Computational and Theoretical Chemistry 1017 (2013) 72–77

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Computational and Theoretical Chemistry

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Reinvestigation of homoaromaticity of cyclohepta-1,3,5-triene

2210-271X/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.comptc.2013.05.001

⇑ Corresponding author. Tel.: +91 141 2651030; fax: +91 141 2652730.E-mail address: bansalrk43@yahoo.com (R.K. Bansal).

Preeti Saini, Parul Bhasin, R.K. Bansal ⇑Department of Chemistry, The IIS University, Jaipur 302 020, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 23 March 2013Received in revised form 1 May 2013Accepted 1 May 2013Available online 11 May 2013

Keywords:HomoaromaticityCyclohepta-1,3,5-trieneHypohomodesmotic reactionValence tautomerizationDFT calculationNBO analysis

A reinvestigation of the homoaromaticity of cyclohepta-1,3,5-triene has been done at the DFT(B3LYP/6-31+G�) level. The determination of the aromatic stabilization energies based on the hypoho-modesmotic reactions gives either too high value (�19.58 kcal mol�1 using ethane as the hydrogen donormolecule) or too low values (�0.46 kcal mol�1 using cycloheptane or �4.27 kcal mol�1 using cyclopen-tane molecules as the hydrogen donor molecules), as the ring strains on the two sides of the reactionsare not compensated. The isomerisation reaction of methylenecyclohepta-1,3-diene to 1-methylcyclo-hepta-1,3,5-triene gives a value of �10.68 kcal mol�1 as the isomerisation energy. Investigation of thevalence tautomerization of cyclohepta-1,3,5-triene to norcaradiene and back to cyclohepta-1,3,5-trienereveals that a dynamic equilibrium exists between the two valence tautomers due to small activationenergy barriers, which causes strong interactions between the p orbitals of the triene moiety and theAHCACH2ACHAr orbitals. The NBO analysis of the two valence tautomers and the transition structureinvolved therein support these interactions. The Frontier Molecular Orbitals of cyclohepta-1,3,5-triene,norcaradiene and the transition structure depict unambiguously the formation of the annular electroncloud, which confers homoaromatic character on cyclohepta-1,3,5-triene.

� 2013 Elsevier B.V. All rights reserved.

�

1. Introduction

The molecule of cyclohepta-1,3,5-triene (tropilidine) may per-haps be having the unique distinction of being the subject of thehighest number of claims and counter-claims about its homoaro-matic stabilization. Thiele for the first time in 1901 attributed theweakly acidic character of the methyl protons of cycloheptatrieneto a partial 1,6-interaction conferring ‘‘benzene like character’’ [1].Doering et al. termed cycloheptatriene as ‘‘mono-homobenzene’’,and supported the concept of 1,6-p electrons interaction, althoughits structure was assumed planar incorrectly [2,3].

On the basis of thermochemical and structural evidence, Rogerset al. concluded that a stabilization energy of ca. 6 kcal mol�1 ofcyclohepta-1,3,5-triene comes mainly from homoaromatic delocal-ization across the sp3 carbon [4]. Most recently, Schleyer and co-workers [5] determined various magnetic properties, namely mag-netic susceptibility exaltation, NICS values and anisotropy of thecurrent-induced density (ACID) of cyclohepta-1,3,5-triene and itsvalence-isomer, norcaradiene and concluded that cyclohepta-1,3,5-triene is a neutral homoaromatic system, although norcarad-iene does not display aromatic character. However, the transitionstructure involved in the electrocyclization of the former to the lat-ter is highly aromatic in accordance with the pericyclic mecha-nism. On the contrary, Conrow [6] attributed homoaromaticity

only a minor stabilizing role on the basis of a small DGisom . in favorof 2,3,7,7-tetramethylcyclohepta-1,3,5-triene than its isomer, 1-methylene-2,6,6-trimethylcyclohepta-2,4-diene. Williams et al.calculated two-centre energy partitioning term for the molecularorbitals of cyclohepta-1,3,5-triene molecule at the semiempiricalMNDO and AM1 levels and concluded that there was no apprecia-ble homoaromatic stabilization across the sp3 carbon atom [7]. Lewand Capon [8] also came to the same conclusion on the basis ofelectrophilic addition reaction of isomeric cycloheptatrienols.However, Herndon and Párkányi [9] supported homoaromatic sta-bilization on the grounds of structure resonance theory calcula-tions. Cremer and co-workers [10,11] carried out ab initiocalculations and interestingly were cautious in their postulation;they suggested that although the triene part of the seven-mem-bered ring is flattened resulting in the improved p-delocalizationand consequently stabilization of cycloheptatriene, it is not neces-sary to invoke homoaromaticity for it.

