The Cope rearrangement of 1 (5)-monosubstituted semibullvalenes and their BCO-derivatives

Pei Xiaoqin, Zhang Xiaoqing , Wu Haishun
(Department of Chemistry, Shanxi Normal University, Linfen, 041004, China)

Received Mar.18, 2006; Supported by NNSFC (20471034) and Youth Foundation of Shanxi (20051011)

Abstract Transition structures, activation energies, energies differences and NICS values were calculated by ab initio quantum mechanical methods for the Cope rearrangements of a series of 1 (5)-monosubstituted semibullvalenes ( and ) and 1, 5-disubstituted semibullvalenes ( and ). In considering-electron donating or accepting substituents at position 1 or 5 of semibullvalenes, the calculation results are in accordance with Hoffmann’s early prediction. While in the 1, 5-disubstituted semibullvalenes, which we emphasized on,-electron groups all shift the equilibrium toward , as can be ascribed to the BCO stabilization effects.-electron donors also reduce the Cope barriers in the 1, 5-disubstituted semibullvalenes. Most of the transition states (except for TS0e) are delocalized, neutral bishomoaromatic. The halogen substituents’parameters of the Cope rearrangement also have corresponding varieties with the change of the main quantum number.
Keywords Transition State,Geometry Configuration,Aromaticity,Reaction Barrier,Energies Difference

Fluxional semibullvalene[1] is quite well-known for its small reaction barrier (4.8-5.2 kcal/mol)[2-3] to the [3,3]-shift degenerate Cope rearrangement. Semibullvalene and its derivatives have intrigued chemists for years. A series of theoretical and experimental studies in the Cope rearrangement have been reported[4-13]. Recently, with the development of “boron carbonyl chemistry”[14-19], novel results have been reported: Wu H.-S.[19] et al suggest that the barriers to the degenerate Cope rearrangement in the semibullvalenes which are substituted by BCO at appropriate positions are eliminated, namely, the traditional transition states have been led to delocalized stabilities. Based on these work and the remarkable isolobal analogy[20] between the two fragments CH and BCO, we replace CH by BCO at appropriate positions after considering the-electron accepters (R=CN, COH) and-electron donors (R=F, Cl, Br, OH) substituting at certain positions of semibullvalene, in order to study the Cope rearrangement of semibullvalene ulteriorly and extend the emerging field of boron carbonyl chemistry. This article will first focus on the study of 1, 5-disubstituted semibullvalenes.

Complete geometric optimizations were done at the B3P86 levels which give better agreement than B3LYP with the known experimental Cope barriers, by using the 6-311+G**basis set with the Gaussian 03 suite of programs[21]. Vibrational frequencies (at B3P86/6-311+G**) were used to characterize the nature of geometries [either were energy minima (Nimag= 0) or transition states (TS) with one imaginary frequency (Nimag = 1)], without scaling. Nucleus independent chemical shifts (NICS)[22] were computed at HF-GIAO/6-31+G*// B3P86/6-311+G** with G03W to indicate the aromatic character. Considering the validity of the data, we dealt the heavy halogen substituents with the same computational method.

Consider the Cope rearrangement equilibrium between 1-R-semibullvalenes (1) and 5-R-semibullvalenes (2). (see Fig. 1).

Fig. 1 The Cope rearrangement between 1-substituted semibullvalenes () and 5-substituted semibullvalenes (

In , the substituent R is on the cyclopropane ring, while in it is just on a normal tertiary carbon. The cyclopropane ring moiety influences much on the stabilization of semibullvalene. In the Walsh model, the carbon atoms of the cyclopropane are bonded with sp hybridization, and their residual p orbitals form cyclopropane’s HOMO frontier orbitals whose energies are higher than those of the inner sp hybridized orbitals. These frontier orbitals are some closing to π orbitals and have greater radial extension of the orbitals, so they can easily react with π-electron accepters. When π-electron accepters substitute on the cyclopropane ring, the semibullvalene will be more stabilized, i.e. in Fig. 1, a π-electron accepter will shift the Cope rearrangement toward , and a π-electron donor will shift the equilibrium in the opposite direction, toward
Fig. 2 gives the sketch maps of the substituted semibullvalenes (, , and ) and the transition states (TS0 and TS1) for Cope rearrangement. The computed energy differences, ΔE, are listed in Table 1, a positive value implying that (or ) is higher in energy and less stable than (or ), while the negative value implying the opposite. The computed activation free energies of the Cope rearrangement, Δ, are listed in Table 2 and key distances are listed in Table 3.

