  Wavefunctions constructed from electron-pair states can accurately model
strong electron correlation effects and are promising approaches especially for
larger many-body systems. In this article, we analyze the nature and the type
of electron correlation effects that can be captured by wavefunctions
restricted to electron-pair states. We focus on the Antisymmetric Product of
1-reference orbital Geminal (AP1roG) method combined with an orbital
optimization protocol presented in [Phys. Rev. B, 89, 201106(R), 2014] whose
performance is assessed against electronic structures obtained form DMRG
reference data. Our numerical analysis covers model systems for strong
correlation: the one-dimensional Hubbard model with periodic boundary condition
as well as metallic and molecular hydrogen rings. Specifically, the accuracy of
AP1roG is benchmarked using the single-orbital entropy, the orbital-pair mutual
information as well as the eigenvalue spectrum of the one-orbital and
two-orbital reduced density matrices. Our study indicates that contributions
from singly occupied states become important in the strong correlation regime
which highlights the limitations of the AP1roG method. Furthermore, we examine
the effect of orbital rotations within the AP1roG model on correlations between
orbital pairs.
