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Polynuclear transition metal complexes such as the P-cluster and theFeMo-cofactor of nitrogenase with eight transition metal centers represent agreat challenge for current electronic structure methods. In this work, weinitiated the use of comb tensor network states (CTNS), whose underlyingtopology has a one-dimensional backbone and several one-dimensional branches,as a many-body wavefunction ansatz to tackle these challenging systems. As animportant first step, we explored the expressive power of CTNS with differentunderlying topologies. To this end, we presented an algorithm to express aconfiguration interaction (CI) wavefunction into CTNS based on the Schmidtdecomposition. The algorithm was illustrated for representing approximate CIwavefunctions obtained from selected CI calculations for the P-cluster and theFeMo-cofactor into CTNS with three chemically meaningful comb structures, whichsuccessively group orbitals belonging to the same atom into branches. Theconventional matrix product states (MPS) representation was obtained as aspecial case. We also discussed the insights gained from such decompositions,which shed some light on the future developments of efficient numerical toolsfor polynuclear transition metal complexes.

Expressibility of comb tensor network states (CTNS) for the P-cluster and the FeMo-cofactor of nitrogenase