Fe 3d Orbital Evolution in Ferrocene Ionization: Insights from ΔSCF, EOES, and Orbital Momentum Distribution

The ionization of ferrocene (Fc) remains an active topic of interest due to its complex, ulti-electron character. Accurate prediction of its first ionization potential (IP) requires methods that go beyond single-particle approximations, as Koopmans' theorem, Janak's theorem, and the outer valence Green function (OVGF) approach prove inadequate. Using the ΔSCF method, the first IP of Fc was calculated to be ~6.9 ± 0.1 eV, which is in close agreement with experimental values (6.72-6.99 eV). To benchmark computational accuracy, 42 models were evaluated using the CCSD, CCSD(T), and B3LYP methods with Pople and Dunning basis sets, including Fe-specific modifications to better capture 3d electron behavior. The results underscore the importance of proper treatment of Fe 3d orbitals, with B3LYP/m6-31G(d) offering the best compromise between accuracy and computational efficiency. Notably, the singly occupied molecular orbital (SOMO) in Fc⁺ is identified as the 8a₁' orbital, which is dominated by its Fe 3d character. This orbital, although not the α-HOMO in Fc⁺, becomes the LUMO upon ionization. Analysis of the excess orbital energy spectrum (EOES) reveals substantial energy shifts upon ionization, particularly in Fe-centered orbitals spanning both the core and valence regions. Theoretical momentum distribution (TMD) analysis of the 8a₁' orbital further quantifies orbital differences before and after ionization, providing complementary insights in momentum space. Finally, energy decomposition analysis (EDA) shows that while most interaction energy components become less stabilizing upon ionization, steric and Pauli terms contribute a small stabilizing effect.