Direct optical generation of long-range charge-transfer states in organic photovoltaics

Theoretical investigation of distal charge separation in a perylenediimide trimer

An exciton-phonon (ex-ph) model based on our recently developed block interaction product basis framework is introduced to simulate the distal charge separation (CS) process in aggregated perylenediimide (PDI) trimer incorporating the quantum dynamic method, i.e., the time-dependent density matrix renormalization group. The electronic Hamiltonian in the ex-ph model is represented by nine constructed diabatic states, which include three local excited (LE) states and six charge transfer (CT) states from both the neighboring and distal chromophores. These diabatic states are automatically generated from the direct products of the leading localized neutral or ionic states of each chromophore's reduced density matrix, which are obtained from ab initio quantum chemical calculation of the subsystem consisting of the targeted chromophore and its nearest neighbors, thus considering the interaction of the adjacent environment. In order to quantum-dynamically simulate the distal CS process with massive coupled vibrational modes in molecular aggregates, we used our recently proposed hierarchical mapping approach to renormalize these modes and truncate those vibrational modes that are not effectively coupled with electronic states accordingly. The simulation result demonstrates that the formation of the distal CS process undergoes an intermediate state of adjacent CT, i.e., starts from the LE states, passes through an adjacent CT state to generate the intermediates (∼200 fs), and then formalizes the targeted distal CS via further charge transference (∼1 ps). This finding agrees well with the results observed in the experiment, indicating that our scheme is capable of quantitatively investigating the CS process in a realistic aggregated PDI trimer and can also be potentially applied to exploring CS and other photoinduced processes in larger systems.

Surface hopping simulations on charge separation in an organic donor-acceptor system

Charge separation in organic solar cells is a long-lasting and heavily debated issue. Here, we use the surface hopping method based on the Pariser-Parr-Pople (PPP) Hamiltonian and configuration interaction singles (CIS) approximation to simulate the charge separation process in an organic donor-acceptor system. The system is composed of one donor polymer chain and four acceptor polymer chains, and they are all stacked face-to-face. We let the system to relax from a photoexcited state, and then we observed that the electron is transferred from the donor chain to different acceptor chains and the hole is left on the donor chain, forming polaron pairs with different electron-hole distances. By performing statistical analysis on a number of trajectories, we found that the electron and the hole are fully separated before the system relaxes to its lowest excited state. The yield of free charges shows a significant dependence on the donor-acceptor band offset which provides the driving force for charge separation, while showing negligible dependence on the photoexcitation energy. The external electric field has a remarkable effect on the yield of free charges.

Short and long-range electron transfer compete to determine free-charge yield in organic semiconductors

Understanding how Frenkel excitons efficiently split to form free-charges in low-dielectric constant organic semiconductors has proven challenging, with many different models proposed in recent years to explain this phenomenon. Here, we present evidence that a simple model invoking a modest amount of charge delocalization, a sum over the available microstates, and the Marcus rate constant for electron transfer can explain many seemingly contradictory phenomena reported in the literature. We use an electron-accepting fullerene host matrix dilutely sensitized with a series of electron donor molecules to test this hypothesis. The donor series enables us to tune the driving force for photoinduced electron transfer over a range of 0.7 eV, mapping out normal, optimal, and inverted regimes for free-charge generation efficiency, as measured by time-resolved microwave conductivity. However, the photoluminescence of the donor is rapidly quenched as the driving force increases, with no evidence for inverted behavior, nor the linear relationship between photoluminescence quenching and charge-generation efficiency one would expect in the absence of additional competing loss pathways. This behavior is self-consistently explained by competitive formation of bound charge-transfer states and long-range or delocalized free-charge states, where both rate constants are described by the Marcus rate equation. Moreover, the model predicts a suppression of the inverted regime for high-concentration blends and efficient ultrafast free-charge generation, providing a mechanistic explanation for why Marcus-inverted-behavior is rarely observed in device studies.

