Local integrals and their globally connected invariant structure in phase space giving rise to a promoting mode of chemical reaction

Abstract

We develop a method to extract local integrals, that is, integrals defined locally in the linear regime of an arbitrary point in phase space. The individual integral represents a vibrational mode. We also propose an index that quantifies the extent of connection between neighboring local integrals. Those pieces that are smoothly connected over a wide range represent a global structure of phase space. With a six-atomic Lennard-Jones cluster, we show that it is possible to identify which vibrational mode in the potential basin correlates smoothly to that in the area of transition state, which is nothing but a reactive mode. As an application of the method, we attempt to enhance the structural transition by exciting the reactive mode thus found. This method works successfully as shown in numerical calculations.

A new method to improve validity range of Lie canonical perturbation theory: with a central focus on a concept of non-blow-up region

“…We demonstrated our method in the two systems and showed that the actions constructed by our method have larger validity ranges than those by the conventional ones and our previous method proposed in [1,2]. Previously, Padé approximations have also been used to improve validity ranges of LCPT [81][82][83][84][85][86]. Empirically, these approximations work well and poles of the Padé approximation tend to clump together in the regions where chaotic motion is observed, such as separatrices or other chaotic regions [81,84].…”