06
|
34.46
|
68.28
|
(2)
|
46.00
|
52.27
|
39.77
|
33.43
|
85.95
|
(3)
|
45.31
|
53.22
|
42.27
|
37.09
|
67.96
|
|
|
δβav =
|
(1) 0.49
|
Sy =
|
(1) 0.88
|
|
|
|
(2) 0.51
(3) 0.49
|
|
(2) 0.83
(3) 0.88
|
The %EV shows us that in the transition state the C-N bond breaking processes are quite advanced processes for the decomposition reactions. We could relate this to an increase in the degrees of freedom of the structure representing the transition state and consequently a higher entropy, which fits the kinetic data reported in Table 1.
The methyl substituent at position 5 stabilizes the same carbon, perhaps due to its ability to induce electrons, which is why the C-N bond breaking process is the most advanced, approximately 86% compared to 68 % for the H and Br atoms. The substituent at C5 delays the alkene formation and slightly delays oxygen migration as well.
Bromine as a substituent, likely due to its electron-scattering effect, decreases the availability of carbon-carbon double bond formation and increases the advance of O-H and N-O bond formation perhaps due to chain effects on the hydrogen electron cloud.
The average relative variation of the bond indices, δβav, with values of 0.49 and 0.51 for the reactions, indicates symmetric transitions states whose structure is intermediate between reactants and products.
The reaction that occurs for the molecule with the methyl substituent presents an imbalance between bond formation and bond breaking events, evidenced by a value of 0.83 for the reaction synchronicity.