Computational and data driven molecular material design assisted by low scaling quantum mechanics calculations and machine learning

Electronic structure methods based on quantum mechanics (QM) are widely employed in the computational predictions of the molecular properties and optoelectronic properties of molecular materials. The computational costs of these QM methods, ranging from density functional theory (DFT) or time-dependent DFT (TDDFT) to wave-function theory (WFT), usually increase sharply with the system size, causing the curse of dimensionality and hindering the QM calculations for large sized systems such as long polymer oligomers and complex molecular aggregates. In such cases, in recent years low scaling QM methods and machine learning (ML) techniques have been adopted to reduce the computational costs and thus assist computational and data driven molecular material design. In this review, we illustrated low scaling ground-state and excited-state QM approaches and their applications to long oligomers, self-assembled supramolecular complexes, stimuli-responsive materials, mechanically interlocked molecules, and excited state processes in molecular aggregates. Variable electrostatic parameters were also introduced in the modified force fields with the polarization model. On the basis of QM computational or experimental datasets, several ML algorithms, including explainable models, deep learning, and on-line learning methods, have been employed to predict the molecular energies, forces, electronic structure properties, and optical or electrical properties of materials. It can be conceived that low scaling algorithms with periodic boundary conditions are expected to be further applicable to functional materials, perhaps in combination with machine learning to fast predict the lattice energy, crystal structures, and spectroscopic properties of periodic functional materials.

Free Charge Carriers in Homo-Sorted π-Stacks of Donor-Acceptor Conjugates

Inspired by the high photoconversion efficiency observed in natural light-harvesting systems, the hierarchical organization of molecular building blocks has gained impetus in the past few decades. Particularly, the molecular arrangement and packing in the active layer of organic solar cells (OSCs) have garnered significant attention due to the decisive role of the nature of donor/acceptor (D/A) heterojunctions in charge carrier generation and ultimately the power conversion efficiency. This review focuses on the recent developments in emergent optoelectronic properties exhibited by self-sorted donor-on-donor/acceptor-on-acceptor arrangement of covalently linked D-A systems, highlighting the ultrafast excited state dynamics of charge transfer and transport. Segregated organization of donors and acceptors promotes the delocalization of photoinduced charges among the stacks, engendering an enhanced charge separation lifetime and percolation pathways with ambipolar conductivity and charge carrier yield. Covalently linking donors and acceptors ensure a sufficient D-A interface and interchromophoric electronic coupling as required for faster charge separation while providing better control over their supramolecular assemblies. The design strategies to attain D-A conjugate assemblies with optimal charge carrier generation efficiency, the scope of their application compared to state-of-the-art OSCs, current challenges, and future opportunities are discussed in the review. An integrated overview of rational design approaches derived from the comprehension of underlying photoinduced processes can pave the way toward superior optoelectronic devices and bring in new possibilities to the avenue of functional supramolecular architectures.

Charge-transfer electronic states in organic solar cells: a TDDFT study

The prediction of new organic photovoltaic materials in organic solar cells (OSCs) must include a precise description of charge-transfer states because they are involved in electron-transfer processes such as charge separation and charge recombination which govern the device efficiency. Also, as the experimental performance of an optoelectronic device is measured for nonequilibrium nanostructures, computational approaches need models that can incorporate morphology effects. Usually, this aspect is treated by molecular dynamics simulation (MDS) methodologies; however, methodologies and formalisms to calculate the electron-transfer processes are still controversial and sometimes do not connect their information with the phase morphologies. In this work we propose a simple and fast characterization of electron-transfer processes to find the rate constants by analysing the distribution of vertical excitation energies of both local excitation (LE) and charge-transfer (CT) states using TD-DFT calculations in the donor-acceptor pair structures which were extracted from MDS. This proposal assumes that conformational changes are prevented and equilibria are not achieved while the electron-transfer events take effect, and thus the only pathway that connects the LE and CT states is their surface crossing point where an ideal distribution might exist. Different density functionals and dialectric models were tested. The results indicate a close relationship between the proposal and experimental data for electron-transfer events, suggesting the application of this method in the rational design of new photovoltaic materials.

