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 (1 and 2) and 1, 5-disubstituted semibullvalenes (3 and 4). In considering p-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, p-electron groups all shift the equilibrium toward 4, as can be ascribed to the BCO stabilization effects. p-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

1 INTRODUCTION
Fluxional semibullvalene^[1] is quite well-known for its small reaction barrier (4.8-5.2 kcal/mol)^[2-3] to the [3,3]-s 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 p-electron accepters (R=CN, COH) and p-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.

2 COMPUTIONAL METHODS
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.

3 RESULT AND DISCUSSION
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 (1) and 5-substituted semibullvalenes (2)

In 1, the substituent R is on the cyclopropane ring, while in 2 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 sp² hybridization, and their residual p orbitals form cyclopropane’s HOMO frontier orbitals whose energies are higher than those of the inner sp² 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 1, and a π-electron donor will shift the equilibrium in the opposite direction, toward 2.
    Fig. 2 gives the sketch maps of the substituted semibullvalenes (1, 2, 3 and 4) 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 2 (or 4) is higher in energy and less stable than 1 (or 3), while the negative value implying the opposite. The computed activation free energies of the Cope rearrangement, ΔG^#, are listed in Table 2 and key distances are listed in Table 3.

Fig. 2 The optimized structures of the substituted semibullvalenes (1, 2, 3 and 4) and the transition states (TS0 and TS1) for Cope rearrangement

3.1 The Direction of the Cope Rearrangement
In monosubstituted semibullvalenes, p-electron donors shift the Cope equilibrium markedly toward 2, while p-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.

At B3P86/6-311+G**

Fig. 3 The frontier molecular orbitals of semibullvalene, 1-BCOsemibullvalene and 5-BCOsemibullvalene

    In 1, 5-disubstituted semibullvalenes, p-electron groups all shift the Cope rearrangement equilibrium markedly toward 1-BCO-5-R-semibullvalenes (4).
    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 p-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 4.
    In disubstituted systems, p-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. p-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 1 and 2 (or 3 and 4) is declined, too.

3.2 The Reaction Barrier
Vide supra, in the monosubstitued systems, p-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 p-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 2 Computed Activation Free Energies

At B3P86/6-311+G**

    In the disubstituted systems, p-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 p-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 p-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 R_2,8 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 R_2,8 single bonds in these configurations. The reason for that is the weak combination of the frontier orbitals of cyclopropane ring and p-electron donors. We can also find that the eigenvalues of R_2,8 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 3 Computed Bond Lengths(R)^a and NICS Values ^b