On the connection between Gaussian statistics and excited-state linear response for time-dependent fluorescence

Area of Science:

• Physical Chemistry
• Computational Chemistry
• Spectroscopy

Background:

• Time-dependent fluorescence (TDF) is often simulated using linear-response approximations.
• Understanding the dynamics of chromophores in solvents is crucial for various chemical and biological processes.

Purpose of the Study:

• To investigate the relationship between linear-response approximations and Gaussian statistics for TDF Stokes shift calculations.
• To provide a deeper understanding of the Carter and Hynes approximation for TDF.

Main Methods:

• Derivation of a linear-response approximation for TDF Stokes shift based on excited-state dynamics.
• Comparison of the derived approximation with results obtained by assuming Gaussian statistics for the energy gap.

Main Results:

• The linear-response approximation derived by Carter and Hynes yields the same result as assuming Gaussian statistics for the energy gap.
• Subtle differences between linear response and Gaussian statistics were identified, suggesting broader applicability of the result.
• The Gaussian statistics assumption allows for straightforward computational checks of the approximation's validity.

Conclusions:

• The study clarifies the connection between linear response and Gaussian statistics in TDF simulations.
• The findings suggest that the Carter and Hynes approximation may be more generally applicable than previously thought.
• The assumption of Gaussian statistics provides a practical method for validating the approximation without increased computational cost.