A new library called libreta for the evaluation of electron repulsion integrals (ERIs) over segmented and contracted Gaussian functions is developed. Our libreta is optimized from three aspects: (1) The Obara–Saika, Dupuis–Rys–King, and McMurchie–Davidson method are all employed. The recurrence relations involved are optimized by tree-search for each combination of angular momenta, and in the best case, 50% of the intermediates can be eliminated to reduce the computational cost. (2) The optimized codes for recurrence relations are combined with different contraction orders, each of which is suitable for ERIs of different angular momenta and contraction patterns. In practice, libreta will determine and use the best scheme to evaluate each ERI. (3) libreta is also optimized at the coding level. For example, with common subexpression elimination and local memory access, the performance can be increased by about 6% and 20%, respectively. The performance was compared with libint2. For both popular segmented and contracted basis sets, libreta can be faster than libint2 by 7.2–912.0%. For basis sets of heavy elements that contain Gaussian basis functions of large contraction degrees, the performance can be increased 20–30 times. We also tested the performance of libreta in direct self-consistent field (SCF) calculations and compared it with NWChem. In most cases, the average time for one SCF iteration by libreta is less than NWChem by 144.2–495.9%. Finally, we discuss the origin of redundancies occurring in the recurrence relations and derive an upper bound of the least number of intermediates required to be calculated in a McMurchie–Davidson recurrence, which is confirmed by ours as well as previous authors’ results. We expect that libreta can become a useful tool for theoretical and computational chemists to develop their own algorithms rapidly.

中文翻译：

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libreta：电子排斥综合评估的计算机优化和代码综合

开发了一个名为libreta的新库，用于评估分段和收缩的高斯函数上的电子排斥积分（ERI）。我们的自由度从三个方面进行了优化：（1）全部采用了Obara–Saika，Dupuis–Rys–King和McMurchie–Davidson方法。通过对角矩的每种组合进行树形搜索来优化所涉及的递归关系，并且在最佳情况下，可以消除50％的中间体以降低计算成本。（2）递推关系的优化代码结合了不同的收缩阶次，每个阶次都适用于不同角动量和收缩模式的ERI。实际上，libreta将确定并使用最佳方案来评估每个ERI。（3）libreta也已在编码级别进行了优化。例如，使用常见的子表达式消除和本地内存访问，性能可以分别提高大约6％和20％。将该性能与libint2进行了比较。对于流行的分段和收缩基集，libreta的速度可以比libint2快7.2–912.0％。对于包含大收缩度的高斯基函数的重元素的基集，性能可以提高20–30倍。我们还在直接自洽场（SCF）计算中测试了libreta的性能，并将其与NWC hem进行了比较。在大多数情况下，libreta进行一次SCF迭代的平均时间比NWC下摆小144.2–495.9％。最后，我们讨论了重复关系中出现的冗余的起源，并得出了在McMurchie-Davidson重复中需要计算的最少中间体数量的上限，这一点已被我们以及先前的作者的结果所证实。我们期望libreta可以成为理论和计算化学家快速开发自己的算法的有用工具。