As one can observe in the equations above, one needs only to provide a functional for electron-electron exchange-correlation (⌫ ee xc ) and for electron-proton correlation (⌫ ep c ). This is because both proton-proton exchange and correlation are negligible for chemically relevant systems. In our implementation, in order to exclude self-interaction, the diagonal elements of the Hartree-Fock exchange term are added to the protonic e↵ective potential. In comparison to standard electronic structure theory, this only leaves the definition of the electron-proton correlation functional unresolved. It should be noted that since one is dealing with fermionfermion correlation, any correlation functional form derived from first-principles should be directly applicable, even if it was designed with electrons in mind. In the context of this work, however, we will stray away from this discussion and restrict ourselves to the use of one of the most widely used functionals, the epc-17.2 functional proposed by Hammes-Schi↵er and coworkers. The expression is based on the Colle-Salvetti formulae and is provided as