In this work we used DFT B3LYP/6-31G (d) to study the mechanism, the regio- and stereoselectivity of the [1+2] cycloaddition reaction between β-himachalene and dihalogenocarbene. Analysis of the reactivity indices and calculation of the activation energies of the transition states showed that this reaction is stereoselectives, the treatment of β-himachalene with one equivalent of dibromocarbene leads via an exothermic reaction to the formation of a single product P1 resulting from the attack of the most substituted double bond C6=C7 of β-himachalene. Treatment of product P1 with one equivalent of dichlorocarbene leads, again via an exothermic reaction, to formation of the two products P3 and P4, but dibromocarbene does not react with the product P1 due to the high activation energy of this reaction

Benharref, A

El Hajbi, A.

Hammal, R.

ZEROUAL, Abdellah zeroual

English

Revues Scientifiques Marocaines

Zeroual & al. / Mor. J. Chem. 3 N°4 (2015) 698-704  698   The regio- and stereoselective addition of dibromocarbene and dichlorocarbene onto β-himachalene  A. Zeroual a*, R. Hammal a, A. Benharref b and A. El Hajbi a  a Laboratory of Physical Chemistry, Department of Chemistry, Faculty of Science Chouaib Doukkali University, El Jadida, Morocco b Laboratory of Biomolecular Chemistry, Natural Substances and Reactivity, URAC 16 Semlalia Faculty of Sciences, Cadi Ayyad University, Marrakech, Morocco   Corresponding author. E-mail address: zeroual19@yahoo.fr  Received 16 May2015, Revised 24 May 2015, Accepted 02 Oct 2015  Abstract  In this work we used DFT B3LYP/6-31G (d) to study the mechanism, the regio- and stereoselectivity of the [1+2] cycloaddition reaction between β-himachalene and dihalogenocarbene. Analysis of the reactivity indices and calculation of the activation energies of the transition states showed that this reaction is stereoselectives, the treatment of β-himachalene with one equivalent of dibromocarbene leads via an exothermic reaction to the formation of a single product P1 resulting from the attack of the most substituted double bond C6=C7 of β-himachalene. Treatment of product P1 with one equivalent of dichlorocarbene leads, again via an exothermic reaction, to formation of the two products P3 and P4, but dibromocarbene does not react with the product P1 due to the high activation energy of this reaction.  Key words: Nucleophilicity; electrophilicity; [1+2] cycloaddition; stereoselectivity; regioselectivity, DFT.  I. Introduction The classic route to prepare cyclopropanes is a cycloaddition [2+1], concerted and stereospecific, between an olefin and a carbene. Deprotonation of chloroform or bromoform with a strong base (for example t-BuOK) in organic medium, or with sodium hydroxide in catalysis by phase transfer, is an excellent method for synthesizing cyclopropane compounds [1]. It method was therefore implemented to prepare all cyclopropanes used in this study. In the first reaction the β- himachaléne reacted with one equivalent of dibromocarbene, chemo-specifically results in a single compound P1 resulting from the attack of the double bond C6= C7 with the α side (Figure 1), the structure was determined by spectral data (NMR, 1H, 13C) [2], and the stereochemistry was confirmed by X-ray diffraction [3]. Thus, the action at a temperature of 0 °C, with a stoichiometric amount of dichlorocarbene (generated in situ under the conditions of the transfer catalysis solid-liquid phase (CTP-LS) from chloroform and sodium hydroxide) in presence of benzyltriethylammonium chloride (TEBA-Cl) as a catalyst on the product P1 leads at the end of two hours to the products P3 and P4. The structures of the products P3 and P4 were determined by spectral data (NMR, 1H, Zeroual & al. / Mor. J. Chem. 3 N°4 (2015) 698-704  699  13C) and the stereochemistry was confirmed by X-ray diffraction [4]. For the same conditions against solid-liquid phase transfer P1 product does not react with dibromocarbene (reaction 3). (Figure 1).   