Phonon-Driven Femtosecond Dynamics of Excitons in Crystalline Pentacene from First Principles

Nonradiative exciton relaxation processes are critical for energy transduction and transport in optoelectronic materials, but how these processes are connected to the underlying crystal structure and the associated electron, exciton, and phonon band structures, as well as the interactions of all these particles, is challenging to understand. Here, we present a first-principles study of exciton-phonon relaxation pathways in pentacene, a paradigmatic molecular crystal and optoelectronic semiconductor. We compute the momentum- and band-resolved exciton-phonon interactions, and use them to analyze key scattering channels. We find that both exciton intraband scattering and interband scattering to parity-forbidden dark states occur on the same $\sim 100\mathrm{fs}$ timescale as a direct consequence of the longitudinal-transverse splitting of the bright exciton band. Consequently, exciton-phonon scattering exists as a dominant nonradiative relaxation channel in pentacene. We further show how the propagation of an exciton wave packet is connected with crystal anisotropy, which gives rise to the longitudinal-transverse exciton splitting and concomitant anisotropic exciton and phonon dispersions. Our results provide a framework for understanding the role of exciton-phonon interactions in exciton nonradiative lifetimes in molecular crystals and beyond.

Figure 1

(a) Atomic structure of pentacene crystal (carbon and hydrogen in teal and gray, respectively). (b) Top: exciton band structure of the low-lying bright ($S_B$, blue) and dark ($S_D$, black) singlet excitons interpolated from the computed GW-BSE exciton dispersion along the reciprocal $\widehat{\mathbf{a}}\text{−}\widehat{\mathbf{b}}$ plane of the Brillouin zone. A longitudinal-transverse splitting of the bright state at $\mathrm{\Gamma }$ results in band intersection of the two states (black line). Bottom: the exciton band structure along the $Y-\mathrm{\Gamma }-X$ $k$ path (in crystal coordinates, shaded area marks the region displayed in the top panel).

Figure 2

Analysis of the computed exciton-phonon scattering for intraband (blue, left) and interband (black, right) transitions: (a) rates per phonon mode $\nu$, (b) rates per phonon momentum $\mathbf{q}$, (c) scattering times per exciton momentum $\mathbf{Q}$.

Figure 3

(a) Exciton wave packet occupation, computed from Eq. (4) for the first 1 ps after excitation, with the scattering rates constructing Fig. 2. The exciton evolution consists of the change in populations of $S_B$ state at $\mathbf{Q}\approx \mathrm{\Gamma }$ (within the area $\eta$ around $\mathrm{\Gamma }$, yellow), $S_B$ state at the remainder of $\mathbf{Q}$ space (blue), total $S_B$ state population (light blue), and $S_D$ state at all $\mathbf{Q}$ points (gray). (b) Spatial propagation of the wave packet during the first 500 fs. Blue distribution shows the bright state occupation, normalized, and amplified with respect to the initial step. MSD along the $\widehat{\mathbf{x}}$ (purple) and $\widehat{\mathbf{y}}$ (teal) are shown on the right.