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

Authors: Sana El Hamidi; Malika Khnifira; El Mokhtar Lemdek; Redouan Hammal; Noureddine Barka; M’hamed Sadiq; Ahmed Benharref; Ahmed Chekroun; Hssaine Zgou; Mohamed Abdennouri
Journal: Heteroatom Chemistry
 (2020)

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## Abstract

This study was performed to understand the site selectivity in the reaction betweenβ-himachalene and meta-chloroperbenzoic acid (m-CPBA) in the first step followed by the addition of dibromocarbene (CBr2) to the main monoepoxidation product Pα 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 Pα product thereafter treated with dibromocarbene leads via an exothermic reaction to the six-membered ring double bond position of α-monoepoxide. The major products Pαα are kinetically and thermodynamically favored with a high stereoselectivity in perfect correlation with the experimental observations.


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## Body

## 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 γ-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]. The 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 seven-membered ring double bond of β-himachalene is attacked, producing a majority of the α-stereoisomer referred to as Pα (Figure 1). When treated with dibromocarbene, these later leads, via an exothermic reaction, to two products Pαα and Pαβ (Figure 1) formed at the α and β sides of the six-membered ring double bond of Pα, respectively. The product Pαα 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.Figure 1
Addition scheme reactions of m-CPBA and dibromocarbene toβ-himachalene.This work aims to understand the site selectivity of theβ-himachalene reaction with m-CPBA and CBr2. 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 6-311 + 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 β-himachalene by m-CBPA and the second part will treat the cyclopropanation reaction between the major product Pα 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 (Pk+,Pk−) [9, 10] and the Fukui functions (fk+,fk−) [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 (EHOMO) and lowest unoccupied molecular orbital (ELUMO) according to the following equations:(1)μ=EHOMO+ELUMO2,(2)η=ELUMO−EHOMO.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]:(3)ω=μ22η.The nucleophilicity indexN (equation (4)) is calculated from the difference of the HOMO energy of the reactant and tetracyanoethylene (TCE) as a reference [8]:(4)N=EHOMONu−EHOMOTCE.The local electrophilicityωk [14] and nucleophilicity Nk [15] indices are calculated by the following equations, respectively:(5)ωk=ω×Pk+,(6)Nk=N×Pk−,where electrophilic Pk+ and nucleophilic Pk− 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: fk+ for nucleophilic attack (equation (7)), fk− for electrophilic attack (equation (8)), and fk0 for radical attack (equation (9)):(7)fk+=ρkN+1−ρkN,(8)fk−=ρkN−ρkN−1,(9)fk0=ρkN+1−ρkN−12,where ρk(N), ρk(N − 1), and ρk(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 6-311 + 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).


## 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 (Pk+,Pk−) [9, 10] and the Fukui functions (fk+,fk−) [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 (EHOMO) and lowest unoccupied molecular orbital (ELUMO) according to the following equations:(1)μ=EHOMO+ELUMO2,(2)η=ELUMO−EHOMO.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]:(3)ω=μ22η.The nucleophilicity indexN (equation (4)) is calculated from the difference of the HOMO energy of the reactant and tetracyanoethylene (TCE) as a reference [8]:(4)N=EHOMONu−EHOMOTCE.The local electrophilicityωk [14] and nucleophilicity Nk [15] indices are calculated by the following equations, respectively:(5)ωk=ω×Pk+,(6)Nk=N×Pk−,where electrophilic Pk+ and nucleophilic Pk− 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: fk+ for nucleophilic attack (equation (7)), fk− for electrophilic attack (equation (8)), and fk0 for radical attack (equation (9)):(7)fk+=ρkN+1−ρkN,(8)fk−=ρkN−ρkN−1,(9)fk0=ρkN+1−ρkN−12,where ρk(N), ρk(N − 1), and ρk(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 6-311 + 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

Table1 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). The 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. This means that there is a global electron density transfer (GEDT) [22] of β-himachalene to m-CPBA. The 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. There results suggest that m-CPBA behaves as an electrophile, while the β-himachalene behaves as a nucleophile.Table 1
Electronic chemical potential (μ), chemical hardness (η), electrophilicity (ω), and nucleophilicity (N) of β-himachalene and m-CPBA (eV).
Reactantsµη⍵Nβ-Himachalene−2.995.900.763.19m-CPBA−4.745.232.141.77


