Steepest descent reaction paths, potential

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. 

In developing an ab initio PES for a chemical reaction in terms of a single reaction path potential, we first located the stationary points on the PES, then followed the reaction path by the steepest descent or distinguished coordinate methods, then chose coordinates, natural collision coordinates or internals, and finally expressed the PES as a series expansion about the... 

Fig. 16 (a) R (D + RX) and P (D,+ + R + X ) zero-order potential energy surfaces. Rc and Pc are the caged systems, (b) Projection of the steepest descent paths on the X-Y plane J, transition state of the photoinduced reaction j, transition state of the ground state reaction W, point where the photoinduced reaction path crosses the intersection between the R and P zero-order surfaces R ., caged reactant system, (c) Oscillatory descent from W to J on the upper first-order potential energy surface obtained from the R and P zero-order surfaces. 

At the transition state the reaction coordinate is defined to be in the direction of the one normal coordinate which has a negative eigenvalue. Fukui (22) suggested that the reaction coordinate be defined as the line of steepest descents from the transition state to reactant or product regions on the potential surface. However, this definition fails to acknowledge the non-orthogonality of the internal coordinates and it would appear more satisfactory to define the reaction coordinate with respect to normal coordinates Q for all points on its path so that the line of steepest descent will be that for which (9r/9(2r) is a maximum (correspondingly all other derivatives (9V/ds r will be zero). 

The choice of reaction path definition used as the reference for such a constrained dynamics is arbitrary any path may be used in practice. However, a natural choice in order to ensure that the simulation moves along the bottom of the potential energy valley connecting reactants/products with TS is the intrinsic reaction path (IRP) of Fukui.46,47 IRP by definition goes along the bottom of such a valley. IRP simply corresponds to a steepest descent path in a mass-weighted coordinates ... 

Carpenter and Borden made two important conclusions that raise significant concerns about the traditional physical organic notions of reaction mechanisms. First, nonstatistical dynamics can occur even when intermediates exist in relatively deep potential energy wells, not just on flat caldera-like surfaces. Second, multiple products can be formed from crossing a single TS. The steepest descent path from a TS can only link to a single product, but reactions can follow nonsteepest descent paths that reach different products. 

The most common assumption is one of a reaction path in hyperspace (Miller et al. 1980). A saddle point on the PES is found and the steepest descent path (in mass-weighted coordinates) from this saddle point to reactants and products is defined as the reaction path. The information needed, except for the path and the energies along it, is the local quadratic PES for motion perpendicular to the path. The reaction-path Hamiltonian is only a weakly local method since it can be viewed as an approximation to the full PES and since it is possible to use any of the previously defined global-dynamical methods with this potential. However, it is local because the approximate PES restricts motion to lie around the reaction path. The utility of a reaction-path formalism involves convenient approximations to the dynamics which can be made with the formalism as a starting point. 

Potential Energy Minima and Saddle Points Distinguished Reaction Cowdinate (DRO Steepest Descent Path (SDP)... 

This paper reviews recent (and current) work in my research group which is aimed at developing practical methods for describing reaction dynamics in polyatomic systems in as ab initio a framework as possible. To overcome the dimensionality dilemma of polyatomic systems—i.e., the fact that the potential energy surface depends on 3N-6 internal coordinates for an N atom system—we have developed dynamical models based on the intrinsic reaction path", i.e., the steepest descent path which connects reactants and products through the transition state (i.e., saddle point) on the potential energy surface. ... 

Fig. 13. The computational methods used for constructing a photochemical reaction path. The full path is computed by joining different MEPs, each one providing information on a specific part of the excited- or ground-state potential-energy surface. The IRD method is used to compute the steepest relaxation directions departing from the FC point (excited-state relaxation) or Cl (ground-state relaxation). The IRC method is used to compute the steepest-descent line defined by the computed IRDs. The CIO method is used to compute the lowest-energy conical intersection point directly. With TSO we indicate the standard transition structure optimization procedure.

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