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

TL;DR

This paper investigates the use of comb tensor network states (CTNS) to represent complex polynuclear transition metal systems like the P-cluster and FeMo-cofactor, demonstrating their expressive power and potential for future electronic structure calculations.

Contribution

The study introduces an algorithm to express CI wavefunctions as CTNS with various topologies, including the special case of MPS, for challenging transition metal complexes.

Findings

CTNS can effectively represent CI wavefunctions of complex metal clusters.

Different comb topologies provide insights into orbital groupings and system structure.

The approach offers a pathway for developing efficient numerical tools for transition metal systems.

Abstract

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.