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We extend the CCSDTQ implementation in CFOUR to UHF and ROHF references and demonstrate its efficiency. We apply it to basis set convergence of post-CCSDT(Q) corrections for the W4-08 thermochemical dataset. Convergence of (Q)–(Q) is relatively rapid. For difficult species (e.g., B2, O3), CCSDTQ–CCSDT(Q) may converge more slowly than (5), but the effects and and basis-set trends oppose each other. Consequently, a single-shot CCCSDTQ(5)-CCSDT(Q) correction appears most efficient. For radicals with bifurcating UHF solutions, energetics of the `less spin-contaminated’ solution are clearly more well-behaved. Our best computed adiabatic electron affinity of ozone is in excellent agreement with experiment.

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