Research Article  Open Access
Sana El Hamidi, Malika Khnifira, El Mokhtar Lemdek, Redouan Hammal, Noureddine Barka, M’hamed Sadiq, Ahmed Benharref, Ahmed Chekroun, Hssaine Zgou, Mohamed Abdennouri, "Understanding the Mechanism and Selectivities of the Reaction of MetaChloroperbenzoic Acid and Dibromocarbene with βHimachalene: A DFT Study", Heteroatom Chemistry, vol. 2020, Article ID 8885991, 8 pages, 2020. https://doi.org/10.1155/2020/8885991
Understanding the Mechanism and Selectivities of the Reaction of MetaChloroperbenzoic Acid and Dibromocarbene with βHimachalene: A DFT Study
Abstract
This study was performed to understand the site selectivity in the reaction between βhimachalene and metachloroperbenzoic acid (mCPBA) in the first step followed by the addition of dibromocarbene (CBr_{2}) to the main monoepoxidation product P_{α} formed in the first reaction. Calculations were performed using the Becke threeparameter hybrid exchange functional and the Lee–Yang–Parr correlation functional (B3LYP) with the 6311 + G (d, p) basis set. Transition states were located by QST2, and their highlighting was validated by the existence of only one imaginary frequency in the Hessian matrix. The action of mCPBA on βhimachalene was analyzed on the two double bonds of βhimachalene whose theoretical calculations show that the attack affects the most substituted double bond on α side containing hydrogen of ring junction. The obtained P_{α} product thereafter treated with dibromocarbene leads via an exothermic reaction to the sixmembered ring double bond position of αmonoepoxide. The major products P_{αα} are kinetically and thermodynamically favored with a high stereoselectivity in perfect correlation with the experimental observations.
1. Introduction
Aromatic plants contain a variety of essential oils in their wood, leaves, fruits, bark, seeds, and/or roots. These oils exhibit antiseptic, cytotoxic, antibacterial, and antioxidant activities allowing them many applications in perfume, agrofood, cosmetic, and pharmaceutical industries [1]. For example, Cedrus atlantica essential oil is essentially composed of α, β, and γhimachalene [2]. βHimachalene is an optically active bicyclic sesquiterpene representing approximately 50% of the essential oils isolated by fractional distillation of the essential oil of the Atlas and Himalayan cedar [3]. The structure of βhimachalene includes two double bonds, one in sixmembered ring double bond and the other in sevenmembered ring double bond.
In order to obtain new therapeutic agents in medicinal chemistry and new compounds with interesting olfactory properties in perfumery, βhimachalene has been epoxidized by mchloroperbenzoic acid. Indeed, when these reactants are used in stoichiometric proportions, only the sevenmembered ring double bond of βhimachalene is attacked, producing a majority of the αstereoisomer referred to as P_{α} (Figure 1). When treated with dibromocarbene, these later leads, via an exothermic reaction, to two products P_{αα} and P_{αβ} (Figure 1) formed at the α and β sides of the sixmembered ring double bond of P_{α}, respectively. The product P_{αα} is kinetically and thermodynamically favored with a high stereoselectivity. The quantum chemistry can provide very reliable information and verify results already found through the experiment.
This work aims to understand the site selectivity of the βhimachalene reaction with mCPBA and CBr_{2}. The computational calculations are performed using the digital chemistry software (Gaussian 09W) which is recognized by its advanced capabilities in the electronic modelling of chemical structures. The DFT method is chosen, which is the most relevant method in quantum chemistry and allows the study of the electronic structure in principle in an exact way, with the 6311 + G (d, p) basis set, which gives more precise results. This work is divided into two parts: the first is dedicated to the epoxidation of βhimachalene by mCBPA and the second part will treat the cyclopropanation reaction between the major product P_{α} resulting from the first reaction and dibromocarbene according to the reaction sequences proposed in Figure 1.
2. Theoretical and Computational Methods
2.1. Global and Local Reactivity Indices
Conceptual density functional theory (CDFT) [4, 5] has provided powerful tools in the study of chemical reactivity by defining many descriptors such as the electronic chemical potential µ [6], the electrophilicity ⍵ [7] and the nucleophilicity N [8] indices, and local condensed indices such as the Parr functions () [9, 10] and the Fukui functions () [11, 12].
