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Wave functions based on electron-pair states provide inexpensive and reliablemodels to describe quantum many-body problems containing strongly-correlatedelectrons, given that broken-pair states have been appropriately accounted forby, for instance, a posteriori corrections. In this article, we analyse theperformance of electron-pair methods in predicting orbital-based correlationspectra. We focus on the (orbital-optimized) pair-coupled cluster Doubles(pCCD) ansatz with a linearized coupled-cluster (LCC) correction. Specifically,we scrutinize how orbital-based entanglement and correlation measures can bedetermined from a pCCD-tailored CC wave function. Furthermore, we employ thesingle-orbital entropy, the orbital-pair mutual information, and the eigenvaluespectra of the two-orbital reduced density matrices to benchmark theperformance of the LCC correction for the one-dimensional Hubbard model withperiodic boundary condition as well as the N$_2$ and F$_2$ molecules againstDMRG reference calculations. Our study indicates that pCCD-LCC accuratelyreproduces the orbital-pair correlation patterns in the weak-correlation limitand for molecules close to their equilibrium structure. Hence, we can concludethat pCCD-LCC predicts reliable wave functions in this regime. In thestrong-correlation limit and for molecules with stretched bonds, the LCCcorrection, generally, overestimates orbital-pair correlations.

Orbital entanglement and correlation from pCCD-tailored Coupled Cluster wave functions