Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory

Intermolecular singlet fission (SF) is the conversion of a photogenerated singlet exciton into two triplet excitons residing on different molecules. SF has the potential to enhance the conversion efficiency of solar cells by harvesting two charge carriers from one high-energy photon, whose surplus energy would otherwise be lost to heat. The development of commercial SF-augmented modules is hindered by the limited selection of molecular crystals that exhibit intermolecular SF in the solid state. Computational exploration may accelerate the discovery of new SF materials. The GW approximation and Bethe-Salpeter equation (GW+BSE) within the framework of many-body perturbation theory is the current state-of-the-art method for calculating the excited-state properties of molecular crystals with periodic boundary conditions. In this Review, we discuss the usage of GW+BSE to assess candidate SF materials as well as its combination with low-cost physical or machine learned models in materials discovery workflows. We demonstrate three successful strategies for the discovery of new SF materials: (i) functionalization of known materials to tune their properties, (ii) finding potential polymorphs with improved crystal packing, and (iii) exploring new classes of materials. In addition, three new candidate SF materials are proposed here, which have not been published previously.

Cluster-Based Approach Utilizing Optimally Tuned TD-DFT to Calculate Absorption Spectra of Organic Semiconductor Thin Films

The photophysics of organic semiconductor (OSC) thin films or crystals has garnered significant attention in recent years since a comprehensive theoretical understanding of the various processes occurring upon photoexcitation is crucial for assessing the efficiency of OSC materials. To date, research in this area has relied on methods using Frenkel-Holstein Hamiltonians, calculations of the GW-Bethe-Salpeter equation with periodic boundaries, or cluster-based approaches using quantum chemical methods, with each of the three approaches having distinct advantages and disadvantages. In this work, we introduce an optimally tuned, range-separated time-dependent density functional theory approach to accurately reproduce the total and polarization-resolved absorption spectra of pentacene, tetracene, and perylene thin films, all representative OSC materials. Our approach achieves excellent agreement with experimental data (mostly ≤0.1 eV) when combined with the utilization of clusters comprising multiple monomers and a standard polarizable continuum model to simulate the thin-film environment. Our protocol therefore addresses a major drawback of cluster-based approaches and makes them attractive tools for OSC investigations. Its key advantages include its independence from external, system-specific fitting parameters and its straightforward application with well-known quantum chemical program codes. It demonstrates how chemical intuition can help to reduce computational cost and still arrive at chemically meaningful and almost quantitative results.

The charge-transfer states and excitation energy transfers of halogen-free organic molecules from first-principles many-body Green's function theory

The organic solar cells based on halogen-free components, have been the new favorites to develop green and renewable energy. PBDB-T and its derivatives are considered the superior electron donors to construct the solar cells. Although there are plenty of researches about them, the charge-transfer mechanisms and excitation energy transfers of relative organic solar cells are still unclear, the developments of photovoltaic devices are restricted consequently. In this work, we calculate the electronic structures and excited-state properties of PBDB-T, PBT1-C, PBT1-O and PBT1-S donors in the gas phase from the many-body Green's function theory. With BTP-IC and BTP-IS as the acceptors, we consider the Förster, Dexter, and overlap electronic couplings to compute the excitation energy transfers of the dimers. The ionization energies and excited-state energies of the four donors calculated by GW + BSE are in good agreement with experiments, and they are sensitive to the functionals in the computation. We find two charge transfer schemes. The thienyl of PBDB-T molecule makes its charge-transfer state at the lowest energy, and the total electronic coupling of PBDB-T based dimer is the strongest. The Dexter, and overlap types electronic couplings are significant to study the excitation energy transfer of organic heterojunctions. We provide a theoretical guide in the design and synthesis of higher-performance halogen-free donors.

Crucial Role of Defect States in the Ultralong Phosphorescence of Organic Molecular Crystals

Ultralong organic phosphorescence (UOP) in pure organic molecular crystals has attracted a lot of interest recently. There is much debate on the emission mechanism of this UOP. Two recent experimental works published in Nat. Photonics 2019, 13, 406-411 and Nat. Mater. 2021, 20, 175-180 attribute UOP in the 2,4,6-trimethoxy-1,3,5-triazine (TMOT) crystals and the carbazole crystals to H-aggregation of the TMOT molecules or the formation of charge-transfer excitons between the carbazole and impurity molecules. Our first-principles many-body Green's function theory calculations show that the lowest triplet states of these two crystals are in fact the localized defect states originating from the twisted TMOT molecules and the impurities, respectively. Energies of the H-aggregation-induced exciton and the charge-transfer exciton are too high to account for UOP. UOP should be mainly due to the little orbital overlap between the localized defect state and the delocalized band edges of the crystal. Strong intermolecular interactions suppress nonradiative decay of the triplet exciton localized on the defect.

