SHADOWING, RARE EVENTS, AND RUBBER BANDS - A VARIATIONAL VERLET ALGORITHM FOR MOLECULAR-DYNAMICS
SHADOWING, RARE EVENTS, AND RUBBER BANDS - A VARIATIONAL VERLET ALGORITHM FOR MOLECULAR-DYNAMICS
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DOI：
10.1063/1.463163
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发表时间：
1992-08-01
影响因子：
4.4
通讯作者：
WILSON, KR
中科院分区：
文献类型：
--
作者：
GILLILAN, RE;WILSON, KR
我们提出了一个变分实现分子动力学的Verlet算法，这是概念上和计算上的吸引力。 给定一个近似路径，该变分Verlet算法计算接近路径的实际轨迹。我们指定端点条件而不是初始条件，这使得计算具有固定端点的轨迹以及精确周期性轨迹（非线性振动模式）成为可能。 通过简单的符号变换，该方法得到了近似的反应途径。 我们提出了几个应用程序，说明这种替代方法的动力学可以产生不寻常的轨迹，是难以实现的常规手段。 在我们的第一个模型系统中，一个简单的双井，我们研究了看似矛盾的经典力学的阴影引理，它声称，尽管累积的数值误差，导致快速偏离正确的路径，计算的轨迹仍然可以接近一些真实的轨迹系统在一个相对较长的时间段。 我们明确计算这种所谓的阴影轨迹。 我们还研究了异构化事件中的轨迹从一个潜在的交叉到另一个，从简单的线段和动力学上的扰动版本的双势阱获得猜测。 在计算大振幅非线性振动模式时，轨迹中短暂循环运动的闭合回路可以作为初始猜测。 最后，我们用一个稀有气体溶液中的AB+C反应模型来说明计算多自由度分子体系的可行性。 A，B，和C原子的气相反应轨迹，与变分Verlet算法，转化为一个类似的解决方案相轨迹，反之亦然。 这种计算表明，罕见的事件，如在溶液中的反应，可以通过细化扰动或解耦系统的初始路径，这样的事件更容易计算。
We present a variational implementation of the Verlet algorithm for molecular dynamics which is both conceptually and computationally attractive. Given an approximate path, this variational Verlet algorithm computes an actual trajectory close to the path. Instead of initial conditions, we specify end-point conditions, which makes it possible to compute trajectories with fixed end points as well as trajectories that are exactly periodic (nonlinear modes of vibration). With a simple sign change, the method yields approximate reaction pathways. We present several applications which illustrate how this alternative approach to dynamics can yield unusual trajectories that are difficult to attain by conventional means. In our first model system, a simple double well, we examine the seemingly paradoxical shadowing lemma of classical mechanics which claims that, in spite of the cumulative numerical errors which cause rapid deviation from the correct path, a calculated trajectory can still be close to some true trajectory of the system over a relatively long time period. We explicitly calculate such so-called shadowing trajectories. We also study isomerization events in which trajectories cross from one potential well to another, obtaining guesses from simple line segments and from dynamics on a perturbed version of the double-well potential. A closed loop of briefly recurrent motion in a trajectory can serve as an initial guess in the computation of a large-amplitude nonlinear mode of vibration. Finally, we use a model AB+C reaction in rare-gas solution to demonstrate the feasibility of calculations on molecular systems with many degrees of freedom. A gas-phase reactive trajectory of the A, B, and C atoms is, with the variational Verlet algorithm, transformed into a similar solution-phase trajectory and vice versa. This calculation suggests that rare events, such as reactions in solution, may be obtained through refining initial paths of perturbed or decoupled systems where such events are more easily computable.