Revisiting the Charge-Transfer States at Pentacene/C60 Interfaces with the GW/Bethe-Salpeter Equation Approach

Molecular orientations and interfacial morphologies have critical effects on the electronic states of donor/acceptor interfaces and thus on the performance of organic photovoltaic devices. In this study, we explore the energy levels and charge-transfer states at the organic donor/acceptor interfaces on the basis of the fragment-based GW and Bethe-Salpeter equation approach. The face-on and edge-on orientations of pentacene/C60 bilayer heterojunctions have employed as model systems. GW+Bethe-Salpeter equation calculations were performed for the local interface structures in the face-on and edge-on bilayer heterojunctions, which contain approximately 2000 atoms. Calculated energy levels and charge-transfer state absorption spectra are in reasonable agreements with those obtained from experimental measurements. We found that the dependence of the energy levels on interfacial morphology is predominantly determined by the electrostatic contribution of polarization energy, while the effects of induction contribution in the edge-on interface are similar to those in the face-on. Moreover, the delocalized charge-transfer states contribute to the main absorption peak in the edge-on interface, while the face-on interface features relatively localized charge-transfer states in the main absorption peak. The impact of the interfacial morphologies on the polarization and charge delocalization effects is analyzed in detail.

Strong optical response and light emission from a monolayer molecular crystal

Excitons in two-dimensional (2D) materials are tightly bound and exhibit rich physics. So far, the optical excitations in 2D semiconductors are dominated by Wannier-Mott excitons, but molecular systems can host Frenkel excitons (FE) with unique properties. Here, we report a strong optical response in a class of monolayer molecular J-aggregates. The exciton exhibits giant oscillator strength and absorption (over 30% for monolayer) at resonance, as well as photoluminescence quantum yield in the range of 60–100%. We observe evidence of superradiance (including increased oscillator strength, bathochromic shift, reduced linewidth and lifetime) at room-temperature and more progressively towards low temperature. These unique properties only exist in monolayer owing to the large unscreened dipole interactions and suppression of charge-transfer processes. Finally, we demonstrate light-emitting devices with the monolayer J-aggregate. The intrinsic device speed could be beyond 30 GHz, which is promising for next-generation ultrafast on-chip optical communications.

The optical response of inorganic two-dimensional semiconductors is dominated by Wannier-Mott excitons, but molecular systems can host localised Frenkel excitons. Here, the authors report strong optical response in a class of monolayer molecular J-aggregates due to the coherent Coulomb interaction between localised Frenkel excitons.

Charge-transfer excited states in the donor/acceptor interface from large-scale GW calculations

Predicting the charge-transfer (CT) excited states across the donor/acceptor (D/A) interface is essential for understanding the charge photogeneration process in an organic solar cell. Here, we present a fragment-based GW implementation that can be applied to a D/A interface structure and thus enables accurate determination of the CT states. The implementation is based on the fragmentation approximation of the polarization function and the combined GW and Coulomb-hole plus screened exchange approximations for self-energies. The fragment-based GW is demonstrated by application to the pentacene/C₆₀ interface structure containing more than 2000 atoms. The CT excitation energies were estimated from the quasiparticle energies and electron-hole screened Coulomb interactions; the computed energies are in reasonable agreement with experimental estimates from the external quantum efficiency measurements. We highlight the impact of the induced polarization effects on the electron-hole energetics. The proposed fragment-based GW method offers a first-principles tool to compute the quasiparticle energies and electronic excitation energies of organic materials.

Thousand-atom ab initio calculations of excited states at organic/organic interfaces: toward first-principles investigations of charge photogeneration

