Testing exact-factorization-based density functional approximation on a continuous density model.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• The Born-Oppenheimer approximation is a cornerstone of molecular quantum mechanics, but neglects electron-nuclear correlation.
• Developing accurate methods beyond the Born-Oppenheimer approximation is essential for describing phenomena like nonadiabatic dynamics.
• Previous work established an exact-factorization-based density functional approximation (DFA) for electron-nuclear correlation.

Purpose of the Study:

• To test the performance of a novel exact-factorization-based density functional approximation (DFA).
• To investigate electron-nuclear correlation beyond the Born-Oppenheimer approximation in a realistic model system.
• To assess the DFA's ability to capture nonadiabatic effects.

Main Methods:

• Implementation of coupled Kohn-Sham equations incorporating nonadiabatic corrections.
• Solution of the nuclear Schrödinger equation alongside electronic equations using advanced iteration techniques.
• Application to a two-electron Shin-Metiu model with continuous electronic density in one dimension.

Main Results:

• The DFA successfully captures nonadiabatic effects arising from electron-nuclear correlation.
• A correct shift in the critical nuclear position for proton-coupled electron transfer was observed.
• Nonadiabatic corrections to the Kohn-Sham potential were shown to shift orbital energies.

Conclusions:

• The tested DFA provides a viable approach for including electron-nuclear correlation beyond the Born-Oppenheimer approximation.
• The method accurately describes key nonadiabatic phenomena, such as proton-coupled electron transfer.
• The findings suggest potential applications in studying electron-phonon interactions and band renormalization in materials.