#### 3.1.2. Prediction of Site Selectivity

The most favored interaction between two polar centers is related to the local indices (ωk and Nk). The most favored product is associated with the highest local electrophilicity index ωk of the electrophile and the highest local nucleophilicity index Nk of the nucleophile. From Figure 2, it is clear that the oxygen atom O∗ of m-CPBA is the most electrophilic active site (ωO∗ = 0.29 eV). We can observe from the surface map illustrated in Figure 3 that the C6 = C7 double bond (NC6 = 0.64, NC7 = 0.70 eV) is very nucleophilic than C2 = C3 (NC2 = 0.10, NC7 = 0.26 eV). In addition, the analysis of the nucleophilic Pk− Parr functions at the reactive sites of β-himachalene indicates that the C6 and C7 carbon atoms, with Pk−values of 2.23 and 3.04, respectively, are more nucleophilically active than the C2 and C3 carbon atoms, with Pk−values of 1.42 and 0.69, respectively. This result confirms that the attack is preferentially done on the double bond C6 = C7 in good agreement with experimental observations [23].Figure 2
The density map and electrophilicity index of m-CPBA.Figure 3
The density map and nucleophilicity index ofβ-himachalene.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. 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.Table 2
Local reactivity properties of reagents calculated using the DFT method for NPA-derived charges.
fk+fk−Pk+Pk−ωk+ωk−C20.00450.03180.05931.42911.42910.0242C30.00430.08260.10760.69730.00330.0629C60.02010.20220.29762.23630.01530.1539C70.03400.22140.30243.04260.02590.1686


#### 3.1.3. Structural Analysis of the Transition States of the Cyclopropanation Reaction

The study of the stereoselectivity of C6 = C7 and C2 = C3 bonds indicates that the attack of the seven-membered ring double bond of β-himachalene 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, TSα,TSβ, TSα’, and TSβ’ transition state energies at the C6=C7 and C2=C3 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. The activation energies corresponding to the attack at the two sides of the C6 = C7 double bond of β-himachalene 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 C2 = C3 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 Pα, Pβ, Pα’, and Pβ’ is an exothermic reaction, with −53.3, −45.8, −51.9, and −45.4 kcal·mol−1, respectively. The 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. This result allows us to conclude that the α-attack is kinetically and thermodynamically favored and that the C6=C7 double bond of β-himachalene is more reactive than the other C2=C3, and this is in good agreement with the experimental results [23].Table 3
Thermodynamic energies of the reaction betweenβ-himachalene and m-CPBA calculated using DFT/6-311 + G (d, p).
E (a.u.)∆E (kcal/mol)H (a.u)∆H (kcal/mol)G (a.u.)∆G (kcal/mol)ν (cm−1)m-CPBA−955.721212—−955.602614—−955.649316—β-Himachalene−586.183305—−585.813259—−585.870499—TSα−1541.88212313.8−1541.39305014.3−1541.48003924.9−375.75TSβ−1541.87613917.5−1541.38617918.6−1541.47263929.6−416.05TSα’−1541.88022514.2−1541.39009714.5−1541.47898625.2−376.66TSβ’−1541.86929917.8−1541.38126818.9−1541.47097730.3−418.89Pα−661.413885−53.3−661.037817−52.4−661.095788−51.0Pβ−661.401320−45.8−661.024962−44.3−661.083388−43.6Pα’−661.413022−51.9−661.036573−50.7−661.094555−49.8Pβ’−661.401101−45.4−661.024790−44.1−661.077968−42.3


#### 3.1.4. Analysis of the IRC of the Reaction betweenβ-Himachalene and M-CPBA

The molecular system during the reaction betweenβ-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). 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 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. The 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.Figure 4
IRC of the reaction betweenβ-himachalene and m-CBPA calculated using DFT at B3LYP/6-311 + G (d, p) level. Structural analysis of the transition states of the reaction.