Figure 1: Cycloaddition of dihalogenocarbene and β-himachlene  In this work we study these reactions by the method of density functional theory (DFT) B3LYP/6-31(d) and compare them with experimental results. DFT (density functional theory) computations were carried out using the B3LYP [5-6] exchange-correlation functionals, together with the standard 6-31G(d) basis set.[7] The optimizations were carried out using the Berny analytical gradient optimization method.[8-9] The stationary points were characterized by frequency computations in order to verify that TSs have one and only one imaginary frequency. The IRC paths [10] were traced in order to check the energy profiles connecting each TS (transition state energy) to the two associated minima. All computations were carried out with the Gaussian 09 suite of programs. [11].  The global electrophilicity index, [12] ω, is given by the following expression,  𝝎 =𝝁𝟐𝟐𝜼, in terms of the electronic chemical potential μ and the chemical hardness η. Both quantities may be approached in terms of the one-electron energies of the frontier molecular orbital HOMO and LUMO, as    𝜀𝐻𝑂𝑀𝑂  and  𝜀𝐿𝑈𝑀𝑂 , 𝜇 =  𝜀𝐻𝑂𝑀𝑂 +𝜀𝐿𝑈𝑀𝑂2   and 𝜂 =  𝜀𝐿𝑈𝑀𝑂−𝜀𝐻𝑂𝑀𝑂 , respectively.[13-14] Th nucleophilicity index[15-16] N, based on the HOMO energies obtained within the Kohn–Sham scheme,[17] and defined as 𝑵 =(𝑬𝑯𝑶𝑴𝑶 𝑵𝒖 − 𝑬𝑯𝑶𝑴𝑶 𝑻𝑪𝑬 ). The nucleophilicity is referred to tetracyanoethylene (TCE). The 𝑃𝑘+ electrophilic and 𝑃𝑘− nucleophilic Parr functions, [18-28] which allow for the characterisation of the electrophilic and nucleophilic centers of a molecule, were obtained through the analysis of the Mulliken atomic spin density of the radical anion and the radical cation of the studied molecules, respectively.   HBrBrH HBrBrHBrBrHBrBrClClHBrBrClClHBrBrBrBrHBrBrBrBr+++CHCl3 / NaOH TBEA-Cl /  CTP-LSTBEA-Cl /  CTP-LS CHBr3 / NaOHCHBr3 / NaOHTBEA-Cl /  CTP-LSP1 100% P2 0%P3 85% P4 15%P5 P6 P1 B-HimachaleneReaction 1Reaction 2Reaction 3Zeroual & al. / Mor. J. Chem. 3 N°4 (2015) 698-704  700  II.Results and Discussion II.1. The intramolecular chemical descriptors of the β-himachalène and the dibromocarbene. Electronic chemical potential (μ), the index of the electrophilicity (ω) and the nucleophilicity index (N) calculated for β-himachalène and dibromocarbene are shown in table 1.  Table 1: Electronic chemical potential (μ), global electrophilicity (ω), and global nucleophilicity (N), in eV.  μ ω N β-himachalene -2.499 0.489 3.427 Dibromocarbene -5.332 4.107 2.469   The electronic chemical potential of β-himachalène (-2.499 eV) is higher than dibromocarbene (-5.332 ev), which means that the electron transfer takes place of β-himachalène to dibromocarbene.  The global electrophilicity of the dibromocarbene (4.107eV) is greater than that of β-himachalène (0.489 eV). Therefore, in this cycloaddition the dibromocarbene will behave as electrophilic while the β-himachalène will behave as nucleophilic, we can conclude the same thing from the nucleophilicity values.  II.2. Comparative analysis of local indexes for the reactants in the first reaction. The local electrophilicity values ωk for carbene and local nucleophilicity Nk for C2 atoms, C3, C6 and C7 of the β-himachalene calculated with the function Parr (atomic spin density) are reported in table 2.  