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Hyperconjugation enhances electrophilic addition to monocyclic monoterpenes: a Fukui function perspective

  • Jorge A. Amador-Balderas
  • Ramsés E. RamírezEmail author
  • Francisco MéndezEmail author
  • Francisco J. Meléndez
  • Arlette Richaud
Original Paper
  • 98 Downloads
Part of the following topical collections:
  1. International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday

Abstract

The local and condensed Fukui functions as well as the principle of hard and soft acids and bases were used to study the addition of free radicals to the exocyclic and endocyclic double bonds of seven monocyclic monoterpenes of formula C10H16. The results obtained showed that, in general, the most reactive double bond was the one with the most substituents on the double-bonded carbon atoms, and that the reaction of a double bond with an electrophile is a soft–soft interaction. The effects of substituents on the double-bonded carbon atoms and the stabilization of the monoterpenes were interpreted by invoking hyperconjugated structures, which led us to propose a simple rule: the larger the value of the Fukui function for the double bond, the greater the hyperconjugative stabilization and the susceptibility of the double bond to electrophilic attack. In general, our results are in good accordance with relevant experimental and theoretical results published in the literature.

Graphical abstract

The specific electrophilic addition to monocyclic monoterpenes.

Keywords

Monoterpene Fukui function Inductive character Endocyclic and exocyclic double bonds Methyl and isopropyl groups Hyperconjugative structures Hyperconjugative stabilization 

Introduction

The formation of several atmospheric contaminants is linked to the presence of monoterpenes (MTPs). The addition of ozone, nitrate, and hydroxyl radicals (present in the troposphere) to MTPs can increase the concentrations of other contaminants such as nitrogen oxides and secondary organic aerosols (SOAs), which have serious effects on the environment [1]. The reactivities of MTPs (of formula C10H16) have been investigated both experimental and theoretically, and have been found to depend on the exocyclic or endocyclic double bonds present and to increase with the number of methyl and/or isopropyl substituents on the double-bonded carbon atoms [1, 2, 3]. Data on the reactivities of MTPs derive mainly from the observed yields of the reactions of various radicals under similar conditions to those present in the troposphere [1, 4, 5, 6]. In a previous study, Jiang et al. studied the ozonolysis of limonene and reported that this reaction produces four stabilized Criegee intermediates. The reaction of ozone with a double bond in limonene (Fig. 1) produces the primary ozonide (1,2,3-trioxolane) and then a Criegge intermediate [3]. They concluded that the formation of exocyclic intermediates and the subsequent final products is explained by the higher reactivity of the exocyclic double bond [5]. Fry et al. reached the same conclusion after studying the production of SOAs through the oxidative reaction of limonene with O3 and NO3 [6].
Fig. 1

The primary ozonide obtained in the first step of the addition of ozone to a double bond

In this paper, we present theoretical studies of the reactivities of the exocyclic and endocyclic double bonds of seven monoterpenes of formula C10H16 (see Fig. 2). Investigating these MTPs allowed us to analyze the influence of the methyl (Me) and isopropyl (i-Pr) groups on the susceptibilities of the endocyclic and exocyclic double bonds in the MTPs to electrophilic attack (see Table 1), which leads to the generation of SOAs and other atmospheric contaminants. The inductive character of the Me and i-Pr groups can be explained by invoking hyperconjugative structures and hyperconjugative stabilization. In the present work, the electrophilic attack of the MTPs by radicals was studied using the local and condensed Fukui functions. Our results show the same trends as seen in corresponding experimental results and other theoretical results.
Fig. 2

The structural formulae of β-terpinene (I), α-phellandrene (II), limonene (III), terpinolene (IV), β-phellandrene (V), α-terpinene (VI), and γ-terpinene (VII)

Table 1

Numbers of endocyclic double bonds, exocyclic double bonds, methyl groups (CH3), and isopropyl groups (i-Pr) in the seven monocyclic monoterpenes (MTPs; formula C10H16) of interest

Molecule

Endocyclic double bonds

Exocyclic double bonds

CH3 groups

i-Pr groups

I

C4=C5

C1=C2

0

1 (C5)

II

C2=C3, C6=C7

1 (C2)

1 (C5)

III

C2=C3

C8=C9

1 (C2), 1 (C9)

0

IV

C2=C3

C5=C9

2 (C9), 1 (C2)

0

V

C6=C7

C1=C2

0

1 (C5)

VI

C2=C3, C4=C5

1 (C2)

1 (C5)

VII

C2=C7, C4=C5

-

1 (C2)

1 (C5)

The location of each methyl/ispropyl group (i.e., the particular carbon atom on which the group is situated) is shown in parentheses

Methodology and computational details

Figure 2 shows the structures of the seven MTPs of formula C10H16 studied in this work. The geometries of β-terpinene (I), α-phellandrene (II) limonene (III), terpinolene (IV), β-phellandrene (V), α-terpinene (VI), and γ-terpinene (VII) were optimized at the MP2/6–311++G(d,p) level of theory [7] using the GAUSSIAN 09 software package [8]. All of the resulting structures were local minima with positive vibrational frequencies.

