  In this article, we investigate the numerical and theoretical aspects of the
coupled-cluster method tailored by matrix-product states. We investigate
chemical properties of the used method, such as energy size extensivity and the
equivalence of linked and unlinked formulation. The existing mathematical
analysis is here elaborated in a quantum chemical framework. In particular, we
highlight the use of a so-called CAS-ext gap describing the basis splitting
between the complete active space and the external part. Moreover, the behavior
of the energy error as a function of the optimal basis splitting is discussed.
We show numerical investigations on the robustness with respect to the bond
dimensions of the single orbital entropy and the mutual information, which are
quantities that are used to choose the complete active space. Furthermore, we
extend the mathematical analysis with a numerical study on the complete active
space dependence of the error.
