Importance of Vibronic Effects in the UV-Vis Spectrum of the 7,7,8,8-Tetracyanoquinodimethane Anion.

We present a computational method for simulating vibronic absorption spectra in the ultraviolet-visible (UV-vis) range and apply it to the 7,7,8,8-tetracyanoquinodimethane anion (TCNQ-), which has been used as a ligand in black absorbers. Gaussian broadening of vertical electronic excitation energies of TCNQ- from linear-response time-dependent density functional theory produces only one band, which is qualitatively incorrect. Thus, the harmonic vibrational modes of the two lowest doublet states were computed, and the vibronic UV-vis spectrum was simulated using the displaced harmonic oscillator approximation, the frequency-shifted harmonic oscillator approximation, and the full Duschinsky formalism. An efficient real-time generating function method was implemented to avoid the exponential complexity of conventional Franck-Condon approaches to vibronic spectra. The obtained UV-vis spectra for TCNQ- agree well with experiment; the Duschinsky rotation is found to have only a minor effect on the spectrum. Born-Oppenheimer molecular dynamics simulations combined with calculations of the electronic excitation energies for a large number of molecular structures were also used for simulating the UV-vis spectrum. The Born-Oppenheimer molecular dynamics simulations yield a broadening of the energetically lowest peak in the absorption spectrum, but additional vibrational bands present in the experimental and simulated quantum harmonic oscillator spectra are not observed in the molecular dynamics simulations. Our results underline the importance of vibronic effects for the UV-vis spectrum of TCNQ-, and they establish an efficient method for obtaining vibronic spectra using a combination of linear-response time-dependent density functional theory and a real-time generating function approach.