Enthalpies of stepwise hydrogenation of polyenes and cyclo-polyenes reveal stabilization resulting from the delocalization ofthe p electrons. Conn et al. [12] reported experimental values ofthe stepwise hydrogenation of tropilidine obtained in the gasphase at 355 k. These values are shown above the arrows in the fol-lowing equation.

Tropilidine����!�21:58�0:33

�21:27�0:40H2trop� 1;3

����!�24:74�0:15

�24:77�0:12

H4trop ����!�26:52�0:15

�26:55�0:26H6trop ð1Þ

CH3CH2

isomerization

Scheme 1. Isomerisation of non-aromatic methylene derivative to aromatic methylderivative.

Scheme 3. Isomerisation of methylenecyclohepta-1,3-diene to 1-methylcyclohep-ta-1,3,5-triene.

P. Saini et al. / Computational and Theoretical Chemistry 1017 (2013) 72–77 73

These values agree well with the data (shown below arrows inEq. (1)) determined calorimetrically using glacial acetic acid [13]after making solvent correction [14].

Isodesmic reactions were introduced by Pople [15] as ‘‘theexamples of (hypothetical) chemical changes in which there isretention of the number of bonds of a given formal type (CAH,CAC, C„C) but with a change in their formal relation to one an-other.’’ The quantum and thermochemical errors cancel, so ‘‘theenergies of isodesmic reactions measure deviations from the addi-tivity of bond energies.’’ Difference of the enthalpies obtained fromthe isodesmic reaction(s) and independently measured heats offormation gives a very good approximation of the ring strain orthe resonance energy. Although isodesmic reactions are not a sub-stitute for quantum mechanical calculations of the energies, theyhave been used conveniently for the estimation of ring strain andconjugation energies of a large number of systems without muchcomputational costs [16,17]. Following this approach, Rogerset al. [4] calculated 6 kcal mol�1 as the stabilization energy ofcyclohepta-1,3,5-triene at the MM2ERW level.

Recently Schleyer and Puhlhofer [18] reported a simple andcomputationally inexpensive method for determining resonanceenergies (RE). This method is based on determining isomerisationenergy (ISE) of methylene derivatives of a non-aromatic systemto its methyl derivative of the aromatic system (Scheme 1). The

Scheme 2. Hypohomodesmotic reactions of cyclohe

ISE so obtained compared well with the resonance energies ofthe corresponding aromatic systems.

By following this approach, a resonance energy of�9.8 kcal mol�1 was determined as the stabilization energy ofcyclohepta-1,3,5-triene at the B3LYP/6-311+G(d,p) level. However,in this approach, contribution of the hyperconjugation has notbeen taken into account.

Although these studies either establish cyclohepta-1,3,5-trieneto be homoaromatic or otherwise, the question, ‘‘why is cyclohep-ta-1,3,5-triene homoaromatic at all?’’ has not been addressed to.

In order to get answer to this question, the process of valence tau-tomerization [19] of cyclohepta-1,3,5-triene to bicyclo[4.1.0]hepta-2,4-diene (norcaradiene) and back to the former and the FMOs in-volved therein need to be investigated and analyzed. In the presentstudies, we first determined stabilization energy of cyclohepta-1,3,5-triene by the methods of isodesmic reaction and isomerisationand then analyzed the FMOs involved in the valence tautomeriza-tion process along with natural bond orbital (NBO) analysis.

pta-1,3,5-triene at the B3LYP/6-31+G(d) level.

74 P. Saini et al. / Computational and Theoretical Chemistry 1017 (2013) 72–77

2. Computational method and models

All calculations were carried out using Gaussian 03 suite of pro-grams [20]. The geometry optimization of the reactants, productsand the transition structure were done in the gas phase at theB3LYP/6-31+G(d) level of theory.

Frequency calculations were done at the same level to deter-mine zero-point energies and to characterize the transition struc-ture by the presence of one and only one imaginary frequencycorresponding to the movement in the direction of the reactioncoordinate. The intrinsic reaction coordinate (IRC) [21,22] calcula-tions starting at the transition structure were carried out at theB3LYP/6-31+G(d) level to confirm its connection with the corre-sponding reactant and the product. The optimized geometriesand the FMOs were plotted using Chemcraft [23].

Fig. 1. Relative activation enthalpies of valence tautomerization of cyclohepta-1,3,5-triene (1) into norcaradiene (11) and back into cyclohepta-1,3,5-triene (1).

3. Results and discussion

3.1. Hypohomodesmotic reactions

To determine stabilization energy of cyclohepta-1,3,5-triene,following hypohomodesmotic reactions [24] were computed(Scheme 2).

