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Boletín de la Sociedad Chilena de Química

versión impresa ISSN 0366-1644

Bol. Soc. Chil. Quím. v.46 n.4 Concepción dic. 2001 



(1) Grupo de Quimica Teorica y computacional Facultad de Ciencias Químicas
Universidad de Concepción Casilla 160-C, Concepción CHILE
(2) Sandra T.Madariaga Centro Superior de Ciencias Basicas
Universidad Austral Puerto Montt CHILE


Thermodynamic parameters for the benzene oxide Û oxepin system have been calculated at MP4(SDQ)/6-31+G**//HF/6-31G** level of theory. The calculated enthalpy for this valence tautomeric equilibrium differs from that reported by Vogel et al in 1967, but agree well with the value calculated by Kollman using the MINDO/3 method. Large deviations in the experimental tautomerization entropies lead to unreliable D Go values. The differences in D Ho and D So can be due to the lack of band shape analysis of the 1H-NMR spectra. The effect of solvent polarity on the above equilibrium has been studied using the isodensity polarized continuum method (IPCM). Low polar solvents favor the oxepin formation whereas medium to high polar solvents leads to benzene oxide formation. The transition state for the tautomerization reaction has been fully characterized and the activation energies for the forward and reverse reaction are estimated to be ca. 9.5 and 11.0 kcal/mol,respectively. The solvent polarity exerts a reasonable effect decreasing the activation energies up to 4 kcal/mol.

KEYWORDS: benzene oxide/oxepin, equilibrium, valence tautomerism, solvent effect.


En el presente trabajo se han calculado teóricamente los parámetros termodinámicos para el sistema beceno oxido = oxepina al nivel MP4(SQD)/6-31 +G**//HF/6-31 G**. La entalpia calculada para este equilibrio tautomerico difiere de la reportada por Vogel y colaboradores en 1967, pero concuerda bien con el valor calculado por Kollman usando el método MINDO/3. Las desviaciones standard en las entropías determinadas experimentalmente conducen a valores de ßGo no confiables. Las diferencias entre los ßHo y ßSo experimentales y los calculados pueden tener su origen en la falta de un análisis de forma de las bandas de el espectro 1H-NMR. EI efecto de la polaridad del solvente sobre este equilibrio ha sido estudiado usando el método IPCM. Solventes de baja polaridad favorecen la formación de oxepina, mientras aquellos de polaridad mediana a alta lIevan a la formación de benceno oxido. EI estado de transición para la reacción de tauromerización ha sido completamente caracterizado y las energías de activación para las reacciones directa e inversa son de alrededor de 9.5 y 11.0 kcal/mol, respectivamente. La polaridad del solvente ejerce un razonable efecto sobre las energías de activación, disminuyéndolas en casi 4 kcal/mol.

PALARAS CLAVES: benceno oxido/oxepin equilibrio, tautomerismo de valencia, efecto del solvente.


