Thermodynamics of the Isomerization of Monoterpene Epoxides.

In this contribution, the thermodynamic analysis of α- and β-pinene epoxide isomerization over Fe and Cu supported on MCM-41 is presented using computational chemistry and group contribution methods (GCMs). Some physical-chemical data (T c, P c, v c, Z c, ω, T b, T fus) and thermodynamic (S°298.15, C p,298.15 °, C v,298.15 °, ΔH f,298.15 °, ΔG f,298.15 °, ΔH vb °, ΔH fus, C pL) properties obtained by different GCMs are reported for several monoterpenes and monoterpenoids, which significantly contribute to the knowledge of the properties of these compounds. Density functional theory (DFT), PBE-D3/6-311G(d,p), was employed for determining the Gibbs free energy and the heat of reaction associated with the transformation of monoterpene epoxides into aldehydes, ketones, and related oxygenated compounds in the presence of different solvents and at several temperatures. The calculations were compared with available data reported and the experimental results of the catalytic reactions. The transformation of α- and β-pinene epoxides into aldehydes appears to be more spontaneous and favorable than their transformations into alcohols in a wide range of temperatures. These results are in agreement with the experiments over Fe/MCM-41 and Cu/MCM-41, where α-pinene epoxide isomerization yields campholenic aldehyde (50-80% selectivity) as the main product. The 1.7Fe/MCM-41 material was more active in all solvents than 1.3Cu/MCM-41 for both α- and β-pinene epoxide isomerization. However, perillyl alcohol (20-70% selectivity) was the most favored for the isomerization reaction, except when ethyl acetate was the solvent. Enthalpy and Gibbs free energy of the studied reactions estimated by both GCMs and DFT calculations did not show large differences for most of the reactions at evaluated temperatures.

Introduction

Essential oils are one of the most important mixtures in organic chemistry because they contain a lot of compounds that can be transformed into value chemicals of use in different fields in chemistry. These mixtures are composed of different fractions of volatile compounds of similar chemical structure and may be extracted directly from biomass.[1−3] Some of these constituents are monoterpenes, which can be biologically obtained by the isoprene pathway.[1,4−7] Monoterpenes are synthesized using 1,4-butadiene molecule and present a wide spectrum of application in fine chemistry as flavors, in agriculture and medicine.[5,8−10] Among a lot of these molecules, α- and β-pinenes are bicyclic monoterpenes that may be purified from turpentine oil.[1,5,11−13] Because of the high reactivity of the double bond, terpenes can be oxidized into epoxides that are very valuable chemicals used as precursors or intermediates in many chemical processes.[1,13−21]

Isomerization of epoxides is an interesting and sensitive reaction that can be performed with the use of nucleophiles as well as with acid-based materials.[22−24] α-Pinene epoxide isomerization in acidic medium gives as main products campholenic aldehyde and carveol with stoichiometric amounts of fencholenic aldehyde, pinocarveol, isopinocamphone, among others (Figure ).[25−28] From β-pinene epoxide, myrtanal, myrtenol, perillyl alcohol, and their isomers such as perillyl aldehyde, perillyl acid, among others are obtained (Figure ).[6,29] These compounds present important applications in fine chemistry; for example, campholenic aldehyde is a precursor of the sandalwood fragrance[30] while trans-carveol has been tested as a precursor of potential substances in the pharmaceutical field.[31−33] Furthermore, myrtanal is a very attractive chemical and intermediate compound in the synthesis of fragrances.[34] On the other hand, myrtenol has been tested as a potential anxiolytic[8] and perillyl alcohol inhibits telomerase activity in prostate cancer cells.[35,36] Isomerization of α- and β-pinene epoxides has been carried out with homogeneous and heterogeneous catalysts and with nucleophiles such as amines and hydroxyl groups.[37−41] Nevertheless, the use of heterogeneous materials is preferred since they can be easily separated and used in several catalytic cycles in contrast to the use of homogeneous ones. Transition metals supported on micro- and mesostructures have been reported as heterogeneous catalysts.[29,42−44] However, the thermodynamics of these reactions have been scarcely considered.

Figure 1

Isomerization products of α- and β-pinene epoxides.

The most acceptable way of studying a process is by experimentally obtaining the properties of its components; nevertheless, this information is not always available for all chemical compounds and the processes involving them are costly and sometimes difficult to implement in the laboratory. Thus, it is relevant and pertinent to estimate the physicochemical and thermodynamic properties through computational simulation using mathematical models and empirical correlations based on group contribution methods (GCMs) instead of (or in combination with) experimental evaluations.[45−49] Thermodynamics plays an important role in the understanding of chemical reactions, and it gives state parameters such as enthalpy, Gibbs free energy, entropy, internal energy, among others, which provide information on whether a particular reaction is energetically possible in one direction, spontaneous, and gives the composition of the reaction system at equilibrium. The knowledge of ideal gas thermochemistry is also crucial for calculating several thermochemical properties in fluids, including the changes of phases, and different interactions such as solute–solvent, solvent–solvent, among others.[50]

