Conical Intersections and Electronic Momentum as Viewed from Phase Space Electronic Structure Theory.

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Chemical Physics

Background:

• Conical intersections are crucial in photochemistry, but standard Born-Oppenheimer approximations limit their understanding.
• The standard framework treats nuclear and electronic motions separately, potentially missing key quantum effects.

Purpose of the Study:

• To investigate the structure of two-state conical intersections using a phase space electronic Hamiltonian.
• To explore the role of electronic momentum in conical intersection dynamics.
• To challenge the limitations of the Born-Oppenheimer framework in describing these phenomena.

Main Methods:

• Developed a phase space electronic Hamiltonian (H_PS(R,P)) that includes nuclear momentum (P).
• Solved the electronic Schrödinger equation in a moving frame, allowing for time-reversal symmetry breaking.
• Analyzed the structure of the conical intersection branching plane in phase space.

Main Results:

• The phase space framework reveals a three-dimensional branching plane for conical intersections, unlike the two-dimensional plane in the Born-Oppenheimer approximation.
• Stationary electronic states in the phase space Hamiltonian exhibit electronic momentum, forming a double-well potential in momentum space.
• Calculated electronic momentum for BeH2 aligns with approximate complex restricted Hartree-Fock predictions.

Conclusions:

• Standard Born-Oppenheimer electronic states cannot capture the electronic momentum inherent in conical intersections.
• This work highlights the need for experimental investigations into photochemical observables beyond the Born-Oppenheimer framework.
• Further research into electronic momentum is essential for a complete understanding of conical intersections.