Explicitly correlated coupled cluster method for accurate treatment of open-shell molecules with hundreds of atoms

We present a near-linear scaling formulation of the explicitly-correlated coupled-cluster singles and doubles with perturbative triples method (CCSD(T)$_{\overline{\text{F12}}}$) for high-spin states of open-shell species. The approach is based on the conventional open-shell CCSD formalism [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)] utilizing the domain local pair-natural orbitals (DLPNO) framework. The use of spin-independent set of pair-natural orbitals ensures exact agreement with the closed-shell formalism reported previously, with only marginally impact on the cost (e.g. the open-shell formalism is only 1.5 times slower than the closed-shell counterpart for the $\text{C}_\text{160}\text{H}_{\text{322}}$ n-alkane, with the measured size complexity of $\approx1.2$). Evaluation of coupled-cluster energies near the complete-basis-set (CBS) limit for open-shell systems with more than 550 atoms and 5000 basis functions is feasible on a single multi-core computer in less than 3 days. The aug-cc-pVTZ DLPNO-CCSD(T)$_{\overline{\text{F12}}}$ contribution to the heat of formation for the 50 largest molecules among the 348 core combustion species benchmark set [J. Klippenstein et al., J. Phys. Chem. A 121, 6580 (2017)] had root-mean-square deviation (RMSD) from the extrapolated CBS CCSD(T) reference values of 0.3 kcal/mol. For a more challenging set of 50 reactions involving small closed- and open-shell molecules [G. Knizia et al., J. Chem. Phys. 130, 054104 (2009)] the aug-cc-pVQ(+d)Z DLPNO-CCSD(T)$_{\overline{\text{F12}}}$ yielded a RMSD of $\sim$0.4 kcal/mol with respect to the CBS CCSD(T) estimate.