Previously kinetics and thermodynamics were performed considering the aspects of solvent effect in the isomerization of α-pinene epoxide. In this case, temperature was varied between 323.15 and 413.15 K over several zeolites, iron-modified zeolites, Fe-H-MCM-41, as well as micro- and mesoporous ZMS-5 materials.[51] It was shown that using the Joback’s group contribution method (GCM), the formation of campholenic aldehyde (Gibbs free energy of formation, −138 kJ mol–1) is more feasible than the formation of trans-carveol (−114 kJ mol–1). Selectivity to trans-carveol was independent of the solvent polarity, while campholenic aldehyde was thermodynamically feasible with nonpolar solvents such as toluene. With a combination of the Benson, Anderson–Bayer–Watson–Yoneda, Verma–Doraiswamy, and Thin-Perry GCMs, the authors[52] calculated the free energy of transformation of α-pinene epoxide into campholenic aldehyde with a Zn triflate catalyst and reported a Gibbs free energy value of −109.35 kJ mol–1 at 298.15 K. Using density functional theory (DFT) calculations, we previously reported thermodynamic values of Gibbs free energy and enthalpy for both isomerization of α- and β-pinene epoxides into value chemicals over Fe-supported catalysts.[53] For β-pinene epoxide isomerization, thermodynamic parameters were calculated with Benson’s methodology; at room temperature, the Gibbs free energies for β-pinene epoxide transformations into myrtanal, myrtenol, and perillyl alcohol were −383.51, −150.46, and −75.27 kJ mol–1, respectively.[6]

Empirical correlation methods and a high set of GCMs have been used to estimate pure compounds properties such as vapor pressure[54] and critical properties.[55−57] Some of them consider interactions between groups and definitions for group mixtures to predict parameters.[58] On the other hand, Benson GCM was used for the estimation of thermochemical properties (formation enthalpy, entropy and heat capacity) and the Joback method to calculate the critical parameters and boiling points of several monoterpenes such as limonene, terpinolene, α-terpineol, 1,8-terpinene, β-terpineol, 2-pinanol, γ-terpineol, 1,4-terpinene, and camphene involved in the α-pinene hydration/isomerization.[59] Vandewiele applied the Benson method for obtaining properties of several monoterpenoids such as linalool, isolinalool, cis/trans-β-terpineol, and pinol derived from the cis/trans-2-pinanol isomerization.[60] Estimation of properties for verbenone, verbenol, and α-pinene epoxide from liquid-phase oxidation of α-pinene, as well as carveol, carvone, and limonene 1,2-epoxide from liquid-phase oxidation of d-limonene over the heterogeneous catalyst FePcCl16-NH2-SiO2 and tert-butyl hydroperoxide has also been reported.[61]

Thermodynamics is an important step for understanding chemical reactions, and there is scarce information about the physicochemical properties of the products obtained from isomerization of α- and β-pinene epoxides. Previously, we published some kinetic data about the performance of this reaction for obtaining aldehydes and alcohols;[62,63] however, thermodynamic analysis of the reaction was not carried out. Prompted by this knowledge, hypothesis, and motivation, the aims of this research are to predict, combining different theoretical and computational methodologies, the thermodynamics properties of the isomerization reaction and to determine the chemical favoring of α- and β-pinene epoxide transformation under several conditions.

Experimental and Computational Methodology

Reagents

Commercial reagents used for the determination of the catalytic activity were used without any further purification unless otherwise noted. Fe(NO3)3·9H2O (99 wt %), Cu(NO3)2·3H2O (99.5 wt %), ethyl acetate (99.5 wt %), and acetonitrile (99.9 wt %) were obtained from Merck. Hydrogen peroxide (30 wt %), cetyl trimethyl ammonium bromide (99 wt %), NH4OH (29 wt %), deionized water type II (≤0.1 μS cm–1), tetraethyl orthosilicate (99 wt %), α-pinene epoxide (98 wt %), β-pinene (98 wt %), toluene (99.8 wt %), and tert-butanol (99.5 wt %) were purchased from Sigma-Aldrich.

Catalyst Preparation and Characterization

Fe/MCM-41 and Cu/MCM-41 were prepared using the incipient wetness impregnation method. In a typical procedure, aqueous solution of Fe(NO3)3·9H2O or Cu(NO3)2·3H2O at 2% of metal concentrations was added dropwise to 0.50 g of support MCM-41 (the synthesis of MCM-41 was previously reported[40]) and stirred at room temperature for 1 h. Then, the materials were dried at 333.15 K for 7 h and calcined at 823.15 K for 4 h. The solids were named as xMe/MCM-41, where x corresponds to the metal content in weight percentage determined by atomic absorption and Me is Fe or Cu. The details of the catalyst characterization were also reported in a previous work.[40]

Catalytic Reactions

The reactions were performed in 2 mL vials covered with inert silicon septa immersed in a heating plate from Radley Tech under magnetic stirring. In a typical experiment, 15 mg of catalyst (previously activated at 823.15 K for 1 h and ground for obtaining a particle size of 200 μm to ensure no diffusional problems related with internal mass transfer) was added to 0.25 mmol of substrate (α- or β-pinene epoxide) in 1 mL of solvent (toluene, ethyl acetate, or tert-butanol) and then stirred at 750 rpm and heated at 343.15 K. β-Pinene epoxide was prepared at 75 wt % by a typical epoxidation procedure and characterized by Fourier transform infrared (FTIR) and gas chromatography coupled with mass spectrometry (CG-MS).[34] The products were quantified by gas chromatography coupled with mass spectrometry (GCMS) in an Agilent 7890A with a flame ionization detector (FID), HP-5 column (30 m × 320 μm × 0.5 μm), carrier gas He (23.80 mL min–1), and a split ratio of 15:1. The oven temperature was kept at 343.15 K for 3 min, increased to 453.15 K at 10 °C min–1, and maintained at this temperature for 1 min.

