The Far-IR Fe-Cp Vibrations of Deuterated Ferrocene: A DFT Benchmark and Physics-Based AI Assessment

Deuteration provides a controlled perturbation for probing isotope and symmetry effects in organometallic vibrational spectra. Here, density functional theory (DFT) is used to systematically examine the evolution of far-infrared (400-600 cm^-1) Fe-Cp vibrational modes in fully protonated, partially deuterated, and fully deuterated ferrocene. All three characteristic modes-the a₂″ torsional mode and the two e₁' bending modes-exhibit monotonic red-shifts with increasing deuteration. The a₂″ mode shows the largest isotope sensitivity, shifting by ~28 cm^-1 across the DFT series, whereas the e₁' modes shift by ~11-12 cm^-1 and undergo symmetry-dependent splitting of up to ~2 cm^-1 under partial deuteration. These results establish the a₂″ band as a sensitive probe of the degree of deuteration and the e₁' splitting as a diagnostic of symmetry reduction. A physics-based AI surrogate model reproduces the overall red-shift trends but deviates at high deuteration, with maximum errors of ~16.6 cm^-1, highlighting the limits of reduced-mass scaling.