The nucleophilic/electrophilic nature of the reactants is evaluated through the electrophilicity ⍵ and nucleophilicity N indices, where the value of ⍵ is found from the electronic chemical potential µ and the global hardness η [6, 13]. These parameters are calculated from the energies of the highest occupied molecular orbital (E_{HOMO}) and lowest unoccupied molecular orbital (E_{LUMO}) according to the following equations:
From equations (1) and (2), we can also calculate the global electrophilicity index ω (equation (3)), defined as the energy stabilization due to charge transfer [7]:
The nucleophilicity index N (equation (4)) is calculated from the difference of the HOMO energy of the reactant and tetracyanoethylene (TCE) as a reference [8]:
The local electrophilicity ω_{k} [14] and nucleophilicity N_{k} [15] indices are calculated by the following equations, respectively:where electrophilic and nucleophilic Parr functions are obtained by analysis of the Mullikan atomic spin density (ASD) of the radical anion and radial cation of the reactants, which allow for the characterization of the electrophilic and nucleophilic centers of a molecule [10, 16].
The Fukui function (FF) is calculated using the procedure proposed by Yang and Mortier [11] based on a finite difference method: for nucleophilic attack (equation (7)), for electrophilic attack (equation (8)), and for radical attack (equation (9)):where (N), (N − 1), and (N + 1) are the gross electronic populations of the site k in neutral, cationic, and anionic systems, respectively.
2.2. Computational Details
All computations of geometry optimization were executed using the Gaussian 09W programs [17]. The geometries of the products were fully optimized through DFT calculations using the hybrid functional B3LYP [18, 19] with the 6311 + G (d, p) basis set [20]. The transition states, resultant to the two α and β reaction sides, were located at the same level by QST2. Their existence was validated by the existence of one and only one imaginary frequency in the Hessian matrix. The intrinsic reaction coordinate (IRC) [21] was performed and plotted to show that the TS is well connected to both minima of reagents and products. The values of enthalpy, entropy, and free energy were calculated from the analysis of the electronic structures of the stationary points and the bond orders (Wiberg indices) using the natural bond orbital method (NBO).
3. Results and Discussion
3.1. Analysis of the Reactivity Indices of the Reactants in the Base State
3.1.1. Prediction of Nucleophilic/Electrophilic Character
Table 1 summarizes the electronic chemical potential μ, chemical hardness η, global electrophilicity ω, and nucleophilicity N of βhimachalene and mCPBA calculated at B3LYP/6311 + G (d, p) level (eV). The table indicates that the electronic chemical potential of βhimachalene, μ = −2.99 eV, is higher than that of mCPBA, μ = −4.74 eV. This means that there is a global electron density transfer (GEDT) [22] of βhimachalene to mCPBA. The mCPBA presents an electrophilicity (ω) index of 2.14 eV and a nucleophilicity (N) index of 1.77 eV, and those corresponding to the βhimachalene are 0.76 eV and 3.19 eV, respectively. There results suggest that mCPBA behaves as an electrophile, while the βhimachalene behaves as a nucleophile.

3.1.2. Prediction of Site Selectivity
The most favored interaction between two polar centers is related to the local indices (ω_{k} and N_{k}). The most favored product is associated with the highest local electrophilicity index ω_{k} of the electrophile and the highest local nucleophilicity index N_{k} of the nucleophile. From Figure 2, it is clear that the oxygen atom O^{∗} of mCPBA is the most electrophilic active site (ω_{O∗} = 0.29 eV). We can observe from the surface map illustrated in Figure 3 that the C_{6} = C_{7} double bond (N_{C6} = 0.64, N_{C7} = 0.70 eV) is very nucleophilic than C_{2} = C_{3} (N_{C2} = 0.10, N_{C7} = 0.26 eV). In addition, the analysis of the nucleophilic Parr functions at the reactive sites of βhimachalene indicates that the C_{6} and C_{7} carbon atoms, with values of 2.23 and 3.04, respectively, are more nucleophilically active than the C_{2} and C_{3} carbon atoms, with values of 1.42 and 0.69, respectively. This result confirms that the attack is preferentially done on the double bond C_{6} = C_{7} in good agreement with experimental observations [23].
In the same perspective, the Fukui functions () are helpful and enable us to distinguish clearly between nucleophilic and electrophilic attacks. However, they have a positive value at sites liable to nucleophilic attack and a negative value at sites liable to electrophilic attack. The values of local reactivity descriptors calculated using the DFT method for natural population analysis (NPA) derived charges of the molecule studied are shown in Table 2.

