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This paper introduces a quaternion-based, atomic orbital (AO) driven direct integral transformation scheme designed to efficiently handle the transformation of relativistic two-electron integrals in electronic structure calculations. By leveraging quaternion density-based contractions and direct Cauchy-Schwarz screening, the method significantly reduces the computational scaling and memory requirements associated with including Breit interaction integrals. The key result demonstrates that this framework enables the routine incorporation of complex relativistic effects in large-scale four-component correlated calculations, enhancing both efficiency and scalability.
Transforming complex relativistic integrals just got easier鈥攖his new quaternion-based method slashes computational costs while boosting scalability for large-scale electronic structure calculations.
High-accuracy correlated four-component relativistic electronic structure methods are typically formulated in terms of integrals over molecular orbital (MO). Consequently, an efficient and scalable strategy is required to deal with the complexity of transforming relativistic two-electron integrals from the atomic orbital (AO) to the MO basis. The transformation bottleneck is particularly acute for approaches that include Breit interaction integrals, whose computational and memory demands further exacerbate the transformation cost. To overcome this challenge, we develop a quaternion-based, AO-driven direct integral transformation scheme. The method operates on scalar AO integrals and combines quaternion density-based contractions with direct Cauchy-Schwarz screening to systematically exploit integral locality. As a result, the proposed framework substantially lowers the practical computational scaling and provides an efficient, memory-conscious, and highly parallelizable pathway for the routine inclusion of relativistic Dirac-Coulomb-Breit integrals in large-scale four-component correlated calculations.