Fig. 2 The optimized structures of the substituted semibullvalenes (, , and ) and the transition states (TS0 and TS1) for Cope rearrangement

3.1 The Direction of the Cope Rearrangement
In monosubstituted semibullvalenes,-electron donors shift the Cope equilibrium markedly toward 2, while-electron acceptors shift the equilibrium in the opposite direction, toward 1 (see Table 1). The calculation results confirm our prediction, and greatly agreed with Hoffmann’s qualitative molecular orbital theory arguments[23]. Note that hydroxyl group shifts the equilibrium to 1d, for it can rotate out of its original configuration to escape this destabilization and reach the global minimum of the potential energy surface.

Table 1Computed total Energies Differences

Δ/(kcal/mol) Δ/(kcal/mol)
1a→2a -3.6 3a→4a -7.2
1b→2b -1.5 3b→4b -5.7
1c→2c -1.4 3c→4c -5.6
1d→2d 0.3 3d→4d -6.0
1e→2e 4.8 3e→4e -2.5
1f→2f 2.6 3f→4f -2.2

At B3P86/6-311+G**
Fig. 3 The frontier molecular orbitals of semibullvalene, 1-BCOsemibullvalene and 5-BCOsemibullvalene

In 1, 5-disubstituted semibullvalenes,-electron groups all shift the Cope rearrangement equilibrium markedly toward 1-BCO-5-R-semibullvalenes ().
It is necessary to discuss how BCO substituent influences the structure and stability of semibullvalene by considering the frontier molecular orbitals of semibullvalene, 1-BCO-semibullvalene and 5-BCO-semibullvalene. These relevant frontier molecular orbitals are depicted in Fig. 3. The replacement of CH by BCO at position 5 leads to the same frontier orbitals as those of the parent semibullvalene, while the replacement of CH by BCO at position 1 has made the original HOMO and HUMO-1 reversal. The HOMO after substituting has lager electron density, due to the-bond between atom B and atom C. The greater radial extension of the orbitals favors the bridged structures and enhances the stabilization of the semibullvalene consumedly. That is the reason for the stabilization of
In disubstituted systems,-electron accepters make the energy differences reduced relative to those in the corresponding monosubstituted systems. It suggests that the kinetic constant of the Cope rearrangement equilibrium is reduced.-electron donors make the energy differences increased, which is advantageous to synthesize. With the reduction of electronegatiuity, the halogen substituents’ ability to offer electrons enhances, and the trend of the energy differences between and (or and ) is declined, too.

3.2 The Reaction Barrier
Vide supra, in the monosubstitued systems,-electron donors (F, Cl, Br) shift the Cope equilibrium toward 2. Their Cope barriers reduced (0.5, 1.9 and 1.8 kcal/mol, respectively) drastically, relative to that of the parent semibullvalene (5.0 kcal/mol). The hydroxyl group and-electron accepters (COH, CN) also reduce their Cope barriers (2.8, 2.6 and 4.3 kcal/mol, respectively). These small barriers suggest that appropriate substituents at appropriate positions of semibullvalene might stabilize the transition state to an energy minimum.

