Gap renormalization of molecular crystals from density-functional theory

Fundamental gap renormalization due to electronic polarization is a basic phenomenon in molecular crystals. Despite its ubiquity and importance, all conventional approaches within density-functional theory completely fail to capture it, even qualitatively. Here, we present a new screened range-separated hybrid functional, which, through judicious introduction of the scalar dielectric constant, quantitatively captures polarization-induced gap renormalization, as demonstrated on the prototypical organic molecular crystals of benzene, pentacene, and C${}_{60}$. This functional is predictive, as it contains system-specific adjustable parameters that are determined from first principles, rather than from empirical considerations.

Figure 1

Fundamental gaps of (a) benzene, (b) pentacene, and (c) C${}_{60}$ for the gas-phase molecule (left) and the molecular crystal (right), calculated with the PBE, HSE, PBE0, OT-RSH, and OT-SRSH functionals, and compared to $\mathit{GW}$. Bulk gaps were aligned to the middle of the gas-phase gap. Gas-phase HOMO and LUMO levels are additionally compared to experimental IP and EA values, taken from Ref. 25. GW values for gas-phase pentacene and benzene were taken from Refs. 20 and 26, respectively.

Figure 2

SRSH-computed HOMO-LUMO gaps [eV] (Ref. 33) of benzene, pentacene, and C${}_{60}$ solids, as a function of $1-1/\varepsilon$, with $\varepsilon$ being the asymptotic potential decay parameter in the SRSH functional. Straight lines are a linear fit.

Figure 3

Energy differences between OT-SRSH/$\mathit{GW}$ and PBE eigenvalues, as a function of OT-SRSH/$\mathit{GW}$ energies, for the benzene, pentacene, and C${}_{60}$ solids. All eigenvalues are shifted to the middle of the HOMO-LUMO gap for each method.