Computing Exchange Coupling constants in Transition metal complexes with Tensor Product Selected Configuration Interaction

TL;DR

This paper compares Tensor Product Selected Configuration Interaction (TPSCI) with DMRG for calculating exchange coupling constants in transition metal complexes, highlighting TPSCI's efficiency, multistate capability, and current limitations due to cluster state truncation.

Contribution

The paper introduces TPSCI as an efficient, interpretable method for strongly correlated transition metal complexes, demonstrating its advantages and limitations compared to DMRG.

Findings

TPSCI yields energies higher than DMRG due to truncation.

Exchange coupling constants from TPSCI are within 10-30 cm$^{-1}$ of DMRG.

TPSCI's multistate capability enables direct J extrapolation.

Abstract

Transition metal complexes present significant challenges for electronic structure theory due to strong electron correlation arising from partially filled $d$-orbitals. We compare our recently developed Tensor Product Selected Configuration Interaction (TPSCI) with Density Matrix Renormalization Group (DMRG) for computing exchange coupling constants in six transition metal systems, including dinuclear Cr, Fe, and Mn complexes and a tetranuclear Ni-cubane. TPSCI uses a locally correlated tensor product state basis to capture electronic structure efficiently while maintaining interpretability. From calculations on active spaces ranging from (22e,29o) to (42e,49o), we find that TPSCI consistently yields higher variational energies than DMRG due to truncation of local cluster states, but provides magnetic exchange coupling constants (J) generally within 10-30 cm$^{-1}$ of DMRG results. Key advantages include natural multistate capability enabling direct J extrapolation with smaller statistical errors, and computational efficiency for challenging systems. However, cluster state truncation represents a fundamental limitation requiring careful convergence testing, particularly for large local cluster dimensions. We identify specific failure cases where current truncation schemes break down, highlighting the need for improved cluster state selection methods and distributed memory implementations to realize TPSCI's full potential for strongly correlated systems.