Alternative forms and transferability of electron-proton correlation functionals in nuclear-electronic orbital density functional theory

Multicomponent density functional theory (DFT) allows the consistent quantum mechanical treatment of both electrons and nuclei. Recently the epc17 electron-proton correlation functional was derived using a multicomponent extension of the Colle-Salvetti formalism and was implemented within the nuclear-electronic orbital (NEO) framework for treating electrons and specified protons quantum mechanically. Herein another electron-proton correlation functional, denoted epc18, is derived using a different form for the functional parameter interpreted as representing the correlation length for electron-proton interactions. The epc18 functional is shown to perform similarly to the epc17 functional for predicting three-dimensional proton densities and proton affinities. Both functionals are shown to be transferable for use with a series of diverse electronic exchange-correlation functionals, indicating that any reasonable electronic exchange-correlation functional may be used in tandem with the epc17 and epc18 electron-proton correlation functionals. Understanding the impact of different forms of the electron-proton correlation functional, as well as the interplay between electron-proton and electron-electron correlation, is critical for the general applicability of NEO-DFT.