Theoretical Study of The Heterocyclic Molecules Reactivity in The Normal Electron Demand Diels-Alder Reaction

Introduction

Experimental study done by auteurs shows that the addition of  2,3-dimethylbutadiene  to a solution of 4-aza-6-nitrobenzofuroxan 1 in CDCl₃ gives the product 3a₁ and 3’a₁.The auteurs carry out another experience, under similar conditions, but with a longer reaction time this reaction did not allow the isolation of 3a₁ and 3’a₁, but  in  adding  advantage water in the solution, he obtained the hydrate 4, likes pale yellow solid, resulting from the reaction of 3a₁. The structure of 4 was determined by X-ray crystallography, which confirm  that  the addition of H₂O has taken place at the C₁₀=N₉ double bond [1].

Figure 1 Click here to View Figure

 

Recently, it has been showed that the nitrobenzofuroxan (DNBF) are able  to react as a dienophile or heterodiene in the Diels-Alder reactions [2-5]. In first stage, we have choice the 6-nitrobenzofuroxane molecules which looks like the 4-aza-6-nitrobenzofuroxan 1. We have only substitue the nitrogen atome number 4 of the molecule 1 by the C-R₃ groupment, then we obtient the molecules 5a-c (figure 2) which seems particulary interessants for experimental study. The diene substitution was studied by substitution of 2,3-dimethylbutadiene 2a₁ by the 2-trimethylsilyloxybuta-1,3-diene 2b₁. In order to find the better calculation method which lead to better convergence for these kind of system, we have optimazed molecule 4 by two different method SCF/6-31G and DFT/B3LYP with the basis set 3-21G. In second stage, we have studied the addition of diene 2a₁-b₁ on the 6-nitrobenzofuroxane 5a-c. In the end, from thermodynamic and orbital  point of view  we have discussed the possibility and the stereoselectivity of normal electron demand  Diels-Alder reaction.

Figure 2 Click here to View Figure

 

Theoretical Study of the Compound 4

Calculation Method

Calculations are done at SCF level with standard basis sets 6-31G of  GAUSSIAN 98 program[6] and while using the DFT method of the same program with The B3LYP hybrid functional [7, 8] and basis sets 3-21G. The choice of this last method is justified by its efficiency in the treatment of  system type [9]. The geometry of the various critical points on the potential energy surface was fully optimized with the gradient method available in GAUSSIAN 98. Calculations of harmonic vibrational frequencies were carry out  to determine the nature of each critical point.

Results

In order to determine the reliability calculation methods in the treatment of this system  type, we optimized the geometry of the compound 4. Putting in mind the stereochemistry of this molecule 4, we compare our theoretical results with the experimental data of the X-ray [1]. Table 1  regroups some geometric parameters of the optimized molecule and the X-ray data.The figure 2 shows the stereochemistry of the molecule 4 optimised at DFT level.

Table 1 : Selected optimized geometrical parameters for the compound  4.

	SCF/6-31G	DFT/3-21G	X-ray [6]
N4-C5	1.457	1.455	1.445
C7-C10	1.525	1.526	1.537
C11-C12	1.348	1.347	1.327
N2-C6	1.565	1.563	1.536
C5-O5	1.414	1.412	1.408
N4-C9	1.354	1.391	1.366
C13-C12	1.487	1.489	1.499
C6-C7	1.473	1.474	1.543
C5-C6	1.449	1.448	1.547
N4-H4	1.001	1.001	0.86
C9-N4-C5	115.373	115.377	115.8
N4-C5-C6	124.34	124.257	109.37
C5-C6-C7	119.587	119.585	111.81
C6-C7-C8	109.287	109.285	105.06
C11-C12-C13	121.03	121.05	122.55
C10-C11-C12	118.347	118.415	123.16
C7-C10-C11	108.642	108.768	116.39
C7-C8-C9	125.381	125.546	125.72

Distances are in Angstrom (A^°) and Angles in degrees (^°)

Figure 3 : DFT/ B3-LYP optimized geometries of the compound  4  Click here to View  Figure

 

The SCF/6-31G and DFT method  give result which  agree with  the experimental  X-ray data of the compound 4. We noticed that the DFT method gives the best results. Therefore the calculation method of DFT/B3-LYP with the standard basis set 3-21G is more reliable with this system type [9]. The geometry parameters data assigned to 4 is in complet agreement with our theoretical results. The distance ( d _H7-H10 =2.47 A°) calculated  by DFT/B3Lyp with the standard basis set 6-31G  was in good accord with the distance obtained by X-Ray crystallography : d _H7-H10 = 2.186 A°.

