Time-resolved fluorescence

Two-dimensional fluorescence spectra of HBDI⁻ were generated based on the AIMS simulations. Spectra were obtained as:

where the sum is restricted to TBFs that are propagating on S₁, h is Planck's constant, n_I(t) is the S₁ population of the I^th TBF, μ_S0/S1(R) is the transition dipole moment between S₀ and S₁ at molecular geometry R, ΔE_S0/S1($\bar{R}$_I) represents the S₀/S₁ energy gap, and $\bar{R}$_I(t) is the position centroid of the I^th TBF at time t.¹⁰² The time-resolved fluorescence spectra were convolved with a Gaussian having FWHM of 0.15 eV in the energy domain (ν) and 100 fs in the temporal domain (t) to simulate the instrument response function of previous fluorescence up-conversion experiments.^27,103 For each two-dimensional fluorescence spectrum, the energy was shifted by 0.13 eV to align the fluorescence intensity maxima obtained from theory and experiment (vide infra).³¹ Once shifted, the decay signal corresponding to an intensity slice at 500 nm was extracted and analyzed to elucidate the fluorescence behavior of HBDI⁻ over the course of the dynamics.