Diffusion quantum Monte Carlo benchmark for metal-ligand binding in first-row metallocenes

The local metal- π bond is the microscopic unit from which metal-organic quantum materials are built. We benchmark this bond with both density-functional theory (DFT) and fixed-node diffusion quantum Monte Carlo (DMC), using Slater-Jastrow (SJ) and Slater-Jastrow-backflow (SJB) trial wave functions, to compute binding-energy curves for the first-row metallocenes M ( C 5 H 5 ) 2 with M = Ti, V, Fe, and Co as the metal-carbon distance d is varied. Both DFT and DMC exhibit a distance-controlled crossover in which Fe and Co are favored under compression, while V and Ti form deeper wells near equilibrium and remain more strongly bound at larger separation. Similar V > Ti > Fe > Co ordering at the binding minima persists from DFT through SJ and SJB DMC. DFT-PBE (Perdew-Burke-Ernzerhof), however, overbinds all four metallocenes relative to the correlated DMC benchmark by a large amount that is close to uniform across the series but grows mildly from early to late transition metals showing that semilocal mean-field DFT captures the qualitative topology of the crossover but is quantitatively inaccurate. DFT + U with standard literature U values does not reliably correct this overbinding and can substantially reorder the binding-strength ranking across the series, showing that U must be determined self-consistently for this bonding environment rather than adopted from unrelated chemistry.