#### 3.1.5. Structural analysis of the transition states of the reaction

The optimized geometries of the TSα, TSβ, TSα, and TSβ’ transition states associated with the reaction between β-himachalene and m-CBPA 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:(10)Δd=dO∗−C6−dO∗−C7,(11)Δd=dO∗−C2−dO∗−C3,where dO∗−C6, dO∗−C7, dO∗−C2, and dO∗−C3 are the length of the bond between the oxygen atom and carbon atoms C6, C7, C2, and C3, respectively. It was found that the asynchronicity of stereoisomer is Δd = 0.16 Å at TSα, while at TSβ, 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 TSβ′.Figure 5
Optimized geometries of the transition states TSα, TSβ, TSα’, and TSβ’of the β-himachalene and m-CBPA (the distances are given in Å).
(a)(b)(c)(d)


### 3.2. Analysis of intramolecular Chemical Descriptors of the Reaction between Pα and Dibromocarbene

After the determination of the chemoselectivity and stereoselectivity of the reaction betweenβ-himachalene and m-CBPA, we subsequently studied the cyclopropanation reaction between the major product (Pα) and dibromocarbene. The electronic chemical potential (μ), chemical hardness (η), electrophilicity index (ω), global nucleophilicity index (N), and maximum charge transfer ΔNmax calculated for Pα and dibromocarbene are shown in Table 4. This table indicates that the electrophilic index of dibromocarbene (4.46 eV) is greater than that of Pα (0.83 eV). This result suggests that dibromocarbene behaves as an electrophile, while Pα behaves as a nucleophile. This behavior is confirmed by the global nucleophilic indices of the reactants. The chemical hardness of Pα is 6.38 eV. This value is greater than that of dibromocarbene (3.41 eV). Also, the electronic chemical potential of Pα (−3.26 eV) is greater than that of dibromocarbene (−5.52 eV). This result indicates that electrons are transferred from Pα to dibromocarbene.Table 4
Electronic chemical potential (μ), chemical hardness (η), electrophilicity (ω), and nucleophilicity (N) of the major product (Pα) and CBr2 calculated at B3LYP/6-311 + G (d, p) level (eV).
PαCBr2µ−3.26−5.52Η6.383.41⍵0.834.46N2.681.91∆Nmax−0.51−1.61


#### 3.2.1. Kinetic Study

The stereoselectivity of the addition of dibromocarbene to the major product (Pα) obtained from the first reaction of β-himachalene with m-CPBA was examined in both α and β sides of Pα. The calculated energies of the reactants, the obtained products (TSαα and TSαβ) at the C2 = C3 double bond of Pα, 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 C2 = C3 (8.9 kcal/mol) is located above the transition state energy of the α side (4.1 kcal/mol). The formation of the products Pαα and Pαβ 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 Pα 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 α-attack is kinetically and thermodynamically favored. It also explains the great stereoselectivity observed experimentally.Table 5
Thermodynamic energies of the cyclopropanation reaction between Pα and dibromocarbene calculated using the DFT method at B3LYP/6-311 + G (d, p) basis set.
E (a.u.)G (a.u.)H (a.u.)∆E (kcal/mol)∆G (kcal/mol)∆H (kcal/mol)Pα−661.413801−661.095710−661.037800CBr2−5186.296500−5186.321500−5186.288610TSαα−5847.703721−5847.389−5847.3187024.117.64.8TSαβ−5847.696000−5847.381512−5847.3109018.922.49.7Pαα−5847.788923−5847.467800−5847.400001−49.3−31.7−46.1Pαβ−5847.781200−5847.460222−5847.392300−44.4−26.9−41.3Figure 6
Energy profile of reaction between Pα and dibromocarbene.


#### 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 Pα and dibromocarbene (Figure 7) shows that the lengths of the bonds formed by stereoisomer 1 are 2.26 Å at d1(C∗ − C3) and 2.59 Å at d2(C∗ − C2) for TSαα. However, those formed by stereoisomer 2 are 2.75 Å at d1(C∗ − C3) and 2.38 Å at d2(C∗ − C2) for TSαβ, where C∗ is the carbon atom of dibromocarbene.Figure 7
Bond lengths (Å) of the transition states of the reaction between Pα and CBr2. (a) TSαα. (b) TSαβ.
(a)(b)The asynchronicity of bond formation in this reaction, measured as the difference between the two lengths of the twoσ bonds formed (Δd), is given by(12)Δd=d1−d2.It was found that the asynchronicity of the stereoisomer 1 is Δd = 0.33 Å at TSαα. However, the asynchronicity of the stereoisomer 2 is Δd = 0.37 Å at TSαβ. From these transition states, we can conclude that the favored stereoisomer is more asynchronous than the other.