Estimation of Thermodynamic Properties Using Group Contribution Methods (GCMs)

The critical properties (pressure pci, temperature Tci, and specific volume vci) of pure monoterpenes and monoterpenoids were estimated by the GCMs of Joback–Reid (JR),[64] Constantinou–Gani (CG),[57] Tahami–Movagharnejad–Ghasemitabar (TGM)[65] and also through Aspen Plus software calculations using the UNIF-DMD thermodynamic model for comparison by Joback (J*) GCM. The critical compressibility factor Zci and the acentric factor ωi were also obtained from Aspen Plus calculations by definition (Def*) equations from critical properties. Normal boiling points Tbi of pure molecules were calculated using the new group contribution methods of Ghasemitabar–Movagharnejad (GM),[56] JR, CG, and J* from Aspen Plus. The standard enthalpy of formation ΔHf,° and Gibbs free energy of formation ΔGf,° were obtained at 298.15 K and 1 atm using the JR, CG, J*, and Benson (B*) GCMs within the software Aspen Plus. The standard enthalpy of vaporization ΔHvb,° was used to determine the thermal properties in the liquid phase with eqs –3 since most of the GCMs estimate the properties as an ideal gas. This property was estimated with the new GCM of Abdi–Movagharnejad–Ghasemitabar (AMG),[66] JR, CG, and through Aspen Plus software calculations using the Ruzicka (R*) method (for a more detailed procedure, see the Supporting Information).The standard heat of reaction ΔHrxn°, standard entropy of reaction ΔSrxn°, and the standard Gibbs free energy of reaction ΔGrxn° at a reference temperature T0 were estimated using the standard enthalpy, standard entropy, and Gibbs free energy of formation and the stoichiometry coefficients γ in the reactions of interest using eqs –6.Dependency on temperature T in eq –12 was estimated based on the Maxwell relations using the isobaric heat capacities in eq , and the heat capacity of the reaction ΔCp° was considered constant at an average temperature Tavg. These parameters give information about the spontaneity and exothermicity of the reactions at a temperature T. The liquid heat capacities were calculated with Aspen Plus simulation using the Ruzicka (R*) method.

Estimation of Thermodynamic Properties Using Computational Quantum Chemistry

Gaussian09 software[67] was used for calculating the typical thermodynamic variables (ΔHrxn, S, Cv, Cp) in the gas phase and including the solvent effect (heptane (ε = 1.92), acetonitrile (ε = 36.64), toluene (ε = 2.38), and 2-propanone (ε = 21.01) in plots, where ε = 0 means free of solvent). The effect of the solvent was included using the conductor-like polarizable continuum model (CPCM) incorporated in the computational package. Optimizations and frequency calculations were performed at the PBE-D3/6-311G(d,p) level of theory (before, each structure was optimized at B3LYP-D3/6-311G(d,p)). Empirical dispersion was included using the Grimme’s D3 model.[68] Basis set like the ones employed in this study has been also used in other studies where thermodynamic data are shown the application of 6-311G (d,p) with the hybrid functional B3LYP for alkanes[50] and PBE for hydrocarbons containing N, C, and O.[69] Minimal structures of the monoterpene epoxides and their isomerization products considered in this study were well characterized by the nonimaginary frequencies (Figure ).

Figure 2

Optimized geometries of some monoterpene epoxides and their isomerization products (PBE-D3 /6-311G(d,p)): (a) α-pinene epoxide, (b) trans-carveol, (c) campholenic aldehyde, (d) β-pinene epoxide, (e) myrtanal, and (f) perillyl alcohol. Red sphere: oxygen, purple sphere: carbon, and pink and smallest sphere: hydrogen.

Results and Discussion

Isomerization Reactions

The isomerization of monoterpene epoxides is drastically affected by the type of catalyst (strength and kind of acidity) as well as solvent. Previously, we elucidated that Fe and Cu supported on MCM-41 are active materials for the isomerization of α- and β-pinene epoxides; however, Cu is less active because of the shape of the oxide (only CuO, detected by XPS, Raman, and TEM techniques) and the size of the clusters over the surface of MCM-41.[40,70] Taking this information into account and for further studies in the thermodynamics of the reactions, Figure shows the effect of the solvent for two selected materials (1.7Fe/MCM-41 and 1.3Cu/MCM-41) on the isomerization of both monoterpene epoxides. In the case of α-pinene epoxide (as it was previously claimed), 1.7Fe/MCM-41 is more active in all solvents than 1.3Cu/MCM-41 (Figure a); nevertheless, as the polarity of solvent increases (from toluene to tert-butanol), a slight decrease in the formation of campholenic aldehyde was achieved, while an increase in the formation of carveol is observed. This result has been explained by the polarization of intermediate carbocation, which could be favored in the presence of polar (or polar basic) solvents and then synthesize carveol over campholenic aldehyde. For 1.3Cu/MCM-41, the behavior is quite different: with toluene and ethyl acetate, the selectivity to campholenic aldehyde is higher (at least 80%), but the conversion decreases as polarity of the solvent increases. Particularly, both ethyl acetate and tert-butanol have free electrons in their valence shell and they can coordinate to Lewis acid sites such as Cu. Then, the competition between coordination of the acid sites of the catalyst and solvent (or epoxide) results in a decrease in the catalytic activity. For β-pinene epoxide (Figure b), a similar behavior was observed in terms of conversion. Nevertheless, no relationship between polarity of solvent and each isomer of β-pinene epoxide was observed for selectivity. In the case of 1.7Fe/MCM-41, 92% of conversion was achieved with a higher selectivity to perillyl alcohol (70%), which is one of the best results reported to date. An increase in solvent polarity increases the conversion of the epoxide slightly. Selectivity to perillyl alcohol is higher when toluene and tert-butanol are used as solvents, while it is lower when ethyl acetate was used as a solvent. Again, a similar behavior was observed with 1.3Cu/MCM-41, when the solvent changes from toluene to ethyl acetate, conversion decreases. Nevertheless, with tert-butanol, a slight increase in conversion was observed.

