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Abstract：
In this work, we propose a multi-level protocol for routine theoretical studies of chemical reaction mechanisms. The initial reaction paths of our investigated systems are sampled using the Nudged Elastic Band (NEB) method driven by a cheap electronic structure method. Forces recalculated at the more accurate electronic structure theory for a set of points on the path are fitted with a machine learning technique (in our case symmetric gradient domain machine learning or sGDML) to produce a semi-local reactive potential energy surface (PES), embracing reactants, products and transition state (TS) regions. This approach has been successfully applied to a unimolecular (Bergman cyclization of enediyne) and a bimolecular (SN2 substitution) reaction. In particular, we demonstrate that with only 50 to 150 energy-force evaluations with the accurate reference methods (here complete-active-space self-consistent field, CASSCF, and coupled-cluster singles and doubles, CCSD) it is possible to construct a semi-local PES giving qualitative agreement for stationary-point geometries, intrinsic reaction coordinates and barriers. Furthermore, we find a qualitative agreement in vibrational frequencies and reaction rate coefficients. The key aspect of the method\'s performance is its multi-level nature, which not only saves computational effort but also allows extracting meaningful information along the reaction path, characterized by zero gradients in all but one direction. Agnostic to the nature of the TS and computationally economic, the protocol can be readily automated and routinely used for mechanistic reaction studies.
摘要：
在这项工作中,我们提出了一个多层次的协议，用于化学反应机理的常规理论研究。我们研究的系统的初始反应路径是使用廉价的电子结构方法驱动的微动弹性带（NEB）方法采样的。用机器学习技术（在我们的例子中，对称梯度域机器学习或sGDML）以更精确的电子结构理论为路径上的一组点重新计算的力，以产生半局部无功势能面（PES），拥抱反应物，产品和过渡状态(TS)区域。该方法已成功应用于单分子（烯二炔的Bergman环化）和双分子（SN2取代）反应。特别是,我们证明，只有50到150个能量力评估与精确的参考方法（这里是完全活动空间自洽场，CASCF,和耦合集群单打和双打，CCSD）可以构造半局部PES，从而为固定点几何形状提供定性协议，内在反应坐标和障碍。此外，我们发现振动频率和反应速率系数在质量上是一致的。该方法性能的关键方面是其多层次的性质，这不仅节省了计算量，而且允许沿着反应路径提取有意义的信息，除一个方向外，所有方向的梯度为零。对TS的性质和计算经济不了解，该方案可以很容易地自动化，并常规用于机械反应研究。