Table 2Computed Activation Free Energies

/(kcal/mol) /(kcal/mol)
1a→TS0a 0.5 2a→TS0a 6.7
3a→TS1a 2.8 4a→TS1a 9.0
1b→TS0b 1.9 2b→TS0b 3.5
3b→TS1b 4.3 4b→TS1b 9.0
1c→TS0c 1.8 2c→TS0c 3.2
3c→TS1c 4.1 4c→TS1c 8.8
1d→TS0d 3.1 2d→TS0d 2.8
3d→TS1d 3.7 4d→TS1d 8.8
1e→TS0e 7.7 2e→TS0e 2.6
3e→TS1e 8.4 4e→TS1e 9.9
1f→TS0f 6.7 2f→TS0f 4.3
3f→TS1f 8.1 4f→TS1f 9.6

At B3P86/6-311+G**

In the disubstituted systems,-electron donors (F, Cl, Br, OH) reduce the activation free energies (2.8, 4.3, 4.1 and 3.7 kcal/mol, respectively), while π-electron accepters (COH, CN) increase the barriers (8.4 and 8.1 kcal/mol, respectively). However, the activation barriers to the Cope rearrangement are increased in the disubstituted semibullvalenes, compared with those in the monosubstituted semibullvalenes. That was caused by the enhanced stabilization of both transition states and reactants, but the latter more so.

3.3 The Geometry Configuration and Aromatic Character
The distance between atom 2 and atom 8 is an important geometry index of the effects of the substituents. In the monosubstituted semibullvalenes, if R is a-electron accepter, it will strengthen the 2-8 bond in 1 but will have little effects on 2. Thus 1 should be more stable than 2. Similarly if R is a-electron donor it will weaken the 2-8 bond of 1 and shift the Cope equilibrium to 2[23]. By calculation, we find that the same argument can be applied to the disubstituted semibullvalenes. As shown in Table 3, the R2,8 values of 1a, 3a, 1b, 3b, 1c, 3c, 1d, 3d (1.670,1.648,1.631, 1.623, 1.633, 1.624, 1.603 and 1.639Å, respectively) are evidently longer than that of the parent semibullvalene (1.601Å). There are no typical R2,8 single bonds in these configurations. The reason for that is the weak combination of the frontier orbitals of cyclopropane ring and-electron donors. We can also find that the eigenvalues of R2,8 of 3 are shorter than those in 1, which can be ascribed to the BCO stabilization effects at the bridging position 5 of semibullvalene.

Table 3Computed Bond Lengths(R) and NICS Values

Nimag 2,8/(Å 2,3/(Å 3,4/(Å 4,6/(Å NICS/(ppm)
1a/ Cs 1.670 1.459 1.345 2.331 -12.7
2a/ Cs 1.618 1.463 1.344 2.345 -12.9
TS0a/ Cs 1.973 1.412 1.366 2.217 -20.8
3a/ Cs 1.648 1.464 1.348 2.542 -11.8
4a/ Cs 1.536 1.475 1.341 2.349 -8.8
TS1a/ Cs 2.152 1.397 1.383 2.148 -22.6
1b/ Cs 1.631 1.463 1.342 2.34 -11.3
2b/ Cs 1.616 1.463 1.343 2.338 -11.9
TS0b/ Cs 2.069 1.395 1.378 2.144 -22.3
3b/ Cs 1.623 1.466 1.346 2.547 -10.9
4b/ Cs 1.535 1.475 1.341 2.347 -8.0
TS1b/ Cs 2.131 1.383 1.397 2.140 -22.3
1c/ Cs 1.633 1.463 1.342 2.340 -11.2
2c/ Cs 1.615 1.463 1.343 2.339 -11.6
TS0c/ Cs 2.102 1.391 1.381 2.123 -21.8
3c/ Cs 1.624 1.467 1.346 2.547 -10.7
4c/ Cs 1.535 1.474 1.342 2.348 -7.8
TS1c/ Cs 2.136 1.382 1.397 2.140 -22.2
1d/ C1 1.635 1.462 1.343 2.333 -11.9
2d/ C1 1.615 1.463 1.343 2.335 -12.3
Ts0d/ C1 2.053 1.396 1.379 2.130 -22.7
3d/ Cs 1.639 1.465 1.347 2.542 -11.1
4d/ Cs 1.535 1.474 1.341 2.342 -8.4
Tsd1/ C1 2.137 1.396 1.384 2.127 -24.7
1e/ Cs 1.558 1.471 1.340 2.347 -9.4
2e/ C1 1.605 1.466 1.341 2.336 -11.0
Ts0e/ Cs 2.072 1.381 1.391 2.016 -11.3
3e/ Cs 1.552 1.471 1.343 2.547 -29.3
4e/ C1 1.526 1.475 1.339 2.363 -7.0
TS1e/ C1 2.097 1.384 1.393 2.143 -22.5
1f/ Cs 1.577 1.470 1.339 2.346 -9.7
2f/ Cs 1.603 1.464 1.340 2.343 -11.1
TS0f/ Cs 2.080 1.383 1.387 2.048 -23.4
3f/ Cs 1.576 1.471 1.343 2.545 -9.8
4f/ Cs 1.530 1.473 1.338 2.355 -7.6
TS1f/ Cs 2.118 1.394 1.381 2.083 -23.1