Figure 3

Effect of solvent on the isomerization of (a) α- and (b) β-pinene epoxides over Fe and Cu supported on MCM-41. Reaction conditions: 15 mg of catalyst, 343.15 K, 750 rpm, 0.25 mmol of monoterpene oxide. CA: campholenic aldehyde, FA: fencholenic aldehyde, CV: carveol, MAL: myrtanal, MOL: myrtenol, PAL: perillyl alcohol, O: others. Conversion of reagents X = (C0 – Cf)/C0 and selectivity of products S = Cf/∑Cproducts, where C is initial (0) and final (f). Mass balance verification by comparing GC areas after and before the reactions around (95–100%).

Standard Thermodynamic Data of Terpenes and GCM Analysis

The thermodynamic analysis of the isomerization of α- and β-pinene epoxides was carried out through the estimation of different standard thermodynamic properties combining group contribution methods and computational quantum chemistry calculations. These thermodynamic data give important information about the nature of the substances and their chemical transformations. In the case of computational quantum chemistry, calculations carried out with Gaussian software take the partition functions of each contribution (vibrational, electronic, translational, rotational, and nuclear) and measure the thermodynamic parameters toward an exhaustive statistical treatment. In these calculations, the rigid rotor-harmonic oscillator approximation could be considered, but in many of the cases, it is computationally expensive because it is carried out using path integral methods, which are affordable only for small molecules.[50] On the other hand, the group contribution methods use additive groups obtained from known experimental data of pure components and mixtures, empirical correlations, and sometimes groups interactions atoms to predict the properties. Table S4 (Supporting Information) shows some of the thermodynamics data obtained by computational chemistry for the oxo-monoterpene derivatives from α- and β-pinene epoxides. As can be seen, the highest value of both ideal gas heat capacity and entropy are obtained for campholenic and fencholenic aldehydes. Nonetheless, it is important to take into account that all substances present very similar thermodynamic values because of the similarity of their chemical structure.

The thermodynamic properties estimated using the group contribution methods are reported in Table S5 (Supporting Information) and Table . The critical properties of the terpenes obtained from the isomerization of both α- and β-pinene epoxides are also presented in Table S5 (Supporting Information). These properties are related to critical compressibility factor, pressure, temperature, volume, and acentric factor. Under the critical conditions, the phase equilibrium boundary vanishes, the substances may coexist in the two states vapor and liquid, and the gas cannot be liquefied by pressure alone. For these reasons, it is important to determine these properties for chemical compounds. At the critical pressure, similar values are obtained with all of the group contribution methods selected with the highest standard deviation of 3.4 bar for α-pinene and the lowest deviation of around 0.9 bar for trans-carveol. Even for α- and β-pinene epoxides and their isomers, the critical pressure of this set of monoterpenoids is around (29.5 ± 1.9) bar, and this is expected due to the similar structure in all substances. Thus, the values of critical pressure seem not to depend on the group contribution method since the differences are not significant.

Table 1

Ideal Gas Standard Enthalpy of Formation and Gibbs Free Energy of Formation of Terpenes Present in α- and β-Pinene Epoxide Isomerizationa

property	ΔHf,298.15° (kJ mol–1)				ΔGf,298.15° (kJ mol–1)
substance/method	JR	CG	B*	Avg.	JR	CG	J*	Avg.
α-pinene	–69.08	19.8	28.3	–7.0 ± 54	149.85	291.8	216.00	219.2 ± 71
β-pinene	–31.15	26.2	38.7	11.2 ± 37	182.60	301.8	247.00	243.8 ± 60
α-pinene epoxide	–167.37	–80.5	–112.9	–120.2 ± 44	115.15	311.4	115.15	180.6 ± 113
β-pinene epoxide	–153.19	–94.0	–94.4	–113.8 ± 34	110.76	306.6	110.76	176.0 ± 113
trans-carveol	–206.03	–132.2	–206.0	–181.4 ± 43	12.86	48.9	12.86	24.9 ± 21
isopinocamphone	–273.43	–58.8	–302.7	–211.6 ± 133	–0.78	238.8	–0.78	79.1 ± 138
pinocarveol	–203.72	–151.6	–203.7	–186.3 ± 30	38.07	149.6	38.07	75.2 ± 64
fencholenic aldehyde	–233.62	–181.6	–187.9	–201.0 ± 28	–22.52	85.4	–22.52	13.5 ± 62
campholenic aldehyde	–233.62	–181.6	–187.9	–201.0 ± 28	–22.52	85.4	–22.52	13.5 ± 62
perillyl alcohol	–185.69	–155.7	–142.7	–161.4 ± 22	20.57	50.4	20.57	30.5 ± 17
myrtanal	–221.31	–179.0	–177.7	–192.7 ± 25	22.29	122.3	22.29	55.6 ± 58
myrtenol	–221.31	–139.9	–129.9	–163.7 ± 50	13.03	148.2	13.03	58.1 ± 78

JR: Joback–Reid, CG: Constantinou–Gani, GM: Ghasemitabar–Movagharnejad, J*: Joback from Aspen Plus, B*: Benson from Aspen Plus, Avg.: average.