Vibrational Analysis

IR spectra calculate by DFT/3-21G method are also in accord with the experimental one (n_C6=C5(theo) =1755 cm^-1 et n_C6=C5(exp) =1609 cm^-1). We noticed that the DFT method using the functional B3LYP and the standard basis set 3-21G gives  the most resultats with this type of heterocyclic molecules. Therefore, we continuous  the thermodynamic study on  Diels-Alder reaction between  the heterocyclic molecules such as 4-aza-6-nitrobenzofuroxan 1 and 6-nitrobenzofuroxan 5a-c with the diene 2a₁-b₁, by using the DFT method with  the functional B3LYP and the standard basis set 3-21G of the GAUSSIAN 98  program [ 6 ].

DFT  Study of Diels-Alder Reaction

Like the figure 4 shows, we have studied the possibility and also the stereoselectivity of normal electron demand Diels-Alder reaction between heterocyclic molecules such as 4-aza-6-nitrobenzofuroxan 1 and 6-nitrobenzofuroxan 5a-c with the diene 2a₁-b₁. The diene is activated by the substituant groupement – ( CH₃) or – (OSi (CH₃)₃. In the case of diene 2a₁-b₁ addition on the 6-nitrobenzofuroxane 5a-c, we have focussed our attention to study the R3 groupement on the Diels-Alder reaction. This study seems to be interessant from synthetic point of view.

Figure 4 Click here to View Figure

 

The orbitals Border Study

We have determinated the LUMO and the HOMO of diene 2a₁-b₁, by DFT/B3LYP with standard basis set method, and as well the LUMO and the HOMO of molecules 1 and 5a-c see table I. In each case of these reactions, the orbital  diagramm between the molecules 1 and the diene 2a₁-b₁, give a very good quantitatively indication about the reactivity of our system. The most predominant interaction existe between the LUMO of dienophile and the HOMO of diene 2a₁-b₁. Therefore these reactions could be considered like the Diels-Alder reaction with normal electron demand [10, 11]. As example, we presente figure 5

Figure 5 : orbital  diagramm between molecule 5c with le diene 2a1. DFT/3-21G Click here to View Figure

 

The table I  shows, that the difference of energy HOMO-LUMO is smaller in the case of the diene 2b₁ reaction with the molecule 5a that in the case of the reaction between 2b₁ with 5c. Therefore the reaction should be easier in the case of the diene 2b₁ addition on the molecule 5a.

Table I: The LUMO and the HOMO of diene 2a₁-b₁ and  heterocyclic molecules such as 4-aza-6-nitrobenzofuroxan 1 and 6-nitrobenzofuroxan 5a-c

	LUMO	HOMO
1 5a 5b 5c	-0.132 -0.179 -0.149 -0.151	-0.254 -0.289 -0.256 -0.264
2a1 2b1	-0.005 -0.021	-0.225 -0.217

 

 Study of Regioselectivity Reaction

The study of (2pz) coefficients of the border orbitals by DFT/3-21G level for the  4-aza-6-nitrobenzofuroxan 1 and 6-nitrobenzofuroxan 5a-c show that the LUMO coefficient of carbone C5 is always less then  carbone C7 (Table II).This means that the addition of diene 2a₁-b₁, appear more reactif on the molecules 1 and the 5a-c is obtained firstly on carbone C7. This constatation is agree with experimental resultats in the case of diene 2a₁ add on the 4-aza-6-nitrobenzofuroxan 1  [1 ].

Scheme 1 Click here to View Scheme

 

Table II : The LUMO Coefficient of carbone C5, C6 and C7of  molecule 1 and 5a-c, The HOMO coefficient of carbone C’1 and C’4 of diene 2a₁-b₁.

