Predicting fluorescence quantum yields for molecules in solution: A critical assessment of the harmonic approximation and the choice of the lineshape function

Abstract

For the rational design of new fluorophores, reliable predictions of fluorescence quantum yields from first principles would be of great help. However, efficient computational approaches for predicting transition rates usually assume that the vibrational structure is harmonic. While the harmonic approximation has been used successfully to predict vibrationally resolved spectra and radiative rates, its reliability for non-radiative rates is much more questionable. Since non-adiabatic transitions convert large amounts of electronic energy into vibrational energy, the highly excited final vibrational states deviate greatly from harmonic oscillator eigenfunctions. We employ a time-dependent formalism to compute radiative and non-radiative rates for transitions and study the dependence on model parameters. For several coumarin dyes, we compare different adiabatic and vertical harmonic models (AS, ASF, AH, VG, VGF, and VH), in order to dissect the importance of displacements, frequency changes, and Duschinsky rotations. In addition, we analyze the effect of different broadening functions (Gaussian, Lorentzian, or Voigt). Moreover, to assess the qualitative influence of anharmonicity on the internal conversion rate, we develop a simplified anharmonic model. We address the reliability of these models considering the potential errors introduced by the harmonic approximation and the phenomenological width of the broadening function.

Luminescence in Crystalline Organic Materials: From Molecules to Molecular Solids

“…[ 142 ] In any case, it is noted that the application of the underlying harmonic approximation for the S 0 potential at such high energies might induce large errors in the calculated rates. [ 247 ] For molecules with comparable molecular (rigid) skeleton, in particular oligomer series such as oligoacenes n Ac (Scheme 3), such approach predicts an increase of k nr with decreasing energy gap between the i and f states (thus for increasing n ). [ 205 ] This “energy gap law” (EGL) was identified as the main reason for the validity of Kasha's rule (emission from S 1 in fluid solution under steady‐state conditions) due to the usually small energy separation found between higher excited states.…”

First-principles calculations of anharmonic and deuteration effects on the photophysical properties of polyacenes and porphyrinoids

“…where IC k is internal conversion (IC) rate constant between electronic states with the same spin multiplicity and ISC k is the intersystem crossing (ISC) rate constant between electronic states with different spin multiplicities [21]. The IC k and ISC k rate constants can be calculated using various softwares at different levels of theory [19,20,[22][23][24][25][26][27]. The most popular method is based on correlation functions for estimating Franck-Condon contributions [22][23][24][25].…”

Evaluating the anharmonicity contributions to the molecular excited state internal conversion rates with finite temperature TD-DMRG

“…Humeniuk et al assessed the validity of HA for several coumarin dyes when predicting the fluorescence quantum yields in solution. 32 They found that the accuracy of HA for the radiative decay rate is remarkable, while HA will underestimate the IC rates. Hence, HA will lead to an unreliable prediction of fluorescence quantum yield compared to the experiments.…”