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

## TL;DR

This paper compares hybrid and double-hybrid density functionals for predicting nuclear quadrupole splittings in iron-containing molecules, identifying the most accurate and efficient methods.

## Contribution

The study introduces a systematic evaluation of newly developed and widely used density functionals for Mössbauer spectroscopy predictions.

## Key findings

- PBE-0DH double-hybrid functional achieves the lowest mean absolute error (0.20 mm/s) for 57Fe NQS predictions.
- rSCAN38 hybrid functional offers a balance of accuracy (0.25 mm/s MAE) and computational efficiency.
- Double-hybrid functionals outperform hybrid ones for strongly correlated systems like ferrocene.

## Abstract

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.