Multicomponent density-functional theory for electrons and nuclei

We present a general multicomponent density-functional theory in which electrons and nuclei are treated completely quantum mechanically, without the use of a Born-Oppenheimer approximation. The two fundamental quantities in terms of which our theory is formulated are the nuclear N-body density and the electron density expressed in coordinates referring to the nuclear framework. For these two densities, coupled Kohn-Sham equations are derived, and the electron-nuclear correlation functional is analyzed in detail. The formalism is tested on the hydrogen molecule H₂ and its positive ion H₂⁺, using several approximations for the electron-nuclear correlation functional.