The atmospheric chemistry of polycyclic aromatic hydrocarbons (PAH) is mainly dominated by their photo oxidation by ozone, some organic volatile compounds and nitrogen oxides (1). These photooxidants formed by sunlight induced oxidations react with PAH (mainly benzene,xylene,toluene and other alkylated derivatives) present in the atmosphere (2). The pathways for PAH degradation primary involve the reaction with OH radicals to produce hydroxycyclohexadienyl (HCH) radicals. These radicals might react with molecular oxygen to either yield: i) hydroxycyclic hexadienyl peroxyl radicals that engage in reaction with NO to end up in dicarbonyl compounds, ii) the corresponding phenols and iii) the formation of arene oxides such as benzene oxide. These arene oxides are known to be primary metabolites in biological systems (3,4,5). In fact, benzene metabolism leads to the benzene oxide/oxepin, which might be re responsible for the carcinogenecity of this compound. A theoretical study has shown that the reaction of HCH radicals with O2 to yield phenol is favored compared with the HCH-peroxyl radicals formation (6). Although, there is no evidence for arene oxides formation (7), the atmospheric chemistry of the species has been investigated (2). Arene oxides are highly tensioned species that easily isomerize to oxepins or phenols. Benzene oxide (Bzoxide) was first prepared by Vogel et al by dehydrohalogenation of 1,2-epoxy-4,5-dibromocyclohexene with sodium metoxide in boiling ether (8,9). The orange product C6H6O turned to be a mixture of Bzoxide and oxepin (10). These valence tautomeric forms are in equilibrium which can be displaced by either temperature, suitable substituents or solvent polarity. In fact, a semiempirical MINDO/3 and ab initio calculations at STO-3G level studies on several C2 and/or C3 substituted Bzoxide/oxepin system reveal that substitution on C2 normally conduct to oxepin formation, whereas substitution on C3 leads to Bzoxide(11). Vogel et al (9,10) studied the 1H-NMR and UV spectra of this tautomeric system and showed that the equilibrium can be readily displaced to the Bzoxide formation by both decreasing the temperature and increasing the solvent polarity. The UV spectra of the orange product C6H6O shows an isosbestic point in solvents of different polarities (10). Approximate estimation, since the extinction coefficients of both species are unknown, points to a Bzoxide concentration in isooctane of ca. 30%, whereas in water/methanol (85:15) mixture its concentration is ca. 90%. The Bzoxide Û oxepin equilibrium was further confirmed by temperature dependence 1H-NMR studies in CF3Br/pentane mixture. The DH and DG values for the tautomerization reactions well as some activation parameters were reported. Ab initio calculations on this molecular system at QCISD(T)/6-31G*//MP2/6-31G* level of theory has been recently reported (12). Pye et al found that Bzoxide is ca. 0.14 kcal/mol lower in enthalpy than oxepin. This value is much lower than the one reported by Vogel et al ( 1.7 kcal/mol) (11), though a variety of D H values were found for calculations at different levels of theory. At this point, it is worth noting that Pye et al (12) computed the vibrational frequencies at HF/6-31G* , whereas the geometry optimizations were carried out at MP2/6-31G*. Under these conditions the calculated frequencies have no validity (13) and hence the derived thermodynamic properties. In addition, we feel that a more flexible basis set than 6-31G* is needed for a better description of the thermodynamics of this system. Accordingly, the 6-31+G** basis set that includes polarization functions on the heavy and hydrogen atoms as well as diffuse functions on the former, have been used to restudy the Bzoxide/oxepin equilibrium both in the gas phase and in solution of various solvents (isooctane, methanol, diethyl sulfoxide, H2O/methanol and H2O/DMSO mixtures. Despite we have explored other basis sets, 6-31+G** is the one that reproduces best the Bzoxide Û oxepin equilibrium yielding reasonable D Go values both in the gas phase and in solution, which is the aim of the present work In addition, we have fully characterized the transition state for the tautomeric reaction. The experimental thermodynamic properties are discussed and a comparison with previously reported theoretical values is also given.


Standard ab initio calculations were carried out using GAUSSIAN 98 series of programs (14). Geometry optimizations of Bzoxide and oxepin were performed at HF/6-31G** level. Initial geometries were taken from references 12 and 15. Frequency calculations and IR intensities were predicted at the equilibrium geometries in both cases all real frequencies; hence both structures are local minima. Energy calculations were carried out using various basis sets to determine the effect of including polarization and diffuse functions. In all cases electronic correlation was taken into account at the second , third and fourth order MÆller-Plesset theory in the frozen core approximation. Because of limited computational resources available in our laboratory, our best estimate was at MP4SDQ/6-31+G** level. These energies were corrected for zero point vibrational energies (ZPE) and enthalpies and free energies changes of tautomerization were determined from the corresponding sums of electronic and thermal enthalpies and free energies, respectively.

