  We introduce the concept of self-adaptive tensor network states (SATNS) based
on multi-site correlators. The SATNS ansatz gradually extends its variational
space incorporating the most important next-order correlators into the ansatz
for the wave function. The selection of these correlators is guided by
entanglement-entropy measures from quantum information theory. By sequentially
introducing variational parameters and adjusting them to the system under
study, the SATNS ansatz achieves to keep their number significantly smaller
than the total number of full-configuration interaction parameters. The SATNS
ansatz is studied for manganocene in its lowest-energy sextet and doublet
states, the latter of which is known to be difficult to describe. It is shown
that the SATNS parametrization solves the convergence issues found for previous
correlator-based tensor network states.