	LUMO coefficient of C7	LUMO coefficient of C6	LUMO coefficient of C5
1	0.241	0.255	-0.145
5a 5b 5c	0.201 0.183 0.153	0.241 0.226 0.186	-0.145 -0.134 -0.138
	HOMO coefficient of C’1		HOMO coefficient of C’4
2a 2b	0.285 0.236		0.285 0.264

 

In purpose to determine the stereoselectivity of the reaction between the molecules 5a-c and the diene 2b₁, we have calculated the (2pz) coefficient of LUMO for diene 2b₁ and also the 2pz coefficient of  LUMO which correspond to carbone C7 and C6 of molecules 5a-c and this leads to the formation of product 6. The formation of (1’)-(7) and (4’)-(6) liaisons are more favorised. See the example on  Figure 5

Figure 5: orbitalairy interaction between the HOMO coefficient of the diene 2b1 with LUMO coefficient of the dienophile 5a.    Click here to View Figure

 

Thermodynamic Approach

As it is shows in figure 6, we studied the interaction of this heterocyclic molecules1 and 5a-c with the diene 2a₁-b₁. The heterocyclic molecules  react as  dienophile and the molecules of  2,3-dimethylbutadiene 2a₁ and  2-trimethylsilyloxybuta-1,3-diene  2b₁  react as  a diene, Therefore we have a normal electron demand Diels-Alder (NEDDA). We found, it is interesting to examine from a thermodynamic approach the possibility and  the stereoselectivity of Diels-Alder  reactions. In each case of these reactions, we calculated by the DFT / B3LYP with the standard basis set 3-21G, the variation  of  free energy  Δ_rG (Kcal.mol^-1) correspond to every type of reaction.The table III regroups the different values obtained by the DFT method.

Figure 6 : DFT study of normal electrons demand Diels-Alder reaction between the diene  2a1-b1 with some heterocyclic molecules such as the 4-aza-6-nitrobenzofuroxane 1 and 6-nitrobenzofuroxane 5a-c.     Click here to View Figure

 

The reactions (I) and (II) between the 2,3-dimethylbutadiene 2a₁ with the benzofuroxane molecules 5a-c and molecule 1 are possible, since the variation of free energy are negative. On the other hand , we sudy the add of  the 2-trimethylsilyloxybuta-1,3-diene  2b₁ to the molecules 5a-c and 1. We notice that reactions (I) and (II) are possible and favored  thermodynamically.

We also notice that the variation of free energy corresponding to reaction (I ) are more important in absolute value, than the variation of free energy relative to reaction (II). This is confirm the possibility of these reactions. Therefore the reactions (I ) give always the main product.

Table III: Thermodynamic results for some reaction calculated at the DFT/B3LYP level of theory. (Kcal.mol ^–1)

	Product of reaction	Dr E	Dr H	Dr G
REaction I	3a1 3b1 6aa1 6ab1 6ba1 6bb1 6ca1 6cb1	-23.4 -26.7 -17.4 -29.4 -18.9 -16.3 -12.5 -13.1	19.3 23.4 27.2 31.4 21.5 22.3 18.9 14.7	-15.6 -17.1 -20.1 -25.3 -15.6 -17.3 -10.4 -12.3
Réaction II	3’a1 3’b1 6’aa1 6’ab1 6’ba1 6’bb1 6’ca1 6’cb1	-13.9 -21.1 -15.3 -20.2 -13.7 -14.8 -9.7 -11.5	16.3 15.2 21.3 25.7 17.3 10.4 12.3 15.2	-10.4 -12.3 -19.5 -23.2 -12.4 -13.6 -8.4 -10.1

 

From these results, we can give answer about some experimently question [ 1]. In fact, the addition of H₂O molecule could  be done only on the majority of the reaction product. For this reason, the addition of H₂O is done only on the C₁₀=N₉ bond of product 3a₁ which could be considered from our calculation as the majority reaction product.

In each case of reactions (I ) and (II ), we have determine the energy which leads to the formation of reaction product. We have make the follow constatation that the energy formation of endo products  6 is more weak then the energy formation of exo products 6’. This is a new confirmation of the stability of endo products which is considered as major product part of Diels-Alder reaction between the molecules 1 and 5a-c with the diene 2a₁-b₁.

Conclusion

We study the Diels-Alder reaction between a diene 2 like 2,3-dimethylbutadiene and 2-trimethylsilyloxybuta-1,3-diene with 6-nitrobenzofuroxane 5a-c, which is specially interesting for scientist in experimental workshop. Therefore the diene is actived by differents substituants and the 6-nitrobenzofuroxane 5 substituate by –NO₂, -OH and -H. We also study the influence by R₁ and R₂ in the Diels-Alder reactions.Our theoretical results show, that the reactions (I) give always the main product which is the endo products.the reaction between the diene 2-trimethylsilyloxybuta-1,3-diene 2b₁ and DNBF 5a gives most results than DNBF 5a with the diene  2,3-dimethylbutadiene 2a₁.

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