Assembly of 1H-pyrrole from cyclopentanone oxime and acetylene: a quantum-chemical model

Quantum-chemical modeling of the mechanism of 1,4,5,6-tetrahydrocyclo-penta[b]pyrrole assembly from cyclopentanone oxime and acetylene has been carried out. The kinetic and thermodynamic characteristics of all reaction stages are calculated. The computation results have revealed a fundamental possibility of 1,4,5,6-tetrahydro-cyclopenta[b]pyrrole formation via the Trofimov reaction.


Computational details
The geometries of the complexes and transition states were obtained using anionic model, with the geometry optimizations being performed in solution (DMSO) using the continuum solvent model IEFPCM [7] and the B3LYP/6-31+G* method. The vibrational corrections to enthalpies and Gibbs free energies were calculated at a standard temperature of 298.15 K. The energies were refined with the double-hybrid B2PLYP method and the 6-311++G** basis set. Effects of nonspecific solvation were additionally estimated using a solvation free energy correction within the IEFPCM model. The combined approach B2PLYP//B3LYP has already been successfully applied for the mechanistic study of the reaction in superbasic media and has shown good agreement with the high-precision CCSD(T)/6-311+G**//CCSD/6-31+G* method [8].
The connection of the transition states with the corresponding minima on the potential energy surface (PES) was proved with the reaction coordinate following, performed using the local quadratic approximation algorithm (LQA) [9]. To describe the kinetic and thermodynamic characteristics of the reactions, thermal effects ΔH and free activation energies ΔG ‡ were used.
To estimate changes of entropy in solution, we used Wertz approach [10,11] applied for a solution of dimethyl sulfoxide [12]. According to this approach the entropy in solution Ssol can be evaluated as follows: Ssol = 0.74Sharm -3.21cal·mol -1 ·K -1 , where Sharm is entropy of the ideal gas obtained within the harmonic approximation.
All calculations were carried out using the Gaussian 09 program package [13].

Results and discussion
The mechanism of the Trofimov reaction comprises the following key steps: vinylation of oxime by acetylene; 1,3-prototropic rearrangement of O-vinyloxime into O-vinylhydroxylamine; [3,3]sigmatropic shift in O-vinylhydroxylamine; intramolecular cyclization of iminoaldehyde; transformation of 5-hydroxypyrroline to 3H-pyrrole; rearrangement of 3H-pyrrole into 1H-pyrrole. All stages will be discussed in detail in the sections below.

O-vinyloxime formation
The pyrrole assembly by the Trofimov reaction mechanism begins with the stage, which is classical for the base-promoted reactions. This is the formation of a nucleophile. The proton abstraction from cyclopentanone oxime 1 occurs with no activation barrier yielding a stable complex 2 of the oximate ion and a water molecule (ΔG = -11.5 kcal/mol). After introducing acetylene, nucleophilic addition of the oximate ion to the C≡C bond occurs with an activation barrier ΔG ‡ = 22.4 kcal/mol (figure 2). The resulting carbanion is barrier-free protonated by a water molecule to form a complex 5 of O-vinyl oxime and hydroxide ion. It should be noted that in the case of cyclohexanone oxime, the vinylation stage was rate-determining with an activation barrier ΔG ‡ = 25.0 kcal/mol.

1,3-Prototropic rearrangement and [3,3]-sigmatropic shift
The α-carbon atom deprotonation occurs with an activation barrier ΔG ‡ = 7.8 kcal/mol (figure 3) and leads to the formation of complex 6 with an increase in the system free energy by ΔG = 4.7 kcal/mol. The migration of a water molecule from a carbon atom to a nitrogen one gives more stable complex 7 (ΔG0 = -12.4 kcal/mol). The protonation of the nitrogen atom affords complex 8 of Ovinylhydroxylamine and hydroxide anion and increases the energy to ΔG0 = -7.1 kcal/mol. The next stage of the mechanism is [3,3]-sigmatropic shift. In the transition state, N−O bond is cleaved and the C−C bond between the second carbon atom of the cyclopentene ring and the β-carbon atom of the vinyl fragment is formed, yielding C=O and C=N bonds. The transition state of [3,3]-sigmatropic shift is higher than that of 1,3-prototropic rearrangement. Thus, the resulting activation barrier of two these stages is ΔG ‡ Σ = 18.3 kcal/mol. The decrease in the system energy relative to the initial compounds in complex 9 of iminoaldehyde with hydroxide anion is ΔG0 = -62.4 kcal/mol.

