Basis-Set Limit CCSD(T) Energies for Large Molecules with Local Natural Orbitals and Reduced-Scaling Basis-Set Corrections

The calculation of
density-based basis-set correction
(DBBSC),
which remedies the basis-set incompleteness (BSI) error of the correlation
energy, is combined with local approximations. Aiming at large-scale
applications, the procedure is implemented in our efficient local
natural orbital-based coupled-cluster singles and doubles with perturbative
triples [LNO-CCSD(T)] scheme. To this end, the range-separation function,
which characterizes the one-electron BSI in space, is decomposed into
the sum of contributions from individual localized molecular orbitals
(LMOs). A compact domain is constructed around each LMO, and the corresponding
contributions are evaluated only within these restricted domains.
Furthermore, for the calculation of the complementary auxiliary basis
set (CABS) correction, which significantly improves the Hartree–Fock
(HF) energy, the local density fitting approximation is utilized.
The errors arising from the local approximations are examined in detail,
efficient prescreening techniques are introduced to compress the numerical
quadrature used for DBBSC, and conservative default thresholds are
selected for the truncation parameters. The efficiency of the DBBSC-LNO-CCSD(T)
method is demonstrated through representative examples of up to 1000
atoms. Based on the numerical results, we conclude that the corrections
drastically reduce the BSI error using double-ζ basis sets,
often to below 1 kcal/mol compared to the reliable LNO-CCSD(T) complete
basis set references, while significant improvements are also achieved
with triple-ζ basis sets. Considering that the calculation of
the DBBSC and CABS corrections only moderately increases the wall-clock
time required for the post-HF steps in practical applications, the
proposed DBBSC-LNO-CCSD(T) method offers a highly efficient and robust
tool for large-scale calculations.