Quantum‐Classical Calculation of the Absorption and Emission Spectral Shapes of Oligothiophenes at Low and Room Temperature by First‐Principle Calculations

Abstract

We report a thorough computational characterization of the low- and room-temperature absorption and emission spectra of a series of oligothiophenes that contain between three and seven thiophene units. Our computational approach is based on time-dependent (TD) density functional calculations with the CAM-B3LYP functional. The effect of vibrations is included without resorting to any empirical parameters either at a fully quantum level or with a hybrid quantum-classical protocol. This latter approach is introduced to describe the relevant broadening effects in absorption at room temperature and is based on the partition of the vibrational modes into two sets: the inter-ring torsions treated at the anharmonic level in a classical way and the remaining modes described at the quantum level. The contribution of the quantum modes to the spectrum is computed by using a harmonic approximation, which accounts for Duschinsky mixing and changes in the vibrational frequencies associated with the electronic transition; a path-integral TD approach is adopted to account for the effect of temperature. The spectra simulated at low temperatures are in very good agreement with their experimental counterparts, which indicates that our calculations can quantitatively reproduce the effect of chain lengthening on the position and the shape of the spectra. Good agreement is also obtained at room temperature, for which we show that the classical description of the broadening, owing to the inter-ring torsions, reproduces the loss of the vibronic structure observed in the experiment and introduces only a slight overestimation of the spectral width.

A Joint Theoretical and Experimental Study of the Behavior of the DIDS Inhibitor and its Derivatives

“…In some cases (e.g. oligothiophene), the flexibility of the compound is responsible for breaking the mirror symmetry rule between absorption and emission spectra, which is also the case for DIDS . The experimental DIDS fluorescence spectrum (data not shown) is less broadened than the absorption spectrum.…”

Going beyond the vertical approximation with time‐dependent density functional theory

“…This is particularly true for the AH model, since the necessity to project S 0 and S 1 normal modes computed at very different geometries, yields huge broadenings caused by exaggerated Duschinsky mixings, an artifact connected to the inadequacy of normal coordinates to describe large distortions of the molecular structure. Several groups are currently working to extend the capability of available models toward large and flexible compounds, adopting for instance a description of normal modes in internal coordinates and/or separating few large‐amplitude anharmonic motions to be treated at quantum or classical levels of theory . Different schemes for introducing anharmonic corrections on the frequencies and vibrational wavefunctions have been proposed considering either a perturbation expansion of the anharmonic potential, or exploiting prescreening techniques similar to those adopted in TI harmonic approaches .…”

“…If a quantum approach is required, all the above strategies are limited to cases where the anharmoncities are confined in a small subset of modes. In contrast, classical approaches can, in principle, deal with many anharmonic modes, at the cost of describing their contributions to the spectrum as a broadening line shape without considering their individual vibronic transitions …”

Toward a general mixed quantum/classical method for the calculation of the vibronic ECD of a flexible dye molecule with different stable conformers: Revisiting the case of 2,2,2‐trifluoro‐anthrylethanol

“…MQC approaches are attractive because they combine the usual procedures based on the harmonic approximation to describe the stiff quantum coordinates and simpler classical methods for the flexible modes, provided the associated frequencies are low. Different simple MQC schemes have been recently proposed in literature, for standard absorption and emission properties . The major challenge for these approaches is how to account, at least approximately, for the couplings between rigid and flexible coordinates.…”

“…Different simple MQC schemes have been recently proposed in literature, for standard absorption and emission properties. 24,[30][31][32][33][34] The major challenge for these approaches is how to account, at least approximately, for the couplings between rigid and flexible coordinates. For ECD spectra, a further challenge arises from the possibly drastic dependence of the RS on both soft and stiff coordinates.…”