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Modeling the emission spectra of polycyclic aromatic hydrocarbons by recurrent fluorescence

Damien Borja, Florent Calvo, Pascal Parneix, Cyril Falvo

Abstract

Recurrent fluorescence (RF) is an important relaxation mechanism in polycyclic aromatic hydrocarbons (PAHs), which could stabilize them and contribute to the production of aromatic infrared bands that are observed in the infrared spectra of the interstellar medium (ISM). In this theoretical work, a statistical model of relaxation by recurrent fluorescence is formally developed, including Herzberg-Teller and Duschinsky rotation effects as well as a full account of vibrational progressions. Using canonical and harmonic approximations, the RF rate constants can be determined from the transition dipole moment time autocorrelation functions. Application to the naphthalene, anthracene, and pyrene cations is presented based on quantum chemical inputs obtained from time-dependent density-functional theory. For these highly symmetric molecules, the low-lying, symmetry-forbidden electronic transitions are predicted to contribute possibly even more than higher energy, non-forbidden transitions. Such an unexpected contribution could increase the cooling efficiency of PAHs and, in turn, stabilize them further under the highly ionized environments of the ISM.

Modeling the emission spectra of polycyclic aromatic hydrocarbons by recurrent fluorescence

Abstract

Recurrent fluorescence (RF) is an important relaxation mechanism in polycyclic aromatic hydrocarbons (PAHs), which could stabilize them and contribute to the production of aromatic infrared bands that are observed in the infrared spectra of the interstellar medium (ISM). In this theoretical work, a statistical model of relaxation by recurrent fluorescence is formally developed, including Herzberg-Teller and Duschinsky rotation effects as well as a full account of vibrational progressions. Using canonical and harmonic approximations, the RF rate constants can be determined from the transition dipole moment time autocorrelation functions. Application to the naphthalene, anthracene, and pyrene cations is presented based on quantum chemical inputs obtained from time-dependent density-functional theory. For these highly symmetric molecules, the low-lying, symmetry-forbidden electronic transitions are predicted to contribute possibly even more than higher energy, non-forbidden transitions. Such an unexpected contribution could increase the cooling efficiency of PAHs and, in turn, stabilize them further under the highly ionized environments of the ISM.
Paper Structure (15 sections, 53 equations, 12 figures, 1 table)

This paper contains 15 sections, 53 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical model for RF relaxation
  3. Recurrent fluorescence differential rate constant
  4. Harmonic model
  5. Computational details
  6. Results
  7. Electronic structure of the cations
  8. Effective canonical temperature
  9. RF rate constants
  10. Experimental comparison
  11. Conclusions and perspectives
  12. Duschinsky parameters
  13. Calculation of the dipole moment time autocorrelation function
  14. Comparison between the computed and experimental absorption spectra of the D$_0$ $\rightarrow$ D$_2$ band of Np$^+$
  15. Validity of the harmonic and HT approximations

Figures (12)

  • Figure 1: Jablonski diagram showcasing some of the most important processes involved in the stochastic heating mechanism: initial excitation, IR photon emission, fragmentation, internal conversion (IC), inverse internal conversion (IIC) and recurrent fluorescence (RF).
  • Figure 2: PAH cations studied in this work. (a) Naphthalene; (b) anthracene; (c) pyrene, together with the reference frame used to identify appropriate symmetries.
  • Figure 3: Simulated photoelectron spectra for (a) Np$^+$; (b) An$^+$; and (c) Py$^+$. The spectra are shifted horizontally to match experimental lines. The original positions of the states, calculated by our model, are shown by dashed vertical lines, while the full lines show the shifted positions. All spectra are convoluted with a Gaussian with FWHM of 50 $\text{cm}^{-1}$.
  • Figure 4: Simulated absorption spectrum for Np$^+$ at zero temperature, convoluted using a Gaussian function with FWHM of 400 $\text{cm}^{-1}$. The inset highlights the 0.6--1.8 eV energy range.
  • Figure 5: Mode-specific Herzberg-Teller oscillator strength $f_{e,k}^{\text{HT}}(T)$ for the D$_0$$\rightarrow$ D$_1$ transition of the cations (a) Np$^+$; (b) An$^+$; and (c) Py$^+$, at $T=2000$ K and as a function of the harmonic frequency $\omega_{e,k}$. The gerade vibrational modes have no contribution. The oscillator strengths in the CH stretching region are given in logarithmic scale for better visualization.
  • ...and 7 more figures