The Role of Crystal Packing on the Optical Response of Trialkyltetrelethynyl Acenes

The electronic and optical responses of an organic semiconductor (OSC) are dictated by the chemistries of the molecular or polymer building blocks and how these chromophores pack in the solid state. Understanding the physicochemical natures of these responses are not only critical for determining OSC performance for a particular application, but the UV/visible optical response may also be of potential use to determine aspects of the molecular-scale solid-state packing for crystal polymorphs or thin-film morphologies that are difficult to determine otherwise. To probe these relationships, we report the quantum-chemical investigation of a series of trialkyltetrelethynyl acenes (tetrel = silicon or germanium) that adopt the brickwork (BW), slip-stack (SS), or herringbone (HB) packing configurations; the π-conjugated backbones considered here are pentacene (PEN) and anthradithiophene (ADT). For comparison, HB-packed (unsubstituted) pentacene is also included. Density functional theory (DFT) and G0W0 (single-shot GW) electronic band structures, G0W0-BSE (Bethe-Salpeter Equation)-derived optical spectra, polarized ϵ2 spectra, and distributions of both singlet and triplet exciton wave functions are reported. Configurational disorder is also considered. Further, we evaluate the probability of singlet fission in these materials through energy conservation relationships.

Accurate Polarization-Resolved Absorption Spectra of Organic Semiconductor Thin Films Using First-Principles Quantum-Chemical Methods: Pentacene as a Case Study

Theoretical studies using clusters as model systems have been extremely successful in explaining various photophysical phenomena in organic semiconductor (OSC) thin films. But they have not been able to satisfactorily simulate total and polarization-resolved absorption spectra of OSCs so far. In this work, we demonstrate that accurate spectra are predicted by time-dependent density functional theory (TD-DFT) when the employed cluster reflects the symmetry of the crystal structure and all monomers feel the same environment. Additionally, long-range corrected optimal tuned functionals are mandatory. For pentacene thin films, the computed electronic spectra for thin films then reach an impressive accuracy compared with experimental data with a deviation of less than 0.1 eV. This allows for accurate peak assignments and mechanistic studies, which paves the way for a comprehensive understanding of OSCs using an affordable and easy-to-use cluster approach.

The Excited State and Charge Transfer of Two Nonfullerene Acceptors from First-Principles Many-Body Green’s Function Theory

Nonfullerene acceptors (NFAs) have shown an outstanding performance upon producing highly efficient and sustainable organic solar cells (OSC). Recently, a growing group of researchers denoted to modify the structures of acceptor−donor−acceptor-type NFAs to raise the power conversion efficiencies (PCEs) when they are blended with a variety of polymer donors in OSC. In 2020, the ketone on the ending groups of BTP-IC were substituted for sulfonyl; the new NFA named BTP-IS was synthetized. The PCE of BTP-IS based OSC is 5.25% higher than that of the BTP-IC device. Based on this, the many-body Green’s function theory, combined with other quantum chemical methods, is conducted to study their ground electronic structures, excited states, and absorption spectra. The ground-state geometries, ionization energies, and the excited state energies are deeply sensitive to exchange-correlation functionals used in calculations. The lowest excited state energies calculated by full-BSE method using DFT-PBE as the starting point is 0.07~0.14 eV smaller than that by TDDFT-PBE method, which is more consistent with experimental data. This provided a methodology for future research on similar NFA systems. The first charge-transfer states and transfer mechanism of two molecules are proposed in this paper. Furthermore, we found that the reason for more efficient charge transport in BTP-IS-based OSC is the larger ionization energies and much weaker electron-hole interaction in BTP-IS. This finding is conducive to the better application of BTP-IS in OSC field.