To localize the transition state (TS) for the Bzoxide Û oxepin tautomerization reaction , the "Synchronous Transit-Guided Quasi-Newton" (STQN) method (16,17) implemented in GASSIAN 98 was used. This method uses a quadratic synchronous transit approach to get closer to the quadratic region of TS that is further optimized by a quasi-Newton or eigenvector-following algorithm (14). Both QST2 and QST3 options to this method produced the same TS structure. The TS was characterized by: a) a frequency calculation which yielded only one imaginary frequency ( 776 cm-1) , b) animation of the imaginary normal mode with either GaussView (18) or Gopenmol (19) programs clearly shows that the mode conduct to either Bzoxide or oxepin. In fact, the most important atom movements involve C2, O1 and C7. As C2 and C7 get closer or away one from each other, the oxygen atom goes up and down producing a closing and opening of the C2O1C7 ( a ) angle. In the former case (closing), the TS looks Bzoxide alike, whereas in the later (opening) resembles oxepin. As a opens the C3 and C6 are below their plane recovering their position when a closes. The angles C2C3C4 and C7C6C5 decrease along with the a decreasing and c) TS Þ Bzoxide and TS Þ oxepin reactions paths were followed by using the intrinsic reaction coordinates (IRC) (14). For the IRC calculations to proceed the initial force constants, previously calculated after geometry optimization were provided. The IRC calculations connect with the reagent (Bzoxide) and the product (oxepin). According to a,b and c , it can be concluded that a true TS for the tautomerization reaction has been found.

The solvent effect on the Bzoxide Û Oxepin tautomerization as well as on the forward and reverse Ts reactions was taken into account by using the isodensity polarized continuum method (IPCM). IPCM is essentially Tomasi’s PCM model modified by Wiberg et al (20a-d). The method calculates the electric field analytically and the solute cavity is defined upon an isosurface of the total electron density. In this way, the cavity is uniquely derived from the electronic environment. Thus, the solvent effect is derived from the surface potential and the dielectric continuum interaction. This is equivalent to going to infinite order in the electric moments. IPCM was applied to gas phase molecular geometries, since structural parameters change very little in going from the gas phase to the solution and hence no large effect on solvation energies can be expected (21). The free energies of solvation (DGos) and in solution ( Gosoln.) were calculated as reported previously (22).


The dehalogenation reaction of 1,2-epoxy-4,5-dibromocyclohexene with sodium methoxide yields a compound of formula C6H6O which readily isomerizes to a mixture of Bzoxide and oxepin in variable proportions (8,9). Is seems clear that these species are part of a bond fluctuating valence isomerism Bzoxide Û oxepin equilibrium that can be driven in either directions by solvent, temperature and substituents effects.

In the present work, we have theoretically studies the above equilibrium both in the gas phase and in solution of various solvents in an attempt to see whether the solvent polarity has any effect on the equilibrium and on the calculated activation energies.

Molecular structures

Figure 1 shows the optimized geometries of Bzoxide , oxepin and their transition state (TS) at the HF/6-31G** level, whereas table 1 lists some selected bond distances and angles. From this table it can be inferred that Bzoxide possesses a bicyclic structure, where a regular benzene and an epoxy rings are fused.. Thus, in the epoxy ring the C-O bond distances are equal making and angle of ca. 63o . The C2 C7 bond length, common to the fused rings, is ca. 1.47Å. The six-membered ring shows two types of C ¾ C bond distances: a) those next to the exopy ring with values of ca. 1.48 Å and b) those involving C3 ¾ C4 and C5 ¾C6 bonds where the carbon atoms are separated by ca. 1.33Å. Accordingly, in this ring the carbon ¾ carbon bond distances of 1.48 Å correspond to single C ¾ C bons,whereas those separated by 1.33Å are consistent with a double bond character. In the benzene ring of Bzoxide all angles are ca. 120o. the C3C2C7 and C6C7C2 are ca. 3o smaller than the above value. Oxepin possesses an heptacyclic structure where the C2¾ C3 , C6 ¾ C7 and C4 ¾ C5 bond lengths are ca. 1.32Å (double bond character) , C3 ¾ C4 and C5 ¾ C6 distances are ca. 1.47Å (single bond character). The C ¾O distances are slightly smaller than in Bzoxide and all internal angles are ca. 125o ,i.e, larger than in byciclic Bzoxide. Both effects are most likely due to the breaking of the C2 ¾ C7 bond, the incorporation of the oxygen atom to the ring and the fluctuation of the C ¾C bond characters. The dihedral angles produce interesting relationships. Both the bicyclic Bzoxide and the seven membered oxepin can be divided into three planes : a) a plane A formed by C2 , O1 and C7 atoms, b) plane B made up of C3, C2, C7 and C6 atoms and c) plane C involving atoms C3, C4, C5 and C6. Plane A makes an angle with plane B of ca. 106 and 132o in Bzoxide and oxepin,respectively, whereas the angles between planes B and C are 5 and 20o , respectively. From table 1 it can be inferred that the six-membered ring in Bzoxide is quasi-planar and that the epoxy ring is standing quite upright. In this sense, oxepin is a more flat structure. This feature is also revealed by the C2O1C7 angle that varies from 63o to 116o in Bzoxide and oxepin,respectively.. According to Pye et al (12) and Cremer et al (15) , we have calculated the curvature and boat character for the species. Curvature (360 ¾ C6C7C2O1 ¾ C5C6C3C2) reveals that Bzoxide is more curved than oxepin by ca. 7o. This effect, which is not visually apparent from the optimized structure drawings, is due to the much smaller C6C7C2O1 dihedral in Bzoxide (106o) than in oxepin (131.9o). The calculation of boat character yields too close values (0.97 and 0.99 for Bzoxide and oxepin,respectively) to allow a clear distinction between these species. Finally, both species do not possess a boat ¾like structure, Bzoxide possesses an almost sofa conformation.

