Quantum Chemical and Experimental Studies on the Mechanism of Alkylation of β-Dicarbonyl Compounds . The Synthesis of Five and Six Membered Heterocyclic Spiro Derivatives

The alkylation of β-dicarbonyl compounds in a K2CO3/DMSO system was found to afford Oand C-alkylated derivatives, depending on the type of the β-dicarbonyl compound involved. The alkyl derivatives obtained were used in the synthesis of some new spiro barbituric acid derivatives. Quantum chemical calculations were carried out to elucidate the reaction mechanisms for some typical synthesis.


Theoretical Approaches
There is no doubt that one of the most versatile methods for elucidating reaction mechanisms nowadays is the use of theoretical calculations.The superiority of computations comes from the fact that they let us to simultaneously calculate more than one parameter, such as dihedral angles, bond lengths, atomic charges, etc. that are related to structure and thermodynamic parameters, which in turn are related to thermodynamics and kinetics.In the present work we aimed to elucidate the reaction mechanism of some synthesis using semi-empirical calculation approach.

Discussion of Computational Work
The aqueous phase PM3 calculation data are given in Table 1.Using appropriate computed parameters and related equations the tautomeric equilibrium constants, K T , were calculated for the Keto Enol tautomerism of the main molecules and the obtained data is collected in Table 2.For the formation of products 1 and 2 (Scheme 1), although the K T value of 0.06 for the R1K R1E equilibrium suggests the predominance of the keto form (i.e. the R1K form) in aqueous media, it seems that this situation is reversed in basic media and the enolate form R1E1(a) predominates over the carbene form R1K(a) and the reaction proceeds by the nucleophilic attack of R1E1(a) on R2 to first form compound 1 and then it proceeds via a second attack of R1E1(a) on 1 to form compound 2. Further evidence to support this argument is the higher nucleophilicity, η; and the higher basicity (i.e.smaller pK a value for deprotonation) of R1E1(a) compared to the R1K1(a) form (Tables 1 and 2) .For the formation of products 3 and 4 (Scheme 1), although K T values of 0.04 and 0.05 for the R3K R3E1 and R3K R3E2 equilibria, respectively, suggest the predominance of the keto form (i.e.R3K) in aqueous media, it appears that in basic media a competition among two enolate ions and one carbene ion becomes inevitable.Although the respective nucleophilicity values are ranked in the increasing order R3E1(a) < R3K(a) < R3E2(a), the magnitudes of the differences are not too large (Table 1).The same analogy exists within the pK a values: the basicity increases (or acidity decreases) in the order R3K(a) < R3E1(a) < R3E2(a) and again the magnitudes of the differences might allow for competition.It seems that in this case the competition was won by the R3E1(a) enolate ion which attacks R2 to form compound 3 in 57 % yield.An attack of the second R3E1(a) enolate ion on compound 3 then afforded compound 4 in 16 % yield.
For the formation of products 5-7 (Scheme 2) a K T value of 0.02 for the R4K R4E equilibrium suggests the predominance of the keto form (i.e.R4K) in aqueous media, but again in basic media it would seem that a competition exists between the enolate ion R4E(a), formed by deprotonation of the enol form R4E, and the carbene ion R4K(a), which forms by deprotonation of the keto form R4K. Since the yield of compound 5 (46%) is the highest, that implies that the R4E(a) enolate ion attacks R2 to form compound this compound.A further attack of enolate R4E(a) ion on compound 5 affords compound 7 in 12 % yield.Alternatively, when carbene ion R4K(a) attacks R2 then compound 6 is formed (in 24 % yield) by an intramolecular ring closure reaction as follows: The slightly higher nucleophilicity and stronger basic strength of R4E(a) compared to R4K(a) are indicative of a high yield for compound 5 than that of compound 6 (Tables 1 and 2).For the formation of compounds 8-10 (Scheme 3) K T values of 0.10 and 0.11 for the R5K R5E1 and R5K R5E2 equilibria indicate the favorability of the keto form R5K over the enol forms R5E1 and R5E2 (Table 2).However, in basic media there seems to be a competition among the enolate ions and carbene ion.When we consider the higher yield of compound 8 it seems that this time the enolate ion R5K(a) is favored and this ion attacked R2 to afford compound 8 in 55 % yield.A competitive reaction is the attack of enolate ion R5E1(a) on R2 to afford compound 9 in a yield of 49 %.Attack of the same enolate ion R5E1(a) on compound 9 affords the molecule 10 in 10 % yield.The nucleophilicity of those three species were found to be in the increasing order: R5E1(a) < R5K(a) < R5E2(a), which accounts for the higher yield of the R5E2(a) enolate initiated reaction giving compounds 9 and 10 (total yield is 59 %) (Table 1).The basicity order is found be be in the increasing order R5E1(a) < R5K < R5E2(a) (Table 2).The higher basicity (or lower acidity) of R5E2(a) is further evidence for the higher yield of compounds 9 and 10.
For the formation of compounds 11-13 (Scheme 3) a K T value of 0.02 for the R6K R6E equilibrium suggests the ketone form R6K is favored (Table 2).When we take into account the percent yield and the structures of the products 11-13 it seems that only the carbene ion R6K(a), formed by deprotonation of R6K in basic media, acts as nucleophile to attack R2 and give compound 12 in 10 % yield and a subsequent intramolecular rearrangement of compound 12 in basic media produces compound 11 in a 57 % yield.Alternatively, attack of the carbene ion on 12 produces compound 13 in 14 % yield.The nucleophilicities of enolate and carbene ions are almost the same (Table 1) but the basicity of the carbene ion is greater than that of the enolate ions (Table 2) which explains why the enolate ion is inactive in this reaction.For the formation of compounds 14-OH, 14-NH 2 and 14-NHPh (Scheme 4) the K T value of 0.01 for the R7K R7E equilibrium suggests the keto form R7K is favored (Table 2).It seems that the formation of compounds 14-OH, 14-NH 2 and 14-NHPh occurs by nucleophilic attack of R8, R9 and R10 on R7K, which is more electropositive compared to R7E.These products were found to produced in about 91 % yield.These products rearrange into compounds 15, 16 and 17 respectively.The overall mechanism can be summarized as follows:

