Csóka József, Hégely Bence, Nagy Péter R, Kállay Mihály
Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary.
HUN-REN-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary.
J Chem Phys. 2024 Mar 28;160(12). doi: 10.1063/5.0194463.
The theory of analytic gradients is presented for the projector-based density functional theory (DFT) embedding approach utilizing the Huzinaga-equation. The advantages of the Huzinaga-equation-based formulation are demonstrated. In particular, it is shown that the projector employed does not appear in the Lagrangian, and the potential risk of numerical problems is avoided at the evaluation of the gradients. The efficient implementation of the analytic gradient theory is presented for approaches where hybrid DFT, second-order Møller-Plesset perturbation theory, or double hybrid DFT are embedded in lower-level DFT environments. To demonstrate the applicability of the method and to gain insight into its accuracy, it is applied to equilibrium geometry optimizations, transition state searches, and potential energy surface scans. Our results show that bond lengths and angles converge rapidly with the size of the embedded system. While providing structural parameters close to high-level quality for the embedded atoms, the embedding approach has the potential to relax the coordinates of the environment as well. Our demonstrations on a 171-atom zeolite and a 570-atom protein system show that the Huzinaga-equation-based embedding can accelerate (double) hybrid gradient computations by an order of magnitude with sufficient active regions and enables affordable force evaluations or geometry optimizations for molecules of hundreds of atoms.
本文提出了基于投影算子的密度泛函理论（DFT）嵌入方法的解析梯度理论，该方法利用了胡齐纳加方程。文中展示了基于胡齐纳加方程公式的优势。特别指出的是，所采用的投影算子不出现在拉格朗日量中，从而在梯度计算时避免了数值问题的潜在风险。对于混合密度泛函理论、二阶莫勒-普莱塞特微扰理论或双混合密度泛函理论嵌入到低层次密度泛函理论环境中的方法，本文给出了解析梯度理论的有效实现方式。为了证明该方法的适用性并深入了解其准确性，将其应用于平衡几何结构优化、过渡态搜索和势能面扫描。我们的结果表明，键长和键角随嵌入体系大小迅速收敛。在为嵌入原子提供接近高水平质量的结构参数的同时，嵌入方法也有潜力使环境坐标得到松弛。我们在一个171个原子的沸石和一个570个原子的蛋白质体系上的演示表明，基于胡齐纳加方程的嵌入方法在有足够活性区域时能将（双）混合梯度计算加速一个数量级，并能对数百个原子的分子进行经济实惠的力计算或几何结构优化。