3.1.3. Structural Analysis of the Transition States of the Cyclopropanation Reaction
The study of the stereoselectivity of C_{6} = C_{7} and C_{2} = C_{3} bonds indicates that the attack of the sevenmembered ring double bond of βhimachalene is preferred. The thermodynamic energies and relative energies were calculated and are presented in Table 3. The analysis of the energies of the reactants, the products obtained, TS_{α},TS_{β}, TS_{α’}, and TS_{β’} transition state energies at the C_{6}=C_{7} and C_{2}=C_{3} double bonds, respectively, of βhimachalene, and the difference in transition energy shows that the attack is kinetically preferred at α side of the double bond of the sevenmembered ring. The activation energies corresponding to the attack at the two sides of the C_{6} = C_{7} double bond of βhimachalene are 17.5 kcal·mol^{−1} at β and 13.8 kcal·mol^{−1} at α and those corresponding to the attack on both sides of the C_{2} = C_{3} double bond are of the order of 14.2 and 17.8 kcal·mol^{−1} at α′ and β′, respectively, showing that the formation of α isomers is kinetically preferred to the formation of β isomers. The formation of P_{α}, P_{β}, P_{α}’, and P_{β’} is an exothermic reaction, with −53.3, −45.8, −51.9, and −45.4 kcal·mol^{−1}, respectively. The examination of mCPBA epoxidation of the βhimachalene using the data given in Table 3 indicates that the energy barrier corresponding to the approach to the α side is lower than that corresponding to the other sides. This result allows us to conclude that the αattack is kinetically and thermodynamically favored and that the C_{6}=C_{7} double bond of βhimachalene is more reactive than the other C_{2}=C_{3}, and this is in good agreement with the experimental results [23].

3.1.4. Analysis of the IRC of the Reaction between βHimachalene and MCPBA
The molecular system during the reaction between βhimachalene and mCPBA was studied by calculating the intrinsic reaction coordinate (IRC) in order to show that the transition state is indeed linked to the two minima (reactants and products). The plots of the total energy E vs intrinsic reaction coordinate (IRC) corresponding to all possible pathways are shown in Figure 4. This figure indicates that the reaction takes place by onestep mechanism characterized by the formation of the first bond followed by closure of the cycle without the formation of a stable intermediary reactant. The analysis of the IRC calculated using DFT at B3LYP/6311 + G (d, p) basis set shows that whatever quantity of mCPBA is used in the interaction with βhimachalene, the transition states are reached without going through a stable intermediary stage.
3.1.5. Structural analysis of the transition states of the reaction
The optimized geometries of the TS_{α}, TS_{β}, TS_{α,} and TS_{β’} transition states associated with the reaction between βhimachalene and mCBPA are shown in Figure 5. The asynchronicity of bond formation in this reaction can be measured as the difference between the two lengths of the two σ bonds formed, namely, Δd given in Å:where , , , and are the length of the bond between the oxygen atom and carbon atoms C_{6}, C_{7}, C_{2}, and C_{3}, respectively. It was found that the asynchronicity of stereoisomer is Δd = 0.16 Å at TS_{α}, while at TS_{β}, the asynchronicity of stereoisomer is Δd = 0.31 Å. On the other hand, the asynchronicity of the stereoisomer was 0.16 Å at TSα′ and 0.23 Å TS_{β′}.
(a)
(b)
(c)
(d)
3.2. Analysis of intramolecular Chemical Descriptors of the Reaction between P_{α} and Dibromocarbene
After the determination of the chemoselectivity and stereoselectivity of the reaction between βhimachalene and mCBPA, we subsequently studied the cyclopropanation reaction between the major product (P_{α}) and dibromocarbene. The electronic chemical potential (μ), chemical hardness (η), electrophilicity index (ω), global nucleophilicity index (N), and maximum charge transfer ΔN_{max} calculated for P_{α} and dibromocarbene are shown in Table 4. This table indicates that the electrophilic index of dibromocarbene (4.46 eV) is greater than that of P_{α} (0.83 eV). This result suggests that dibromocarbene behaves as an electrophile, while P_{α} behaves as a nucleophile. This behavior is confirmed by the global nucleophilic indices of the reactants. The chemical hardness of P_{α} is 6.38 eV. This value is greater than that of dibromocarbene (3.41 eV). Also, the electronic chemical potential of P_{α} (−3.26 eV) is greater than that of dibromocarbene (−5.52 eV). This result indicates that electrons are transferred from P_{α} to dibromocarbene.

