Kumar Anup, DeGregorio Nicole, Iyengar Srinivasan S
Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States.
J Chem Theory Comput. 2021 Nov 9;17(11):6671-6690. doi: 10.1021/acs.jctc.1c00065. Epub 2021 Oct 8.
We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree-Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graph-theoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree-Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.
我们提出了一种基于图论的多拓扑分子碎片化方法，用于计算与后哈特里 - 福克理论水平相符但成本为密度泛函理论的多维势能面。分子聚集体被粗粒化为一组图论节点，然后用边连接起来，以表示一组局部相互作用的子系统，其相互作用可达任意阶。每个子系统在两个电子结构理论水平上进行处理，结果用于构建嵌入在ONIOM方案中的多体展开式。这些展开式随着子系统的多体阶数（或图形秩）迅速收敛，并能准确有效地捕捉多体相互作用。然而，在分子构型空间中可能会定义多个图，从而产生多个碎片化拓扑结构，这可能出现在构象采样过程中，或者源于反应、键断裂和键形成等事件。考虑到所需的电子结构计算数量，获得由此产生的势能面是一个指数缩放问题。我们在变分方案中利用一族图论表示，以降低成本获得多维势能面。随着多体相互作用阶数的增加，图论展开式的快速收敛减轻了计算势能面的指数缩放成本，因为与整个系统相比，只需要使用包含较少量子核自由度的分子片段。这是因为片段子系统采样构象空间的维度比整个分子构型空间小得多。此外，我们还引入了一种基于物理定义标准的多维聚类算法，将能量计算的数量减少几个数量级。所测试的分子系统包括质子化水线中的耦合质子运动。所获得的势能面和多维核本征态与显式后哈特里 - 福克计算结果非常吻合，而随着量子核维度数量的增加，后者的计算变得难以实现。这里的进展为这个重要的化学物理问题提供了一种严格而有效的替代方法。