The critical temperature was also calculated for all substances and products involved in the isomerization of α- and β-pinene epoxides. In this case, more significant differences between the group contribution methods were observed than critical pressure. The highest standard deviation values were reported for isopinocamphone and myrtenol since the CG GCM predicted low critical temperature values than the other methods, and the lowest for α-pinene epoxide. Although in general, all critical temperature values were in the same order of magnitude for all substances 696.9 ± 29.4 K, it seems to increase from hydrocarbons to alcohols in this order: α- and β-pinenes < epoxides < aldehydes ∼ ketones < alcohols. Furthermore, the highest critical molar volume was assigned to perillyl alcohol with the lowest standard deviation value between the GCMs selected. In general, the selected terpenes have similar critical specific volume values around 486 ± 34 cm3 mol–1. The critical compressibility factor Zci of the selected terpenes was around 0.256 ± 0.012. The compressibility factor Z describes the deviation of a real gas from ideal gas behavior (Z = 1) due to attractive and repulsive intermolecular forces. At given temperature and pressure, repulsive forces increase the volume larger than for an ideal gas (Z > 1). However, when attractive forces dominate, as in the case of the critical conditions, the molecules are free to move and Z <1. The reason is that the closer the gas is to its critical point or its boiling point, the more Z deviates from the ideal case. The acentric factor ω of the selected terpenes is also included in Table S2 (Supporting Information). This property is a measure of the nonsphericity (centricity) of the molecules, and as it increases, the molecules have higher boiling points (see Figure ). This nonsphericity was higher for alcohols > aldehydes > ketones > epoxides > monoterpenes hydrocarbons. Table shows the calculations of ideal gas standard enthalpy of formation and ideal gas Gibbs free energy of formation of the selected terpenes obtained from the isomerization of both α- and β-pinene epoxides. For all of the compounds, significant differences are observed for all of the GCMs used; isopinocamphone has the highest standard deviation in the calculation and the estimation of the Gibbs free energy of formation by the CG method.

Figure 4

Acentric factor vs average normal boiling point for the selected terpenes.

The phase change properties of the selected terpenes are listed in Table S6 (Supporting Information). Normal boiling point, heat of vaporization, fusion temperature, and heat of fusion were also calculated using different GCMs, and the obtained values were compared with available reports. Differences between values obtained with the methods are associated mainly with the methodology used, which involves the use of electronic and steric contributions in the total values of the thermodynamic parameters. Although most normal boiling temperatures have the same order of magnitude for the selected terpenes 479.9 ± 18.6 K, they show signs of increase from hydrocarbons to alcohols in this order: α- and β-pinenes < epoxides < aldehydes < ketones < alcohols. The α- and β-pinenes and myrtanal presented the lowest standard deviation 6–8 K, whereas isopinocamphone and pinocarveol had the highest standard deviation for the normal boiling point 28–41 K and isopinocamphone and myrtenol for the melting point 37–51 K, estimated for all of the selected GCMs. Differences in the normal boiling point of these terpenes are associated not only to physical properties such as sphericity and the type of GCMs employed but also to intermolecular forces that are different for each compound. In general, boiling points are affected by the number of carbons in the molecule, branching of the structure, and the relative strength of the intermolecular forces (ionic > hydrogen bonding > dipole–dipole > van der Waals/London forces) that are influenced by the functional groups. As hydrocarbon monoterpenes α- and β-pinenes do not have heteroatoms, the oxygenated derivatives monoterpenoids will have a higher boiling point. In this last set of terpenes, the epoxide functional groups are dominated by dipole–dipole forces, whereas alcohols have a stronger intermolecular force due to the hydrogen bonding in the hydroxyl groups. Normal heat of vaporization was also in the same order of magnitude for the selected terpenes 47.1 ± 5.5 kJ mol–1, with the highest standard deviation for pinocarveol estimation 55.54 ± 11 kJ mol–1 for all of the selected GCMs. However, when the Trouton’s rule of eq was applied to evaluate the entropy of vaporization as the ratio between the enthalpy of vaporization and the normal boiling point, the values obtained for the average GCMs calculations were close (98.3 ± 8.9 J mol–1 K–1) to the highest values for the monoterpenoid alcohols trans-carveol, pinocarveol, perillyl alcohol, and myrtenol. Although Trouton’s rule states that the entropy of vaporization is almost the same value, about 85–88 J mol–1 K–1, for several liquids at their boiling points, there are exceptions in which some deviations can be explained due to interactions between molecules such as alcohols with hydrogen bonding.

Finally, the constant-pressure heat capacities for the liquid terpenes in Table S7 (Supporting Information) were obtained through simulation using the Ruzicka method in the software Aspen Plus to be used in the determination of the heat, entropy, and Gibbs free energy of liquid phase reactions for the transformation of α- and β-pinene epoxides at 298.15 and 343.15 K summarized in Table . The results for the epoxidation of their precursors α- and β-pinenes are also presented. The formation enthalpies in the liquid phase at 298.15 K were calculated with eq as an average value from the data of formation enthalpy in the gas phase and heat of vaporization obtained from the different GCMs of Joback–Reid, Constantinou–Gani, Benson, and Ruzicka. The entropy of the reaction in the liquid phase at 298.15 K was obtained with eq from the quantum chemistry estimation of the formation entropy and the average GCMs of the heat of vaporization and normal boiling point estimations through Trouton’s rule with eq . These values were corrected at the temperature of the reaction of the isomerization of α- and β-pinenes (343.15 K) using eqs –12. The results obtained suggest that all of the reactions are exothermic, including the epoxidation of the monoterpenes hydrocarbons α- and β-pinenes, and that they are thermodynamically feasible and spontaneous since the values of the Gibbs free energy of the reactions ΔGrxn,L° are negative. No significant differences were observed for the values at 298.15 and 343.15 K. The group contribution methodology suggests that the most exothermic and spontaneous reactions in α-pinene epoxide isomerization correspond to the synthesis of isopinocamphone, fencholenic, and campholenic aldehydes. From the β-pinene epoxide isomerization, myrtenol production was less spontaneous in comparison with the formation of myrtanal and perillyl alcohol.