The local [f(r) = ρN(r) − ρN − 1(r)] and condensed [\( {f}_k^{-}={q}_N-{q}_{N-1} \) ] Fukui functions for electrophilic attack [9, 10, 11] on the seven MTPs were calculated at the MP2/6–311++G(d,p) level of theory using GAUSSIAN 09 [8]. The electronic densities and the Hirshfeld populations for the neutral [ρN(r) and qN, respectively] and monocationic [ρN − 1(r) and qN − 1, respectively] species were evaluated using the geometries of the neutral species.

Results and discussion

Table 1 shows the positions of the exocyclic and endocyclic double bonds as well as the methyl (Me) and isopropyl (i-Pr) groups in the seven monocyclic monoterpene structures.

Experimental results show that the endocyclic double bond is the more reactive of the two double bonds in β-terpinene (I) and limonene (III) (C4=C5 and C2=C3, respectively) [4, 5, 6], while the exocyclic double bond is the more reactive of the two double bonds in terpinolene (IV) and β-phellandrene (V) (C5=C9 and C1=C2, respectively) [12, 13]. Furthermore, the experimental and theoretical rate constants for the reactions of limonene (III) and terpinolene (IV) with O3, OH, and NO3 are in good accord with previous results (see Table 2) [14, 15, 16, 17]. When two endocyclic double bonds exist in the same ring—as is the case in α-phellandrene (II) (C2=C3 and C6=C7) [18], α-terpinene (VI) (C2=C3 and C4=C5), and γ-terpinene (VII) (C2=C7 and C4=C5) [1]—the electrophile (O3, OH, or NO3) attacks the double bond in which one of the carbon atoms has a methyl (C2=C3 for II and VI and C2=C7 for VII) or isopropyl (C4=C5 for VI and VII) substituent.
Table 2

Reported rate constants for the reactions of limonene and terpinolene with O3, OH, and NO3

Monoterpenes

Reaction at exocyclic double bond

Reaction at endocyclic double bond

Limonene [14]

1.2 × 10−17 cm3 molecule−1 s−1

43 × 10−17 cm3 molecule−1 s−1

Limonene [14]

51.4 × 10−12 cm3 molecule−1 s−1

86.9 × 10−12 cm3 molecule−1 s−1

Limonene [15]

7 × 10−18 cm3 molecule−1 s−1

3 × 10−16 cm3 molecule−1 s−1

Limonene [16]

2 × 10−13 cm3 molecule−1 s−1

6 × 10−12 cm3 molecule−1 s−1

Terpinolene [17]

120 × 10−17 cm3 molecule−1 s−1

43 × 10−17 cm3 molecule−1 s−1

Terpinolene [17]

110 × 10−12 cm3 molecule−1 s−1

87 × 10−12 cm3 molecule−1 s−1

Figure 3 shows the f(r) isosurfaces for the electrophilic attack of the seven monoterpenes studied. For α-phellandrene (II), the highest value of f(r) occurs at the double bond in which one of the carbon atoms has a methyl group substituent. According to the Yang and Parr postulate [10] and the principle of hard and soft acids and bases (HSAB) [19, 20, 21, 22, 23, 24], the addition of a soft electrophile is more favored at C2=C3 than at C6=C7. Studies of the potential energy surface have reached the same conclusion [18]. The Fukui function values for α-phellandrene (II) and limonene (III) suggest that ozone will react with the double bond with the most substituents on the double-bonded carbon atoms, i.e., C2=C3 in both structures, as the methyl substituent at the C2 atom increases the reactivity of the double bond C2=C3.
Fig. 3

The f (r) isosurfaces for the seven MTPs (plotted at 0.016 a.u.)

