Optimization of the Linear-Scaling Local Natural Orbital CCSD(T) Method: Improved Algorithm and Benchmark Applications

An
optimized implementation of the local natural orbital (LNO)
coupled-cluster (CC) with single-, double-, and perturbative triple
excitations [LNO–CCSD­(T)] method is presented. The integral-direct,
in-core, highly efficient domain construction technique of our local
second-order Møller–Plesset (LMP2) scheme is extended
to the CC level. The resulting scheme, which is also suitable for
general-order LNO–CC calculations, inherits the beneficial
properties of the LMP2 approach, such as the asymptotically linear-scaling
operation count, the asymptotically constant data storage requirement,
and the completely independent domain calculations. In addition to
integrating our recent redundancy-free LMP2 and Laplace-transformed
(T) algorithms with the LNO–CCSD­(T) code, the memory demand,
the domain and LNO construction, the auxiliary basis compression,
and the previously rate-determining two-external integral transformation
have been significantly improved. The accuracy of all of the approximations
is carefully examined on medium-sized to large systems to determine
reasonably tight default truncation thresholds. Our benchmark calculations,
performed on molecules of up to 63 atoms, show that the optimized
method with the default settings provides average correlation and
reaction energy errors of less than 0.07% and 0.34 kcal/mol, respectively,
compared to the canonical CCSD­(T) reference. The efficiency of the
present LNO–CCSD­(T) implementation is demonstrated on realistic,
three-dimensional examples. Using the new code, an LNO–CCSD­(T)
correlation energy calculation with a triple-ζ basis set is
feasible on a single processor for a protein molecule including 2380
atoms and more than 44000 atomic orbitals.