Table 2

Liquid-Phase Gibbs Free Energy, Entropy, and Heat of Reaction in α- and β-Pinene Epoxide Isomerization

reaction	ΔHrxn,L,298.15°(kJ mol–1)	ΔSrxn,L,298.15° (J mol–1 K–1)	ΔGrxn,L,298.15rxn° (kJ mol–1)	ΔHrxn,L,343.15° (kJ mol–1)	ΔSrxn,L,343° (J mol–1 K–1)	ΔGrxn,L,343.15°(kJ mol–1)
α-pinene → α-pinene epoxide	–116.0	–22.0	–109.5	–115.3	–19.7	–108.5
β-pinene → β-pinene epoxide	–130.4	–4.3	–129.1	–129.8	–2.5	–129.0
α-pinene epoxide → trans-carveol	–79.0	–0.4	–78.8	–81.6	–8.7	–78.6
α-pinene epoxide → isopinocamphone	–90.6	45.8	–104.3	–89.2	50.4	–106.5
α-pinene epoxide → pinocarveol	–83.7	–2.0	–83.1	–86.2	–9.7	–82.8
α-pinene epoxide → campholenic aldehyde	–86.5	43.7	–99.6	–84.6	49.6	–101.7
α-pinene epoxide → fencholenic aldehyde	–86.5	55.7	–103.1	–84.6	61.6	–105.8
β-pinene epoxide → perillyl alcohol	–64.3	14.0	–68.5	–61.5	22.6	–69.3
β-pinene epoxide → myrtanal	–81.1	–7.4	–78.9	–80.6	–5.8	–78.6
β-pinene epoxide → myrtenol	–65.8	–27.6	–57.5	–63.7	–21.2	–56.4

Computational Quantum Chemistry Analysis

Effect of Solvent Polarity

It has been reported that solvent polarity drastically affects the product distribution of the isomerization reaction of α- and β-pinene epoxides.[44,71,72] The effect of the solvent on the reaction is related with the rearrangement of the intermediate carbocation that can favor the electronic migration instead of steric breaking. The thermodynamics of product formation will depend on heat, spontaneity, solvent polarity, molecular structure, and reaction conditions. As we previously stated, over Fe-supported materials and a natural zeolite, it is possible to obtain campholenic aldehyde and trans-carveol from α-pinene epoxide and myrtanal, and myrtenol and perillyl alcohol from β-pinene epoxide.[6,40] Myrtanal is favored over Fe/MCM-41 materials, while perillyl alcohol and myrtanal are favored over natural zeolite. The main explanation about the selectivity dependence of the catalyst was related with the architecture of the catalyst that affects the transition-state shape and also the kinetics. Gibbs free energy of reaction (ΔG) is an important parameter that gives information about spontaneity and evolution direction of the transformation of reactants into products, and some qualitative aspects into the equilibrium. In this way and because of our previous study in the kinetics of the isomerization of α-pinene epoxide over Fe/MCM-41 and Fe/SBA-15, herein, we will explain, from a thermodynamic point of view, the connection between experimental results and thermodynamics modeling. ΔG = 0 means that the reaction is in equilibrium, ΔG <0 means that the reaction is spontaneous (thermodynamically favorable), and ΔG> 0 means that the reaction is nonspontaneous or nonfavorable. ΔG was calculated for the isomers of α- and β-pinene epoxides in the presence of solvents of different polarities. Figure shows the change in the enthalpy and free energy of isomerization of the α-pinene epoxide. In all cases, the incorporation of the solvent (independent of polarity, defined by the dielectric constant decreases both enthalpy and Gibbs free energy. As it was obtained using the GCM approach, the most exothermic and spontaneous reactions correspond to the synthesis of campholenic aldehyde (CA), its isomer fencholenic aldehyde (FA), and isopinocamphone. However, this last one is more exothermic and spontaneous in comparison with campholenic aldehyde in almost all of the solvents evaluated. In the case of isopinocamphone, no effect of the solvent is observed, while for FA and CA, it is more notorious. Also, for both trans-carveol and pinocarveol, free energy is lower than zero but is less spontaneous in comparison with CA, FA, and isopinocamphone. As the polarity of the solvent increases (in terms of dielectric constant), the exergonic behavior of the transformation for FA and CA slightly increases (up to ∼−111 kJ mol–1 with regard to isopinocamphone). The general difference between the value of Gibbs energy without solvent and with the highest polar solvent is around 13 kJ mol–1. We report that not only solvent polarity is an important factor that significantly affects the distribution of the products, but also other factors such as viscosity and basicity of the solvent also modify the synthesis of alcohols (mainly trans-carveol) and aldehydes (mostly campholenic aldehyde).[73] Low values of polarity (nonbasic solvents) and viscosity increase the formation of campholenic aldehyde. In addition, and taking into account the kinetic constants obtained in our previous study[62] (over Fe/MCM-41), the solvent that presents a lower energetic barrier is toluene (30.99 kJ mol–1), followed by tert-butanol and ethyl acetate (47.42 and 52.39 kJ mol–1, respectively). These results are in agreement with our thermodynamic study and also with the catalytic activity.