3.2.1. Kinetic Study
The stereoselectivity of the addition of dibromocarbene to the major product (P_{α}) obtained from the first reaction of βhimachalene with mCPBA was examined in both α and β sides of P_{α}. The calculated energies of the reactants, the obtained products (TS_{αα} and TS_{αβ}) at the C_{2} = C_{3} double bond of P_{α}, and the difference in transition energies are listed in Table 5. From this table, we can deduce that the transition state energy of the β side of double bond C_{2} = C_{3} (8.9 kcal/mol) is located above the transition state energy of the α side (4.1 kcal/mol). The formation of the products P_{αα} and P_{αβ} occurred via exothermic reaction with −49.3 and −44.4 kcal/mol, respectively, and is strongly exergonic, by −31.7 and −26.9 kcal/mol, respectively. These values indicate that the reaction between P_{α} and dibromocarbene is energetically exothermic. We also notice that the energy barrier corresponding to the approach to the α side is less than the corresponding one to the β side (Figure 6). These results allow us to conclude that αattack is kinetically and thermodynamically favored. It also explains the great stereoselectivity observed experimentally.

3.2.2. Structural Analysis of the Transition States of the Epoxy Reaction
The analysis of the geometries of the transition states associated with the reaction between P_{α} and dibromocarbene (Figure 7) shows that the lengths of the bonds formed by stereoisomer 1 are 2.26 Å at d_{1}(C^{∗} − C_{3}) and 2.59 Å at d_{2}(C^{∗} − C_{2}) for TS_{αα}. However, those formed by stereoisomer 2 are 2.75 Å at d_{1}(C^{∗} − C_{3}) and 2.38 Å at d_{2}(C^{∗} − C_{2}) for TS_{αβ}, where C^{∗} is the carbon atom of dibromocarbene.
(a)
(b)
The asynchronicity of bond formation in this reaction, measured as the difference between the two lengths of the two σ bonds formed (Δd), is given by
It was found that the asynchronicity of the stereoisomer 1 is Δd = 0.33 Å at TS_{αα}. However, the asynchronicity of the stereoisomer 2 is Δd = 0.37 Å at TS_{αβ}. From these transition states, we can conclude that the favored stereoisomer is more asynchronous than the other.
4. Conclusions
The reaction of metachloroperbenzoic acid and dibromocarbene with βhimachalene was studied using the DFT method at the B3LYP/6311 + G (d, p) level. The results confirm that this theory gives a conceptual framework to the study of the reactivity and selectivity of the chemical reaction through local and global descriptors. The latter allows one to show that the double bond of the sevenmembered ring of βhimachalene is more reactive with a high stereoselectivity with mCPBA through its α face than the sixmembered one forming the major product P_{α}. The reaction of the latter with CBr_{2} takes place according to an exothermic mechanism in a single step in which the product P_{αα} is kinetically and thermodynamically favored over P_{αβ} according to the energetic parameters of the transition states in good agreement with experimental observations.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this article.
Acknowledgments
The authors are thankful to the Sultan Moulay Slimane University for facilitating infrastructure and equipment use.
References
 A. Sivropoulou, E. Papanikolaou, C. Nikolaou, S. Kokkini et al., “Antimicrobial and cytotoxic activities of OriganumEssential oils,” Journal of Agricultural and Food Chemistry, vol. 44, no. 5, pp. 1202–1205, 1996. View at: Publisher Site  Google Scholar
 R. Hammal, A. Benharref, and A. El Hajbi, “Theoretical study of the chemo, regio and stereoselectivity of the interaction between dichlorocarbene and αtranshimachalene using density functional theory (DFT) B3LYP/631G (d, p),” International Journal of Innovation and Applied Studies, vol. 6, pp. 734–745, 2014. View at: Google Scholar
 H. Eljamili, A. Auhmani, M. Dakir et al., “Oxydation et addition des dihalocarbènes sur le βhimachalène,” Tetrahedron Letters, vol. 43, no. 37, pp. 6645–6648, 2002. View at: Publisher Site  Google Scholar
 P. Geerlings, F. De Proft, and W. Langenaeker, “Conceptual density functional theory,” Chemical Reviews, vol. 103, no. 5, pp. 1793–1874, 2003. View at: Publisher Site  Google Scholar
 L. Domingo, M. RíosGutiérrez, and P. Pérez, “Applications of the conceptual density functional theory indices to organic chemistry reactivity,” Molecules, vol. 21, no. 6, p. 748, 2016. View at: Publisher Site  Google Scholar
