One-centre corrected two-electron integrals in inner projection-based integral evaluations

Cholesky decomposition (CD) of the two-electron integrals and the resolution-of-identity (RI) techniques are established inner projection methods to efficiently evaluate two-electron integrals. Both approaches share the notion of an auxiliary basis set as a mean to reduce the scaling. In the past years, the close relationship between the two approaches has fostered developments on how to systematically derive unbiased auxiliary basis sets – atomic CD (aCD) and atomic compact CD (acCD) auxiliary basis sets, different to the precomputed auxiliary basis sets. The accuracy of these approximations in the RI approach can be further improved via an explicit correction of the one-centred two-electron integrals, which is the main object of this research. Correcting the one-centred two-electron integrals directly, which scales linear with system size, is expected to provide a new degree of freedom to the design of auxiliary basis sets. This can either be used to gain faster convergence towards the conventional treatment of the two-electron integrals or as a mean to design lighter auxiliary basis sets while maintaining the same accuracy as of the uncorrected approach. The benchmarks of the one-centre corrections applied to several auxiliary basis set types were investigated in this paper.双电子积分的乔列斯基分解（Cholesky decomposition, CD）与分辨率恒等（resolution-of-identity, RI）技术，是两类用于高效计算双电子积分的经典内投影方法。二者均借助辅助基组以降低计算的标度复杂度。过往数年中，二者间的紧密联系推动了系统性推导无偏辅助基组的研究发展，相继提出了原子型CD（atomic CD, aCD）与原子紧致型CD（atomic compact CD, acCD）辅助基组，区别于传统预计算辅助基组。在RI方法框架下，通过对单中心双电子积分进行显式校正，可进一步提升上述近似方法的计算精度，这也是本研究的核心目标。直接校正随体系规模呈线性缩放的单中心双电子积分，有望为辅助基组的设计提供新的自由度。该自由度既可用于加速双电子积分传统处理方式的收敛速度，也可在保持与未校正方法同等精度的前提下，构建更轻量化的辅助基组。本文针对多种辅助基组类型开展了单中心校正的基准测试研究。