The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction

Area of Science:

• Molecular Quantum Mechanics
• Theoretical Chemistry

Background:

• The Born-Oppenheimer approximation is a cornerstone of molecular science, simplifying calculations by separating electronic and nuclear motion.
• This approximation assumes electronic and nuclear wavefunctions can be treated independently due to their mass difference.

Purpose of the Study:

• To introduce a variational principle demonstrating the exact factorization of the total molecular wavefunction.
• To present an exact method for separating electronic and nuclear motion, overcoming limitations of the Born-Oppenheimer approximation.

Main Methods:

• Development of a variational principle to derive the exact factorization of the molecular wavefunction.
• Definition of a modified electronic Hamiltonian and derivation of the corresponding Schrödinger equation.
• Exact separation of the center of mass motion.

Main Results:

• The total molecular wavefunction can be exactly expressed as a product of electronic and nuclear wavefunctions.
• Nuclear motion is governed by a potential derived from the electronic energy, similar to the Born-Oppenheimer approximation.
• The proposed method allows for exact separation of the center of mass, which is not possible in the standard Born-Oppenheimer approximation.

Conclusions:

• A theoretically exact factorization of the molecular wavefunction is achievable.
• This exact method provides a more rigorous foundation for molecular quantum mechanics, including exact center of mass separation.
• The study validates the approach with a simple, exactly solvable model.