  Tailored coupled cluster theory represents a computationally inexpensive way
to describe static and dynamical electron correlation effects. In this work, we
scrutinize the performance of various tailored coupled cluster methods
externally corrected by electronic wave functions of polynomial cost.
Specifically, we focus on frozen-pair coupled-cluster (fpCC) methods, which are
externally corrected by pair-coupled cluster doubles (pCCD), and coupled
cluster theory tailored by matrix product state wave functions optimized by the
density matrix renormalization group (DMRG) algorithm. As test system, we
selected a set of various small- and medium-sized molecules containing
diatomics (N$_2$, F$_2$, C$_2$, CN$^+$, BN, BO$^+$, and Cr$_2$) and molecules
(ammonia, ethylene, cyclobutadiene, benzene) for which conventional
single-reference coupled cluster singles and doubles (CCSD) is not able to
produce accurate results for spectroscopic constants, potential energy
surfaces, and barrier heights. Most importantly, DMRG-tailored and
pCCD-tailored approaches yield similar errors in spectroscopic constants and
potential energy surfaces compared to multireference and/or experimental
reference data and generally outrank the conventional single-reference CCSD
approach. Although fpCC methods provide a reliable description for the
dissociation pathway of molecules featuring single and quadruple bonds, they
fail in the description of triple or hextuple bond-breaking processes or
avoided crossing regions.