 R. G. Parr and R. G. Pearson, “Absolute hardness: companion parameter to absolute electronegativity,” Journal of the American Chemical Society, vol. 105, no. 26, pp. 7512–7516, 1983. View at: Publisher Site  Google Scholar
 R. G. Parr, L. V. Szentpály, and S. Liu, “Electrophilicity index,” Journal of the American Chemical Society, vol. 121, no. 9, pp. 1922–1924, 1999. View at: Publisher Site  Google Scholar
 L. R. Domingo, E. Chamorro, and P. Pérez, “Understanding the reactivity of captodative ethylenes in polar cycloaddition reactions. A theoretical study†,” The Journal of Organic Chemistry, vol. 73, no. 12, pp. 4615–4624, 2008. View at: Publisher Site  Google Scholar
 R. G. Parr and W. Yang, “Density functional approach to the frontierelectron theory of chemical reactivity,” Journal of the American Chemical Society, vol. 106, no. 14, pp. 40494050, 1984. View at: Publisher Site  Google Scholar
 L. R. Domingo, P. Pérez, and J. A. Sáez, “Understanding the local reactivity in polar organic reactions through electrophilic and nucleophilic Parr functions,” RSC Advances, vol. 3, no. 5, pp. 1486–1494, 2013. View at: Publisher Site  Google Scholar
 W. Yang and W. J. Mortier, “The use of global and local molecular parameters for the analysis of the gasphase basicity of amines,” Journal of the American Chemical Society, vol. 108, no. 19, pp. 5708–5711, 1986. View at: Publisher Site  Google Scholar
 E. Chamorro, P. Pérez, and L. R. Domingo, “On the nature of Parr functions to predict the most reactive sites along organic polar reactions,” Chemical Physics Letters, vol. 582, pp. 141–143, 2013. View at: Publisher Site  Google Scholar
 L. R. Domingo, M. RíosGutiérrez, and P. Pérez, “A new model for CC bond formation processes derived from the Molecular Electron Density Theory in the study of the mechanism of [3 + 2] cycloaddition reactions of carbenoid nitrile ylides with electrondeficient ethylenes,” Tetrahedron, vol. 72, no. 12, pp. 1524–1532, 2016. View at: Publisher Site  Google Scholar
 L. R. Domingo, M. J. Aurell, P. Pérez, and R. Contreras, “Quantitative characterization of the local electrophilicity of organic molecules. Understanding the regioselectivity on DielsAlder reactions,” The Journal of Physical Chemistry A, vol. 106, no. 29, pp. 6871–6875, 2002. View at: Publisher Site  Google Scholar
 P. Pérez, L. R. Domingo, M. DuqueNoreña, and E. Chamorro, “A condensedtoatom nucleophilicity index. An application to the director effects on the electrophilic aromatic substitutions,” Journal of Molecular Structure: THEOCHEM, vol. 895, no. 1–3, pp. 86–91, 2009. View at: Publisher Site  Google Scholar
 A. Zeroual, R. Hammal, A. Benharref, and A. El Hajbi, “The regio and stereoselective addition of dibromocarbene and dichlorocarbene onto βhimachalene,” Moroccan Journal of Chemistry, vol. 3, pp. 698–704, 2015. View at: Google Scholar
 M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., Gaussian 09, Gaussian Inc., Wallingford, CT, USA, 2009.
 A. D. Becke, “Density‐functional thermochemistry. III. The role of exact exchange,” The Journal of Chemical Physics, vol. 98, no. 7, pp. 5648–5652, 1993. View at: Publisher Site  Google Scholar
 C. Lee, W. Yang, and R. G. Parr, “Development of the ColleSalvetti correlationenergy formula into a functional of the electron density,” Physical Review B, vol. 37, no. 2, pp. 785–789, 1988. View at: Publisher Site  Google Scholar
 W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, NY, USA, 1986.
 H. B. Schlegel, “Geometry optimization on potential energy surfaces,” in Modern Electronic Structure Theory, D. R. Yarkony, Ed., pp. 459–500, World Scientific Publishing, Singapore, 1995. View at: Google Scholar
 L. R. Domingo, “A new CC bond formation model based on the quantum chemical topology of electron density,” RSC Advances, vol. 4, no. 61, pp. 32415–32428, 2014. View at: Publisher Site  Google Scholar
 A. Chekroun, A. Jarid, A. Benharref, and A. Boutalib, “Regio and stereoselectivity of βhimachalene epoxidation bymCPBA. A theoretical study,” The Journal of Organic Chemistry, vol. 65, no. 14, pp. 4431–4434, 2000. View at: Publisher Site  Google Scholar
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Copyright © 2020 Sana El Hamidi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.