Fukui Function and Fukui Potential for Solid-State Chemistry: Application to Surface Reactivity

The Fukui function and its associated potential serve as essential descriptors of chemical reactivity within the framework of conceptual density functional theory (c-DFT). While c-DFT is well-established for molecular systems, it encounters formal and technical challenges when applied to extended systems. This comprehensive study addresses the complexities involved in calculating the Fukui function and its potential in systems with periodic boundary conditions (PBC). We specifically investigate the introduction of a fictitious potential associated with a compensating background of charge (CBC) in these calculations, examining its implications for the reliability of these reactivity descriptors. To explore this issue, we analyze a diverse range of metallic and semiconductor surfaces, including elemental metals such as Ti and Pt, metal oxides like TiO₂, SnO₂, and MgO, and transition metal carbides such as TiC and ZrC. By encompassing this varied selection, this work aims to uncover both the limitations and advantages of various computational approaches in accurately capturing the intrinsic chemical reactivity of extended systems. Our findings indicate that while certain methods yield reliable results, others introduce artifacts that can significantly distort interpretations of surface reactivity. We advocate for the calculation of the Fukui function and potential using finite differences with self-consistent potential correction whenever feasible. Interpolation methods may also be employed if delocalization errors are manageable. Furthermore, we demonstrate that a reliable method for computing the Fukui potential, in combination with perturbation theory, can predict the interaction energies of reducing agents such as sodium and oxidants like chlorine with TiO₂ surfaces, thus supporting the application of c-DFT in heterogeneous catalysis. This research contributes critical insights to the field, offering practical methodologies to address the inherent challenges in predicting surface reactivity. By elucidating the complexities of the Fukui function under PBC, we not only enhance theoretical frameworks but also equip researchers with robust tools for advancing materials science and surface chemistry.