## 3.1. Analysis of the Reactivity Indices of the Reactants in the Base State

### 3.1.1. Prediction of Nucleophilic/Electrophilic Character

Table1 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). The 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. This means that there is a global electron density transfer (GEDT) [22] of β-himachalene to m-CPBA. The 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. There results suggest that m-CPBA behaves as an electrophile, while the β-himachalene behaves as a nucleophile.Table 1
Electronic chemical potential (μ), chemical hardness (η), electrophilicity (ω), and nucleophilicity (N) of β-himachalene and m-CPBA (eV).
Reactantsµη⍵Nβ-Himachalene−2.995.900.763.19m-CPBA−4.745.232.141.77


### 3.1.2. Prediction of Site Selectivity

The most favored interaction between two polar centers is related to the local indices (ωk and Nk). The most favored product is associated with the highest local electrophilicity index ωk of the electrophile and the highest local nucleophilicity index Nk of the nucleophile. From Figure 2, it is clear that the oxygen atom O∗ of m-CPBA is the most electrophilic active site (ωO∗ = 0.29 eV). We can observe from the surface map illustrated in Figure 3 that the C6 = C7 double bond (NC6 = 0.64, NC7 = 0.70 eV) is very nucleophilic than C2 = C3 (NC2 = 0.10, NC7 = 0.26 eV). In addition, the analysis of the nucleophilic Pk− Parr functions at the reactive sites of β-himachalene indicates that the C6 and C7 carbon atoms, with Pk−values of 2.23 and 3.04, respectively, are more nucleophilically active than the C2 and C3 carbon atoms, with Pk−values of 1.42 and 0.69, respectively. This result confirms that the attack is preferentially done on the double bond C6 = C7 in good agreement with experimental observations [23].Figure 2
The density map and electrophilicity index of m-CPBA.Figure 3
The density map and nucleophilicity index ofβ-himachalene.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. 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.Table 2
Local reactivity properties of reagents calculated using the DFT method for NPA-derived charges.
fk+fk−Pk+Pk−ωk+ωk−C20.00450.03180.05931.42911.42910.0242C30.00430.08260.10760.69730.00330.0629C60.02010.20220.29762.23630.01530.1539C70.03400.22140.30243.04260.02590.1686


### 3.1.3. Structural Analysis of the Transition States of the Cyclopropanation Reaction

The study of the stereoselectivity of C6 = C7 and C2 = C3 bonds indicates that the attack of the seven-membered ring double bond of β-himachalene 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, TSα,TSβ, TSα’, and TSβ’ transition state energies at the C6=C7 and C2=C3 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. The activation energies corresponding to the attack at the two sides of the C6 = C7 double bond of β-himachalene 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 C2 = C3 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 Pα, Pβ, Pα’, and Pβ’ is an exothermic reaction, with −53.3, −45.8, −51.9, and −45.4 kcal·mol−1, respectively. The 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. This result allows us to conclude that the α-attack is kinetically and thermodynamically favored and that the C6=C7 double bond of β-himachalene is more reactive than the other C2=C3, and this is in good agreement with the experimental results [23].Table 3
Thermodynamic energies of the reaction betweenβ-himachalene and m-CPBA calculated using DFT/6-311 + G (d, p).
E (a.u.)∆E (kcal/mol)H (a.u)∆H (kcal/mol)G (a.u.)∆G (kcal/mol)ν (cm−1)m-CPBA−955.721212—−955.602614—−955.649316—β-Himachalene−586.183305—−585.813259—−585.870499—TSα−1541.88212313.8−1541.39305014.3−1541.48003924.9−375.75TSβ−1541.87613917.5−1541.38617918.6−1541.47263929.6−416.05TSα’−1541.88022514.2−1541.39009714.5−1541.47898625.2−376.66TSβ’−1541.86929917.8−1541.38126818.9−1541.47097730.3−418.89Pα−661.413885−53.3−661.037817−52.4−661.095788−51.0Pβ−661.401320−45.8−661.024962−44.3−661.083388−43.6Pα’−661.413022−51.9−661.036573−50.7−661.094555−49.8Pβ’−661.401101−45.4−661.024790−44.1−661.077968−42.3


### 3.1.4. Analysis of the IRC of the Reaction betweenβ-Himachalene and M-CPBA

The molecular system during the reaction betweenβ-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). 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 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. The 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.Figure 4
IRC of the reaction betweenβ-himachalene and m-CBPA calculated using DFT at B3LYP/6-311 + G (d, p) level. Structural analysis of the transition states of the reaction.


