Software for Chemistry and Materials NV, NL-1081HV Amsterdam, The Netherlands.
Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands.
J Chem Theory Comput. 2023 Mar 14;19(5):1499-1516. doi: 10.1021/acs.jctc.2c01201. Epub 2023 Feb 14.
Pair atomic density fitting (PADF) has been identified as a promising strategy to reduce the scaling with system size of quantum chemical methods for the calculation of the correlation energy like the direct random-phase approximation (RPA) or second-order Møller-Plesset perturbation theory (MP2). PADF can however introduce large errors in correlation energies as the two-electron interaction energy is not guaranteed to be bounded from below. This issue can be partially alleviated by using very large fit sets, but this comes at the price of reduced efficiency and having to deal with near-linear dependencies in the fit set. One posibility is to use global density fitting (DF), but in this work, we introduce an alternative methodology to overcome this problem that preserves the intrinsically favorable scaling of PADF. We first regularize the Fock matrix by projecting out parts of the basis set which gives rise to orbital products that are hard to describe by PADF. After having thus obtained a reliable self-consistent field solution, we then also apply this projector to the orbital coefficient matrix to improve the precision of PADF-MP2 and PADF-RPA. We systematically assess the accuracy of this new approach in a numerical atomic orbital framework using Slater type orbitals (STO) and correlation consistent Gaussian type basis sets up to quintuple-ζ quality for systems with more than 200 atoms. For the small and medium systems in the S66 database we show the maximum deviation of PADF-MP2 and PADF-RPA relative correlation energies to DF-MP2 and DF-RPA reference results to be 0.07 and 0.14 kcal/mol, respectively. When the new projector method is used, the errors only slightly increase for large molecules and also when moderately sized fit sets are used the resulting errors are well under control. Finally, we demonstrate the computational efficiency of our algorithm by calculating the interaction energies of large, non-covalently bound complexes with more than 1000 atoms and 20000 atomic orbitals at the RPA@PBE/CC-pVTZ level of theory.
对原子密度拟合（PADF）的研究表明，这是一种很有前途的策略，可以降低直接随机相位近似（RPA）或二阶 Møller-Plesset 微扰理论（MP2）等计算相关能量的量子化学方法的系统规模缩放。然而，PADF 可能会在相关能量中引入较大的误差，因为不能保证双电子相互作用能有下界。通过使用非常大的拟合集可以部分缓解这个问题，但这是以降低效率和处理拟合集中的近似线性依赖关系为代价的。一种可能性是使用全局密度拟合（DF），但在这项工作中，我们引入了一种替代方法来克服这个问题，同时保留了 PADF 固有的有利缩放。我们首先通过投影基组的一部分来正则化 Fock 矩阵，这部分基组导致难以用 PADF 描述的轨道乘积。因此，获得可靠的自洽场解后，我们还将该投影器应用于轨道系数矩阵，以提高 PADF-MP2 和 PADF-RPA 的精度。我们在数值原子轨道框架中使用 Slater 型轨道（STO）和相关一致的高斯型基组，系统规模达到 200 个原子以上的 quintuple-ζ 质量，系统地评估了这种新方法的准确性。对于 S66 数据库中的小和中型系统，我们表明 PADF-MP2 和 PADF-RPA 相对于 DF-MP2 和 DF-RPA 参考结果的最大相对相关能量偏差分别为 0.07 和 0.14 kcal/mol。当使用新的投影器方法时，对于大分子，误差仅略有增加，并且当使用适度大小的拟合集时，结果误差也得到很好的控制。最后，我们通过在 RPA@PBE/CC-pVTZ 理论水平上计算具有超过 1000 个原子和 20000 个原子轨道的大非共价键复合物的相互作用能，展示了我们算法的计算效率。
