Zhu Xiaolei, Thompson Keiran C, Martínez Todd J
Department of Chemistry, Stanford University, Stanford, California 94305, USA.
J Chem Phys. 2019 Apr 28;150(16):164103. doi: 10.1063/1.5090303.
The development of high throughput reaction discovery methods such as the ab initio nanoreactor demands massive numbers of reaction rate calculations through the optimization of minimum energy reaction paths. These are often generated from interpolations between the reactant and product endpoint geometries. Unfortunately, straightforward interpolation in Cartesian coordinates often leads to poor approximations that lead to slow convergence. In this work, we reformulate the problem of interpolation between endpoint geometries as a search for the geodesic curve on a Riemannian manifold. We show that the perceived performance difference of interpolation methods in different coordinates is the result of an implicit metric change. Accounting for the metric explicitly allows us to obtain good results in Cartesian coordinates, bypassing the difficulties caused by redundant coordinates. Using only geometric information, we are able to generate paths from reactants to products which are remarkably close to the true minimum energy path. We show that these geodesic paths are excellent starting guesses for minimum energy path algorithms.
诸如从头算纳米反应器等高通量反应发现方法的发展，需要通过优化最小能量反应路径来进行大量的反应速率计算。这些路径通常是通过反应物和产物端点几何结构之间的插值生成的。不幸的是，在笛卡尔坐标中直接进行插值往往会导致近似效果不佳，进而导致收敛缓慢。在这项工作中，我们将端点几何结构之间的插值问题重新表述为在黎曼流形上寻找测地线曲线。我们表明，不同坐标下插值方法的性能差异是隐式度量变化的结果。明确考虑度量使我们能够在笛卡尔坐标中获得良好的结果，绕过冗余坐标带来的困难。仅使用几何信息，我们就能生成从反应物到产物的路径，这些路径非常接近真实的最小能量路径。我们表明，这些测地线路径是最小能量路径算法的极佳初始猜测。
