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Transition state ensemble optimization for reactions of arbitrary complexity.

In the present work, we use Variational Transition State Theory (VTST) to develop a practical method for transition state ensemble optimization by looking for an optimal hyperplanar dividing surface in a space of meaningful trial collective variables. These might be interatomic distances, angles, electrostatic potentials, etc. Restrained molecular dynamics simulations are used to obtain on-the-fly estimates of ensemble averages that guide the variations of the hyperplane maximizing the transmission coefficient. A central result of our work is an expression that quantitatively estimates the importance of the coordinates used for the localization of the transition state ensemble. Starting from an arbitrarily large set of trial coordinates, one can distinguish those that are indeed essential for the advance of the reaction. This facilitates the use of VTST as a practical theory to study reaction mechanisms of complex processes. The technique was applied to the reaction catalyzed by an isochorismate pyruvate lyase. This reaction involves two simultaneous chemical steps and has a shallow transition state region, making it challenging to define a good reaction coordinate. Nevertheless, the hyperplanar transition state optimized in the space of 18 geometrical coordinates provides a transmission coefficient of 0.8 and a committor histogram well-peaked about 0.5, proving the strength of the method. We have also tested the approach with the study of the NaCl dissociation in aqueous solution, a stringest test for a method based on transition state theory. We were able to find essential degrees of freedom consistent with the previous studies and to improve the transmission coefficient with respect to the value obtained using solely the NaCl distance as the reaction coordinate.