Development of local natural orbital arbitrary order coupled cluster methods and assessment through connected quadruples

We present the development of local natural orbital (LNO) based arbitrary-order coupled-cluster (CC) methods, and rigorous assessment of the beyond CCSD(T)-level correlation through LNO-CCSDTQ. Both the closed-and open-shell implementations inherit from our LNO family of methods the asymptotically linear-scaling framework, support for point group symmetry, multi-level embedding, as well as greatly reduced memory and disk use. The accuracy of LNO approximations and basis set completeness is benchmarked for thermochemistry and non-covalent interactions through CCSDTQ. Even for complicated atomizations and barrier heights, the CCSDT−CCSD(T), (Q), and especially the CCSDT(Q)−CCSD(T) contributions are obtained reliably within 85-95% relative and 0.05-0.1 kcal/mol absolute accuracy, already with the default LNO threshold set. Tightening LNO settings generally improves this performance, useful when aiming at high relative accuracy in even smaller effects, such as in non-covalent interactions or when pursuing the basis set limit of post-CCSD(T) atomization contributions. Thus, the LNO approximation greatly expands the reach of post-CCSD(T) methods, especially beyond a few atoms and small (double-ζ) basis sets, i.e., above ca. 100 orbitals. For example, via our multi-level approach, we report an unprecedented CCSDT(Q)−CCSD(T) reaction energy correction computation for a real-life enzyme reaction. Thus, LNO-based higher-order CC methods enable thermochemistry protocols aiming at kJ/mol accuracy for practical, 3D molecular systems that are much larger than previously accessible.