text: Results. The method is validated for small PAHs, i.e., naphthalene and pyrene. We find that the semiempirical method PM3 produces accurate band positions with an error <5 cm−1. Furthermore, we calculate the spectra at multiple temperatures and find a clear trend toward band shifting and broadening.
  It is commonly accepted that polycyclic aromatic hydrocarbon molecules (PAHs) are the carriers of discrete emission features at 3.3, 6.2, 7.7, 8.6, 11.2, and 12.7 μm bands in the infrared (IR) spectra of a variety of astrophysical environments from young stellar objects, to planetary and reflection nebulae, to the diffuse interstellar medium, and even in the emission from entire galaxies (Tielens 2008). In order to identify relevant molecular structures and characterize the physical and chemical conditions of PAHs in various astrophysical environments, experimentalists and theoreticians have been working together closely to study the IR spectra of PAHs.
  From the theoretical point of view, IR vibrational spectra can be calculated using several methods. Previous computations were performed using a static/time-independent method within the framework of density functional theory (DFT), in which the double harmonic approximation is used for vibrational IR intensities. A scaling factor has to be implemented to downscale the calculated harmonic frequencies to correct the anharmonic effects or match with matrix-isolation experimental features (Langhoff 1996). As a first-order approximation, this approach has been successful enough in roughly reproducing the overall IR spectrum of certain individual PAHs, but serious problems persist when comparing this with high-resolution experiments (Mackie et al. 2015). Specifically, the IR features in the C-H stretching region are poorly modeled using harmonic level analysis, owing to the effects of mode couplings and resonances that are not described at the harmonic level (Mackie et al. 2015).
  Second-order vibrational perturbations theory (VPT2) produce accurate anharmonic spectra, which compare well with experimental spectra (Chen 2018). In the VPT2 method, IR intensity can be redistributed among fundamentals, combination bands, and overtones due to resonances. A recent study shows that the standard VPT2 contains caveats with resonances; for example, the singularities that occur in resonant calculations of intensities cannot be handled correctly and this often leads to the overestimation of the intensity of certain combination bands on the spectrum. Therefore additional corrections are necessary (Mackie et al. 2015). In addition, VPT2 suffers from low efficiency of calculation and only works for small molecules (less than 24 C-atoms). Moreover, highly symmetric molecules with symmetry of D6h, for example, coronene and circumcoronene, cannot be calculated with this method. However, such species are actually expected to be highly abundant in space given their high stability (Bauschlicher et al. 2008). Circumcoronene has special interest for astronomers, as the aromatic infrared bands are believed to be carried by PAHs with more than 50 carbon atoms (Allamandola et al. 1989; Li & Draine 2001; Tielens 2008).