Basis Set Limit CCSD(T) Energies for Extended Molecules via a Reduced-Cost Explicitly Correlated Approach

Several approximations are introduced and tested to reduce
the
computational expenses of the explicitly correlated coupled-cluster
singles and doubles with perturbative triples [CCSD(T)] method for
both closed and open-shell species. First, the well-established frozen
natural orbital (FNO) technique is adapted to explicitly correlated
CC approaches. Second, our natural auxiliary function (NAF) scheme
is employed to reduce the size of the auxiliary basis required for
the density fitting approximation regularly used in explicitly correlated
calculations. Third, a new approach, termed the natural auxiliary
basis (NAB) approximation, is proposed to decrease the size of the
auxiliary basis needed for the expansion of the explicitly correlated
geminals. The performance of the above approximations and that of
the combined FNO-NAF-NAB approach are tested for atomization and reaction
energies. Our results show that overall speedups of 7-, 5-, and 3-times
can be achieved with double-, triple-, and quadruple-ζ basis
sets, respectively, without any loss in accuracy. The new method can
provide, e.g., reaction energies and barrier heights well within chemical
accuracy for molecules with more than 40 atoms within a few days using
a few dozen processor cores, and calculations with 50+ atoms are still
feasible. These routinely affordable computations considerably extend
the reach of explicitly correlated CCSD(T).