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A Mechanical String Model of Adiabatic Chemical Reactions
The paper deals with the mathematical description of adiabatic chemical reactions by reaction paths. The main subject is a new reaction path concept which is based on a mechanical reaction model (Chap. 4). The reaction path which results from the model differs from the known reaction paths in the following points: (i) It possesses a clear physical meaning, (ii) it starts at the educt-minimizer, (iii) its initial direction is determined by a vibrational mode of the educt-molecule and (iv) it admits to determine the points where the reactive domain is left/entered in a simple manner. Each point of the path is associated with a quasi-stationary solution of an equation of motion.
A numerical procedure for following the reaction path is proposed (Chap. 5). The procedure requires only the gradient of the energy function and the Hessian matrix at the initial point (educt-minimizer). In the last chapter (Chap. 6) the results of some path tracings are reported.
In Chap. 3 the reaction path concept is discussed against the background of the Mountain-Pass Theorem. Chap. 2 deals with molecular systems from a mathematical point of view. In particular, the configuration space and some subspaces which simplify the mathematical treatment are studied and some theorems pertaining to the consequences of the invariance of the potential energy with respect to overall translation/rotation are proven.