Table 2: Electrophilic and nucleophilic Parr functions, and the local electrophilicity and local nucleophilicity. Reactifs N° carbone P + P - ωk Nk Dibromocarbene CBr2 0.979 0.706 4.020 1.743  β-himachalene C2 C3 C6 C7 0.08 0.13 0.27 0.28 0.14 0.09 0.25 0,27 0.05 0.09 0.18 0.19 0.47 0.30 0.85 0.92  These results show that the most favored interaction takes place between the carbene carbon atom (with the highest value of ωk) and atoms C6 and C7 β-himachalène (with the highest value of Nk). Therefore, the regioselectivity observed experimentally is correctly predicted by Parr functions. At the end highlight that the attack of the double bond C6 = C7 β-himachalene is preferred, we are studying stereo-selectivity of binding C6 = C7.  II.3. Study of stereoselectivity of the double bond C6 = C7. It was found the attack of the double bond C6=C7 by the α side of β-himachalene is preferred. We determined the energies of reactants, the energies of the products, the energies of TSα, TSβ and deference of transition energy (Table 3).  Zeroual & al. / Mor. J. Chem. 3 N°4 (2015) 698-704  701  Table 3: Total (E, in au) and relative (ΔE, in kcal /mol) energies of the stationary points involved in the cycloaddition [1+2] between β-himachalene and dibromocarbene.  E (u.a) ΔE*(kcal/mol) (E – ER) Δ(TSβ–TSα) Kcal/mol Reactifs  (β-himachalene +CBr2)  -5767.430  ---------    8.157   ETS α 1 -5767.424 3.765 ETS β 2 -5767.411 11.922 Product P1 -5767.534 -65.262 Product P2 -5767.509 -49.573  The difference between the activation energies of products P1 and P2 is 8.16 kcal/mol indicating that the formation of the alpha isomer is kinetically favored over the beta isomer. The calculation is in agreement with the experimental results.  II.4. Theoretical studies of the stereoselectivity of the cycloaddition reaction [1+2] between the P1 and the dihalogenocarbene.  Table 4: The chemical descriptors intramolecular (in eV) for the product P1, dichlorocarbene and dibromocarbene.  μ ω N Product P1 -3.44 1.06 3.3 Dichlorocarbene -5.45 3.90 2.17 Dibromocarbene -5.33 4.10 2.46   Table 5: Total (E, a.u) and Relative (ΔE, kcal/mol) Energies of the Stationary Points Involved in the Addition Reaction to the product P1 and dihalogenocarbene.  E (u.a) ΔE*(Kcal/mol) (E – ER) Δ(TSβ–TSα) (Kcal/mol) (P1+CCl2) -6725.917 ---------   16.315 ETS α 3 -6725.892 15.687 ETS β 4 -6725.866 32.002 Product 3 -6725.997 -50.200 Product 4 -6725.999 -51.455 (P1+CBr2) -10948.934 ---------   17.570  ETS α 5 -10948.903 19.452 ETS β 6 -10948.875 37.023 Product 5 -10949.021 -54.593 Product 6 -10949.025 -57.103  Zeroual & al. / Mor. J. Chem. 3 N°4 (2015) 698-704  702  * The electrophilicity index of dibromocarbene and dichlorocarbene (4.10 eV and 3.90 eV), respectively, are higher than that of the product P1 (1.06 eV). Therefore, in this cycloaddition the dihalogenocarbene behaves as an electrophile while the product P1 will behaves as nucleophile. (Table 4) * The chemical potential of the product P1 (-3.44 eV) is higher than dihalogenocarbenes (-5.33 eV, -5.45 eV), which implies that the electron transfer takes place from the product P1 to dihalogenocarbenes. Experimentally the attack of the double bond C2 = C3 by the α side of the product P1: ((1S, 3R, 8S) -2,2-dibromo-3,7,7,10- tetramethyltricyclo [6.4.0.01,3] Dodec -9-ene is preferred, we determined the energies of reactants, the energies of the products, the transition energy TSα, the transition TSβ and deference of the transition energy (table 5).  Table 6 :activations energies of alpha and bita faces for reactions 2 and 3  ΔE*(kcal/mol) Δ [ΔE*(kcal/mol] ETS α 3 (dichlorocarbene) 15.687 3.765 ETS α 5 (dibromocarbene) 19.452 ETS β 4 (dichlorocarbene) 32.002 5.021 ETS β 6 (dibromocarbene) 37.023  𝑽 =𝟏𝟑𝝅.