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Theoretical implications involved in the DDRP method

机译:DDRP方法涉及的理论含义

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The aim of this paper is to prove that safe success in finding reaction paths (RPs) can only be expected from global path-determining methods. Some extensions of the mathematical arguments leading to the introduction of the DDRP (dynamically defined reaction path) method have been sketched. Four cases involving relaxation of analyticity, variability of the gradient field, minimum energy (reaction) paths (MEPs) and "golf pocket holes" on the potential energy surface (PES), and the rather strange consequences of the main theorem of the DDRP method giving a rigorous mathematical basis to chemical intuition in reaction kinetics have been discussed. The discussions show that the DDRP method - when changing the conditions and parameters - may, in essence, involve all other global methods. It has been shown that the DDRP method works in a stable way even for non-analytic though smooth energy functions; moreover, the gradient field can be replaced by other vector fields resulting in better convergence to the reaction path. As a by-product, the question of the existence of MEPs can safely be handled and golf pocket holes are constructed on the PES in order to prove that local methods have chance to search faithfully the RPs in complicated systems only if the energy function can be restored from its arbitrarily small pieces.
机译:本文的目的是证明只能通过全局路径确定方法来期望成功找到反应路径(RP)。已经勾勒了导致引入DDRP(动态定义的反应路径)方法的数学论证的一些扩展。涉及解析松弛,梯度场可变性,最小能量(反应)路径(MEP)和势能表面(PES)上的“高尔夫球窝”的四个案例,以及DDRP方法的主要定理的相当奇怪的后果为反应动力学中的化学直觉提供了严格的数学基础。讨论表明,DDRP方法-更改条件和参数时-本质上可能涉及所有其他全局方法。已经证明,即使对于非解析但平滑的能量函数,DDRP方法也可以稳定地工作。此外,梯度场可以用其他矢量场代替,从而更好地收敛到反应路径。作为副产品,可以安全地解决MEP的存在问题,并在PES上构造高尔夫球口袋孔,以证明只有在能量函数为零的情况下,局部方法才有机会忠实地搜索复杂系统中的RP。从其任意小的碎片恢复。

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