Department of Chemistry - Ångström Laboratory, Uppsala University, Box 538, 751 21 Uppsala, Sweden.
Department of Computing Science, Umeå University, Umeå SE-901 87, Sweden.
J Chem Theory Comput. 2021 Mar 9;17(3):1771-1781. doi: 10.1021/acs.jctc.0c01156. Epub 2021 Feb 19.
The Curvature Constrained Splines (CCS) methodology has been used for fitting repulsive potentials to be used in SCC-DFTB calculations. The benefit of using CCS is that the actual fitting of the repulsive potential is performed through quadratic programming on a convex objective function. This guarantees a unique (for strictly convex) and optimum two-body repulsive potential in a single shot, thereby making the parametrization process robust, and with minimal human effort. Furthermore, the constraints in CCS give the user control to tune the shape of the repulsive potential based on prior knowledge about the system in question. Herein, we developed the method further with new constraints and the capability to handle sparse data. We used the method to generate accurate repulsive potentials for bulk Si polymorphs and demonstrate that for a given Slater-Koster table, which reproduces the experimental band structure for bulk Si in its ground state, we are unable to find one single two-body repulsive potential that can accurately describe the various bulk polymorphs of silicon in our training set. We further demonstrate that to increase transferability, the repulsive potential needs to be adjusted to account for changes in the chemical environment, here expressed in the form of a coordination number. By training a near-sighted Atomistic Neural Network potential, which includes many-body effects but still essentially within the first-neighbor shell, we can obtain full transferability for SCC-DFTB in terms of describing the energetics of different Si polymorphs.
曲率约束样条 (CCS) 方法已被用于拟合排斥势，以用于 SCC-DFTB 计算。使用 CCS 的好处是，排斥势的实际拟合是通过二次规划在凸目标函数上进行的。这保证了在单次操作中具有独特的（对于严格凸的）和最优的二体排斥势，从而使参数化过程具有鲁棒性，并且需要的人工努力最小。此外，CCS 中的约束使用户能够根据有关所讨论系统的先验知识来调整排斥势的形状。在此，我们进一步开发了具有新约束和处理稀疏数据能力的方法。我们使用该方法为体硅多型体生成了准确的排斥势，并证明对于给定的 Slater-Koster 表，该表再现了体硅基态的实验能带结构，我们无法找到一个单一的二体排斥势可以准确描述我们训练集中的各种体硅多型体。我们进一步证明，为了提高可转移性，需要调整排斥势以适应化学环境的变化，这里以配位数的形式表示。通过训练一种近视原子神经网络势，它包含多体效应，但仍然基本上在第一近邻壳内，我们可以获得 SCC-DFTB 在描述不同硅多型体的能量学方面的完全可转移性。
