Prediction of ⁵⁷Fe Mössbauer Nuclear Quadrupole Splittings with Hybrid and Double-Hybrid Density Functionals

As a crucial parameter in Mössbauer spectroscopy, nuclear quadrupole splitting (NQS) exhibits a strong dependence on quantum chemistry methods, which makes accurate theoretical predictions challenging. Meanwhile, the continuous emergence of new density functionals presents opportunities to advance current NQS research. In this study, we evaluate the performance of eleven hybrid density functionals and twelve double-hybrid density functionals, selected from widely used functionals and newly developed functionals, in predicting the NQS values of the ⁵⁷Fe nuclide for 32 iron-containing molecules within about 70 atoms. The calculations have incorporated scalar relativistic effects using the exact two-component (X2C) Hamiltonian. In general, the double-hybrid functional PBE-0DH demonstrates superior performance compared to the experimental values, achieving a mean absolute error (MAE) of 0.20 mm/s. Meanwhile, rSCAN38 is the best hybrid functional for our database with an MAE = 0.25 mm/s, and it offers a significant advantage in computational efficiency over PBE-0DH. The +/- sign of NQS has also been considered in our error statistics when it has a clear physical meaning; if neglected, the errors of many functionals decrease, but PBE-0DH and rSCAN38 remain unaffected. Notably, when calculating ferrocene [Fe(C₅H₅)₂], which involves strong static correlations, all hybrid functionals that incorporate more than 10% exact exchange fail, while several double-hybrid functionals continue to deliver reliable results. In addition, we encountered two particularly challenging species characterized by strong static correlations: [Fe(H₂O)₅NO]²+ and FeO₂^--porphyrin. Unfortunately, none of the density functionals tested in our study yielded satisfactory results for the two cases since the density functional theory (DFT) is a single-determinant approach, and it is imperative to explore large-scale multi-configurational methods for these species. This research offers valuable guidance for selecting density functionals in Mössbauer NQS calculations and serves as a reference point for the future development of new density functionals.