Exciton mobility control through $\text{sub}-\mathrm{\AA }$ packing modifications in molecular crystals

Exciton mobility in π stacks of organic chromophores is shown to be highly sensitive to the interference between long-range Coulombic coupling and a short-range coupling due to wave function overlap. A destructive interference, which leads to a compromised exciton bandwidth, can be converted to constructive interference (and an enhanced bandwidth) upon sub-Angstrom transverse displacements between neighboring chromophores. The feasibility of the control scheme is demonstrated theoretically on a derivative of terrylene, where the exciton is essentially immobile despite strong Coulombic coupling. A transverse slip of only 0.5 Å along either the short or the long molecular axis boosts the exciton velocity to $2\times {10}^4 \mathrm{m}/\mathrm{s}$. Changes in the mobility are correlated to changes in the absorption spectrum, allowing the latter to be used as a screen for high mobility aggregates.

Figure 1

The crystal structure of TAT nanopillars, [18] viewed down the stacking axis, is shown on the left. Here, X and Y denote the long and short molecular axes, respectively. The chemical structure of TAT is shown on the right.

Figure 2

(a) The calculated short-range coupling $J_{SR}$ and (b) the NN Coulombic coupling $J_C$ as a function of the transverse displacement in a cofacial TAT dimer. The origin indicates the eclipsed geometry. Blue regions indicate a positive coupling and hence H aggregation, while red regions indicate a negative coupling and J aggregation. The natural geometry of TAT (green dot) lies in a red region of the short-range coupling and a blue region of the long-range (Coulombic) coupling, making TAT an HJ aggregate. A slight shift along either molecular axis (yellow dots) has virtually no effect on the Coulombic coupling but leads to a sign change of the short-range coupling, transforming TAT into an HH aggregate with enhanced exciton transport properties. The transfer integrals $t_e$ and $t_h$ are found from the dimer energy splitting method, where the ab initio calculations set the intermolecular stacking distance to 3.3 Å and employ the B3LYP functional coupled with the 6-31G(d) basis set. $J_{SR}$ is subsequently evaluated using Eq. (4) with $U-V_{\mathrm{CT}}\left(1\right)=1209\mathrm{c}{\mathrm{m}}^{-1}$ (see the Supplemental Material, Tables S.1 and S.2 [33] for TAT parameters). The Coulombic couplings were evaluated using the transition-charge method [28, 29] and subsequently scaled by the procedure outlined in Ref. [17].

Figure 3

Calculated optical and dynamical properties of a TAT π stack, which behaves as an HJ aggregate, and a hypothetical π stack obtained by reversing the sign of $t_e$ (HH aggregate). (a) The calculated TAT absorption spectrum (red) is compared to the experimental nanopillar spectrum from Ref. [17]. Also shown is the HH aggregate spectrum (blue). The HH spectrum shows enhanced H-like behavior as the 0-0/0-1 peak ratio is suppressed due to a redistribution of oscillator strength to higher vibronic peaks. (b)–(d) The evolution of the wave function for a π stack containing 10 molecules when initially the first molecule is excited. (b) The amount of population that has accumulated in the trap at the end of the chain as a function of time. In the HJ aggregate, the excitation cannot efficiently reach the end of the chain, leading to a slow buildup of population in the trapping state; however, for the HH aggregate, the exciton moves swiftly across the chain so that the excitation reaches the trap quickly. (c) and (d) The exciton populations at each site on the chain for the HJ and HH aggregates with data points at 10 fs intervals. The HJ aggregate shows essentially zero movement of the exciton, while the HH aggregate moves rapidly across the chain. Parameters for these calculations are reported in the Supplemental Material, Tables S.1 and S.2 [33].

Figure 4

(a) Contour plot of the trap population as a function of time over a range of $J_{SR}$ values using the Hamiltonian in Eq. (2) with ${\widehat{H}}_{el}$ from Eq. (1). The parameters for the Hamiltonian are identical to those corresponding to a TAT HJ aggregate in Fig. 3, with the exception of $t_e$ and $t_h$. The latter were taken to be the TAT values (respectively, 435 and $402\mathrm{c}{\mathrm{m}}^{-1}$) multiplied by a scaling factor $\sqrt{\mathit{q}}$ so that the corresponding short-range coupling in Eq. (4) is scaled by $q$, i.e., $J_{SR}=q{J}_{SR}^{\mathrm{TAT}}$ with $J_{SR}^{\mathrm{TAT}}=-290\mathrm{c}{\mathrm{m}}^{-1}$. To obtain the negative scaling $J_{SR}=-q{J}_{SR}^{\mathrm{TAT}}, t_e$ was additionally multiplied by −1. (b) Calculated absorption spectra for a π stack containing 20 chromophores.

Figure 5

(a) The temperature dependent broadening of the 0-0 absorption peak is used to determine the relative contributions of static and dynamic disorder in TAT. (b) The population of the trapping site for the disordered HJ and HH aggregate, showing that the contrasting behaviors of constructive and destructive couplings are robust against disorder and dephasing and may even be enhanced by such effects.