### 3.1.5. Structural analysis of the transition states of the reaction

The optimized geometries of the TSα, TSβ, TSα, and TSβ’ transition states associated with the reaction between β-himachalene and m-CBPA 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:(10)Δd=dO∗−C6−dO∗−C7,(11)Δd=dO∗−C2−dO∗−C3,where dO∗−C6, dO∗−C7, dO∗−C2, and dO∗−C3 are the length of the bond between the oxygen atom and carbon atoms C6, C7, C2, and C3, respectively. It was found that the asynchronicity of stereoisomer is Δd = 0.16 Å at TSα, while at TSβ, 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 TSβ′.Figure 5
Optimized geometries of the transition states TSα, TSβ, TSα’, and TSβ’of the β-himachalene and m-CBPA (the distances are given in Å).
(a)(b)(c)(d)


## 3.1.1. Prediction of Nucleophilic/Electrophilic Character

Table1 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). The 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. This means that there is a global electron density transfer (GEDT) [22] of β-himachalene to m-CPBA. The 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. There results suggest that m-CPBA behaves as an electrophile, while the β-himachalene behaves as a nucleophile.Table 1
Electronic chemical potential (μ), chemical hardness (η), electrophilicity (ω), and nucleophilicity (N) of β-himachalene and m-CPBA (eV).
Reactantsµη⍵Nβ-Himachalene−2.995.900.763.19m-CPBA−4.745.232.141.77


## 3.1.2. Prediction of Site Selectivity

The most favored interaction between two polar centers is related to the local indices (ωk and Nk). The most favored product is associated with the highest local electrophilicity index ωk of the electrophile and the highest local nucleophilicity index Nk of the nucleophile. From Figure 2, it is clear that the oxygen atom O∗ of m-CPBA is the most electrophilic active site (ωO∗ = 0.29 eV). We can observe from the surface map illustrated in Figure 3 that the C6 = C7 double bond (NC6 = 0.64, NC7 = 0.70 eV) is very nucleophilic than C2 = C3 (NC2 = 0.10, NC7 = 0.26 eV). In addition, the analysis of the nucleophilic Pk− Parr functions at the reactive sites of β-himachalene indicates that the C6 and C7 carbon atoms, with Pk−values of 2.23 and 3.04, respectively, are more nucleophilically active than the C2 and C3 carbon atoms, with Pk−values of 1.42 and 0.69, respectively. This result confirms that the attack is preferentially done on the double bond C6 = C7 in good agreement with experimental observations [23].Figure 2
The density map and electrophilicity index of m-CPBA.Figure 3
The density map and nucleophilicity index ofβ-himachalene.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. 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.Table 2
Local reactivity properties of reagents calculated using the DFT method for NPA-derived charges.
fk+fk−Pk+Pk−ωk+ωk−C20.00450.03180.05931.42911.42910.0242C30.00430.08260.10760.69730.00330.0629C60.02010.20220.29762.23630.01530.1539C70.03400.22140.30243.04260.02590.1686


## 3.1.3. Structural Analysis of the Transition States of the Cyclopropanation Reaction

The study of the stereoselectivity of C6 = C7 and C2 = C3 bonds indicates that the attack of the seven-membered ring double bond of β-himachalene 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, TSα,TSβ, TSα’, and TSβ’ transition state energies at the C6=C7 and C2=C3 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. The activation energies corresponding to the attack at the two sides of the C6 = C7 double bond of β-himachalene 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 C2 = C3 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 Pα, Pβ, Pα’, and Pβ’ is an exothermic reaction, with −53.3, −45.8, −51.9, and −45.4 kcal·mol−1, respectively. The 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. This result allows us to conclude that the α-attack is kinetically and thermodynamically favored and that the C6=C7 double bond of β-himachalene is more reactive than the other C2=C3, and this is in good agreement with the experimental results [23].Table 3
Thermodynamic energies of the reaction betweenβ-himachalene and m-CPBA calculated using DFT/6-311 + G (d, p).
E (a.u.)∆E (kcal/mol)H (a.u)∆H (kcal/mol)G (a.u.)∆G (kcal/mol)ν (cm−1)m-CPBA−955.721212—−955.602614—−955.649316—β-Himachalene−586.183305—−585.813259—−585.870499—TSα−1541.88212313.8−1541.39305014.3−1541.48003924.9−375.75TSβ−1541.87613917.5−1541.38617918.6−1541.47263929.6−416.05TSα’−1541.88022514.2−1541.39009714.5−1541.47898625.2−376.66TSβ’−1541.86929917.8−1541.38126818.9−1541.47097730.3−418.89Pα−661.413885−53.3−661.037817−52.4−661.095788−51.0Pβ−661.401320−45.8−661.024962−44.3−661.083388−43.6Pα’−661.413022−51.9−661.036573−50.7−661.094555−49.8Pβ’−661.401101−45.4−661.024790−44.1−661.077968−42.3


