Phonon-Induced Localization of Excitons in Molecular Crystals from First Principles

The spatial extent of excitons in molecular systems underpins their photophysics and utility for optoelectronic applications. Phonons are reported to lead to both exciton localization and delocalization. However, a microscopic understanding of phonon-induced (de)localization is lacking, in particular, how localized states form, the role of specific vibrations, and the relative importance of quantum and thermal nuclear fluctuations. Here, we present a first-principles study of these phenomena in solid pentacene, a prototypical molecular crystal, capturing the formation of bound excitons, exciton-phonon coupling to all orders, and phonon anharmonicity, using density functional theory, the ab initio $GW$-Bethe-Salpeter equation approach, finite-difference, and path integral techniques. We find that for pentacene zero-point nuclear motion causes uniformly strong localization, with thermal motion providing additional localization only for Wannier-Mott-like excitons. Anharmonic effects drive temperature-dependent localization, and, while such effects prevent the emergence of highly delocalized excitons, we explore the conditions under which these might be realized.

Figure 1

Isosurfaces of electron distributions of singlet [blue (a)] and triplet [green (b)] excitons for a hole fixed at the center of the plotted area and corresponding dispersions [(c), same color scheme] in molecular crystals. A typical low-frequency (top) and high-frequency (bottom) phonon of pentacene is shown in (d).

Figure 2

Singlet (blue) and triplet (green) exciton radii within the different cases and temperatures (a). Representative configuration showing electronic isosurfaces for fixed hole positions, indicating localization of the singlet (triplet) at 0 K toward the region in blue (green), shown in (b) [(c)]. Red represents electronic wave function amplitude that disappears in the presence of phonons.

Figure 3

The difference between the rms displacement of phonons in the harmonic and anharmonic distributions of pentacene (a). Singlet exciton radii (b) along the highly anharmonic phonon shown in (a). Phonon displacements $u$ are given in units of their zero-point width $1/\sqrt{2{\omega }_{\mathit{q}\nu }}$ [32]. The dotted line in (b) is a guide to the eye.