When Do Band Gap Calculations Agree with Experiments in Monolayer-Protected Cu 14 and Au 20 Atomically Precise Nanoclusters? A (TD)-DFT Comparison of HOMO–LUMO, Fundamental, Optical, and Electrochemical 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: [Cu 14 H 10 (MBN) 3 (PPh 3 ) 8 ] + and Au 20 (TBBT) 16 . Through UV/visible spectroscopy and differential pulse voltammetry, we measure optical and electrochemical band gaps in those systems. We then compare these experimentally determined gaps to HOMO−LUMO gaps, fundamental gaps, vertical excitation energies, and E o ox − E o red potentials computed using different density functional theory (DFT) or time-dependent DFT (TDDFT) methods. Specifically, in both copper and gold nanoclusters, we test the effect of truncating inert ligands from the model and compare density functionals with varying degrees of Hartree−Fock (HF) exchange from 0 to 50%, range-separated hybrids with a varying long-range tuning parameter, different correlation functionals, basis sets, and (equilibrium and nonequilibrium) continuum solvation models. Despite having different frontier orbital characters (the copper nanocluster has a metal-to-ligand charge transfer character while the gold nanocluster has metal-centered frontier orbitals), both nanoclusters display a similar sensitivity of the HOMO−LUMO gap to the HF exchange that is partially mitigated when computing the fundamental, optical, and electrochemical gaps. 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 guidelines for factors of varied importance for correlating computed and experimental band gap values.