At B3P86/6-311+G** HF-GIAO/6-31+G*//B3P86/6-311+G** and at the unweighted centers of the Cope systems (atoms2-4 and 6-8)

We also pay attention to the geometric configuration of the transition states, see Fig. 4, each of whom has an imaginary frequency (Nimag=1). Whether in the monosubstitued or the disubstituted systems, the C-C bonds around the periphery of a Cope system are of approximately equal length. The average lengths of C-C bonds (Rav) are between the value of single bonds (1.54Å) and the value of the double bonds (1.34Å), more close to the double ones. The Rav values of the disubstituted semibullvalenes are all increased relative to those in monosubstituted semibullvalenes, which indicate that the replacement of CH by BCO favors the delocalized semibullvalenes substantially. Due to the interaction of the symmetric combination of the allyl nonbonding orbitals with an antibonding skeletal orbital, the C-C bonds (R1,5) of the disubstituted semibullvalenes are weakened, and the R1,5 bond lengths are elongated.

Fig. 4 Structures and bond lengths of some transition states

On the base of the geometric, energetic, and the nucleus independent chemical shifts, NICS, C semibullvalene itself is not aromatic, but its C2v transition state for the Cope rearrangement is highly neutral bishomoaromatic[24-27]. The cyclopropane unit in semibullvalene is largely responsible for the NICS value and there is no significant contribution from homoconjugation. The C2v transition state’s calculated NICS value of geometric center of the active atoms (C2, 3, 4, 6, 7, 8) is -22.7. Once deleting the contribution of the cyclopropane ring, the NICS value of the C2v transition state is still largely negative. After substituting, as shown in Table 3, all the transition states have largely negative NICS values. They are all delocalized, neutral bishomoaromatic. The substitutions we have done are at the bridging 1,5-positions that are not in the Cope active system in semibullvalene, which do little contribution to the aromaticity, so the NICS values are almost as much as that of the parent system. Interestingly, 3e has the largest negative NICS value (-29.3), while TS0e has little NICS value (-11.3). The cause is that 3e has aromatic character, while its theoretic transition state has no aromatic character.
With the enhancement of the main quantum numbers, the halogen substituents will reduce the overlap of the p orbitals between themselves and the carbons, which causes the reduction of the delocalization of electron and the smaller NICS value. Take for example, the order of the NICS value is as follows: 1a (-12.7)>1b (-11.3)>1c (-11.2). The NICS values of the 1b and 1c are almost the same, which is caused by the deflection of computational methodology. In theory, 1c should have smaller NICS value.

Calculations on the 1 (5)-monosubstitued semibullvalenes, 1, 5-disubstituted semibullvalenes and their transition states for the Cope rearrangement with the Gaussian 03 suite of programs were carried out. The energy differences show that in the disubstituted semibullvalenes, π-electron groups shift the Cope rearrangement toward 1-BCO-5-R- semibullvalenes (). π-electron donors substituting on the position 1 or 5 of semibullvalene also reduce the Cope barriers relative to that of the parent semibullvalene in the disubstituted semibullvalenes. Most of the transition states are delocalized, neutral bishomoaromatic. Frontier molecular orbital theory and the geometrical features of the transition states elucidate the effects of BCO substitutent. With the change of the main quantum number, the halogen’s series parameters of the Cope rearrangement have corresponding varieties. A series of such work will be reported in the future.