Computing Exchange Coupling Constants in Transition Metal Complexes with Tensor Product Selected Configuration Interaction

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.过渡金属配合物因部分填充d轨道产生的强电子关联效应，给电子结构理论研究带来了显著挑战。我们将新近开发的张量积选择组态相互作用（Tensor Product Selected Configuration Interaction，TPSCI）与密度矩阵重整化群（Density Matrix Renormalization Group，DMRG）进行对比，以计算六种过渡金属体系的交换耦合常数，体系包括双核铬、铁、锰配合物以及四核镍立方烷配合物。TPSCI采用局域关联张量积态基组，可在保持可解释性的同时高效描述电子结构。通过对活性空间范围从(22e,29o)到(42e,49o)的体系开展计算，我们发现：由于局域簇态的截断处理，TPSCI的变分能始终高于DMRG，但其给出的磁交换耦合常数（J）普遍与DMRG结果的偏差在10~30 cm⁻¹以内。其核心优势包括具备天然的多态处理能力，可直接进行J值外推且统计误差更小，同时对高难度体系具备更高的计算效率。但簇态截断是一项根本性局限，需要进行细致的收敛性测试，尤其是在局域簇维度较大的情况下。我们还识别出当前截断方案失效的具体场景，这凸显出需要改进簇态选择方法与分布式内存实现方案，以充分发挥TPSCI在强关联体系中的应用潜力。