Electronic properties of oligoacenes from first principles

We present the electronic band structures and dielectric tensors for a series of crystalline linear oligoacenes—i.e., naphthalene, anthracene, tetracene, and pentacene—calculated within the density functional framework. The band dispersions, the effective charge carrier masses, and the optical response are discussed as a function of the oligomer length compared to previously reported calculations. The total band dispersions of the two topmost valence and lowest conduction bands are between 0.14 and $0.52\mathrm{eV}$, which, however, are strongly anisotropic. Regarding the charge transport properties, the band dispersions are large enough for bandlike transport only along crystalline directions within the herringbone plane. Except for naphthalene, the conduction bands are more dispersive than the valence bands. This indicates that the electron transport is favored compared to hole migration. The revised stable pentacene single-crystal structure exhibits the largest conduction-band dispersions among the series. Consequently the effective electron masses in pentacene are only $0.8m_0$, whereas the hole masses are in the order of $1.3m_0$. The electronic and optical gaps and thus the onset of the optical response decrease almost linearly, when going from naphthalene to pentacene.

Figure 1

(Color online) The anthracene $\left(3A\right)$ molecule as well as the herringbone arrangement of two inequivalent molecules in the $\mathbf{a}\mathbf{b}$ plane of crystalline $3A$. The number of repeating phenyl rings is indicated by $n$ in $nA$ and equals 2, 3, 4, and 5, for naphthalene, anthracene, tetracene, and pentacene, respectively.

Figure 2

(Color online) The $\mathbf{a}\mathbf{c}$ plane of the pentacene crystal reported by Campbell et al. (Refs. 18, 20) (top) and the revised structure by Mattheus et al. (Refs. 13, 19) (bottom).

Figure 3

(Color online) The band structures $E\left(\mathbf{k}\right)$ and DOS of monoclinic $2A$ (top) and $3A$ (middle), as well as the IBZ of $3A$ (bottom) illustrating the $\mathbf{k}$ path along which the energies have been calculated for the oligoacenes. The high-symmetry points in units of $(2\pi ∕a,2\pi ∕b,2\pi ∕c)$ are $\Gamma =(0,0,0)$, $\mathrm{Y}=(0.5,0,0)$, $\mathrm{Z}=(0,0,0.5)$, $\mathrm{A}=(0.5,0.5,0)$, $\mathrm{B}=(0,0.5,0)$, and $\mathrm{D}=(0.5,0.5,-0.5)$. The Fermi level is indicated by the dashed line. The subbands of the VB and CB as well as their DOS are given in gray.

Figure 4

Analogous to Fig. 3 from top to bottom: the band structures $E\left(\mathbf{k}\right)$ and DOS of the triclinic systems $4A$, $5A\text{−}C$, and $5A\text{−}M$.

Figure 5

The GGA energy gap $E_g^{\mathrm{GGA}}$ compared to data available in literature (Refs. 30, 40) as a function of the oligomer length $n$ (left) as well as a function of the inverse oligomer length $1∕n$ (right). The open symbols correspond to the $5A\text{−}M$ structure.

Figure 6

The band splitting of the highest occupied VB (left) and the lowest unoccupied CB (right) at high-symmetry points in the IBZ as a function of the oligomer length $n$. The open symbols correspond to the $5A\text{−}M$ structure.

Figure 7

Linear optical response ${\epsilon }_2\left(\omega \right)$ to incoming light with an electric field vector $\mathbf{E}$ parallel to the crystal axes $a$, $b$, and $c$, respectively. A lifetime broadening of $0.05\mathrm{eV}$ has been included. The amplitude of the strong $c$-polarized absorption given in gray is plotted against the right $y$ axis.