Electronic-nuclear entanglement in Born-Oppenheimer wave functions and beyond

Area of Science:

• Quantum chemistry
• Molecular physics
• Theoretical chemistry

Background:

• Electronic and nuclear motions in molecules are often treated separately using approximations.
• Understanding the entanglement between these motions is crucial for accurate molecular modeling.

Purpose of the Study:

• To analyze the entanglement in molecular wave functions under various theoretical frameworks.
• To assess entanglement as a measure of nonadiabatic couplings.

Main Methods:

• Analysis of four common molecular wave function treatments: Born-Oppenheimer factorization, diabatic picture, Born-Huang expansion, and the full molecular Hamiltonian eigenfunction.
• Utilized one-dimensional models: H2+ and the Shin-Metiu Hamiltonian.

Main Results:

• Even within the Born-Oppenheimer approximation, molecular states exhibit entanglement.
• Entanglement content correlates with the variation of electronic wave functions and is influenced by avoided crossings.
• Sharp avoided crossings favor a diabatic picture, while broad ones favor the adiabatic picture.
• Electron-nuclear entanglement effectively identifies strong or weak nonadiabatic couplings.

Conclusions:

• Entanglement is an inherent property of molecular wave functions, not just an artifact of approximations.
• The Born-Huang expansion shows slow convergence for entanglement trends compared to the full molecular eigenfunction.
• Electron-nuclear entanglement provides a valuable tool for characterizing molecular dynamics and nonadiabatic effects.