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Pandey P., Naik S., Keshavamurthy S.
Classical and Quantum Dynamical Manifestations of Index-2 Saddles: Concerted Versus Sequential Reaction Mechanisms
2021, vol. 26, no. 2, pp. 165-182
The presence of higher-index saddles on a multidimensional potential energy surface is usually assumed to be of little significance in chemical reaction dynamics. Such a viewpoint requires careful reconsideration, thanks to elegant experiments and novel theoretical approaches that have come about in recent years. In this work, we perform a detailed classical and quantum dynamical study of a model two-degree-of-freedom Hamiltonian, which captures the essence of the debate regarding the dominance of a concerted or a stepwise reaction mechanism. We show that the ultrafast shift of the mechanism from a concerted to a stepwise one is essentially a classical dynamical effect. In addition, due to the classical phase space being a mixture of regular and chaotic dynamics, it is possible to have a rich variety of dynamical behavior, including a Murrell – Laidler type mechanism, even at energies sufficiently above that of the index-2 saddle. We rationalize the dynamical results using an explicit construction of the classical invariant manifolds in the phase space.
Lyu W., Naik S., Wiggins S.
The Role of Depth and Flatness of a Potential Energy Surface in Chemical Reaction Dynamics
2020, vol. 25, no. 5, pp. 453-475
In this study, we analyze how changes in the geometry of a potential energy surface in terms of depth and flatness can affect the reaction dynamics.We formulate depth and flatness in the context of one and two degree-of-freedom (DOF) Hamiltonian normal form for the saddlenode bifurcation and quantify their influence on chemical reaction dynamics [1, 2]. In a recent work, García-Garrido et al.  illustrated how changing the well-depth of a potential energy surface (PES) can lead to a saddle-node bifurcation. They have shown how the geometry of cylindrical manifolds associated with the rank-1 saddle changes en route to the saddle-node bifurcation. Using the formulation presented here, we show how changes in the parameters of the potential energy control the depth and flatness and show their role in the quantitative measures of a chemical reaction. We quantify this role of the depth and flatness by calculating the ratio of the bottleneck width and well width, reaction probability (also known as transition fraction or population fraction), gap time (or first passage time) distribution, and directional flux through the dividing surface (DS) for small to high values of total energy. The results obtained for these quantitative measures are in agreement with the qualitative understanding of the reaction dynamics.