The theory of non-orthogonal spin-adaptation for closed-shell molecular systems is applied to coupled cluster methods with quadruple excitations (CCSDTQ). The advantages of the non-orthogonal spin-adaption with respect to simplification and factorization of the working equations and to efficient implementation are presented and discussed. Additionally, specific optimizations of the implementation for often-overlooked issues such as tensor transposition, disk access, and removal of redundant and/or unnecessary operations are detailed. The resulting algorithm is implemented in the CFOUR program suite for CCSDT, CCSDTQ, and various approximate methods [CCSD(T), CC3, CCSDT-n, and CCSDT(Q)]. The performance of these implementations is one to two orders of magnitude better than in prior implementations.