Fig.1.- Optimized Geometries and atoms numbering for Bzoxide, Oxepin and TS

The transition state

The structure of the transition state (TS) for the isomerization reaction studied here is somewhat in between Bzoxide and oxepin isomers. In fact, some geometrical parameters are close to Bzoxide and other resemble oxepin . Looking at the dihedrals defining planes A, B and C one can infer that the angle between planes A and B is closer to Bzoxide, whereas the angle made by planes B and C is very similar to oxepin. In fact , TS looks like a distorted oxepin since the C2 ¾ C7 bond is already broken ( C2 ¾ C7 distance = 1.8178Å).


Table 2 gives the energetics and thermodynamic properties of the Bzoxide/ oxepin molecular system calculated at MP4SDQ/6-31+G**//HF/6-31G** level. The vibrational frequencies were calculated at the equilibrium geometries and employing the same basis set (HF/6-31G**) used in the optimization procedure. It is well known that thermodynamics calculated at other level than the one used to obtain the optimized structures are of no validity.

In an attempt to see whether the thermodynamical results give or not support to the experimental values (8-10) ,we have carried out ab initio calculations using various basis sets and including electron correlation at the second, third and fourth order Moler-Plesett theory in the frozen core approximation. From table 2 , it can be inferred that electron correlation produces stabilization in the entire system and that the use of a moderate flexible basis set such as 6-31+G** allows to obtain a reasonable description of the system energetics. Studying the temperature dependence of the equilibrium constant (k) above and below the coalescence temperature,Vogel et al (8-10) have derived a value of 1.70 kcal/mol for the tautomerization enthalpy. k was determined from the ratio of the signal areas and the position of the a -protons ( attached to C2 and C7) signals. The ratio of the frequency factors yielded an entropy change of 10.5 ± 8.3 cal/K mol , whereas using the equilibrium constant a value of 11.0 ± 5.0 cal/K mol. Accordingly, from these values it was inferred that : a) Bzoxide is ca. 1.7 kcal/mol lower in enthalpy than oxepin and b) at room temperature the entropy gain associated to the isomerization process leads to a D Go value of ca. ¾1.3 kcal/mol. If the experimental data, D Hotaut. and D Sotaut., are used to calculate D Go taut., one arrives to a value of ca. ¾1.3 kcal/mol for the later parameter if the large deviation of the entropy change is neglected. Otherwise, D Gotaut. must lie between ¾3.07 and -0.09 kcal/mol. Our best estimate for the enthalpy and entropy of tautomerization are ca. ¾1.3 kcal/mol and 2.00 cal/K mol ,respectively. These values leads to a free energy change of ¾1.887 kcal/mol in the gas phase in good agreement with the fact that the Bzoxide Û oxepin equilibrium is displaced to the oxepin formation. The small deviation of our DGotaut. value with respect to that proposed by Vogel at al (10) can be attributed to the solvent effect . Pye et al(12) reported values of 0.14 kcal/mol and 2.0 cal/K mol for the enthalpy and entropy of tautomerization,respectively. Accordingly, DGotaut. is to be ¾0.46 kcal/mol, a value away from the experimental and the one reported in the present work. The diffence between our and Pye at al values is most probably due to the fact that in the later the thermodynamic properties were derived from the vibrational frequencies calculated at a different level (HF/6-31G*) than the geometry optimization one (MP2/6-31G*) and hence they have no validity. Finally, the reported activation energies (Ea) for the forward (Bzoxide® TS) and reverse (Oxepin® TS) reactions are 9.1 and 7.2 kcal/mol, respectively. In the present work (see table 3) we have found values of 0.49 and 11.07 kcal/mol for the corresponding reactions in the gas phase. Despite the good agreement in our forward Ea ,the reverse one appears to be larger as it should be. In fact, at room temperature the higher entropy oxepin is energetically the most stable species and hence the Ea for the reverse reaction ought to be larger than the forward one. However, a direct comparison cannot be made between the calculated gas phase thermodynamic parameters and Ea with the experimental values as the later were obtained at ¾113 oC in a CF3Br/pentane (2:1) mixture.

