Nonequilibrium Fermi golden rule for electronic transitions through conical intersections.

Area of Science:

• Physical Chemistry
• Quantum Chemistry
• Computational Chemistry

Background:

• Photoinduced electronic transitions are crucial in photochemistry and photophysics.
• Conical intersections play a key role in facilitating these transitions in large molecules.
• Understanding these processes at finite temperatures is essential for accurate modeling.

Purpose of the Study:

• To develop a simple analytical expression for the time evolution of electronic populations during photoinduced transitions.
• To provide a nonequilibrium generalization of the Fermi golden rule applicable to photoinduced processes.
• To validate the model against quantum dynamics simulations for relevant molecular systems.

Main Methods:

• Utilizing the linear vibronic model Hamiltonian.
• Applying a second-order cumulant expansion for linear diabatic couplings.
• Deriving an analytical expression for electronic population dynamics at finite temperatures.
• Obtaining model parameters from electronic structure calculations and a diabatization procedure.

Main Results:

• A simple analytical expression for time-dependent electronic populations was derived.
• The expression represents a nonequilibrium generalization of the Fermi golden rule.
• The model shows good agreement with quantum dynamics simulations for fulvene and related cations.

Conclusions:

• The developed analytical model accurately describes photoinduced electronic transitions through conical intersections.
• The model provides a computationally efficient alternative to full quantum dynamics simulations.
• This work advances the theoretical understanding of photochemical processes in complex molecules.