Figure 5

Values of ΔHrxn and ΔGrxn as a function of dielectric constant (ε) for the transformation of α-pinene epoxide into campholenic aldehyde (CA), fencholenic aldehyde (FA), isopinocamphone (ipCA), trans-carveol (CV), and pinocarveol (POL). ε = 0 indicates free of solvent. Computational conditions: 343.15 K and 1 atm. Lines were included to guide the eye.

The isomerization of β-pinene epoxide into myrtanal, myrtenol, and perillyl alcohol was also analyzed. Figure shows enthalpy and Gibbs free energy values for this transformation. As it was demonstrated using the group contribution methodology, the quantum chemistry calculations suggest that myrtenol formation is less spontaneous than perillyl alcohol and myrtanal. Furthermore, when the polarity of the solvent increases, the production of perillyl alcohol shows drastic changes in these thermodynamic parameters. However, for the whole analyzed range, the more spontaneous transformation corresponds to β-pinene epoxide isomerization into myrtanal, which is in agreement with previous results.[6,34] Myrtanal and perillyl alcohol are the more exothermic transformations, while that for myrtenol corresponds to the less exothermic isomerization. This could explain that in many of the heterogeneous and homogeneous catalytic systems used for this reaction, the highest yields are for the synthesis of myrtanal and perillyl alcohol instead of myrtenol, since its C–O breaking and H-proton transfer are not easy due to transition-state shape and the energetic barriers.[40] Compared with the kinetics study performed using computational methods and published previously by our group,[63] synthesis of myrtanal is favored over myrtenol and perillyl alcohol at 343 K and using toluene as a solvent. Although myrtanal production requires the same number of steps as myrtenol, the transfer of hydrogen from intermedia carbocation to the adjacent carbon is faster than in the case of myrtenol. On the other hand, perillyl alcohol requires more steps and the kinetic constants (calculated using the transition states) are lower than in the case of both myrtanal and myrtenol. Considering these findings, it is plausible to conclude that although myrtanal, myrtenol, and perillyl alcohol production is thermodynamically favored, kinetics limits the formation of myrtenol and perillyl alcohol in toluene as a solvent.

Figure 6

Values of ΔHrxn and ΔGrxn as a function of dielectric constant (ε) for the transformation of β-pinene epoxide into myrtanal (MAL), myrtenol (MOL), and perillyl alcohol (PAL). ε = 0 indicates free of solvent. Computational conditions: 343.15 K and 1 atm. Lines were included to guide the eye.

Thus, the GCMs and quantum chemistry calculations suggest the thermodynamic favorability of aldehyde formation instead of alcohols, and this can also be explained in terms of the chemical nature of the terpenes. The isomerization of α-pinene epoxide becomes more spontaneous and exothermic independently of the type of solvent in comparison with β-pinene epoxide. This is because the location of the oxirane group (epoxide) is strainer in the position endo with respect to exo position.

For a better understanding of the solvent effect on the thermodynamics of isomerization of both monoterpene epoxides, the values of Gibbs free energy and enthalpy of the reaction were plotted as a function of the reciprocal of dielectric constant (1/ε). Figure S1 (Supporting Information) shows the typical tendencies obtained for α- and β-pinene epoxide isomers. In the case of α-pinene epoxide isomers (Figure S1a in Supporting Information), it seems that as the reciprocal value of dielectric constant increases, both ΔG and ΔH increase. Clearly, nonpolar solvents favor the synthesis of campholenic aldehyde from α-pinene oxide and the synthesis of myrtanal from β-pinene oxide. It has been reported that when reactions are performed with solvents, the solvation effect can affect thermodynamic variables, which is the tendency found in this research.

Gibbs free energy is related with the equilibrium constant (K) as shown in eq where R is the gas ideal constant (8.3145 × 10–3 kJ K–1 kmol–1), T is the temperature in K, and ΔGrxn is the Gibbs free energy of the reaction.

Table shows the values of the equilibrium constant at the computational conditions tested in this research. As no apparent change in the thermodynamic parameters was achieved with different solvents, an average value was taken for the calculation of the equilibrium constant. In all cases, all equilibrium constants are higher than 1, which allows deducing that, based on the Le Châtelier principle, all transformations are favored in the direction of the products.

Table 3

Equilibrium Constants for α- and β-Pinene Epoxide Isomerizationa

epoxide	product	equilibrium constants (au)
α-pinene epoxide	campholenic aldehyde	4.13 × 1017
	fencholenic aldehyde	1.34 × 1018
	pinocarveol	1.03 × 104
	isopinocamphone	3.15 × 1016
	trans-carveol	6.08 × 1010
β-pinene epoxide	myrtanal	1.84 × 1011
	myrtenol	3.37 × 104
	perillyl alcohol	3.08 × 109

Computational conditions: 343.15 K, 1 atm in gas phase.

Effect of Temperature on the Thermodynamics of the Isomerization of α- and β-Pinene Epoxides

One of the most important parameters that affect the equilibrium and the thermodynamics of the reactions can be described by enthalpy and Gibbs free energy, which depend on temperature and pressure. Equations and 15 are obtained using Legendre transformation from the internal energy.where dH corresponds to the total differential enthalpy, T is the temperature, dS is the differential of entropy, V is the volume of the system, dp is the differential of pressure, μ is the chemical potential under the established conditions, and n is moles. Because isomerization of α- and β-pinene epoxides occurs at constant pressure and moles, eqs and 15 are transformed to dH = T dS and dG = −S dT.

