Inelastic X-Ray Scattering Study of Exciton Properties in an Organic Molecular Crystal

Excitons in a complex organic molecular crystal were studied by inelastic x-ray scattering (IXS) for the first time. The dynamic dielectric response function is measured over a large momentum transfer region, from which an exciton dispersion of 130 meV is observed. Semiempirical quantum chemical calculations reproduce well the momentum dependence of the measured dynamic dielectric responses, and thus unambiguously indicate that the lowest Frenkel exciton is confined within a fraction of the complex molecule. Our results demonstrate that IXS is a powerful tool for studying excitons in complex organic molecular systems. Besides the energy position, the IXS spectra provide a stringent test on the validity of the theoretically calculated exciton wave functions.

Figure 1

A unit cell of Py-SO molecular crystal.

Figure 2

(a) IXS data of Py-SO with $q$ along the $a$ axis. The spectral intensities are divided by $q^2$. (b), (c) Enlargements of spectra shown in (a) with elastic line removed. ZINDO/SCI simulated $S(q,\omega )/q^2$ for $q$ along the $a$ axis based on (d) the aggregate and (e) a single molecule. The dashed lines in panels (a), (c), and (e) indicate the calculated HOMO-LUMO gap energy.

Figure 3

Integrated intensity as a function of momentum transfer for experimental features and single molecule calculations: (a) $A$ and I integrated over [1.5 eV, 3 eV], (b) $B+B^{\prime }$ and $\mathrm{II}+{\mathrm{II}}^{\prime }$ integrated over [4 eV, 5.4 eV], and (c) $C$ and III integrated over [5.4 eV, 8 eV]. Broken and dashed lines in (b) and (c) show the $q$ dependence of two main excitations of features $B$ and $C$, respectively. The false color plots for the calculated possibility $P(x,y)$ of finding an electron at site $x$ and a hole at site $y$ for (d) the lowest energy exciton; (e), (f) two main excitations of feature $B$; (g), (h) two main excitations of feature $C$. The atom sites are numbered in the top right corner. The atoms plotted in gray scale on the Py-SO molecule structure in the inset represent the probability $P(x)\equiv \sum _{y}P(x,y)$ of finding the electron or hole at site $x$ for Py-SO molecule.

Figure 4

(a) Experimental data with background removed. Momentum transfer $q$ is perpendicular to $a$ axis. (b) ZINDO/SCI simulated $S(q,\omega )/q^2$ based on a single molecule with $q$ perpendicular to $a$ axis in the $ac$ plane