The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wave-function theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a given basis set. The derivation of the exact equations are based on the Levy-Lieb formulation of DFT, which helps us to define a complementary functional which corrects uniquely for the basis-set error of WFT. The coupling of DFT and WFT is done through the definition of a real-space representation of the electron-electron Coulomb operator projected in a one-particle basis set. Such an effective interaction has the particularity to coincide with the exact electron-electron interaction in the limit of a complete basis set, and to be finite at the electron-electron coalescence point when the basis set is incomplete. The non-diverging character of the effective interaction allows one to define a mapping with the long-range interaction used in the context of range-separated DFT and to design practical approximations for the unknown complementary functional. Here, a local-density approximation is proposed for both full-configuration-interaction (FCI) and selected configuration-interaction approaches. Our theory is numerically tested to compute total energies and ionization potentials for a series of atomic systems. The results clearly show that the DFT correction drastically improves the basis-set convergence of both the total energies and the energy differences. For instance, a sub kcal/mol accuracy is obtained from the aug-cc-pVTZ basis set with the method proposed here when an aug-cc-pV5Z basis set barely reaches such a level of accuracy at the near FCI level.
Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory
提出了一种基于插值可分密度拟合的张量超压缩（THC）分解方法。我们说明算法的细节，以实现这一目标的框架内，贝克的原子为中心的正交网格。单个ISDF参数$c_\text{ISDF}$控制精度和成本之间的权衡。具体地，$c_\text{ISDF}$设置在THC中使用的内插点的数量，$N_\text{IP} = c_\text{ISDF}\times N_\text{X}$，其中$N_\text{X}$是辅助基函数的数量。结合身份解析（RI）技术，我们开发并研究了用于Hartree-Fock和范围分离混合体（例如，$ω$ B 97 X-V）和四次标度二阶和三阶Møller-Plesset理论（MP2和MP3）。这些算法在W 4 -11热化学（原子化能）集和A24非共价相互作用基准集与标准Dunning基组（cc-pVDZ、cc-pVTZ、aug-cc-pVDZ和aug-cc-pVTZ）上进行了评价。我们证明了收敛的THC-RI算法的数值精确RI结果使用ISDF点。在此基础上，我们对每个基组和方法的$c_\text{ISDF}$提出了建议。我们还演示了THC-RI精确交换和MP2对于水团簇和$\text{C}_{20}$等大型系统的实用性。我们强调，更多的挑战等待在获得准确的和数值稳定的THC分解波函数振幅，以及在大基组的虚拟轨道所跨越的空间，并实现稀疏意识的THC-RI算法。
Systematically Improvable Numerical Atomic Orbital Basis Using Contracted Truncated Spherical Waves
Institute of Microelectronics, Chinese Academy of Sciences（中国科学院微电子研究所）；AI for Science Institute（人工智能科学研究所）；DP Technology（北京智源人工智能研究院）；HEDPS, CAPT, School of Mechanics and Engineering Science and School of Physics , Peking University（北京大学力学与工程科学学院、物理学院）
Rigorous ab initio quantum embedding for quantum chemistry using Green's function theory: screened interaction, non-local self-energy relaxation, orbital basis, and chemical accuracy
Smoothed truncated Coulomb potential for periodic Gaussian-basis Hartree--Fock exchange
Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算机科学联合中心）；Department of Mathematics, University of Maryland（马里兰大学数学系）；Department of Chemistry and Biochemistry, University of Maryland（马里兰大学化学与生物化学系）；Institute for Physical Science and Technology, University of Maryland（马里兰大学物理科学与技术研究所）
