Excitonic splitting in conjugated molecular materials: A quantum mechanical model including interchain interactions and dielectric effects

We present a quantum mechanical model for the calculation of the excitonic splitting of conjugated molecular materials; both short- and long-range interchain effects are explicitly included. The model is based on the time-dependent (TD) density functional approach and it introduces the effects of the proximate molecular systems in a perturbative framework. The new important aspect of our model is that both the single chain properties and the interchain effects are evaluated in the presence of an embedding environment which is modeled to mimic the dielectric interactions of the distant chains. This environment is here approximated with a continuum anisotropic dielectric. Such anisotropy is introduced to take into account the different dielectric properties of crystals (or films) of conjugated molecular systems along and perpendicular to the direction of the chains. In the model the dielectric environment is directly introduced in the quantum-mechanical equations through proper operators to be added to the Hamiltonian. An application to oligomers of polyacetylene quantifies the relative importance of the adjacent chains as well as of the dielectric medium showing the fundamental role played by the latter toward a direct comparison with experimental data.

Figure 1

Example of cavity used to simulate the “embedding” effects.

Figure 2

Comparison between perturbative (PT) (full line) and supermolecule (dotted line) approaches to compute excitonic splittings of “embedded” cofacial ${\mathrm{C}}_8{\mathrm{H}}_{10}$ chains at HF/6-31G (upper graph) and B3LYP/6-31G (lower graph) level. The circles refer to two-chain systems and the squares to three-chain systems. All the splittings are in eV and the interchain distances $\left(d\right)$ are in angstroms.

Figure 3

Schematic representation of the herringbone arrangement of the two trans-polyacetylene chains in the unit cell of the orthorombic crystal structure.

Figure 4

B3LYP/6-31G comparison between perturbative (PT) (full line) and supermolecule (dotted line) approaches to compute excitonic splittings of “embedded” ${\mathrm{C}}_8{\mathrm{H}}_{10}$ chains in a herringbone arrangement. The circles refer to two-chain systems and the squares to three-chain systems. All the splittings are in eV and the interchain distances $\left(d\right)$ are in angstroms.

Figure 5

Chain length dependence of the PT excitonic splitting (eV) computed at $\mathrm{B}3\mathrm{LYP}∕6\text{−}31+\mathrm{G}(d,p)$. Three interchain separations are considered, namely 4, 5, and $6\mathrm{\AA }$. The dotted line refers to the dipole-dipole approximation (see text) and the corresponding values have been scaled by 0.5.

Figure 6

Chain length dependence of the PT excitonic splitting (in eV) for chains at distance $d=5\mathrm{\AA }$ when computed without $\left({\Delta }_2^{\mathrm{PT}}\left(\text{gas}\right)\right)$ or with the embedding effects. In the latter case three sets of values are reported, the implicit term $({\Delta }_{\text{implicit}}={\Delta }_{\mathrm{Coul}}+{\Delta }_{\mathrm{xc}}-{\Delta }_{\mathrm{Ovl}})$, the explicit PCM term $\left({\Delta }_{\mathrm{PCM}}\right)$ and their sum $\left({\Delta }_2^{\mathrm{PT}}\right)$.

Figure 7

PT excitonic splittings (in eV) of herringbone polyacetylene in the two-chain $\left({\Delta }_2^{\mathrm{PT}}\right)$ and in the $n$-chain approximation $\left({\Delta }_n^{\mathrm{PT}}\right)$. In the latter case, results referring to the embedded system $({\Delta }_n^{\mathrm{PT}}\left(\text{embedded}\right))$ are also reported.