Ring Expansion Tetrahydropyrimidin-2-ones into Tetrahydro-1 H-1 , 3-diazepin-2-ones : a Theoretical Study

A plausible mechanism for the nucleophile-mediated ring expansion of 4-chloromethyl-1,2,3,4tetrahydropyrimidin-2-one into 2,3,6,7-tetrahydro-1H-1,3-diazepin-2-ones based on DFT calculations at B3LYP/6-31+G(d,p) level is discussed. This mechanism involves the following subsequent steps: N(1)H deprotonation under the action of nucleophile, intramolecular nucleophilic substitution of the chlorine atom to give cyclopropane bicyclic intermediate, nucleophile-promoted cyclopropane ring opening leading to 2,5-dihydro-1H-1,3-diazepin-2-one, and addition of nucleophiles to the C=N bond to afford the final diazepinones.

Principal limitations of this method are poor accessibility and low diversity of starting pyrimidines.
It is of great importance to study mechanism of the above transformation and related ring expansion reactions of nitrogen-containing heterocycles (1,4-dihydropyridines 9 and 9,10-dihydroacridines 10 ) with HN-CC-C-C-LG moiety (A, Scheme 3). 11Obviously, formation of 7-or 6-substituted diazepines could be expected following pathway (a) or (b), respectively.Our experimental and reported data showed that the only isolated products were 7substituted diazepines, which proves that the reaction proceeds via pathway (a).Thus, we attempted to rationalize the mechanism of the pyrimidine ring expansion including the reason of exclusive formation of cyclopropane intermediates.Herein we describe this mechanism based on computational data.

Results and discussion
The calculations were performed for nucleophile-mediated ring expansion reaction of 4-chloromethyl-1,2,3,4-tetrahydropyrimidin-2-one as a model compound.The geometry optimizations of all key stationary points were carried out at the B3LYP level of theory using Gaussian 09 suite of quantum chemical programs. 13Pople's basis sets, 6-31+G(d,p), was employed for geometry optimization in the gas phase and in solution.The effect of continuum solvation was incorporated using the polarizable continuum model.Since MeCN was the typical solvent in the reactions studied, we chose the dielectric constant of MeCN (ε = 36.6) in the condensed-phase calculations.Enthalpies and Gibbs free energies were obtained by adding unscaled zero-point vibration energy corrections (ZPVE) and thermal contributions to the energies.All transition states were optimized and characterized as a first order saddle point by harmonic vibration frequency analysis.The only one imaginary frequency of the firstorder saddle point was subjected to visual inspection to examine whether it represented the desired reaction coordinate.The intrinsic reaction coordinate (IRC) analysis was performed to authenticate that the transition state pertains to the desired reaction coordinate.The IRC calculations were carried out at the B3LYP/6-31+G(d,p) level of theory.
We performed the B3LYP/6-31+G(d,p) calculations for both routes (a and b) of reaction of compound 6 with cyanide-ion in the gas phase and in MeCN solution (Scheme 5).2) electrocyclic opening of cyclopropane ring (C→ G → H).The energy barrier ΔG for transformation of C into G was found to be 10.31 kcal/mol in the gas phase and 8.12 kcal/mol in MeCN.
In contrast, anion E resulted from NH deprotonation of C is extremely unstable.This anion undergoes ring expansion to give diazepine anion F without energy barrier (ΔG = 0 kcal/mol) in the gas phase or with a very low barrier (ΔG = 0.06 kcal/mol) in MeCN.Further detailed calculations using CN-anion as a base showed that the pre-reaction complex of cyclopropane intermediate C with this anion undergoes both the zero-bridge cleavage and NH deprotonation with an activation barrier of ∆G = 4.45 kcal/mol (the gas phase, 298 K, 1 atm) to give the post-reaction complex of anion F with HCN.Ring expansion of the pre-reaction complex of intermediate C and CN-anion in MeCN solution proceeds via zero-bridge cleavage with an energy barrier of G = 6.17 kcal/mol to provide the complex G•CN -.The initial ring expansion products further form dihydrodiazepinone H followed by the addition of HCN to the C=N double bond to give the target diazepine 27.It should be noted that transformation of bicycle C into diazepine H promoted by bases is a thermodynamically favorable process with ∆G = -9.86kcal/mol and ∆G = -8.16kcal/mol in the gas phase and MeCN, respectively (298 K, 1 atm).
We believe that the nucleophile-promoted ring expansion of 5-functionalized pyrimidines 4a-c into diazepines 5 proceeds, in general, analogously to that described above for compound 6 (Scheme 6).
However, we suppose that the presence of an electron-withdrawing group at the C5 in the starting compounds may assist the reaction.

Scheme 5 .
Scheme 5. Two plausible pathways of the ring expansion of pyrimidine 6 into diazepine 7 under the action of cyanide-anion.

Scheme 6 .
Scheme 6. Plausible pathway of ring expansion of pyrimidines 4a-c under action of nucleophiles.