It is obvious that the values of the stabilization energy obtainedfrom the reactions 1 and 2 are too high and too low respectively, asthe ring strains on the two sides of the reaction are not compen-sated. The stabilization energy calculated from the reaction 3 islower than the value reported earlier [4], as the total strain ofthe cyclopentane rings is more than the sum of the strains of onecycloheptane ring and three cyclopentene rings.

3.2. Isomerisation reaction

Computation of the isomerisation reaction of 6-methylenecy-clohepta-1,3-diene (8) to 1-methylcyclohepta-1,3,5-triene (9) atthe B3LYP/6-31+G(d) level gives an energy value of�10.68 kcal mol�1 (Scheme 3). If a value of 4.54 kcal mol�1, calcu-lated from the difference of the total energies of 9 and 10 is takenas the energy corresponding to the extra stabilization of 9 due tohyperconjugation, the value of the stabilization energy due tohomoaromaticity is obtained as 6.14 kcal mol�1. This value is ingood agreement with the reported value [4].

Scheme 4. Valence tautomerization of cyclohepta-1,3,5-triene (1) to norcaradiene(11) and the thermodynamic data at 25 �C.

3.3. Valence tautomerization

We have computed the reaction involving valence tautomeriza-tion of cyclohepta-1,3,5-triene to norcaradiene (Scheme 4).

As expected, entropy change is almost negligible and hencedoes not play any role in the valence tautomeric equilibrium.Due to this, activation enthalpy is primarily the only factor that af-fects the dynamic equilibrium between cyclohepta-1,3,5-trieneand norcaradiene. The value of activation enthalpy for the conver-sion of the former into the latter is 9.87 kcal mol�1, whereaschange of the latter back into the former has a barrier of2.29 kcal mol�1 only. It is obvious that due to small activation bar-riers on both sides, a dynamic equilibrium ensues between 1 and11 even at room temperature (Fig. 1).

3.4. Optimized geometries

Optimized geometries of cyclohepta-1,3,5-triene (1), its valencetautomer, norcaradiene (11) and the transition structure (TS) in-volved therein are shown in Fig. 2.

Optimized geometry of the transition structure, TS revealsinteresting features: formation of the r C1ACA6 bond is quite ad-vanced (occupancy, 1.694e, bond length, 1.861 Å, Wiberg bond in-dex, 0.58). At the same time, the length of the bonds, C1AC2,C2AC3, C3AC4, C4AC5 and C5AC6 as well as their Wiberg bondindices do not differ much and lie between those of the car-bonAcarbon double bond (C@C) and the carbonAcarbon singlebond (CAC), indicating strong interaction between them. The inter-actions resulting from the conjugative and hyperconjugative ef-fects can be estimated using NBO theory [25]. In view of this, wedid NBO calculations of cyclohepta-1,3,5-triene, norcaradiene andthe transition structure. The results reveal strong p–p conjugativeinteractions as also the hyperconjugative interactions with the rorbitals of the methylene group.

Fig. 2. Optimized geometries of cyclohepta-1,3,5-triene (1), transition structure (TS) and norcaradiene (11) along with the bond distances (Å) and Wiberg bond indices (inparantheses) at the B3LYP/6-31+G(d) level.

Table 1NLMO occupancies of r and p orbitals in cyclohepta-1,3,5-triene (1), the transitionstructure (TS) and norcaradiene (11).

Orbitals Occupancy

1 TS 11

r C1AC2 1.985 1.983 1.981r C2AC3 1.984 1.981 1.982r C3AC4 1.981 1.980 1.978r C4AC5 1.985 1.981 1.983r C5AC6 1.984 1.983 1.981r C6AC7 1.984 1.943 1.937r C1AC7 1.985 1.943 1.937r C1AC6 – 1.694 1.886p C1AC2 1.908 – –p C2AC3 – 1.778 1.884p C3AC4 1.871 _ _p C4AC5 – 1.778 1.884p C5AC6 1.909 – –

P. Saini et al. / Computational and Theoretical Chemistry 1017 (2013) 72–77 75

3.5. NBO analysis

The NLMO occupancies of the different r and p orbitals and thesecond order perturbative interactions in cyclohepta-1,3,5-triene,the transition structure and norcaradiene are given in Tables 1and 2 respectively.

