The CNEO methods are based on the multicomponent quantum theory, in which both electrons and nuclei are treated quantum mechanically. Based on the physical intuition that in most chemical and biological systems of interest, nuclei are still relatively localized in space, we treat nuclei as distinguishable particles and use the quantum nuclear expectation positions to denote geometries in the CNEO framework. Thus, for a particular geometry, the multicomponent quantum ground state is obtained by minimizing the total energy subject to the constraint on the quantum nuclear expectation positions: