Scalable Electron Correlation Methods. 7. Local Open-Shell Coupled-Cluster Methods Using Pair Natural Orbitals: PNO-RCCSD and PNO-UCCSD

We
present well-parallelized local implementations of high-spin
open-shell coupled cluster methods with single and double excitations
(CCSD) using pair natural orbitals (PNOs). The methods are based on
the spin-orbital coupled cluster
theory using restricted open-shell Hartree–Fock (ROHF) reference
functions. Two variants, namely, PNO-UCCSD and PNO-RCCSD are implemented
and compared. In PNO-UCCSD, the coupled cluster amplitudes are spin-unrestricted,
while in PNO-RCCSD the linear terms are spin-adapted by a spin-projection
approach as described in J. Chem. Phys. 1993, 99, 5219−5227. Near linear scaling
of the computational cost with the number of correlated electrons
is achieved by applying domain and pair approximations. The PNOs are
spin-independent and obtained using a semicanonical spin-restricted
MP2 approximation with large domains of projected atomic orbitals
(PAOs). The pair approximations of our previously described closed-shell
PNO-LCCSD method are carefully revised so that they are compatible
to the UCCSD theory, and PNO-UCCSD or PNO-RCCSD calculations for closed-shell
molecules yield exactly the same results as corresponding spin-free
closed-shell PNO-LCCSD calculations. The convergence of the results
with respect to the thresholds and options that control the domain
and pair approximations is demonstrated. It is found that large domains
are required for the single excitations in open-shell calculations
in order to obtain converged results. In general, the errors of relative
energies caused by the local approximations can be reduced to below
1 kcal mol–1, even for difficult cases. Presently,
PNO-RCCSD and PNO-UCCSD calculations for molecules with 100–200
atoms and augmented triple-ζ basis sets can be carried out in
a few hours of elapsed time using ∼100 CPU cores. In addition,
the program is also capable of performing distinguishable cluster
(PNO-RDCSD and PNO-UDCSC) calculations. The present work is a critical
step in developing fully local open-shell PNO-RCCSD­(T)-F12 methods.