Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA.
NIMBioS, University of Tennessee Knoxville, Knoxville, Tennessee 37996, USA.
J Chem Phys. 2023 Apr 28;158(16). doi: 10.1063/5.0140667.
Recent work [Mirth et al., J. Chem. Phys. 154, 114114 (2021)] has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in 3 N-dimensions. This includes information about all transition paths between local minima (connected by critical points of index ≥1) and allows for differentiation of energy landscapes that may appear similar when considering only the lowest energy pathways (as tracked by other representations, such as disconnectivity graphs, using index 1 critical points). Using the additive nature of the conformational potential energy landscape of n-alkanes, it became apparent that some topological features-such as the number of sublevelset persistence bars-could be proven. This work expands the notion of predictable energy landscape topology to any additive intramolecular energy function on a product space, including the number of sublevelset persistent bars as well as the birth and death times of these topological features. This amounts to a rigorous methodology to predict the relative energies of all topological features of the conformational energy landscape in 3N dimensions (without the need for dimensionality reduction). This approach is demonstrated for branched alkanes of varying complexity and connectivity patterns. More generally, this result explains how the sublevelset persistent homology of an additive energy landscape can be computed from the individual terms comprising that landscape.
最近的工作[米尔思等人，《化学物理杂志》154, 114114（2021）]表明，亚层持久同调为 3N 维能量景观的复杂特征提供了紧凑的表示。这包括关于所有局部极小值（通过指数≥1 的临界点连接）之间的跃迁路径的信息，并允许区分可能看起来相似的能量景观，而仅考虑最低能量途径（如其他表示方法，如使用指数 1 临界点的不连续图）。利用烷烃构象势能景观的可加性质，很明显可以证明一些拓扑特征，例如亚层持久条的数量。这项工作将可预测的能量景观拓扑结构的概念扩展到乘积空间上的任何加性分子内能量函数，包括亚层持久条的数量以及这些拓扑特征的出现和消失时间。这相当于一种严格的方法，可以预测 3N 维构象能量景观中所有拓扑特征的相对能量（无需降维）。该方法针对具有不同复杂度和连接模式的支链烷烃进行了演示。更一般地说，这个结果解释了如何从构成景观的各个项计算加性能量景观的亚层持久同调。