Predicting electronically excited states across electron-donor/electron acceptor interfaces is essential for understanding the charge photogeneration process in organic solar cells. However, organic solar cells are large and disordered systems, and their excited states cannot be easily accessed by conventional quantum chemistry approaches. Moreover, a large number of excited states must be obtained to fully understand the charge separation mechanism. Recently, we have developed a novel fragment-based excited state method which can efficiently calculate a large number of states in molecular aggregates. In this article, we demonstrate the large-scale excited-state calculations by investigating interfacial charge transfer (ICT) states across the electron-donor/electron acceptor interfaces. As the model systems, we considered the face-on and edge-on configurations of pentacene/C₆₀ bilayer heterojunction structures. These model structures contain approximately 1.8 × 10⁵ atoms, and their local interface regions containing 2000 atoms were treated quantum mechanically, embedded in the electrostatic potentials from the remaining parts. Therefore, the charge delocalization effect, structural disorder, and the resulting heterogeneous electrostatic and polarizable environments were taken into account in the excited-state calculations. The computed energies of the low-lying ICT states are in reasonable agreement with experimental estimates. By comparing the edge-on and face-on configurations of the pentacene/C₆₀ interfaces, we discuss the influence of interfacial morphologies on the energetics and charge delocalization of ICT states. In addition, we present the detailed characterization of excited states and highlight the importance of hybridization effects between pentacene excited states and ICT states. The large-scale ab initio calculations for the interface systems enabled the exploration of the ICT states, leading to first-principles investigation of the charge separation mechanism in organic solar cells.

Investigations on the charge transfer mechanism at donor/acceptor interfaces in the quest for descriptors of organic solar cell performance

Herein, we theoretically and experimentally investigated the mechanisms of charge separation processes of organic thin-film solar cells. PTB7, PTB1, and PTBF2 have been chosen as donors and PC₇₁BM has been chosen as an acceptor considering that effective charge generation depends on the difference between the material combinations. Experimental results of transient absorption spectroscopy show that the hot process is a key step for determining external quantum efficiency (EQE) in these systems. From the quantum chemistry calculations, it has been found that EQE tends to increase as the transferred charge, charge transfer distance, and variation of dipole moments between the ground and excited states of the donor/acceptor complexes increase; this indicates that these physical quantities are a good descriptor to assess the donor-acceptor charge transfer quality contributing to the solar cell performance. We propose that designing donor/acceptor interfaces with large values of charge transfer distance and variation of dipole moments of the donor/acceptor complexes is a prerequisite for developing high-efficiency polymer/PCBM solar cells.

Hot and Cold Charge-Transfer Mechanisms in Organic Photovoltaics: Insights into the Excited States of Donor/Acceptor Interfaces

The evolution of the excited-state manifold in organic D/A aggregates (e.g., the prototypical P3HT/PCBM) is investigated through a bottom-up approach via first-principles calculations. We show how the excited-state energies, the charge transfer (CT) states, and the electron-hole density distributions are strongly influenced by the size, the orientation, and the position (i.e., on-top versus on-edge phases) of P3HT/PCBM domains. We discuss how the structural order influences the excited-state electronic structure, providing an atomistic interpretation of the photophysics of organic blends. We show how the simultaneous presence of on-top and on-edge phases does not alter the optical absorption spectrum of the blend but does affect the photophysics. Photovoltaic processes such as (i) the simultaneous charge generation obtained from hot and cold excitations, (ii) the instantaneous and delayed charge separation, and (iii) the pump-push-probe charge generation can be interpreted based on our study.

Effect of Solid-State Polarization on Charge-Transfer Excitations and Transport Levels at Organic Interfaces from a Screened Range-Separated Hybrid Functional

We develop a robust approach for the description of the energetics of charge-transfer (CT) excitations and transport levels at organic interfaces based on a screened range-separated hybrid (SRSH) functional. We find that SRSH functionals correctly capture the effect of solid-state electronic polarization on transport gap renormalization and on screening of the electrostatic electron-hole interaction. With respect to calculations based on nonscreened optimally tuned RSH (long-range corrected) functionals, the SRSH-based calculations can be performed for both isolated molecular complexes and systems embedded in a dielectric medium with the same range-separation parameter, which allows a clear physical interpretation of the results in terms of solid-state polarization without any perturbation of the molecular electronic structure. By considering weakly interacting donor/acceptor complexes of pentacene with C₆₀ and poly-3-hexylthiophene (P3HT) with PCBM, we show that this new approach provides CT-state energies that compare very well with experimental data.

