Steepest descent reaction paths

Page M, Doubleday C and Mclver J W Jr 1990 Following steepest descent reaction paths. The use of higher energy derivatives with ab initio electronic structure methods J. Chem. Phys. 93 5634 and references therein... 

A reaction-path based method is described to obtain information from ab initio quantum chemistry calculations about the dynamics of energy disposal in exothermic unimolecular reactions important in the initiation of detonation in energetic materials. Such detailed information at the microscopic level may be used directly or as input for molecular dynamics simulations to gain insight relevant for the macroscopic processes. The semiclassical method, whieh uses potential energy surface information in the broad vicinity of the steepest descent reaction path, treats a reaction coordinate classically and the vibrational motions perpendicular to the reaction path quantum mechanically. Solution of the time-dependent Schroedinger equation leads to detailed predictions about the energy disposal in exothermic chemical reactions. The method is described and applied to the unimolecular decomposition of methylene nitramine. 

If there was no curvature coupling, motion along the steepest descent reaction path would be uncoupled from the internal vibrational degrees of freedom. 

A great deal of effort has been expended on efficient calculation of the MEP [12,30-32, 41-50]. At the moment, if relatively inexpensive second derivatives are available, the cubic corrected local quadratic method is most efficient otherwise, reasonably efficient gradient-only methods are available [49]. This is an area where methods are still advancing and recently proposed methods may prove to be better still when these methods have been used with dynamical calculations on real ab initio PES [12,43,48, 50]. At this stage some examples of steepest descent reaction paths might be informative. 

Steepest Descent Reaction Paths. The Use of Higher Energy Derivatives with ab Initio Electronic Structure Methods. 

The steepest descent reaction path (see Reaction Path Following) is usually calculated after the transition structure has been located. There are some approaches that calculate both in the same procedure. These methods start with an approximate reaction path represented by a series of structures interpolated between reactants and products. The path is successively improved by a series of relaxation steps. Elber and Karplus refined the path by minimizing the integral of the energy along the path under the constraint of equally spaced points ... 

CLQA = corrected local quadratic approximation DDRP = dynamically defined reaction path DRP = dynamic reaction path ES = Euler stabilization method GS = Gonzalez and Schlegel method IMK = Ishida-Morokuma-Kormomicld method LQA = local quadratic approximation MB = Miillar-Brown method MEP = minimum energy path ODE = ordinary differential equations SDRP = steepest descent reaction path VRl = valley-ridge inflection. 

To describe the steepest descent reaction path, the coordinates along the path, x s) are written as a parametric function of the arc length along the path, s. The path can then be expanded in a Taylor series ... 

Reaction path following methods yield a discrete set of points Xi along the path rather than a continuous function. These points can be found by starting at the transition structure and using numerical methods to solve equation (2), the differential equation that defines the steepest descent reaction path. A variety of numerical methods are available for solving... 

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