As mentioned earlier, formation of the r C1AC6 bond in thetransition structure is quite advanced, which is accompanied bythe formation of the p C2AC3 (occupancy, 1.778e) and p C4AC5(occupancy, 1.778e) bonds. If the occupancies of these two p orbi-tals in the transition structure are compared with those in the cor-responding p orbitals in the final product, norcaradiene, it becomesobvious that the transition structure approaches the product and

Table 2Second order perturbative interactions in cyclohepta-1,3,5-triene (1), the transition struct

Interactions in 1 Eij (kcal mol�1) Interactions in TS

Donor Acceptor Donor Acceptor

p C1AC2 p� C3AC4 12.97 p C2AC3 p� C4AC5p C1AC2 p� C5AC6 0.57 p C2AC3 r� C1AC7p C1AC2 r� C6AC7 2.16 p C2AC3 r� C7AC6p C3AC4 p� C5AC6 13.04 p C4AC5 p� C2AC3p C3AC4 p� C1AC2 13.04 p C4AC5 r� C1AC6p C5AC6 p� C1AC2 0.57 p C4AC5 r� C6AC7p C5AC6 p� C3AC4 12.97 r C6AH r� C4AC5p C5AC6 r� C1AC7 2.16 r C6AH r� C7AC8r C6AH r� C4AC5 3.34r C6AH r� C7AC8 3.33

Bold values reveal interactions of the p orbitals with the CAC r orbitals of the methyle

resembles it more. In view of a small activation energy barrier be-tween the transition structure and norcaradiene (ca. 2 kcal mol�1),difference between these two species is blurred. Due to this reason,the second-order perturbative interactions in the transition struc-ture and norcaradiene are quite similar (Table 2), although they arestronger in the former. It is noteworthy that appreciably strong p–p conjugative interactions are present in all the three specieswhich are particularly strong in the transition structure. Further-more, hyperconjugative p–r� interactions are ensued betweenthe p orbitals and the r orbitals, C1AC6, C1AC7 and C6AC7, bothin the transition structure and norcaradiene. In cyclohepta-1,3,5-triene, three p orbitals interact among themselves on the one hand,and they interact with the r orbitals, C1AC7 and C6AC7 on theother hand. The existence of hyperconjugative n ? r� interactionsbetween the lone pair of the hetero-atom and the r� CAH orbitalsof the neighboring methylene group in heterocyclic analogues ofcyclohexene have been reported [26,27]. In the present case also,we could detect hyperconjugative interactions with the r CAHorbitals of the neighboring methylene group, as shown in Table 2.Thus, a dynamic equilibrium between cyclohepta-1,3,5-triene andnorcaradiene accompanied by the interactions between the p orbi-tals and the r orbitals make the delocalization of the 6p electronspossible in spite of the presence of an sp3 carbon interruption, con-ferring homoaromatic character on the system.

3.6. Frontier Molecular Orbital (FMO) analysis

The FMOs of cyclohepta-1,3,5-triene (1), the transition structure(TS) and norcaradiene (11) are shown in Fig. 3.

These FMOs, particularly the HOMO-2 orbitals in 1 and TS re-veal unambiguously merging of the p orbitals of the 1,3,5-trienemoiety with the C1AC6, C1AC7 and C6AC7r orbitals resulting in

ure (TS) and norcaradiene (11).

Eij (kcal mol�1) Interactions in 11 Eij (kcal mol�1)

Donor Acceptor

17.19 p C2AC3 p� C4AC5 13.742.62 p C2AC3 r� C1AC7 4.468.77 p C2AC3 r� C7AC6 1.5917.19 p C4AC5 p� C2AC3 13.748.77 p C4AC5 r� C1AC6 1.592.62 p C4AC5 r� C6AC7 4.462.63 r C6AH r� C4AC5 1.872.63 r C6AH r� C7AC8 1.87

ne group.

Fig. 3. FMOs of cyclohepta-1,3,5-triene (1), the transition structure (TS) and norcaradiene (11) obtained at the B3LYP/6-31+G(d) level.

76 P. Saini et al. / Computational and Theoretical Chemistry 1017 (2013) 72–77

the formation of a continuous electron cloud over the whole ring.Thus a dynamic equilibrium between cyclohepta-1,3,5-triene andnorcaradiene resulting from symmetry allowed valence tautomer-ization overcomes the interruption between the three conjugatedcarbonAcarbon double bonds and makes the delocalization of the6 p electrons possible.

4. Conclusion

Isodesmic reactions, which should be termed hypohomodes-motic reactions according to the recently proposed classification,give a lower value of the aromatic stabilization energy of cyclohep-ta-1,3,5-triene. Isomerisation reaction, however, gives a value of ca.6 kcal mol�1 after making adjustment for the extra stabilizationcaused by hyperconjugation. A symmetry-allowed valence tauto-merization establishes dynamic equilibrium between cyclohepta-1,3,5-triene and norcaradiene, separated by an activation barrierof �9 kcal mol�1, even at room temperature, which in fact causesstrong interaction of the p orbitals of the cyclohexadiene part withthe r orbitals of the cyclopropane ring, leading to the formation ofan uninterrupted electron cloud over the whole ring, and thus con-ferring homoaromatic character.

Acknowledgement

Thanks are due to the authorities of the IIS university, Jaipur forproviding necessary facilities.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.comptc.2013.05.001.

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