Quaternion Dirac--Coulomb--Breit Integral Transformation for Relativistic Four-Component Correlated Electronic Structure Theory
Abstract
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.
Versions
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BibTeX
@misc{oele2026quaternion,
title = {{Quaternion Dirac--Coulomb--Breit Integral Transformation for Relativistic Four-Component Correlated Electronic Structure Theory}},
author = {Martijn Oele and Rajat Majumder and Shiv Upadhyay and Tianyuan Zhang and Ryan A Beck and Agam Shayit and Lucas Visscher and Xiaosong Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.04316},
eprint = {2606.04316},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.04316},
}
RIS
TY - UNPB
TI - Quaternion Dirac--Coulomb--Breit Integral Transformation for Relativistic Four-Component Correlated Electronic Structure Theory
AU - Martijn Oele
AU - Rajat Majumder
AU - Shiv Upadhyay
AU - Tianyuan Zhang
AU - Ryan A Beck
AU - Agam Shayit
AU - Lucas Visscher
AU - Xiaosong Li
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2606.04316
UR - https://arxiv.org/abs/2606.04316
AB - 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.
ER -