In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate formal properties of the used method, such as energy size consistency 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 what we have defined as a complete active space-external space gap describing the basis splitting between the complete active space and the external part generalizing the concept of a HOMO-LUMO gap. Furthermore, the behavior of the energy error for an optimal basis splitting, i.e., an active space choice minimizing the density matrix renormalization group-tailored coupled-cluster singles doubles error, 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 a complete active space. Moreover, the dependence of the ground-state energy error on the complete active space has been analyzed numerically in order to find an optimal split between the complete active space and external space by minimizing the density matrix renormalization group-tailored coupled-cluster error.

Department of Physics of Complex Systems Eötvös Loránd University Pf 32 H 1518 Budapest Hungary

Faculty of Mathematics and Physics Charles University 11636 Prague Czech Republic

Hylleraas Centre for Quantum Molecular Sciences Department of Chemistry University of Oslo P O Box 1033 Blindern N 0315 Oslo Norway

J Heyrovský Institute of Physical Chemistry Academy of Sciences of the Czech Republic v v i Dolejškova 3 18223 Prague 8 Czech Republic

Modeling Simulation and Optimization in Science Department of Mathematics Technische Universität Berlin Sekretariat MA 5 3 Straße des 17 Juni 136 10623 Berlin Germany

Strongly Correlated Systems Lendület Research Group Wigner Research Center for Physics H 1525 P O Box 49 Budapest Hungary

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