Understanding the Mechanism and Selectivities of the Reaction of Meta-Chloroperbenzoic Acid and Dibromocarbene with β -Himachalene: A DFT Study

This study was performed to understand the site selectivity in the reaction between β -himachalene and meta-chloroperbenzoic acid (m-CPBA) 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 three-parameter hybrid exchange functional and the Lee–Yang–Parr correlation functional (B3LYP) with the 6-311+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 m-CPBA on β -himachalene was analyzed on the two double bonds of β -himachalene 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 six-membered ring double bond position of α -monoepoxide. The major products P αα are kinetically and thermodynamically favored with a high stereoselectivity in perfect correlation with the experimental observations.


Introduction
Aromatic plants contain a variety of essential oils in their wood, leaves, fruits, bark, seeds, and/or roots. ese 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 c-himachalene [2]. β-Himachalene 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]. e structure of β-himachalene includes two double bonds, one in six-membered ring double bond and the other in seven-membered ring double bond.
In order to obtain new therapeutic agents in medicinal chemistry and new compounds with interesting olfactory properties in perfumery, β-himachalene has been epoxidized by m-chloroperbenzoic acid. Indeed, when these reactants are used in stoichiometric proportions, only the sevenmembered ring double bond of β-himachalene is attacked, producing a majority of the α-stereoisomer 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. e product P αα is kinetically and thermodynamically favored with a high stereoselectivity. e quantum chemistry can provide very reliable information and verify results already found through the experiment.
is work aims to understand the site selectivity of the β-himachalene reaction with m-CPBA and CBr 2 . e 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. e 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 6-311 + G (d, p) basis set, which gives more precise results. is work is divided into two parts: the first is dedicated to the epoxidation of β-himachalene by m-CBPA 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.

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 (P + k ,P − k ) [9,10] and the Fukui functions (f + k , f − k ) [11,12]. e 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]. ese 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]: e nucleophilicity index N (equation (4)) is calculated from the difference of the HOMO energy of the reactant and tetracyanoethylene (TCE) as a reference [8]:   (4) e local electrophilicity ω k [14] and nucleophilicity N k [15] indices are calculated by the following equations, respectively: where electrophilic P + k and nucleophilic P − k 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].
e Fukui function (FF) is calculated using the procedure proposed by Yang and Mortier [11] based on a finite difference method: f + k for nucleophilic attack (equation (7)), f − k for electrophilic attack (equation (8)), and f 0 k for radical attack (equation (9)): where ρ k (N), ρ k (N − 1), and ρ k (N + 1) are the gross electronic populations of the site k in neutral, cationic, and anionic systems, respectively.

Computational Details.
All computations of geometry optimization were executed using the Gaussian 09W programs [17]. e geometries of the products were fully optimized through DFT calculations using the hybrid functional B3LYP [18,19] with the 6-311 + G (d, p) basis set [20]. e transition states, resultant to the two α and β reaction sides, were located at the same level by QST2. eir existence was validated by the existence of one and only one imaginary frequency in the Hessian matrix. e intrinsic reaction coordinate (IRC) [21] was performed and plotted to show that the TS is well connected to both minima of reagents and products. e 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).

Analysis of the Reactivity Indices of the Reactants in the
Base State Table 1 summarizes the electronic chemical potential μ, chemical hardness η, global electrophilicity ω, and nucleophilicity N of β-himachalene and m-CPBA calculated at B3LYP/6-311 + G (d, p) level (eV). e table indicates that the electronic chemical potential of β-himachalene, μ � −2.99 eV, is higher than that of m-CPBA, μ � −4.74 eV. is means that there is a global electron density transfer (GEDT) [22] of β-himachalene to m-CPBA. e m-CPBA presents an electrophilicity (ω) index of 2.14 eV and a nucleophilicity (N) index of 1.77 eV, and those corresponding to the β-himachalene are 0.76 eV and 3.19 eV, respectively.

Prediction of Nucleophilic/Electrophilic Character.
ere results suggest that m-CPBA behaves as an electrophile, while the β-himachalene behaves as a nucleophile.

Prediction of Site Selectivity.
e most favored interaction between two polar centers is related to the local indices (ω k and N k ). e 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 m-CPBA 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 In addition, the analysis of the nucleophilic − Pk Parr functions at the reactive sites of β-himachalene indicates that the C 6 and C 7 carbon atoms, with − Pk values of 2.23 and 3.04, respectively, are more nucleophilically active than the C 2 and C 3 carbon atoms, with − Pk values of 1.42 and 0.69, respectively. is 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 ( + fk , − fk ) 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. e 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.