𝒓𝟐𝒉 𝒉 = 𝑫. 𝐜𝐨𝐬𝜽𝟐 𝒓 = 𝑫. 𝐬𝐢𝐧𝜽𝟐 𝒔 = 𝑫 = 𝟐.𝑹 𝑨𝟏 + 𝟐.𝑹 𝑨𝟐 + 𝒅(𝑨𝟐 − 𝑨𝟏) Dibromocarbene  Dichlorocarbene  R(C) = 70 pm R(Br)=115 pm d1=191.82 pm θ1 (Br-C-Br)= 109.427 D1=561.82 pm h1=324.507 pm r1=458.557 pm V1=0.071 (nm)3 R(C) = 70 pm R(Cl)=100pm d2=175.26 pm θ2 (Cl-C-Cl)= 109.317 D2=515.26 pm h2=298.026 r2=420.297 V2=0.055 (nm)3  Table 5 shows that:   The formation of products P3, P4, P5 and P6 are exothermic by -50.200, -51.455, -54.593 and -57.103 kcal/mol respectively and thermodynamically favorable.   The transition state energy of the β side of double bond C2=C3 is located in front 16.315 and 17.570 kcal/mol below the transition state energy of the α side for reaction 3 and reaction 4 respectively. Zeroual & al. / Mor. J. Chem. 3 N°4 (2015) 698-704  703    The difference between the activation energies of products P3 and P4 is of order 16.315 kcal/ mol, indicating that the formation of alpha stereoisomer are kinetically favored over the beta stereoisomer. The result is in agreement with the experimental results. Under the same experimental conditions P1 does not react with dibromocarbene. To find out why this so, we compare the energy of activation recent reactions (reactions 2 and 3) and the size of dihalogenocarbene used we gather in Table 6 activations energies of alpha and bita faces for reactions 2 and 3, we also collect in this table geometrical parameters of dihalogenocarbene. The bromine atom is larger than the chlorine atom which makes the lengths and bond angles in the dibromo-carbene (d1=191.82 pm, θ1 (Br-C-Br)= 109.4276) greater than in the dichlorocarbene (d2=175.26 pm, θ2 (Cl-C-Cl)= 109.3176) and the free rotation of the molecules in the solvent, it will consider that the carbenes (singlet carbene) have shapes of cones. We gather in Table 6 relations used to calculate the parameters of the cones. We find that the volume of dibromo-carbene (0.071 nm3) is greater than the volume of dichlorocarbene (0.055 nm3), so the steric hindrance created by the methyl carried by the C11 carbon is most important with the dibromo-carbene than dichlorocarbene which make the activation energies of the third reaction greater than those of the second reaction. So the reaction 3 is difficult to achieve experimentally, then it is necessary to estimate the other terms (solvent, temperature, catalyst ...).  IV. Conclusion The regio- and stereoselectivity of the reaction between β-himachalene and dibromocarbene was studied using DFT B3LYP/6-31G (d). Analysis of the global electrophilicity and nucleophilicity indices showed that β-himachalene P1 behaves as a nucleophile, while dibromocarbene and dichlorocarbene behaves as an electrophile. The regioselectivity found experimentally was confirmed by local indices of electrophilicity and nucleophilicity ωk and Nk. Calculation of activation energies shows that this reaction stereoselective reaction takes place at the α side of the double bond C6=C7 of β-himachalene. Treatment of product P1 with one equivalent of dichlorocarbene leads to formation of the two products P3 and P4 we showed that the reaction is stereoselective too, but dibromocarbene does not react with the product P1 because the activation energies of this reaction (α and β sides) are very high.  Reference [1] M. Fedoryński, Chem. Rev., 103 (2003) 1099-1132.  [2] H. Eljamili, A. 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The regio- and stereoselective addition of dibromocarbene and dichlorocarbene onto β-himachalene

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The regio- and stereoselective addition of dibromocarbene and dichlorocarbene onto β-himachalene

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