The most reactive double bond in terpinolene (IV) is the exocyclic bond (C5=C9), as there are two methyl groups at C9. In α-terpinene (VI) and γ-terpinene (VII), there are two endocyclic double bonds. One involves the methyl-bearing C2 atom (C2=C3 and C2=C7 in VI and VII, respectively); the other involves the isopropyl-bearing C5 (C4=C5 in both cases). Our results indicate that both of these substituents (methyl and isopropyl) have similar effects on the reactivities of the corresponding double bonds, as both bonds have similar reactivities (as can be seen in Fig. 3). It is interesting to note that β-terpinene (I) contains an endocyclic double bond, C4=C5, with an isopropyl group attached to C5, which makes this bond more reactive than the exocyclic double bond C1=C2, thus supporting the hypothesis that the isopropyl group has a similar effect to the methyl group on MTP reactivity. Therefore, the degree of substitution of the double-bonded atoms plays an important role, since a higher degree of substitution leads to greater reactivity [3]. This hypothesis is supported by the local Fukui function values obtained in this work. In β-phellandrene (V), there is no methyl group attached to any of the double-bonded atoms, and the degree of substitution is the same for both double bonds (C1=C2 and C6=C7); however, the local Fukui function is mainly localized around the endocyclic double bond (C1=C2), suggesting that the C1=C2 bond is more reactive than the C6=C7 bond. Experimentally, C1=C2 is indeed found to be more reactive than C6=C7, and this can be verified by investigating the condensed Fukui function for electrophilic attack. Table 3 shows that for β-phellandrene (V), \( {f}_{{\mathrm{C}}_1}^{-}>{f}_{{\mathrm{C}}_6}^{-} \) and \( {f}_{{\mathrm{C}}_2}^{-}>{f}_{{\mathrm{C}}_7}^{-} \). Similarly, for the other monoterpenes (IIV and VVII), the condensed Fukui function values for electrophilic attack accurately predict the experimentally determined reactive sites in each MTP.
Table 3

Condensed Fukui function values for electrophilic attack for the seven MTPs studied

Atoms

I (β-terpinene)

II (α-phellandrene)

III (limonene)

IV (terpinolene)

V (β-phellandrene)

VI (α-terpinene)

VII (γ-terpinene)

C1

0.056

0.027

0.034

0.013

0.192

0.027

0.022

C2

−0.022

0.122

0.198

0.016

0.099

0.122

0.097

C3

0.024

0.170

0.222

0.004

0.013

0.100

0.030

C4

0.215

0.021

0.023

0.020

0.011

0.106

0.095

C5

0.196

0.011

0.002

0.192

0.010

0.131

0.087

C6

0.021

0.130

0.007

0.019

0.160

0.019

0.031

C7

0.008

0.077

0.023

0.019

0.087

0.019

0.110

C8

0.011

0.003

−0.010

0.189

0.007

0.009

0.005

C9

0.021

0.008

0.033

0.031

0.006

0.016

0.013

C10

0.001

0.009

0.005

0.031

0.011

0.009

0.009

For the seven MTPs studied here, the effects of the Me and i-Pr substituents on the C=C bonds can be analyzed by considering the hyperconjugation [25, 26, 27, 28]. For the fragment C=C…CH3 of the MTP, electron density shifts from the C–H bonds of the Me group to the C=C bond, leading to the weakening and the strengthening of the C–H and C=C bonds, respectively. For example, in α-phellandrene (II), a hyperconjugative interaction occurs between the Me and the C2=C3 moieties (Fig. 4). There are three hyperconjugative structures (HCSs) due to the presence of the Me substituent (one for each H atom), and the hyperconjugative interaction has a stabilizing effect. Upon also noting the two hyperconjugative structures from the two H atoms in C4, the total number of HCSs for the double bond C2=C3 increases to five, whereas there is only one for C6=C7 (from the H atom at C5). Table 4 shows the number of HCSs in each of the seven monocyclic monoterpenes studied here.
Fig. 4

Hyperconjugative structures of α-phellandrene (II)

Table 4

The number of hyperconjugative structures (HCSs) for each double bond, the difference in hyperconjugative stabilization \( \mid \delta \Delta {H}^{\mathrm{o}}\mid =\mid \Delta {H}_2^{\mathrm{o}}-\Delta {H}_1^{\mathrm{o}}\mid \) (kcal/mol) between the double bonds, and a comparison of the experimental reactivities of the double bonds in each of the seven studied monocyclic monoterpenes (MTPs)

Molecule

δΔHo

HCSs

Comparison of experimental double-bond reactivities

I

3.6 (C4=C5 > C1=C2)

5 (C4=C5), 4 (C1=C2)

C4=C5 > C1=C2

II

3.7 (C2=C3 > C6=C7)

5 (C2=C3), 1 (C6=C7)

C2=C3 > C6=C7

III

4.0 (C2=C3 > C8=C9)

5 (C2=C3), 4 (C8=C9)

C2=C3 > C8=C9

IV

1.4 (C2=C3 > C5=C9)

7 (C2=C3), 10 (C5=C9)

C2=C3 < C5=C9

V

0.7 (C1=C2 > C6=C7)

1 (C6=C7), 2 (C1=C2)

C1=C2 > C6=C7

VI

0.6 (C4=C5 > C2=C3)

5 (C2=C3), 3 (C4=C5)

No difference between C4=C5 and C2=C3

VII

0.6 (C4=C5 > C2=C7)

7 (C2=C7), 5 (C4=C5)