Intramolecular cyclization of iminoaldehyde and 5-hydroxypyrroline vinylation
The iminoaldehyde conformation in complex 9 does not allow closing it into a cycle. Its change is carried out by a slight activation barrier ΔG ‡ = 1.8 kcal/mol and leads to a more stable complex 10 (ΔG0 = -63.1 kcal/mol). Then, carbon atom of carbonyl group undergoes a nucleophilic attack by a nitrogen electron pair with an activation barrier ΔG ‡ = 6.6 kcal/mol ( figure 4). The proton of imino group migrates to hydroxide ion during descent from the transition state yielding complex 11 of the 5hydroxypyrroline anion with a water molecule. The migration of a water molecule to the O-anion results in a more stable complex 12.
It was previously shown that 5-hydroxypyrroline vinylation is one of the key steps in the reaction mechanism [2]. Nucleophilic addition of the 5-hydroxypyrroline anion to acetylene occurs with an activation barrier ΔG ‡ = 24.3 kcal/mol to afford complex 12 of 5-vinyloxypyrroline and hydroxide ion.

Formation of 3H-pyrrole and rearrangement to 1H-pyrrole
We have previously considered various ways of obtaining 3H-pyrrole [2]. The most promising way is realized through a series of transformations, which starts with a hydroxide ion addition to the C=N bond of 5-vinyloxypyrroline. The addition of the hydroxide ion to the C=N carbon atom is carried out with an activation barrier ΔG ‡ = 15.4 kcal/mol. This process is accompanied by the simultaneous elimination of the vinyl alcohol anion ( figure 5). The addition of a hydroxide ion to neutral azolin-2-ol leads to the abstraction of a proton from position 4 of the cycle with a barrier ΔG ‡ = 13.6 kcal/mol. The elimination of the hydroxy group from the intermediate anion with the formation of 3H-pyrrole corresponds to the barrier ΔG ‡ = 11.3 kcal/mol. Rearrangement of 3H-pyrrole to 1H-pyrrole takes place with no activation barrier, and system energy decreases significantly. The formed 1H-pyrrole anion is much more favorable than the neutral form. It is consistent with the high acidity of pyrroles in dimethyl sulfoxide.  Figure 5. . Reaction profile of 3H-pyrrole formation and its rearrangement to 1H-pyrrole.

Comparison of the activation barriers
So, all thermodynamic characteristics of the main stages of the 1,4,5,6-tetrahydrocyclopenta[b]pyrrole assembly had been obtained. Next, they can be compared with characteristics for 4,5,6,7-tetrahydro-1H-indole. It allows to evaluate the possibility of 1,4,5,6-tetrahydrocyclopenta[b]pyrrole synthesis via the Trofimov reaction. Values of the activation barriers are presented in table 1. First of all, it should be noted that the rate-determining step of 4,5,6,7-tetrahydro-1H-indole formation is the O-vinylation of oxime, while the vinylation of 5-hydroxypyrroline represent such a stage for 1,4,5,6-tetrahydrocyclopenta[b]pyrrole. However, the difference in these limiting barriers is insignificant (ΔΔG ‡ = 0.6 kcal/mol), and in the case of 1,4,5,6-tetrahydrocyclopenta[b]pyrrole activation barrier is actually lower. Only at the stage of 3H-pyrrole formation, the activation barrier turns out to be higher by 3.2 kcal/mol for 1,4,5,6-tetrahydrocyclopenta[b]pyrrole, although it is still insignificant in comparison with the barrier of the rate-determining stage.

Conclusion
A quantum-chemical modeling of 1,4,5,6-tetrahydrocyclopenta[b]pyrrole assembly from cyclopentanone oxime and acetylene in superbasic medium has been carried out. It is shown that the activation barriers of the rate-determining stages of 4,5,6,7-tetrahydro-1H-indole and 1,4,5,6tetrahydrocyclopenta[b]pyrrole formation are similar. So, 1,4,5,6-tetrahydrocyclopenta[b]pyrrole formation is theoretically possible under conditions similar to those for obtaining pyrrole from cyclohexanone oxime (~100°C, 1 atm.). However, 1,4,5,6-tetrahydrocyclopenta[b]pyrrole was not experimentally obtained by the Trofimov reaction. Most likely, this is due to various side processes of hydrolysis and condensation, which are characteristic of the basic media. The investigations in this field are under way.