Qin Xinming, Shang Honghui, Yang Jinlong
Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, China.
Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui, China.
Front Chem. 2023 Jul 27;11:1232425. doi: 10.3389/fchem.2023.1232425. eCollection 2023.
The NAO2GTO scheme provides an efficient way to evaluate the electron repulsion integrals (ERIs) over numerical atomic orbitals (NAOs) with auxiliary Gaussian-type orbitals (GTOs). However, the NAO2GTO fitting will significantly impact the accuracy and convergence of hybrid functional calculations. To address this issue, here we propose to use the fitted orbitals as a new numerical basis to properly handle the mismatch between NAOs and fitted GTOs. We present an efficient and linear-scaling implementation of analytical gradients of Hartree-Fock exchange (HFX) energy for periodic HSE06 calculations with fitted NAOs in the HONPAS package. In our implementation, the ERIs and their derivatives for HFX matrix and forces are evaluated analytically with the auxiliary GTOs, while other terms are calculated using numerically discretized GTOs. Several integral screening techniques are employed to reduce the number of required ERI derivatives. We benchmark the accuracy and efficiency of our implementation and demonstrate that our results of lattice constants, bulk moduli, and band gaps of several typical semiconductors are in good agreement with the experimental values. We also show that the calculation of HFX forces based on a master-worker dynamic parallel scheme has a very high efficiency and scales linearly with respect to system size. Finally, we study the geometry optimization and polaron formation due to an excess electron in rutile TiO by means of HSE06 calculations to further validate the applicability of our implementation.
NAO2GTO方案提供了一种有效的方法，用于评估基于数值原子轨道（NAO）和辅助高斯型轨道（GTO）的电子排斥积分（ERI）。然而，NAO2GTO拟合会显著影响杂化泛函计算的准确性和收敛性。为了解决这个问题，我们在此建议使用拟合轨道作为新的数值基，以妥善处理NAO与拟合GTO之间的不匹配。我们在HONPAS软件包中，针对具有拟合NAO的周期性HSE06计算，给出了哈特里-福克交换（HFX）能量解析梯度的高效线性标度实现。在我们的实现中，利用辅助GTO对HFX矩阵和力的ERI及其导数进行解析评估，而其他项则使用数值离散的GTO进行计算。采用了几种积分筛选技术来减少所需ERI导数的数量。我们对实现的准确性和效率进行了基准测试，并证明了我们计算的几种典型半导体的晶格常数、体模量和带隙结果与实验值吻合良好。我们还表明，基于主从动态并行方案的HFX力计算具有很高的效率，并且相对于系统大小呈线性标度。最后，我们通过HSE06计算研究了金红石TiO中由于多余电子导致的几何结构优化和极化子形成，以进一步验证我们实现的适用性。
