Origin of Divergent H/D Isotope Effects on 31P NMR Chemical Shifts in Ferrocene Derivatives: A Multicomponent DFT Study

Abstract The hydrogen-bonded neutral ferrocene-1,1′-diyl-bis(methylphosphinic acid) (FcPMe) and its monoanion (FcPMe(−)) exhibit divergent H/D isotope effects on their 31P NMR chemical shifts (δP). The previous quasi-adiabatic Born–Oppenheimer-based treatment failed to predict even the correct sign of the isotope effect for the monoanion. Herein, we elucidate the origin of this phenomenon using a multicomponent quantum mechanical (MC_QM) approach, which directly incorporates nuclear quantum effects (NQEs) into the electronic structure. Our results reveal that NQEs induce significant changes in the molecular geometry and the associated electronic structure, leading to a qualitative reshaping of the δP profile and a reversal in the sign of the H/D isotope effect. In neutral FcPMe, this coupling reduces the proton-transfer barrier. In FcPMe(−), NQEs eliminate the barrier for the proton, transforming a classical transition state into a stable, symmetric equilibrium structure in which the optimized protonic Gaussian center lies at the O···O midpoint, whereas a residual barrier persists for the heavier deuteron. Crucially, we demonstrate that the structural relaxation induced by NQEs, together with the associated changes in the electronic structure, qualitatively alters the highly nonlinear geometric dependence of the 31P NMR chemical shift. The curvature of the δP profile changes from a classical ″M-shape″ to a nearly quadratic form. Because the proton resides exactly at the minimum of this quadratic curve while the deuteron slightly deviates from it, this qualitative transformation provides the clear mechanistic explanation for the reversed sign of the isotope effect. These findings highlight the importance of incorporating NQE-induced structural changes into electronic structure calculations when analyzing isotope effects on highly nonlinear spectroscopic properties and provide a framework for understanding proton quantum dynamics in complex hydrogen-bonded systems.