Fundamental and excitation gaps in molecules of relevance for organic photovoltaics from an optimally tuned range-separated hybrid functional

The fundamental and optical gaps of relevant molecular systems are of primary importance for organic-based photovoltaics. Unfortunately, whereas optical gaps are accessible with time-dependent density functional theory (DFT), the highest-occupied – lowest-unoccupied eigenvalue gaps resulting from DFT calculations with semi-local or hybrid functionals routinely and severely underestimate the fundamental gaps of gas-phase organic molecules. Here, we show that a range-separated hybrid functional, optimally tuned so as to obey Koopmans’ theorem, provides fundamental gaps that are very close to benchmark results obtained from many-body perturbation theory in the GW approximation. We then show that using this functional does not compromise the possibility of obtaining reliable optical gaps from time-dependent DFT. We therefore suggest optimally tuned range-separated hybrid functionals as a practical and accurate tool for DFT-based predictions of photovoltaically relevant and other molecular systems.

Figure 1

The set of photovoltaically relevant molecules considered in this work: (a) thiophene, (b) 1,2,5-thiadiazole, (c) 2,1,3-benzothiadiazole, (d) benzothiazole, (e) fluorene, (f) 3,4,9,10-perylene tetracarboxylic acid dianhydride (PTCDA), (g) buckminsterfullerene (C${}_{60}$), (h) 21H,23H-porphine (H${}_2$P), (i) tetraphenylporphyrin (H${}_2$TPP), and (j) phthalocyanine (H${}_2$Pc).

Figure 2

Graphical representation of the data in Table : Optimally tuned values of the range parameter $\gamma$ (in atomic units) for the molecules shown in Fig. 1, as a function of the molecular characteristic radius (in Å).

Figure 3

Graphical representation of the data in Table for the ionization potentials of the molecules in Fig. 1. Yellow circles, experimental values; stars, optimally tuned BNL values; blue diamonds, GW values; red triangles, B3LYP values.

Figure 4

Graphical representation of the data in Table for the HOMO-LUMO gaps of the molecules in Fig. 1. Yellow circles, experimental values; stars, optimally tuned BNL values; blue diamonds, GW values; red triangles, B3LYP values.

Figure 5

Graphical representation of the data in Table for the first singlet excitation energies of the molecules in Fig. 1. Red triangles, B3LYP values; stars, optimally tuned BNL values; yellow circles, experimental values.