Correcting hybrid density functionals to model Y6 and other non-fullerene acceptors

Recently developed fused-ring organic electron-acceptors such as Y6 have strong oscillator strength, good charge-carrier transport and low bandgaps. They therefore have enormous current technical application to optoelectronic devices, such as solar cells. Due to the large number of atoms involved in representative aggregates of these materials, we need an efficient electronic structure method to model them. Standard density functional theory poorly describe charge-transfer states, and were developed for vacuum calculations of individual molecules. In this work we tune a range-separated hybrid functional for Y6. We characterise representative dimers of the solid-state and show that Y6 dimers show the extensive solvatochromic effects are due, in part, to oscillator strength borrowing. We provide an explanation for the short optimally-tuned range-separation parameter, based in the Penn model for the frequency dependent dielectric of a semiconductor. We caution that standard range-separated hybrids are less accurate than global hybrids for these, and similar, materials. We show how reducing the range-separation length improves the accuracy of standard functionals, without an involved tuning process.

💡 Research Summary

This paper addresses a pressing challenge in the computational modeling of modern organic photovoltaic (OPV) materials: the accurate description of charge‑transfer (CT) and Frenkel‑exciton (FE) states in low‑band‑gap, high‑oscillator‑strength non‑fullerene acceptors (NFAs) such as Y6. Conventional density functional theory (DFT) and even standard global hybrid functionals (e.g., B3LYP, PBE0) suffer from self‑interaction error and an incorrect long‑range exchange decay, leading to qualitatively wrong CT energies and state ordering. To overcome these limitations, the authors employ a range‑separated hybrid (RSH) functional, LC‑ωhPBE, and perform an optimal‑tuning (OT) procedure that enforces a generalized Koopmans’ condition: the highest occupied and lowest unoccupied Kohn‑Sham eigenvalues must match the ionization potential (IP) and electron affinity (EA) obtained from ΔSCF calculations. Crucially, the tuning incorporates the material’s macroscopic optical dielectric constant (ε_r) by constraining the sum of the short‑ and long‑range Hartree‑Fock exchange fractions (α + β = 1/ε_r). Using an experimentally motivated ε_r ≈ 6 for Y6 thin films, the authors obtain a short‑range separation parameter ω ≈ 0.12 a₀⁻¹, α ≈ 0.23, and a slightly negative β (≈ ‑0.07 to ‑0.09), indicating reduced long‑range exchange relative to the short range.

The tuned functional is applied to the Y6 monomer and six representative “contact‑pair” dimers (D1‑D6) extracted from the crystal structure, all featuring inter‑molecular separations < 3.5 Å where electronic coupling is strong. Benchmarking against high‑level GW/BSE/MM calculations shows that the OT‑SRSH yields the smallest mean‑squared error for the first six singlet and triplet excitations across all dimers. Importantly, it reproduces the correct energetic ordering of CT and FE states, a feature that standard off‑the‑shelf RSHs (CAM‑B3LYP, wB97X‑D) fail to achieve, and that global hybrids capture only by coincidence. The authors further demonstrate the transferability of the tuned parameters: using the monomer‑derived ω, α, β on any dimer yields virtually identical excitation energies and state characters, confirming that a single set of OT‑SRSH parameters can be applied across monomers, dimers, and larger aggregates without re‑tuning.

State‑character analysis is performed with TheoDORE, which evaluates the transition density matrix to extract the CT fraction (ω_CT) and participation ratio (ω_PR). For dimer D2 (a J‑aggregate motif) the two lowest singlet states are pure CT, followed by two FE states, whereas dimer D4 (an H‑aggregate) exhibits four low‑lying mixed CT‑FE states. Triplet manifolds, in contrast, are dominated by FE character with CT states appearing at higher energies. This pronounced dependence of singlet CT‑FE mixing on dimer geometry explains the giant solvatochromic shifts observed experimentally in Y6 films. Reorganization energies calculated via both Nelsen’s four‑point method and Reimers’ normal‑mode approach are comparable to those from PBE0 and B3LYP, indicating that the OT‑SRSH does not distort potential energy surfaces despite its focus on excited‑state accuracy.

A particularly practical insight emerges from the authors’ exploration of “parameter‑reduced” CAM‑B3LYP: by simply decreasing its range‑separation parameter to reflect the high dielectric environment (i.e., using a shorter ω), one can achieve performance on par with the fully tuned OT‑SRSH, without the computational overhead of a full OT procedure. This suggests a straightforward recipe for large‑scale simulations of organic semiconductors: adopt a reduced ω consistent with the material’s ε_r, retain the standard global‑exchange fraction (α ≈ 0.20–0.25), and optionally allow a modest negative β to capture screened long‑range exchange.

In summary, the study provides a robust, transferable, and computationally efficient framework for modeling the excited‑state landscape of Y6 and related NFAs. By integrating dielectric screening into the range‑separation tuning, the authors reconcile the need for accurate CT description with the practical constraints of modeling sizable molecular aggregates. The work not only validates OT‑SRSH against high‑level many‑body methods but also offers a pragmatic shortcut (shortened ω in conventional RSHs) that can be readily adopted by the broader OPV community for the design and optimization of next‑generation organic photovoltaic devices.