Thermal Fluctuations in Conjugation and their Effect on Calculated Excitation Energies: A Case Study on the Astaxanthin Carotenoid

Abstract

A popular approach to the calculation of molecular excitation energies is to consider only equilibrium geometries and neglect the effects of thermal motion. Although this static approach is sensible for molecules with distinct potential-energy minima, its adequacy relative to dynamical approaches appears not to have been thoroughly tested. Here, we report a case study investigating how thermal motion accounted for by molecular dynamics simulations influences the optically bright state of astaxanthin, a carotenoid of broad photobiological interest that features 13 conjugated double bonds. Employing several different density functional methods, it is shown that thermal fluctuations in the conjugation result in the Boltzmann-weighted average excitation energies for this state being shifted by up to 0.05 eV relative to those obtained from purely static calculations. Accordingly, it is concluded that the effects of thermal motion on excitation energies of conjugated systems can be quite large even for molecules with distinct potential-energy minima.

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

“…In addition, errors produced by using different sizes of basis sets are in general higher than 0.01 eV. For instance, differences obtained by the selection of different basis sets with different density functionals for the closely related astaxanthins may reach 0.04 eV [6]. However, if values are extrapolated for higher number of carbon atoms s, the value of becomes more significant.…”

“…At this point, it is worth to compare the results presented herein with that found in the literature. In particular, Wang and Durbeej, found that considering thermal motion on the calculated excitation energies of astaxanthin carotenoids cannot be ignored, since the mean value for different functionals were found to be around 0.03–0.04 eV, depending on the composition of the density functional (only B3LYP density functional shows value around 0.01 eV) [6]. It should be noted, however, that there are some discrepancies in the calculation methods used in the present study and that of Wang et al, in terms of the calculation of excited electronic states (double hybrid versus global hybrids) and the calculation of the MD trajectories (extended tight binding for 200 ps vs. global hybrids for 20 ps) [6].…”

“…In particular, Wang and Durbeej, found that considering thermal motion on the calculated excitation energies of astaxanthin carotenoids cannot be ignored, since the mean value for different functionals were found to be around 0.03–0.04 eV, depending on the composition of the density functional (only B3LYP density functional shows value around 0.01 eV) [6]. It should be noted, however, that there are some discrepancies in the calculation methods used in the present study and that of Wang et al, in terms of the calculation of excited electronic states (double hybrid versus global hybrids) and the calculation of the MD trajectories (extended tight binding for 200 ps vs. global hybrids for 20 ps) [6]. More importantly, carotenoids are in general more “flexible” than linear polyenes of similar size/length due the the presence of two aromatic rings at the two ends of the polyene middle chain, which may results in making them more sensitive to thermal motions than simple linear polyenes.…”

“…the static approximation in the correct description of electronic excited states for molecular systems with distinctive potential energy minimum [6].…”

“…Actually, many studies considered the "dynamical" approach in their calculations of electronic excited states of different chemical systems [14][15][16]. However, Wang and Durbeej explicitly investigated the reliability and the need of the static and dynamic approaches [6]. In particular, they studied three stereoisomeric forms of conjugated astaxanthin carotenoids [6], using different global hybrid and meta global hybrid GGA functionals for the vertical excitation energies and for ab-initio molecular dynamics (AIMD) to generate thermal motion trajectories [6].…”