  Wave functions based on electron-pair states provide inexpensive and reliable
models to describe quantum many-body problems containing strongly-correlated
electrons, given that broken-pair states have been appropriately accounted for
by, for instance, a posteriori corrections. In this article, we analyse the
performance of electron-pair methods in predicting orbital-based correlation
spectra. 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 be
determined from a pCCD-tailored CC wave function. Furthermore, we employ the
single-orbital entropy, the orbital-pair mutual information, and the eigenvalue
spectra of the two-orbital reduced density matrices to benchmark the
performance of the LCC correction for the one-dimensional Hubbard model with
periodic boundary condition as well as the N$_2$ and F$_2$ molecules against
DMRG reference calculations. Our study indicates that pCCD-LCC accurately
reproduces the orbital-pair correlation patterns in the weak-correlation limit
and for molecules close to their equilibrium structure. Hence, we can conclude
that pCCD-LCC predicts reliable wave functions in this regime. In the
strong-correlation limit and for molecules with stretched bonds, the LCC
correction, generally, overestimates orbital-pair correlations.
