Effect of thermal fluctuations on the electronic excitation energies of linear polyenes: A combined molecular dynamics and TD-DFT study

In the present study, thermally averaged electronic excitation energies (the so-called dynamic approach) are quantitatively assessed for a model molecular system composed of a series of increasingly longer chains of simple linear polyenes. The molecular dynamics trajectories are calculated using the semi-empirical “Geometry, Frequency, Noncovalent, eXtended Tight Binding” (GFN2-xTB) method, while TD-DFT vertical excitation energies of selected snapshots are obtained with the spin-component-scaled double hybrid density functional SCS-wPBEPP86. Boltzmann weighted average excitation energies were then calculated in order to take into account the contribution of thermal motions. Excitation energies via the dynamic approach are compared with that of the static approach in which thermal fluctuations are not considered. The differences between the dynamic and the static approaches were found to be around the range $-0.01$ to $+0.01$ eV for polyenes up to 44 carbon atoms. This range of errors is relatively small in comparison with typical errors produced by using different density functionals and/or basis sets. Therefore, the electronic excited states of small to medium lengths of linear polyenes (less than 50 carbon atoms) can be safely modeled via the static approach. However, extrapolation of the results to longer polyenes indicates that the difference between both approaches is estimated to be 0.05 eV for polyenes containing 100 carbon atoms, which suggests that considering thermal motions in the calculations of excitation energies is recommended for such long conjugated molecular systems.