Simple Semiempirical Method for the Location Determination of HOMO and LUMO of Carbon Dots

Carbon dots (C-Dots) have many unique properties, which endow them with a promising platform from catalysis to biology applications. However, quantitative understanding of those properties of C-Dots is still a tremendous challenge, and thus an urgent task is to develop a simple theoretical prediction method to quantitatively determine the energy levels of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) by a simple equation. Here, we determine the energy levels of LUMO and HOMO of C-Dots using the tight-binding method as well as the adjustment from the surface functional groups. A quantitative linear relationship between HOMO and HOMO–LUMO gap of C-Dots was obtained, which allows us to deeply understand the optical and photoelectrochemical properties.