Iyer Gopal R, Whelpley Noah, Tiihonen Juha, Kent Paul R C, Krogel Jaron T, Rubenstein Brenda M
Department of Chemistry, Brown University, Providence, Rhode Island 02912, United States.
Department of Physics, Nanoscience Center, University of Jyväskylä, Jyväskylä 40014, Finland.
J Chem Theory Comput. 2024 Sep 10;20(17):7416-7429. doi: 10.1021/acs.jctc.4c00214. Epub 2024 Aug 22.
The accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH) molecule and the nucleophilic substitution (S2) reaction F + CHF → FCH + F. We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.
准确绘制势能面（PESs）对于我们理解由原子重排介导的众多物理和化学过程至关重要，例如构象变化和化学反应，以及这些过程的热力学和动力学可行性。随机电子结构理论，例如量子蒙特卡罗（QMC）方法，能够进行高精度的总能量计算，原则上可用于构建PES。然而，其随机性质给力和海森矩阵的计算与使用带来了挑战，而在诸如推挤弹性带（NEB）算法及其爬坡图像形式等用于最小能量路径（MEP）和过渡态（TS）识别的算法中，力和海森矩阵通常是必需的。在此，我们提出利用先前为QMC结构优化开发的替代海森矩阵线搜索方法的策略，以在无需随机电子结构理论层面进行力计算的情况下高效识别MEP和TS结构。通过修改替代海森矩阵算法使其在路径正交子空间和鞍点处运行，我们表明可以使用无作用力的QMC方法识别MEP和TS。我们通过两个例子展示了这些策略，即氨（NH）分子的反转以及亲核取代（S2）反应F + CHF → FCH + F。我们使用基于密度泛函理论（DFT）和耦合簇（CCSD、CCSD(T)）的NEB计算验证了我们的结果。然后，我们引入一种混合DFT - QMC方法来计算热力学和动力学量、自由能差、速率常数和平衡常数，该方法纳入了随机优化的结构及其能量，并表明该方案提高了DFT的精度。我们的方法可直接推广到其他系统以及其他同样在计算能量梯度时面临挑战的高精度理论，为以显著降低的计算成本进行高精度的PES映射、过渡态确定以及热力学和动力学计算铺平了道路。
