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 a 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, multilevel embedding, as well as greatly reduced
memory and disk use. The accuracy of LNO approximations and basis
set completeness is benchmarked for thermochemistry and noncovalent
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 noncovalent 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 multilevel
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.