In the last decade, the quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as the method of choice for calculations of strongly correlated molecular systems. Despite its favourable scaling, it is in practice not suitable for computations of dynamic correlation. We present a novel method for accurate "post-DMRG" treatment of dynamic correlation based on the tailored coupled cluster (CC) theory in which the DMRG method is responsible for the proper description of non-dynamic correlation, whereas dynamic correlation is incorporated through the framework of the CC theory. We illustrate the potential of this method on prominent multireference systems, in particular N2, Cr2 molecules and also oxo-Mn(Salen) for which we have performed the first "post-DMRG" computations in order to shed light on the energy ordering of the lowest spin states.The coupled cluster (CC) approach, introduced to quantum chemistry (QC) by Čížek 1 , is one of the most accurate ab initio methods for the treatment of dynamic electron correlation. The advantages of this scheme include a compact description of the wave function, size-extensivity, invariance to orbital rotations together with a systematic hierarchy of approximations converging towards the full configuration interaction (FCI) limit 2 . Despite the great success of QC and in particular the CC methodology 3 in standard (single-reference) cases, the situation is dramatically different for strongly correlated (multireference) systems 4 , where the usual single-reference approaches become inaccurate or even completely break down. One category of methods designed for the treatment of such systems are multireference coupled cluster (MRCC) approaches, which generalize the CC exponential parameterization of the wave function 5-7 . Out of many formulations of MRCC theories, the class of methods relevant to this work are externally corrected CC, which extract information about the most important higher excitations or active space single and double excitations from an "external" calculation performed by a different method like complete active space self-consistent field (CASSCF) or multireference configuration interaction (MRCI) [8][9][10][11][12][13][14][15][16][17][18][19] . In this letter, we present a further development in this field concerning the tailored CC (TCC) method, where the information for external correction is obtained from a density matrix renormalization group (DMRG) calculation.DMRG is a very powerful approach suitable for treatment of strongly correlated systems originally developed in solid state physics [20][21][22] . The success of DMRG in this field motivated its application to QC problems [23][24][25][26][27][28][29][30][31] where it has proven the potential to outperform traditional QC methods for systems which require very large active spaces, like molecules containing several transition metal atoms 32,33 . Despite the favourable scaling of the DMRG method, it is computationally prohibitive to treat the dynamic cor...

We have performed a full configuration interaction (FCI) quality benchmark calculation for the tetramethyleneethane molecule in the cc-pVTZ basis set employing a subset of complete active space second order perturbation theory, CASPT2(6,6), natural orbitals for the FCI quantum Monte Carlo calculation. The results are in an excellent agreement with the previous large scale diffusion Monte Carlo calculations by Pozun et al. and available experimental results. Our computations verified that there is a maximum on the potential energy surface (PES) of the ground singlet state (A) 45° torsional angle, and the corresponding vertical singlet-triplet energy gap is 0.01 eV. We have employed this benchmark for the assessment of the accuracy of Mukherjee's coupled clusters with up to triple excitations (MkCCSDT) and CCSD tailored by the density matrix renormalization group method (DMRG). Multireference MkCCSDT with CAS(2,2) model space, though giving good values for the singlet-triplet energy gap, is not able to properly describe the shape of the multireference singlet PES. Similarly, DMRG(24,25) is not able to correctly capture the shape of the singlet surface, due to the missing dynamic correlation. On the other hand, the DMRG-tailored CCSD method describes the shape of the ground singlet state with excellent accuracy but for the correct ordering requires computation of the zero-spin-projection component of the triplet state (B).

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 groundstate 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.