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

Abstract

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 EVIB≲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.

Vibrational Energy Flow and Chemical Reactions

“…Finding the nonlinear couplings would seem to require high-quality quantum chemical calculations, but the main features of energy flow only depend on their statistical propertiestypical size, variation, etc. The couplings can be modeled as random quantities (hence the “random” of local random matrix theory) subject to certain scaling laws and correlations dependent on the bonding properties of the molecule. ,− , Unperturbed modes often mix stretching and bending of many parts of the molecule, so the magnitude of the nonlinearities depends on the bonding pattern of the molecule. A simple implementation of the scaling, suitable for semiquantitative IVR calculations, is given in refs and .…”

“…The couplings can be modeled as random quantities (hence the "random" of local random matrix theory) subject to certain scaling laws and correlations dependentonthebondingpropertiesofthemolecule. 34,[42][43][44]55 Unperturbed modes often mix stretching and bending of many parts of the molecule, so the magnitude of the nonlinearities depends on the bonding pattern of the molecule. A simple implementation of the scaling, suitable for semiquantitative IVR calculations, is given in refs 26 and 34.…”

How Does Vibrational Energy Flow Fill the Molecular State Space?

“…Spectral features result from the interplay of the transition dipole operator, which weights the full density of eigenstates according to oscillator strength with the hierarchical structure of the vibrational Hamiltonian, which distributes the oscillator strength in a nontrivial fashion . The hierarchical structure has several origins: the size of the potential constants and matrix elements decreases exponentially with the order of the coupling when dimensionless normal or local mode coordinates are used; − a “triangle rule” for vibrational matrix elements due to this exponential scaling restricts energy flow among triplets of states; the local nature of most chemical bonding in large, low symmetry molecules reduces coupling among pairs and higher n -tuplets of vibrational states further. , …”

Quantum dynamics and control of vibrational dephasing

“…where ω is a typical vibrational frequency (100 meV), D is a typical energy scale for dissociating a molecular bond (2 eV), and the masses are for electrons and nuclei. As a result, the potential constant V (n) of a given order n scales as [11,14,22]…”