Optical gaps in pristine and heavily doped silicon nanocrystals: TDDFT versus quantum Monte Carlo benchmarks

We present a time-dependent DFT study of optical gap of light-emitting nanomaterials, the pristine and heavily B and P co-doped silicon crystalline nanoparticles. Twenty DFT exchange-correlation functionals sampled from the best currently available inventory such as hybrids and range-separated hybrids are benchmarked against ultra-accurate quantum Monte Carlo results on small (~1 nm) model Si nanocrystals. Overall, the range-separated hybrids are found to perform best as expected for charge-transfer type transitions. However, even the range-separated hybrids exhibit pronounced quality variation for our limited test set. The quality of TDDFT gaps is correlated with deviation from the Koopmans’ theorem as a possible quality guide. In addition to providing a generic test of the TDDFT ability to describe optical properties of silicon crystalline nanoparticles, the results also open up a route to benchmark-quality DFT studies of nanoparticles sizes approaching those studied experimentally.