High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions

密歇根州立大学的Piotr Piecuch得到了化学部化学理论、模型和计算方法项目的支持，以开发一种全新的方法来求解多粒子薛定谔方程。这种方法是解释电子在原子和分子中运动的关键。通过了解这一动议的细节，皮库赫和他的团队可以精确地确定打破化学键并将反应物转化为产品所需的能量。准确进行这些计算的能力最终将有助于设计新材料、更好的催化剂和更高效的能源。新方法对许多小能量贡献进行重复的随机测试，并保留那些被发现最重要的能量贡献。这种方法将高精度方法的计算成本降低了数量级。一旦完全开发，这些方法将通过开源机制与社区共享。这些活动得出的结果正被用于教学课程，并通过出版物、研讨会和会议报告进行传播。这些想法为皮库奇小组的成员提供了走在物理科学前沿的积极训练经验。这项研究解决了电子结构理论中的关键挑战之一，即开发实用的和系统可改进的从头计算方案，旨在准确描述分子能量学。人们普遍认为，基于耦合团簇理论的尺寸扩展方法是解决这一挑战的优秀候选方法。然而，众所周知，要在不遇到高阶耦合集群方案令人望而却步的计算成本的情况下，结合实现定量描述所需的集群算子的高于两体的组件，已经是出了名的困难。所提出的方法解决了这个问题，即使在电子类简并和高于对的激发变得重要的情况下，人们也可以以很小的计算成本获得相当于高水平耦合团簇计算的精确能量学。通过将确定性形式(简称CC(P；Q))与随机组态相互作用和耦合簇蒙特卡罗方法相结合，保留了传统单参考计算的黑箱特性。形式和算法的进步以及高效的计算机实现将伴随着与光谱学、化学反应机制和动力学以及催化有关的分子势能面的计算。这项工作为研究生和博士后研究员提供了重要的培训，正在开发的项目将与更广泛的理论界广泛分享。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Piotr Piecuch of Michigan State University is supported by an award from the Chemical Theory, Models and Computational Methods program in the Chemistry Division to develop a radically new approach to solving the many-particle Schrodinger equation. This method holds the key to explaining the motion of electrons in atoms and molecules. By understanding the details of this motion, Piecuch and his group can precisely determine the amounts of energy needed to break chemical bonds and transform reactants into products. The ability to do these calculations accurately will ultimately aid in the design of new materials, better catalysts, and more efficient energy sources. The new approach uses repeated random tests of many small energy contributions and retains those found to be most important. This approach reduces the computational costs of high-accuracy methods by orders of magnitude. Once fully developed, the methods will be shared with the community via open-source mechanisms. Findings resulting from the activities are being used in teaching courses and communicated through publications, seminars, and conference presentations. These ideas provide positive training experiences in the forefront of the physical sciences for members of the Piecuch group. This research addresses one of the key challenges in electronic structure theory, namely the development of practical and systematically improvable ab initio computational schemes aimed at an accurate description of molecular energetics. It is widely accepted that size extensive methods based on the coupled-cluster theory are excellent candidates for addressing this challenge. However, it has been notoriously difficult to incorporate higher-than two-body components of the cluster operator, needed to achieve a quantitative description, without running into prohibitive computational costs of higher-order coupled-cluster schemes. The proposed methodology solves the problem, allowing one to obtain accurate energetics equivalent to high-level coupled-cluster calculations, even when electronic quasi-degeneracies and higher-than pair excitations become significant, at a small fraction of the computational cost. It also preserves the black-box character of conventional single-reference computations, by fusing the deterministic formalism, abbreviated as CC(P;Q) with the stochastic configuration interaction and coupled-cluster Monte Carlo approaches. The formal and algorithmic advances and efficient computer implementations will be accompanied by calculations of molecular potential energy surfaces relevant to spectroscopy, chemical reaction mechanisms and dynamics, and catalysis. The work provides important training for graduate students and postdoctoral fellows and the programs being developed will be widely shared with the broader theoretical community.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.