Coupled cluster linear and nonlinear molecular properties across the periodic table

Accurate electronic structure calculations have become and indispensable tool to understand the properties of molecular systems containing elements across the whole periodic table, up to and including superheavy elements. Such approaches help make sense of the underlying complex physical processes probed by experiments, or in case such experiments are unfeasible (due to hazards such as radiotoxicity, short element lifetimes etc). A challenge in such calculations is taking into account both relativistic effects (which require the solution of the Dirac equation in two- or four-component form) and electron correlation (in which wavefunctions and the interactions between particles are represented as large, high-dimensional tensors and tensor contractions respectively). In this presentation we will outline our contributions to the development of relativistic coupled cluster approaches for the determination of linear [1], quadratic [2] and cubic response [3] theories carried out in the ExaCorr module of the DIRAC code [4], as well as strategies to reduce computational bottlenecks by compressing the information of the underlying tensor representations with natural orbital based schemes [5]. Finally, we will evoke efforts to standardize tensor operations [6] and how such efforts allow for simplifying development as well as for leveraging new accelerated architectures to speed up tensor computations. AcknowledgementsANR (ANR-19-CE29-0019, ANR-24-CE29-0904, ANR-11-LABX-0005, ANR-16-IDEX-0004), CDP C2EMPI, CPER WaveTech, GENCI, Oak Ridge Leadership Computing Facility (DE-AC05-00OR22725) References[1] X. Yuan et al., J. Chem. Theory Comput. 20, 677 (2024)[2] X. Yuan, L. Halbert, L. Visscher, A. S. P. Gomes, J. Chem. Theory Comput. 19, 9428 (2023); J. Phys. Chem. A 129, 11695 (2025)[3] M. Le, L. Halbert, A. S. P. Gomes, in preparation [4] J. V. Pototschnig et al., J. Chem. Theory Comput. 17, 5509 (2021); T. Saue et al., J.Chem. Phys. 152, 204104 (2020)[5] X. Yuan, L. Visscher, A. S. P. Gomes, J. Chem. Phys. 156, 224108 (2022); M. Le et al., in preparation[6] J. Brandejs, T. Saue, A. S. P. Gomes, L. Visscher, P. Bientinesi, arXiv:2602.05490 (2026); J. Brandejs et al., arXiv:2601.07827 (2026)