In electronic-structure theory, the most pertinent problem is the eigenvalue problem of the electronic Hamiltonian. For electronic systems with appreciable static correlation, the classical post-Hartree—Fock methods fail spectacularly. Multireference methods are needed, and the hunt for multireference coupled-cluster methods that are affordable and accurate enough to be run by non-experts is ongoing. We present a recently pubished multireference coupled-cluster method (bivar-MRCC) based on Arponen’s bivariational principle, a generalization of the Rayleigh—Ritz variational principle. The bivar-MRCC method is algebraically straightforward, has relatively cheap computational cost, and it can compete with established and extremely complicated MRCC methods. Tensor-network based methods are emerging as alternative powerful tools for resolving static correlation in electronic-sctructure theory, but so far they do not cope too well with the residual correlation, a description of which is essential for accurate calculations. We propose to combine the best of two worlds: let tensor-network methods deal with the static correlation, and (MR)CC methods deal with the remaining correlation. This has been done with the so-called tailored CC method, but in order to correct for the systematical errors present in this approach, the bivariational point of view is needed. The result is a class of hybrid tensor-CC methods which we describe from a mathematical and algorithmic perspective.
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