No difference between C4=C5 and C2=C7

The hyperconjugation can be calculated using several methodologies [29, 30, 31]. We used the one proposed by Houk et al., based on isodesmic reactions [31]. For example, the hyperconjugative stabilization (HC) was calculated at the MP2G3 level of theory for the double bonds C6=C7 and C2=C3 of α-phellandrene (II) as \( \Delta {H}_2^{\mathrm{o}} \) and \( \Delta {H}_1^{\mathrm{o}} \) , respectively, using the isodesmic reactions \( {\mathrm{C}}_{10}{\mathrm{H}}_{18}+\mathrm{C}{\mathrm{H}}_2=\mathrm{C}{\mathrm{H}}_2\overset{\Delta {H}_1^{\mathrm{o}}}{\leftarrow }{\mathrm{C}}_{10}{\mathrm{H}}_{16}+\mathrm{C}{\mathrm{H}}_3-\mathrm{C}{\mathrm{H}}_3\overset{\Delta {H}_2^{\mathrm{o}}}{\to }{\mathrm{C}}_{10}{\mathrm{H}}_{18}+\mathrm{C}{\mathrm{H}}_2=\mathrm{C}{\mathrm{H}}_2 \) (see also Fig. 5). The difference in HC between the double bonds, calculated as \( \delta \Delta {H}^{\mathrm{o}}=\Delta {H}_2^{\mathrm{o}}-\Delta {H}_1^{\mathrm{o}} \), shows that the hyperconjugative stabilization of C2=C3 is 3.7 kcal/mol greater than that of C6=C7. Similar calculations were performed for the other structures, and the results are presented in Table 4.
Fig. 5

Isodesmic reactions for α-phellandrene (II); \( \delta \Delta {H}^{\mathrm{o}}=\varDelta {H}_2^{\mathrm{o}}-\varDelta {H}_1^{\mathrm{o}} \)

The ∣δΔHo∣ and HCS values for structures I, II, III, and V, as shown in Table 4, suggest that one of the double bonds in each structure is more reactive than the other, and the trends seen in the calculated results mirror those observed experimentally. The ∣δΔHo∣ and HCS values for structure IV show the opposite and similar trends, respectively, to the experimental bond reactivities. The HCS values for structures VI and VII suggest that one of the double bonds is more reactive than the other, whereas the small ∣δΔHo∣ values for these MTPs suggest that both double bonds exhibit similar reactivities, which is supported by their experimental reactivities. Therefore, it seems that the larger the value of the Fukui function for the double bond, the greater its hyperconjugative stabilization and susceptibility to electrophilic attack. Electrostatic potential maps (MEPs) were also calculated for IVII on isosurfaces of −0.015 to 0.065 a.u. No differences between the endocyclic and exocyclic double bonds were observed (see the “Electronic supplementary material,” ESM), suggesting that the electrophilic attack of a double bond is a soft–soft interaction.

Conclusions

The electrophilic addition of free radicals to the exocyclic and endocyclic double bonds of seven monocyclic monoterpenes of formula C10H16 was studied by evaluating their local and condensed electrophilic Fukui functions and applying the local HSAB principle. The results obtained show that, in general, the most reactive double bond is the one with the most substituents on the double-bonded carbon atoms. The inductive character of the methyl and isopropyl groups, which can be explained by invoking hyperconjugative structures and hyperconjugative stabilization, prompted us to draw similar conclusions about the relative reactivities of the double bonds to those obtained upon analyzing the Fukui function values of the monoterpenes. This led us to propose a simple rule: the greater the value of the Fukui function for the double bond, the greater the hyperconjugative stabilization and susceptibility of the double bond to electrophilic attacks. Our results for the Fukui functions of the monoterpenes were found to be in good accord with previous results published in the literature.

Notes

Acknowledgments

This work was partially supported by the project VIEP-BUAP RAGR-NAT17-I, Facultad de Ciencias Químicas Benemérita Universidad Autónoma de Puebla, Cuerpo Académico BUAP-CA-263 “Investigación experimental y teórica de nuevos materiales y educación en ciencias,” as well as the Laboratorio Nacional de Supercómputo del Sureste de México (LNS).

Supplementary material

894_2018_3825_MOESM1_ESM.docx (757 kb)
ESM 1 (DOCX 756 kb)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jorge A. Amador-Balderas
    • 1
  • Ramsés E. Ramírez
    • 1
    Email author
  • Francisco Méndez
    • 2
    Email author
  • Francisco J. Meléndez
    • 3
  • Arlette Richaud
    • 2
  1. 1.Departamento de FisicomatemáticasBenemérita Universidad Autónoma de Puebla-Facultad de Ciencias QuímicasPueblaMéxico
  2. 2.Departamento de Química, División de Ciencias Básicas e IngenieríaUniversidad Autónoma Metropolitana-IztapalapaMéxicoMéxico
  3. 3.Departamento de FisicoquímicaBenemérita Universidad Autónoma de Puebla-Facultad de Ciencias QuímicasPueblaMéxico

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