Event Information
Minimum Energy and Steepest Descent Path Algorithms for QM/MM Applications
- Abstract:
- A number of new methods are presented to determine the reaction path both for chemical systems where the transition state(TS) is known and for the more complicated case when only the reactant and product are available. To determine the minimum energy path(MEP) without the TS two algorithms are developed.
The first MEP method is a quadratic string method (QSM) which is based on a multiobjective optimization framework. In the method, each point on the MEP is integrated in the descent direction perpendicular to path. Each local integration is done on an approximate quadratic surface with an updated Hessian allowing the algorithm to take many steps between energy and gradient calls. The integration is performed with an adaptive step size solver, which is restricted in length to the trust radius of the approximate Hessian. The full algorithm is shown to be capable of practical superlinear convergence, in contrast to the linear convergence of other methods. The method also eliminates the need for predetermining such parameters as step size and spring constants, and is applicable to reactions with multiple barriers. The method is demonstrated for the Muller Brown potential, a 7-atom Lennard-Jones cluster and the enolation of acetaldehyde to vinyl alcohol.
The second MEP method is referred to as the Sequential Quadratic Programming Method (SQPM). This method is based on minimizing the points representing the path in the subspace perpendicular to the tangent of the path while using a penalty term to prevent kinks from forming. Rather than taking one full step, the minimization is divided into a number of sequential steps on an approximate quadratic surface. The resulting method is shown to be capable of super-linear convergence. However, the emphasis of the algorithm is on its robustness and its ability to determine the reaction mechanism efficiently, from which TS can be easily identified and refined with other methods. To improve the resolution of the path close to the TS, points are clustered close to this region with a reparametrization scheme. The usefulness of the algorithm is demonstrated for the Muller Brown potential, amide hydrolysis and an 89 atom cluster taken from the active site of 4-Oxalocrotonate tautomerase (4-OT) for the reaction which catalyzes 2-oxo-4-hexenedioate to the intermediate 2-hydroxy-2,4-hexadienedioate.
With the TS known we also present a method for integrating the steepest descent path (SDP), which is based on the diagonally implicit Runge-Kutta framework. This is shown to be a general form for constructing stable, efficient steepest descent reaction path integrators, of any order. With this framework tolerance driven, adaptive step-size methods can be constructed by embedding methods to obtain error estimates of each step without additional computational cost. There are many embedded and non-embedded, diagonally implicit Runge-Kutta methods available from the numerical analysis literature and these are reviewed for orders 2,3 and 4. New embedded methods are also developed which are tailored to the application of reaction path following. All integrators are summarized and compared for three systems.
Ph.D. Dissertation Defense Seminar
Student Exams Seminar