A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the product densities, modeling their contribution to the exchange and second-order correlation energy, and a simple weighted error measure is minimized. Generally contracted Gaussian auxiliary basis sets are optimized to match the wavefunction basis sets [D. N. Laikov, Theor. Chem. Acc. 138, 40 (2019)] for all 102 elements in a scalar-relativistic approximation [D. N. Laikov, J. Chem. Phys. 150, 061103 (2019)].

中文翻译：

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分子二电子积分近似的原子密度拟合基函数优化。

考虑到精度和数值稳定性之间的平衡，设计了优化原子密度拟合基函数的一般程序。给定单电子波函数和能量，将权重分配给乘积密度，对它们对交换和二阶相关能的贡献进行建模，并最小化简单的加权误差度量。对一般收缩的高斯辅助基集进行了优化，以匹配波函数基集[DN Laikov，Theor。化学 累积 138，40（2019）]为在一个标量相对论近似[DN Laikov，J.化学所有102层的元件。物理 150，061103（2019）]。