Structural Analysis of the Transition States of the Cyclopropanation Reaction.
e study of the stereoselectivity of C 6 � C 7 and C 2 � C 3 bonds indicates that the attack of the seven-membered ring double bond of β-himachalene is preferred. e thermodynamic energies and relative energies were calculated and are presented in Table 3. e 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 β-himachalene, and the difference in transition energy shows that the attack is kinetically preferred at α side of the double bond of the seven-membered ring. e activation energies corresponding to the attack at the two sides of the showing that the formation of α isomers is kinetically preferred to the formation of β isomers. e 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. e examination of m-CPBA epoxidation of the β-himachalene 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. is result allows us to   conclude that the α-attack is kinetically and thermodynamically favored and that the C 6 �C 7 double bond of β-himachalene is more reactive than the other C 2 �C 3 , and this is in good agreement with the experimental results [23].

Analysis of the IRC of the Reaction between β-Himachalene and M-CPBA.
e molecular system during the reaction between β-himachalene and m-CPBA 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). e plots of the total energy E vs intrinsic reaction coordinate (IRC) corresponding to all possible pathways are shown in Figure 4. is figure indicates that the reaction takes place by one-step mechanism characterized by the formation of the first bond followed by closure of the cycle without the formation of a stable intermediary reactant. e analysis of the IRC calculated using DFT at B3LYP/6-311 + G (d, p) basis set shows that whatever quantity of m-CPBA is used in the interaction with β-himachalene, the transition states are reached without going through a stable intermediary stage.

Structural analysis of the transition states of the reaction.
e optimized geometries of the TS α , TS β , TS α, and TS β' transition states associated with the reaction between β-himachalene and m-CBPA are shown in Figure 5. e 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 inÅ: 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 � 0.16Å at TS α , while at TS β , the asynchronicity of stereoisomer is Δd � 0.31Å. On the other hand, the asynchronicity of the stereoisomer was 0.16Å at TSα′ and 0.23Å TS β′ .

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 β-himachalene and m-CBPA, we subsequently studied the cyclopropanation reaction between the major product (P α ) and dibromocarbene. e 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. is table indicates that the electrophilic index of dibromocarbene (4.46 eV) is greater than that of P α (0.83 eV). is result suggests that dibromocarbene behaves as an electrophile, while P α behaves as a nucleophile. is behavior is confirmed by the global nucleophilic indices of the reactants. e chemical hardness of P α is 6.38 eV. is 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). is result indicates that electrons are transferred from P α to dibromocarbene.

Kinetic Study.
e stereoselectivity of the addition of dibromocarbene to the major product (P α ) obtained from the first reaction of β-himachalene with m-CPBA was examined in both α and β sides of P α . e 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). e 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. ese 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). ese results allow us to conclude that α-attack is kinetically and thermodynamically favored. It also explains the great stereoselectivity observed experimentally.

Structural Analysis of the Transition States of the Epoxy
Reaction.
e 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 2.26Å at d 1 (C * − C 3 ) and 2.59Å at d 2 (C * − C 2 ) for TS αα . However, those formed by stereoisomer 2 are 2.75Å at d 1 (C * − C 3 ) and 2.38Å at d 2 (C * − C 2 ) for TS αβ , where C * is the carbon atom of dibromocarbene.
e 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 Table 4: Electronic chemical potential (μ), chemical hardness (η), electrophilicity (ω), and nucleophilicity (N) of the major product (P α ) and CBr 2 calculated at B3LYP/6-311 + G (d, p) level (eV).  6 Heteroatom Chemistry It was found that the asynchronicity of the stereoisomer 1 is Δd � 0.33Å at TS αα . However, the asynchronicity of the stereoisomer 2 is Δd � 0.37Å at TS αβ . From these transition states, we can conclude that the favored stereoisomer is more asynchronous than the other.

Conclusions
e reaction of meta-chloroperbenzoic acid and dibromocarbene with β-himachalene was studied using the DFT method at the B3LYP/6-311 + G (d, p) level. e results confirm that this theory gives a conceptual framework to the study of the reactivity and selectivity of the chemical reaction  Figure 6: Energy profile of reaction between P α and dibromocarbene. Heteroatom Chemistry 7 through local and global descriptors. e latter allows one to show that the double bond of the seven-membered ring of β-himachalene is more reactive with a high stereoselectivity with m-CPBA through its α face than the six-membered one forming the major product P α . e 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
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this article.