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.