Accurate and efficient prediction of optical gaps in silicon and germanium nanoparticles using a high-local-exchange density functional

Abstract

We investigated the HOMO-LUMO gaps and the optical gaps of Si and Ge nanoparticles (NPs) with various terminations and sizes using different functionals (HLE16, B3LYP, HSE-HJS) and basis sets (CRENBL, def2-SVP, def2-TZVP). The high-local-exchange functional HLE16, without Hartree–Fock exchange, effectively reproduces optical gaps using HOMO−LUMO gaps, offering a cost-effective alternative to hybrid functionals and TDDFT in nanoscale systems. Size (quantum confinement effects) and termination ligands (surface effects) significantly impact energy gaps: nonpolar CH3 had minimal effects, while polar ligands reduced gaps notably. Finally, ECP basis sets like CRENBL are better suited for NP electronic structures than all-electron basis sets.