## 3.1.4. Analysis of the IRC of the Reaction betweenβ-Himachalene and M-CPBA

The molecular system during the reaction betweenβ-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). 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 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. The 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.Figure 4
IRC of the reaction betweenβ-himachalene and m-CBPA calculated using DFT at B3LYP/6-311 + G (d, p) level. Structural analysis of the transition states of the reaction.


## 3.1.5. Structural analysis of the transition states of the reaction

The optimized geometries of the TSα, TSβ, TSα, and TSβ’ transition states associated with the reaction between β-himachalene and m-CBPA 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:(10)Δd=dO∗−C6−dO∗−C7,(11)Δd=dO∗−C2−dO∗−C3,where dO∗−C6, dO∗−C7, dO∗−C2, and dO∗−C3 are the length of the bond between the oxygen atom and carbon atoms C6, C7, C2, and C3, respectively. It was found that the asynchronicity of stereoisomer is Δd = 0.16 Å at TSα, while at TSβ, 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 TSβ′.Figure 5
Optimized geometries of the transition states TSα, TSβ, TSα’, and TSβ’of the β-himachalene and m-CBPA (the distances are given in Å).
(a)(b)(c)(d)


## 3.2. Analysis of intramolecular Chemical Descriptors of the Reaction between Pα and Dibromocarbene

After the determination of the chemoselectivity and stereoselectivity of the reaction betweenβ-himachalene and m-CBPA, we subsequently studied the cyclopropanation reaction between the major product (Pα) and dibromocarbene. The electronic chemical potential (μ), chemical hardness (η), electrophilicity index (ω), global nucleophilicity index (N), and maximum charge transfer ΔNmax calculated for Pα and dibromocarbene are shown in Table 4. This table indicates that the electrophilic index of dibromocarbene (4.46 eV) is greater than that of Pα (0.83 eV). This result suggests that dibromocarbene behaves as an electrophile, while Pα behaves as a nucleophile. This behavior is confirmed by the global nucleophilic indices of the reactants. The chemical hardness of Pα is 6.38 eV. This value is greater than that of dibromocarbene (3.41 eV). Also, the electronic chemical potential of Pα (−3.26 eV) is greater than that of dibromocarbene (−5.52 eV). This result indicates that electrons are transferred from Pα to dibromocarbene.Table 4
Electronic chemical potential (μ), chemical hardness (η), electrophilicity (ω), and nucleophilicity (N) of the major product (Pα) and CBr2 calculated at B3LYP/6-311 + G (d, p) level (eV).
PαCBr2µ−3.26−5.52Η6.383.41⍵0.834.46N2.681.91∆Nmax−0.51−1.61


### 3.2.1. Kinetic Study

The stereoselectivity of the addition of dibromocarbene to the major product (Pα) obtained from the first reaction of β-himachalene with m-CPBA was examined in both α and β sides of Pα. The calculated energies of the reactants, the obtained products (TSαα and TSαβ) at the C2 = C3 double bond of Pα, 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 C2 = C3 (8.9 kcal/mol) is located above the transition state energy of the α side (4.1 kcal/mol). The formation of the products Pαα and Pαβ 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 Pα 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 α-attack is kinetically and thermodynamically favored. It also explains the great stereoselectivity observed experimentally.Table 5
Thermodynamic energies of the cyclopropanation reaction between Pα and dibromocarbene calculated using the DFT method at B3LYP/6-311 + G (d, p) basis set.
E (a.u.)G (a.u.)H (a.u.)∆E (kcal/mol)∆G (kcal/mol)∆H (kcal/mol)Pα−661.413801−661.095710−661.037800CBr2−5186.296500−5186.321500−5186.288610TSαα−5847.703721−5847.389−5847.3187024.117.64.8TSαβ−5847.696000−5847.381512−5847.3109018.922.49.7Pαα−5847.788923−5847.467800−5847.400001−49.3−31.7−46.1Pαβ−5847.781200−5847.460222−5847.392300−44.4−26.9−41.3Figure 6
Energy profile of reaction between Pα and dibromocarbene.


