A valence bond study of the Bergman cyclization: geometric features, resonance energy, and nucleus-independent...

The Bergman cyclization of (Z)-hex-3-ene-1,5-diynes (1, enediynes), which produces pharmacologically important DNA-cleaving biradicals (1,4-benzyne, 2), was studied by using Hartree-Fock (HF) and density-functional theory (DFT) based valence bond (VB) methods (VB-HF and VB-DFT, respectively). We found that only three VB configurations are needed to arrive at results not too far from complete active space [CASSCF(6 x 6)] computations, while the quality of VB-DTF utilizing the same three configurations improves upon CASSCF(6 x 6) analogous to CASPT2. The dominant VB configuration in 1 contributes little to 2, while the most important biradical configuration in 2 plays a negligible role in 1. The avoided crossing of the energy curves of these two configurations along the reaction coordinate leads to the transition state (TS). As a consequence of the shape and position of the crossing section, the changes in geometry and in the electronic wavefunction along the reaction coordinate are non-synchronous; the TS is geometrically approximately 80% product-like and electronically approximately 70% reactant-like. While the pi resonance in the TS is very small, it is large (64.4 kcal mol(-1)) for 2 (cf. benzene=61.5 kcal mol(-1)). As a consequence, substituents operating on the sigma electrons should be much more effective in changing the Bergman reaction cyclization barrier. Furthermore, additional sigma resonance in 2 results in unusually high values for the nucleus-independent chemical shift (NICS, a direct measure for aromaticity). Similarly, the high NICS value of the TS is due mostly to sigma resonance to which the NICS procedure is relatively sensitive.