How size, edge shape, functional groups and embeddedness influence the electronic structure and partial optical properties of graphene nanoribbons

The armchair and zigzag edge shape makes graphene nanoribbons (GNRs) exhibit interest in different applications. However, the relationship between influencing factors and properties is not clear. Herein, the many-body Green's function theory and the TDDFT method are used to investigate the effect of size, edge shape and functional groups on the electronic and optical properties of GNRs and h-BN-embedded GNRs. We find that ZGNRs have a smaller band gap and absorption edge than AGNRs having the same size and functional groups. The relationship between S₁ and T₁ is mainly determined by the size and edge shape of GNRs, while the redox ability of water splitting mainly relies on the kind of the functional group. When h-BN is embedded in GNRs, the edge shape of GNRs and the contact part between two substances control the direction of electron transfer in both the ground state and the excited state. These results can provide theoretical support for further improvements and applications of GNRs.

Singlet fission relevant energetics from optimally tuned range-separated hybrids

As a promising idea to design high-efficiency organic photovoltaics, singlet fission (SF) mechanism, i.e., generating two triplet excitons out of a single photon absorption, has recently come into the spotlight. Even though much effort has been devoted to this arena, accurately accounting for the SF process from the theoretical perspective has proven to be challenging. Herein, the SF energetics have thoroughly been investigated with the help of optimally tuned range-separated hybrid functionals (OT-RSHs) in both gas and solvent phases. Taking a series of experimentally known SF chromophores as working models, we have proposed and validated several variants of OT-RSH approximations for the reliable prediction of the energy levels which match the crucial criteria for the SF process, namely, the negative singlet-triplet and triplet-triplet energy gaps. We scrutinize the role of the OT-RSH ingredients, i.e., the underlying density functional approximations, short- and long-range exact-like exchange, as well as the range-separation parameter, for our purpose. The newly designed OT-RSHs outperform the standard RSHs and other related schemes such as screened-exchange approximations as well as other density functionals from different rungs for describing the SF energetics. More importantly, it is unveiled that although the OT-RSH coupled with the polarizable continuum model, OT-RSH-PCM, as well as the screened versions, OT-SRSHs, which account for the screening effect by the electron correlation through the scalar dielectric constant have some advantages over gas-phase computations using OT-RSHs, the energetics criteria of the SF process may not necessarily be satisfied. This in turn corroborates the idea of performing both the optimal tuning procedure and subsequent computations of the SF relevant energetics using OT-RSHs as a more reliable and affordable framework, at least for the present purpose. The applicability of the proposed models is also put into broader perspective, where they are used for the computational design of several chromophores as promising candidates prone to utilization in the SF-based materials. Hopefully, our recommended OT-RSHs can function as efficient models for both the theoretical modeling of SF chromophores and confirming the experimental observations in the field.

Global and local aromaticity of acenes from the information-theoretic approach in density functional reactivity theory

In this work, we report a systematic study on the global and local aromaticity of acenes using a series of model structures from 2-acene to 11-acene. A recently developed ansatz, an information-theoretic approach coached into density functional reactivity theory has been employed, which essentially provides different density functionals characterizing the molecular electron density distribution. Based on the correlation analysis of six conventional aromaticity indices with eight information-theoretic quantities, we examined the aromaticity of acenes from both global and local perspectives. From the global aromaticity viewpoint, our results suggest that different descriptors based on various physicochemical properties are intrinsically dependent. A novel laminated feature ruling local aromaticity of acenes has been unveiled, from which we found that the distance from the terminal rings plays the critical role. Based on the shape of the correlation plots between the conventional aromaticity indices and information-theoretic quantities, the latter could be separated into three subgroups. The seemingly contradictory results from global and local aromaticity perspectives not only present us the uniqueness of the acene systems but all demonstrate the effectiveness of the information-theoretic approach from density functional reactivity theory. Besides strengthening the validity of a series of new aromaticity descriptors, our results should lead to more clear insights into the chemical significance of the information-theoretic quantities.