### 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 Pα and dibromocarbene (Figure 7) shows that the lengths of the bonds formed by stereoisomer 1 are 2.26 Å at d1(C∗ − C3) and 2.59 Å at d2(C∗ − C2) for TSαα. However, those formed by stereoisomer 2 are 2.75 Å at d1(C∗ − C3) and 2.38 Å at d2(C∗ − C2) for TSαβ, where C∗ is the carbon atom of dibromocarbene.Figure 7
Bond lengths (Å) of the transition states of the reaction between Pα and CBr2. (a) TSαα. (b) TSαβ.
(a)(b)The asynchronicity of bond formation in this reaction, measured as the difference between the two lengths of the twoσ bonds formed (Δd), is given by(12)Δd=d1−d2.It was found that the asynchronicity of the stereoisomer 1 is Δd = 0.33 Å at TSαα. However, the asynchronicity of the stereoisomer 2 is Δd = 0.37 Å at TSαβ. From these transition states, we can conclude that the favored stereoisomer is more asynchronous than the other.


## 3.2.1. Kinetic Study

The stereoselectivity of the addition of dibromocarbene to the major product (Pα) obtained from the first reaction of β-himachalene with m-CPBA was examined in both α and β sides of Pα. The calculated energies of the reactants, the obtained products (TSαα and TSαβ) at the C2 = C3 double bond of Pα, 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 C2 = C3 (8.9 kcal/mol) is located above the transition state energy of the α side (4.1 kcal/mol). The formation of the products Pαα and Pαβ 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 Pα 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 α-attack is kinetically and thermodynamically favored. It also explains the great stereoselectivity observed experimentally.Table 5
Thermodynamic energies of the cyclopropanation reaction between Pα and dibromocarbene calculated using the DFT method at B3LYP/6-311 + G (d, p) basis set.
E (a.u.)G (a.u.)H (a.u.)∆E (kcal/mol)∆G (kcal/mol)∆H (kcal/mol)Pα−661.413801−661.095710−661.037800CBr2−5186.296500−5186.321500−5186.288610TSαα−5847.703721−5847.389−5847.3187024.117.64.8TSαβ−5847.696000−5847.381512−5847.3109018.922.49.7Pαα−5847.788923−5847.467800−5847.400001−49.3−31.7−46.1Pαβ−5847.781200−5847.460222−5847.392300−44.4−26.9−41.3Figure 6
Energy profile of reaction between Pα and dibromocarbene.


## 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 Pα and dibromocarbene (Figure 7) shows that the lengths of the bonds formed by stereoisomer 1 are 2.26 Å at d1(C∗ − C3) and 2.59 Å at d2(C∗ − C2) for TSαα. However, those formed by stereoisomer 2 are 2.75 Å at d1(C∗ − C3) and 2.38 Å at d2(C∗ − C2) for TSαβ, where C∗ is the carbon atom of dibromocarbene.Figure 7
Bond lengths (Å) of the transition states of the reaction between Pα and CBr2. (a) TSαα. (b) TSαβ.
(a)(b)The asynchronicity of bond formation in this reaction, measured as the difference between the two lengths of the twoσ bonds formed (Δd), is given by(12)Δd=d1−d2.It was found that the asynchronicity of the stereoisomer 1 is Δd = 0.33 Å at TSαα. However, the asynchronicity of the stereoisomer 2 is Δd = 0.37 Å at TSαβ. From these transition states, we can conclude that the favored stereoisomer is more asynchronous than the other.


## 4. Conclusions

The reaction of meta-chloroperbenzoic acid and dibromocarbene withβ-himachalene was studied using the DFT method at the B3LYP/6-311 + 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 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 Pα. The reaction of the latter with CBr2 takes place according to an exothermic mechanism in a single step in which the product Pαα is kinetically and thermodynamically favored over Pαβ according to the energetic parameters of the transition states in good agreement with experimental observations.



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