It seems that increasing temperature does not cause significant changes for the synthesis of neither campholenic nor fencholenic aldehydes (even in all of the isomers) (Figure ). However, at 50 K, a change of around 15 kJ mol–1 is observed for both isomers. This change could be attributed to the reaction mechanism that occurs by the carbocation pathway (mainly affected by the type of charge and its hyperconjugation) or it could also be owing to no changes of the entropy because of small variations in the free grade of translation and rotation. A slight decrease in Gibbs energy was observed for trans-carveol, while no significant changes were seen for pinocarveol. From a statistical thermodynamics point of view, an increase in the temperature generates an increase of the vibration of the bond, as stated in eq where qvib is the vibrational contribution (vibrational partition function), T is the temperature, and Θvib is the normal temperature of vibration, which is characteristic of each substance.

Figure 7

Values of (a) ΔHrxn and (b) ΔGrxn as a function of temperature for the transformation of α-pinene epoxide into campholenic aldehyde (CA), fencholenic aldehyde (FA), isopinocamphone (ipCA), trans-carveol (CV), and pinocarveol (POL). Lines were included to guide the eye.

For isomerization of β-pinene epoxide into myrtanal, myrtenol, and perillyl alcohol, both ΔHrxn and ΔGrxn show a similar profile (Figure ). In all ranges of temperature, no significant changes in the spontaneity and exergonic behavior of myrtanal and myrtenol are observed because of their similar molecular structure (with a difference in the oxygenated-type functional group). On the other hand, myrtenol appears to be less spontaneous and favorable than myrtanal and perillyl alcohol in the whole range of temperature. These conclusions agree with the results over heterogeneous catalysts that show that myrtenol is a product obtained with low selectivity from isomerization of β-pinene epoxide.[34,43,74] Computational efforts to explain the selectivity to these products, over Fe-based catalysts, allowed us to elucidate the kinetic constants with the aim to justify why myrtenol is not obtained (or synthesized with low selectivity) since neither kinetics nor thermodynamic favors this product.[63]

Figure 8

Values of ΔHrxn and ΔGrxn as a function of temperature for transformation of β-pinene epoxide into myrtanal (MAL), myrtenol (MOL), and perillyl alcohol (PAL). Lines were included to guide the eye.

Figure shows the comparison between the average values of enthalpy and Gibbs free energy of the reactions transformation in the isomerization of α- and β-pinene epoxides obtained from GCMs and DFT calculations. The reaction enthalpy of campholenic aldehyde from α-pinene epoxide obtained by computational methods and group contribution methods are similar to reported values.[51,74] The values by DFT calculations and the average of CGMs are −102 and −84.6 kJ mol–1 (liquid phase, 343.15 K), respectively, and the difference between the contribution methods is at least 6 kJ mol–1. The transformation is spontaneous and exothermic in both cases, indicating a thermodynamic favorability toward this aldehyde from the monoterpene epoxide. Concerning Gibbs free energy of the reaction, DFT calculations gave a value of −120 kJ mol–1, which is close to the value obtained with the average GCMs −101.7 kJ mol–1 (liquid phase, 343.15 K). The enthalpy and Gibbs free energy of reaction obtained by DFT calculation for the isomerization of β-pinene epoxide into myrtanal were −69 and −76 kJ mol–1, respectively. The difference of enthalpy of reaction calculated by the average GCMs (−80.6 kJ mol–1) and the Gibbs free energy of the reaction (−78.6 kJ mol–1) from the values predicted by the quantum chemistry could be because DFT calculation involves electronic calculation toward statistical thermodynamics and corrections to the gas phase that are not considered with the group contribution methods. However, there are no significant differences between the group contribution methodology and the DFT calculations used in this study. The highest deviations between both methodologies were from isopinocamphone and myrtenol calculations in the range of temperature evaluated herein.

Figure 9

Comparison of values of ΔHrxn and ΔGrxn of each product in the liquid-phase isomerization of α- and β-pinene epoxides, using group contribution methods (average) and DFT computational chemistry calculations at 298.15 and 343.15 K.

Conclusions

Herein, we presented several valuable thermodynamic results related with the isomerization of α- and β-pinene epoxides using DFT and group contribution methods calculations (JR, CG, GM, J*) to support the transformation of these compounds over Fe and Cu supported on MCM-41 materials. It is plausible to deduce that rearrangement of epoxides into aldehydes is always favorable since the values of Gibbs free energy and the heat of reaction in a wide range of temperature are lower than 0, which were in agreement with the results of the equilibrium constants. Myrtenol production from β-pinene epoxide is less favorable with the change of the solvent and also at any range of temperatures 10–375 K from the thermodynamic point of view. However, the experimental formation of products also depends on the interaction with the active sites in the catalyst with connection of the thermodynamic data. In addition, the difference in the use of a solvent instead of gas phase (or without solvent) does not change significantly the spontaneity of the studied reaction. Thermodynamic data of several oxo-monoterpenes were deduced, and they contribute significantly to the state-of-the-art in the field of thermodynamics. Finally, reaction enthalpy and Gibbs free energy are shown to be in good correspondence using both methodologies (contribution methodology and DFT calculations), except in the case of myrtenol and isopinocamphone, where the values slightly changed.