X =OR and NHR R = H and Ph
The tautomeric equilibrium constants of 1.99 and 3.63 for 20K 18E and 21K 19E (Table 2) indicate the predominance of enol forms 18E and 19E over 20K and 21K respectively (Scheme 5).The bigger nucleophilicity of 18E and 19E well explains the high yields of those compounds (Table 1).

Conclusions
It seems that theoretical calculations can give some clues about the mechanism and the possible yields of some synthetic reactions.However, to be more conclusive further work should be done using other calculation methods and different basis sets which might give better correlation with experimental values.

General
The 1 H-NMR spectra were recorded using a JEOL C-90 MHz spectrometer at room temperature.Elemental analysis were done using a Carlo Erba EA 1108 type instrument.

chloroethoxy)ethane
The appropriate β-dicarbonyl compound (1 mole) was added to a mixture of 2-chloro-1-(2chloroethoxy)ethane (1.2 mole) and K 2 CO 3 (2.5 mole) in DMSO (400 mL) and stirred vigorously at 70 o C for 20h.The reaction mixture was then cooled down and water was added until all the K 2 CO 3 was dissolved.The solution was then extracted with ether a few times.The combined ether extracts were washed with water till neutral and dried over anhydrous Na 2 SO 4 .After filtration and evaporation of the ether the residue was distilled under vacuum to separate the products.

General method for the preparation of barbituric acids.
A mixture of diester 11 (0.05 mol), metallic sodium (0.05 mol) and carbamide or thiocarbamide in absolute ethanol (50 mL) was mixed for 7 h at 100 o C. The precipitated sodium salt was filtered, washed with absolute ethanol and dissolved in water.The solution was acidified with HCl.The precipitate was filtered and recrystallized from water.

Computational Details
Theoretical calculations were carried out at the restricted Hartree-Fock level (RHF) using PM3 semi empirical SCF-MO method in the MOPAC 7.0 program [24], implemented on an Intel Pentium4 400 MHz computer.All the structures were optimized to a gradient norm of <0.1 in the liquid phase.The initial estimates of the geometry of all structures were obtained by a molecular mechanics program of CS ChemOffice Pro for Windows [25], followed by full optimized of all geometrical variables (bond lengths, band angles and dihedral angles), without any symmetry constraint, using semi empirical PM3 quantum chemical methods in the MOPAC 7.0 program.

Table 1 .
Liquid phase PM3 calculated physical parameters of the studied molecules.

Table 2 .
Liquid phase PM3 calculated physical parameters of studied molecules.