In this section, we briefly review the theoretical framework of CNEO-DFT. For simplicity, we only treat protons and electrons quantum mechanically. A detailed formulation of CNEO-DFT, including a full-quantum treatment on all nuclei, can be found in previous work. According to the generalization of the Hohenberg-Kohn theorem to a multicomponent system of electrons and quantum nuclei, the ground-state energy of the multicomponent system is a functional of both electron densities ρ e and proton densities ρ p , E g.s. = E[ρ e , ρ p ].