Intramolecular rate-constant calculations based on the correlation function using temperature dependent quantum Green's functions

Abstract

A theoretical method for calculating rate constants for internal conversion (IC), intersystem crossing (ISC) and radiative (R) electronic transitions is presented. The employed method uses temperature-dependent quantum Green's functions, which give the opportunity to consider almost any nth-order polynomial perturbation operator and the influence of external electromagnetic fields on the rate constants. The rate constants of the IC, ISC and R processes are calculated for two important indocyanine molecules namely indocyanine green (ICG) and heptamethine cyanine (IR808) at the Franck–Condon level using the temperature-dependent quantum Green's function approach. Calculations at the time-dependent density functional theory level with the MN15 functional show that ICG and IR808 have only one triplet state below the S₁ state. The main deactivation channel of the S₁ state is the IC process with a large (k_IC(S₁ → S₀)) rate constant of ∼10⁹–10¹¹ s⁻¹. The estimated quantum yield of fluorescence (φ_fl) is ∼0.001–0.24 for the two studied molecules, which agrees rather well with experimental values. Thus, the present approach enables calculations of the three kinds of rate constants and the quantum yield of fluorescence using the same computational methodology.