Electronic Flux Density beyond the Born-Oppenheimer Approximation.

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Chemical Dynamics

Background:

• The Born-Oppenheimer approximation simplifies molecular simulations by separating electronic and nuclear motion.
• A consequence of this approximation is that electronic flux density, crucial for understanding electron movement, often vanishes.
• This vanishing flux density limits the ability to monitor electronic motion during chemical processes within standard Born-Oppenheimer simulations.

Purpose of the Study:

• To develop a method for calculating a meaningful electronic flux density within the Born-Oppenheimer approximation framework.
• To enable the monitoring of electronic motion coupled to nuclear motion during chemical rearrangements.
• To provide a computationally accessible approach for studying electron dynamics in chemical reactions.

Main Methods:

• Utilizing the exact factorization of electrons and nuclei.
• Applying nuclear velocity perturbation theory to derive a correction to the electronic wave function.
• Calculating the corrected electronic flux density using only the ground state potential energy surface and electronic wave function.

Main Results:

• The proposed electronic flux density effectively approximates the true electronic flux density.
• This approximation holds for both coherent tunneling dynamics and over-the-barrier scattering.
• The method shows good accuracy even for electron-to-nucleus mass ratios significantly larger than those found in reality.

Conclusions:

• A computationally feasible method to calculate electronic flux density has been developed.
• This approach overcomes the limitations of the standard Born-Oppenheimer approximation regarding electronic motion.
• The corrected electronic flux density offers a valuable tool for studying electron dynamics in chemical processes.