Polarized absorbance and Davydov splitting in bulk and thin-film pentacene polymorphs

Pentacene is one of the most studied organic materials and in particular its optical properties have been the subject of intense research during the last two decades. In spite of such a widespread interest and of the extensive knowledge achieved so far, a number of issues are still debated. One of the most relevant questions concerns the role of polymorphism and how it affects the lowest-energy exciton, which appears in the visible region and is subject to a sizable Davydov splitting. We address this problem in a combined theoretical and experimental work, where the optical absorption properties of three pentacene polymorphs are investigated within the whole energy range of visible light. Optical spectra computed from first principles in the framework of many-body perturbation theory are directly compared with the polarization-resolved absorbance, measured for three different pentacene phases (the two bulk polymorphs and the thin-film phase). In this way, we unambiguously identify the two Davydov components of the first exciton and the optical fingerprints of each considered phase. With very good agreement between theory and experiment, we show that all polymorphs exhibit common features at the absorption onset, while phase-dependent characteristics appear only above 2 eV. We discuss the character of the lowest-lying singlet and triplet excitons, including dark ones, highlighting the contributions from the electronic bands and the role of the electron-hole interaction and of the local-field effects.

Combining Wave Function Methods with Density Functional Theory for Excited States

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.

Many-body perturbation theory for understanding optical excitations in organic molecules and solids

Semiconductors composed of organic molecules are promising as components for flexible and inexpensive optoelectronic devices, with many recent studies aimed at understanding their electronic and optical properties. In particular, computational modeling of these complex materials has provided new understanding of the underlying properties which give rise to their excited-state phenomena. This article provides an overview of recent many-body perturbation theory (MBPT) studies of optical excitations within organic molecules and solids. We discuss the accuracy of MBPT within the GW/BSE approach in predicting excitation energies and absorption spectra, and assess the impact of two commonly used approximations, the DFT starting point and the Tamm-Dancoff approximation. Moreover, we summarize studies that elucidate the role of solid-state structure on the nature of excitons in organic crystals. These studies show that a rich physical understanding of organic materials can be obtained from GW/BSE.

The Bethe–Salpeter equation in chemistry: relations with TD-DFT, applications and challenges

We review the Bethe–Salpeter formalism and analyze its performances for the calculation of the excited state properties of molecular systems.

Is the Bethe-Salpeter Formalism Accurate for Excitation Energies? Comparisons with TD-DFT, CASPT2, and EOM-CCSD

Developing ab initio approaches able to provide accurate excited-state energies at a reasonable computational cost is one of the biggest challenges in theoretical chemistry. In that framework, the Bethe-Salpeter equation approach, combined with the GW exchange-correlation self-energy, which maintains the same scaling with system size as TD-DFT, has recently been the focus of a rapidly increasing number of applications in molecular chemistry. Using a recently proposed set encompassing excitation energies of many kinds [J. Phys. Chem. Lett. 2016, 7, 586-591], we investigate here the performances of BSE/GW. We compare these results to CASPT2, EOM-CCSD, and TD-DFT data and show that BSE/GW provides an accuracy comparable to the two wave function methods. It is particularly remarkable that the BSE/GW is equally efficient for valence, Rydberg, and charge-transfer excitations. In contrast, it provides a poor description of triplet excited states, for which EOM-CCSD and CASPT2 clearly outperform BSE/GW. This contribution therefore supports the use of the Bethe-Salpeter approach for spin-conserving transitions.

Benchmark of Bethe-Salpeter for Triplet Excited-States

We have evaluated the accuracy of the Bethe-Salpeter singlet-triplet transition energies as well as singlet-triplet and triplet-triplet splittings for 20 organic molecules, using as reference the CC3 values determined by Thiel and co-workers with both the TZVP and aug-cc-pVTZ atomic basis sets. Our excitation energies are obtained on the basis of GW quasiparticle energy levels that are self-consistently converged with respect to the starting DFT eigenvalues. In its current form, BSE/GW is often unable to provide a balanced description of both singlet and triplet excited-states. While the singlet-singlet and triplet-triplet energy separations are obtained accurately, triplets are located too close in energy from the ground-state, by typically -0.55 eV when using standard functionals to generate the starting eigenstates. Applying the Tamm-Dancoff approximation upshifts the BSE triplet energies and allows reducing this error to ca. -0.40 eV, while using M06-HF eigenstates allows a further increase and hence a reduction of the error for triplet states, but at the cost of larger errors for the singlet excited-states. At this stage, the most accurate TD-DFT estimates therefore remain competitive for computing singlet-triplet transition energies. Indeed, with M06-2X, irrespective of the application or not of the Tamm-Dancoff approximation and of the selected atomic basis set, the deviations obtained with TD-DFT are rather small.