  Polynuclear transition metal complexes such as the P-cluster and the
FeMo-cofactor of nitrogenase with eight transition metal centers represent a
great challenge for current electronic structure methods. In this work, we
initiated the use of comb tensor network states (CTNS), whose underlying
topology has a one-dimensional backbone and several one-dimensional branches,
as a many-body wavefunction ansatz to tackle these challenging systems. As an
important first step, we explored the expressive power of CTNS with different
underlying topologies. To this end, we presented an algorithm to express a
configuration interaction (CI) wavefunction into CTNS based on the Schmidt
decomposition. The algorithm was illustrated for representing approximate CI
wavefunctions obtained from selected CI calculations for the P-cluster and the
FeMo-cofactor into CTNS with three chemically meaningful comb structures, which
successively group orbitals belonging to the same atom into branches. The
conventional matrix product states (MPS) representation was obtained as a
special case. We also discussed the insights gained from such decompositions,
which shed some light on the future developments of efficient numerical tools
for polynuclear transition metal complexes.
