Prediction of approximate transition states by Bell-Evans-Polanyi principle:: I

We propose a specific mathematical model of the Bell-Evans-Polanyi principle (BEP) to locate approximate transition structures of elementary reactions. The BEP adiabatic energy surface is built as a combination of three quadratic energy surfaces. Two of these quadratic energy surfaces are associated with the reactants and products, whereas the third one is associated with the crossing point energy minimum resulting from the intersection of the reactant and product quadratic energy surfaces. In this way, the resonance energy terms are taken into account. The resulting approximate transition structure and the corresponding Hessian matrix can be used as an initial geometry and a Hessian matrix to locate and optimize the true transition state on the real potential energy surface. In addition, the method provides a simple way to analyze the transition in terms of the contribution weights of the reactants and products. This model is illustrated by different numerical examples, such as the analytical Muller-Brown potential energy surface, the ring opening of cyclopropyl radical, the rearrangement of trans-hydroxycarbene to formaldehyde, and the rearrangement of bicyclo[3.1.0]hex-3-en-2-il radical to cyclohexadienyl radical. (C) 1999 John Wiley & Sons, Inc.