Department of Chemistry, Columbia University, New York, New York10027, United States.
College of Chemistry, University of California, Berkeley, California94720, United States.
J Chem Theory Comput. 2022 Dec 13;18(12):7336-7349. doi: 10.1021/acs.jctc.2c00742. Epub 2022 Dec 2.
In this work, we developed and showcased the occ-RI-K algorithm to compute the exact exchange contribution in density functional calculations of solids near the basis set limit. Within the Gaussian planewave (GPW) density fitting, our algorithm achieves a 1-2 orders of magnitude speedup compared to conventional GPW algorithms. Since our algorithm is well suited for simulations with large basis sets, we applied it to 12 hybrid density functionals with pseudopotentials and a large uncontracted basis set to assess their performance on band gaps of 25 simple solids near the basis set limit. The largest calculation performed in this work involves 16 electrons and 350 basis functions in the unit cell utilizing a 6 × 6 × 6 -mesh. With 20-27% exact exchange, global hybrid functionals (B3LYP, PBE0, revPBE0, B97-3, SCAN0) perform similarly with a root-mean-square deviation (RMSD) of 0.61-0.77 eV, while other global hybrid functionals such as M06-2X (2.02 eV) and MN15 (1.05 eV) show higher RMSD due to their increased fraction of exact exchange. A short-range hybrid functional, HSE achieves a similar RMSD (0.76 eV) but shows a notable underestimation of band gaps due to the complete lack of long-range exchange. We found that two combinatorially optimized range-separated hybrid functionals, ωB97X-rV (3.94 eV) and ωB97M-rV (3.40 eV), and the two other range-separated hybrid functionals, CAM-B3LYP (2.41 eV) and CAM-QTP01 (4.16 eV), significantly overestimate the band gap because of their high fraction of long-range exact exchange. Given the failure of ωB97X-rV and ωB97M-rV, we have yet to find a density functional that offers consistent performance for both molecules and solids. Our algorithm development and density functional assessment will serve as a stepping stone toward developing more accurate hybrid functionals and applying them to practical applications.
在这项工作中，我们开发并展示了 occ-RI-K 算法，以计算固体在基组极限附近的密度泛函计算中的精确交换贡献。在高斯平面波 (GPW) 密度拟合中，与传统的 GPW 算法相比，我们的算法实现了 1-2 个数量级的加速。由于我们的算法非常适合具有大基组的模拟，我们将其应用于 12 种带有赝势和大非收缩基组的混合密度泛函，以评估它们在基组极限附近 25 种简单固体的能带隙中的性能。这项工作中进行的最大计算涉及到单位晶胞中的 16 个电子和 350 个基函数，使用的是 6×6×6 网格。具有 20-27%的精确交换，全局混合泛函（B3LYP、PBE0、revPBE0、B97-3、SCAN0）的表现类似，均方根偏差（RMSD）为 0.61-0.77eV，而其他全局混合泛函，如 M06-2X（2.02eV）和 MN15（1.05eV），由于精确交换的比例增加，RMSD 更高。短程混合泛函 HSE 达到类似的 RMSD（0.76eV），但由于完全缺乏远程交换，导致能带隙明显低估。我们发现，两种组合优化的范围分离混合泛函，ωB97X-rV（3.94eV）和 ωB97M-rV（3.40eV），以及另外两种范围分离混合泛函，CAM-B3LYP（2.41eV）和 CAM-QTP01（4.16eV），由于其远程精确交换的比例很高，因此大大高估了能带隙。鉴于 ωB97X-rV 和 ωB97M-rV 的失败，我们还没有找到一种既能在分子又能在固体中表现一致的密度泛函。我们的算法开发和密度泛函评估将为开发更准确的混合泛函并将其应用于实际应用提供一个起点。
