Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction.

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Physics

Background:

• Local scalar potentials are essential for density-functional theory (DFT) calculations, particularly for phenomena like molecular dissociation.
• Existing DFT formalisms often assume real-valued electronic wavefunctions, limiting their applicability to current-carrying states.

Purpose of the Study:

• To generalize existing scalar potentials to complex, current-carrying electronic wavefunctions.
• To introduce and characterize a novel electronic vector potential within the exact factorization formalism.
• To explore the implications of these potentials for molecular systems beyond the Born-Oppenheimer approximation.

Main Methods:

• Generalization of local scalar potentials ($$ and $$) to complex electronic wavefunctions.
• Application of the exact factorization formalism to derive coupled equations for marginal and conditional amplitudes.
• Analysis of the introduced electronic vector potential's relationship with paramagnetic and diamagnetic current densities.

Main Results:

• An unremovable electronic vector potential naturally emerges when extending scalar potentials to complex current-carrying states.
• This vector potential is linked to both paramagnetic and diamagnetic current densities.
• A specific example in a two-electron triplet state demonstrates the vector potential's circulation and a non-vanishing geometric phase.

Conclusions:

• The study successfully generalizes scalar potentials and introduces a crucial electronic vector potential for complex electronic states.
• This framework provides a more accurate description of molecular phenomena involving electronic currents.
• The findings offer new avenues for theoretical investigations beyond the standard Born-Oppenheimer approximation.