Table 2 . Energetics for the Bzoxide-Oxepin System

Energy level












































m (D)
























E0 + ZPE




E0 + Etot




E0 + Hcorr




E0 + Gcorr













  1. Energies in Hartrees;Eo = energy at MP4SDQ/A level, D H and D Gtautomerization for
    Bzoxide Û Oxepin system in kcal/mol; S and D S in cal K-1mol-1
  2. A = 6-31+G** basis set

The experimental DH¹ value of ca. 8.8 kcal/mol correlates well with our estimate of 9.4 kcal/mol. The D S¹ value is ca 6.6 cal/K mol, whereas our calculations produce a slightly negative of ¾0.73 cal/K mol value. Small negative DS¹ values are often found in dynamic NMR studies of intramolecular processes (24-26). At this point, it is worth noting that the error limits in experimentally determined DH¹ and DS¹ depends on the errors in the primary data, i.e., the rate of reaction (k) and temperatures . Thus, insertion of reasonable values of Dk and DT variance and relative error in DG¹ equations ,shows that the later is not sensitive to erros in the primary data. The problems show up when errors in activation enthalpies and entropies are analysed. In fact, both values are normally obtained by a least-square fitting of k and T to a straight line (of the form y = bx+c) in the plot ln(k/T) vs 1/T (24). The errors in these properties are calculated from the standard deviations in b and c. Looking at the activation parameters for N,N’-dimethyl formamide (24) one can see that the reported DH¹ values are in the range of 6 ¾ 27 kcal/mol , whereas DS¹ varies from ¾38 to +18 cal/ K mol. Accordingly, the reported values are to taken just as reference points as they might be contaminated with large errors coming either from the calculated frequency factors, temperature and the way the activation parameters were derived.

Table 3. Activation Parameters for the Bzoxide Þ TS Ü Oxepin Molecular Systema in the Gas Phase.

