Minding the Band gap: Major Factors for Correlating Computations with Experiments in Cu14 and Au20 Atomically Precise Nanoclusters

In a Perspective article titled "Mind the Gap!", Bredas clarifies the distinction between different uses of the term "band gap" in the context of experimentally measured or computationally evaluated energy gaps. In view of the tremendous progress in atomically precise metal nanoclusters where electrochemical and optical energetics are routinely supported by computations to establish structure-function correlations, we explore the relationship between different protocols for measuring and computing band gaps of two distinct organic ligand-protected nanoclusters: [Cu14H10(MBN)3(PPh3)8]+ and Au20(TBBT)16. Through UV/visible spectroscopy and differential pulse voltammetry, we measure optical and electrochemical band gaps in those systems. We then compare these experimental gaps to HOMO-LUMO gaps, fundamental gaps, vertical excitation energies, and Eox - Ered potentials computed using density functional theory (DFT) or time-dependent DFT (TD-DFT). We test functionals with varying degrees of Hartree-Fock (HF) exchange from 0% to 50%, different correlation functionals, basis sets, and (equilibrium and non-equilibrium) continuum solvation models. We find that in both copper and gold nanoclusters, the most important factor affecting the magnitude of the band gap is the % HF exchange, which in the case of the HOMO-LUMO gap can vary by several eV. This sensitivity is partially mitigated when computing the fundamental, optical, and electrochemical gaps. The second most important factor is the proper description of solvation effects. Other factors, such as the nature of the correlation functional, basis set, and geometry relaxation, have a considerably smaller effect on computed band gaps in these systems. Overall, this work provides generalizable guidelines on factors at varied importance for correlating computed and experimental "band gap" values.