Calculations of vibrational state mixing leading to intramolecular vibrational energy redistribution in S₁ anthracene: Comparison with quantum beat experiments

A simple model for the anharmonic coupling constants has been used to calculate vibrational state mixing in S₁ anthracene. The aim of the calculations is to provide insight into the vibrational state mixing responsible for intramolecular vibrational energy redistribution (IVR). The calculations include all vibrations of the appropriate symmetry within a 100 cm^-1 interval centered about the state of interest. The calculations are compared with experimental measurements of quantum beats in S₁ anthracene [P. M. Felker and A. H. Zewail, J. Chem. Phys. 82, 2975 (1985) ]. These experiments involved an investigation of rotational effects that established the coupling to be anharmonic in origin. We show that in order for the experimental data to be explained by anharmonic coupling alone, the high-order anharmonic terms must be reasonably large. This implies that the anharmonic expansion converges quite slowly for E_VIB≲2000 cm^-1 in anthracene, in contrast with spectroscopic data for small molecules. Anthracene does not appear to be unique with regard to its IVR behavior, and consequently we suggest that slow convergence of the anharmonic expansion will prove to be the norm for large molecules. As a consequence of the slow convergence, direct coupling through high-order anharmonic terms is an important coupling mechanism. The model used to determine the anharmonic coupling constants is not specific to anthracene, and it is anticipated that it will be possible to predict vibrational state mixing in other molecules using the parameters deduced for anthracene.