Process DH¹ DS¹ DG¹ Ea

BzoxideÞ TS 9.367 -0.725 9.582 9.485
  11.6560 -2.728 11.469 11.066
Oxepin ÞTS        

a. All Parameters in kcal/mol ; DS¹ in cal k-1 mol-1

Solvent effect

To study the solvent effect on the Bzoxide Û oxepin equilibrium and on the activation energies , the isodensity polarized continuum method (IPCM) (20a-d) at HF/6-31G ** gas phase equilibrium geometries was used. Table 4 gives the D Gos (energy of solvation) , Gosoln. (free energy in solution) and relative D Gosoln. for Bzoxide and oxepin , whereas table 5 shows the effect on the activation energies for the forward and reverse reactions. The solvents, isooctane (e = 1.94), methanol (e =32.63), DMSO ( (e =46.70) , H2O/MeOH (85:15) (e =71.53) and H2O/DMSO (85:15) (e =73.64) were used to match the ones used by Vogel et al (10) in the UV and 1H-NMR spectra. In fact, the UV spectra in isooctane ,MeOH and H2O/MeOH show maxima at 271 and 305 mm that were assigned , by comparison with 8.9-indan oxide and dimethyloxepin, to the Bzoxide and oxepin, respectively. The spectra of the Bzoxide/oxepin system show a strong dependence of the solvent polarity and an isosbestic point demonstrate the presence of both components. Since the extinction coefficients of both valence tautomers are not known, they were estimated from the reference compounds. Thus, Bzoxide concentration was found to be ca. 30% in isooctane whereas in the H2O/MeOH mixture its concentration is ca. 90% concluding that the proportion of Bzoxide increases with the solvent polarity. The present results (tables 2 and 4) indicate that in the gas phase (e =1.0) the Bzoxide concentration is ca. 4%, whereas in the low polarity isooctane is ca. 63%. In a medium polarity solvent such as methanol Bzoxide concentration is ca. 91%. In higher polarity solvents this concentration remains unchanged. From table 4 it can be concluded that IPCM method reproduces well the experimental findings. On the other hand, the gas phase activation energies are lowered by ca. 1 ¾ 2 kcal/mol in isooctane, whereas in high polarity solvents decreases by 3-4 kcal/mol.. In other words, the gas phase Ea(F) decreases from 9.4 to 8.2 kcal/mol in isooctane and to ca. 5.7 kcal/mol in higher polarity solvents. The same trend is observed for Ea( R) .

Table 4. Free Energies of Solvation (DGos)a and in Solution (Gosoln.)b ( kcal/mol) for Benzene Oxide Û Oxepin Equilibrium.


Isooctane (Isoct) -1.56   -1.24
Metanol (MeOH) -4.25   -2.87
Dimethyl Sulfoxide (DMSO) -4.32   -2.92
H2O/MeOH (85:15) -4.37   -2.93
H2O/DMSO (85:15) -4.39   -2.97
H2O -4.39   -2.97
Isoct -3.45   -3.13
MeOH -6.14   -4.76
DMSO -6.21   -4.81
H2O/MeOH -6.25   -4.84
H2O/DMSO -6.26   -4.84
H2O -6.28   -4.86
  DGosoln.   % BZOXIDE
Isooct 0.32   63.2
MeOH 1.38   91.1
DMSO 1.40   91.4
H2O/MeOH 1.41   91.5
H2O/DMSO 1.41   91.5
H2O 1.42   91.7

a) D Gos = Esoln. ¾ Egas
b) Gosoln. = DGogas + DGos

Table 5. Solvent Effect on the Activation Energies (Ea) for the Forward and Reverse Reactions In Benzene Oxide ¾ Oxepin System. (kcal/mol)

Solvent DGos(a ) Ea (F)b Ea(R)c


-1.31 8.175 9.756
MeOH -3.67 5.815 7.396
DMSO -3.74 5.747 7.326
H2O/MeOH -3.79 5.695 7.276
H2O/DMSO -3.80 5.685 7.266
H2O -3.80 5.685 7.266

a) Free Energy of Solvation for the Transition State.
b) Forward : BzoxideÞ TS Reaction.
c) Reverse : Oxepin Þ TS Reaction.


From the above results it can be concluded that:

1.- The optimized gas phase geometries for Bzoxide and oxepin are local minima at thelevel of calculation employed. The vibrational frequency calculated at the samelevel of optimization yielded only one negative frequency for the transition state.

2.- The MP4SDQ level and using a flexible enough basis set like 6-31+G** properly describe the molecular properties of Bzoxide, Oxepin and their TS. The thermodynamics for the Bzoxide Û oxepin equilibrium is well described by the calculated entalphy, entropy and free energy changes.

3.- Activation energies for the forward and reverse reactions are in the range of the experimental reported values.

4.- The Bzoxide/Oxepin equilibrium is easily displaced in one or other direction by using solvents of different polarities. Low and high polar solvents favor oxepin and Bzoxide formation, respectively.

5.- Generally speaking, solvents lower the activation energies for the forward and reverse reactions.


The present work was supported by an operating grant (No 200.021.013-1.0) from the Universidad de Concepcion, Chile.


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