A Valence Bond Study of the Bergman Cyclization: Geometric Features, Resonance Energy, and Nucleus-Independent Chemical Shift (NICS) Values

Abstract

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.

1,3,5-Cyclohexatriene captured in computro; the importance of resonance

“…They therefore used two-center bond-distorted orbitals [28] in the one-structure calculation and completely delocalized orbitals in the full benzene calculation [29,30] to arrive at a VRE-value of )65 kcal/mol [26], which fortuitously agrees with previous estimates (cf. [5,[23][24][25][26]).…”

“…The self-repulsion of the structures is now higher making the individual structure energies higher. The locality of the resonating structures was forced in the calculations by Mo et al [5,28] and Shaik et al [26,29] by making use of only partially delocalized p-orbitals. In their approach the aim was just to reduce the delocalization of the orbitals.…”

The Baldwin rules: revised and extended

“…Alabugin and Manoharan estimated the energy cost for alkyne bending along the Bergman cyclization pathway, comparing hex‐3‐ene‐1,5‐diyne with cyclic enediynes. While a significant reactant destabilization (~13 kcal/mol) is observed upon constricting the parent enediyne with the nine‐membered cycle, the acetylene bond breaking was found to be of only minor importance ,…”

Valence bond theory for chemical dynamics

“…More generally it is necessary to allow the orbitals to delocalize onto neighboring centers to obtain accurate results without ionic terms 61–65, 87, 95…”

“…The present essay will start in next section with some remarks on multireference systems and on localized and delocalized treatments of chemical bonding. This discussion is based both on calculations from the early days of quantum mechanics1, 32–34 and quantum chemistry35, 36 and also on modern computational valence bond theory,13, 37–113 which provides insight into the question of how localized and semilocalized orbitals arise in the treatment of so‐called multireference systems. The section after that presents remarks on the use of VB formalisms and concepts for semiempirical treatments of potential energy surfaces for electronically adiabatic reactions.…”