Organic Planar Heterojunctions: From Models for Interfaces in Bulk Heterojunctions to High-Performance Solar Cells

Recent progress regarding planar heterojunctions (PHJs) is reviewed, with respect to the fundamental understanding of the photophysical processes at the donor/acceptor interfaces in organic photovoltaic devices (OPVs). The current state of OPV research is summarized and the advantages of PHJs as models for exploring the relationship between organic interfaces and device characteristics described. The preparation methods and the characterization of PHJ structures to provide key points for the appropriate handling of PHJs. Next, we describe the effects of the donor/acceptor interface on each photoelectric conversion process are reviewed by examining various PHJ systems to clarify what is currently known and not known. Finally, it is discussed how we the knowledge obtained by studies of PHJs can be used to overcome the current limits of OPV efficiency.

Charge-Transfer States in Organic Solar Cells: Understanding the Impact of Polarization, Delocalization, and Disorder

We investigate the impact of electronic polarization, charge delocalization, and energetic disorder on the charge-transfer (CT) states formed at a planar C₆₀/pentacene interface. The ability to examine large complexes containing up to seven pentacene molecules and three C₆₀ molecules allows us to take explicitly into account the electronic polarization effects. These complexes are extracted from a bilayer architecture modeled by molecular dynamics simulations and evaluated by means of electronic-structure calculations based on long-range-separated functionals (ωB97XD and BNL) with optimized range-separation parameters. The energies of the lowest charge-transfer states derived for the large complexes are in very good agreement with the experimentally reported values. The average singlet-triplet energy splittings of the lowest CT states are calculated not to exceed 10 meV. The rates of geminate recombination as well as of dissociation of the triplet excitons are also evaluated. In line with experiment, our results indicate that the pentacene triplet excitons generated through singlet fission can dissociate into separated charges on a picosecond time scale, despite the fact that their energy in C₆₀/pentacene heterojunctions is slightly lower than the energies of the lowest CT triplet states.

Sub-wavelength modulation of χ(2) optical nonlinearity in organic thin films

Modulating the second-order nonlinear optical susceptibility (χ⁽²⁾) of materials at the nanoscale represents an ongoing technological challenge for a variety of integrated frequency conversion and nonlinear nanophotonic applications. Here we exploit the large hyperpolarizability of intermolecular charge transfer states, naturally aligned at an organic semiconductor donor–acceptor (DA) interface, as a means to control the magnitude and sign of χ⁽²⁾ at the nanoscale. Focusing initially on a single pentacene-C₆₀ DA interface, we confirm that the charge transfer transition is strongly aligned orthogonal to the heterojunction and find that it is responsible for a large interfacial nonlinearity probed via second harmonic generation that is sufficient to achieve d₃₃>10 pm V⁻¹, when incorporated in a non-centrosymmetric DA multilayer stack. Using grating-shadowed oblique-angle deposition to laterally structure the DA interface distribution in such multilayers subsequently enables the demonstration of a χ⁽²⁾ grating with 280 nm periodicity, which is the shortest reported to date.

Materials with spatially modulated nonlinear optical properties are used for quasi-phase matching. Here, Yan et al. exploit the nonlinearity of intermolecular charge transfer states together with oblique-angle deposition to achieve nanoscale modulation of the second-order susceptibility.

Ultrafast Long-Range Charge Separation in Organic Photovoltaics: Promotion by Off-Diagonal Vibronic Couplings and Entropy Increase

The exciton dissociation in a model donor/acceptor heterojunction with electron-phonon couplings is simulated by a full quantum dynamical method, in which ultrafast long-range charge separation is observed. Such a novel scenario does not undergo short-range interfacial (pinned) charge transfer states, but can be mainly ascribed to the quantum resonance between local Frenkel excited states and a broad array of long-range charge transfer (LRCT) states assisted by the moderate off-diagonal vibronic couplings. The entropy-increasing effect associated with the very dense density of states for LRCT states is also found to be beneficial for lowering the free energy barrier for charge generation in organic solar cells.

Extended Intermolecular Interactions Governing Photocurrent-Voltage Relations in Ternary Organic Solar Cells

Efficient organic solar cells are based on (electron) donor-acceptor heterojunctions. An optically generated excited molecular state (exciton) is dissociated at this junction, forming a charge-transfer (CT) state in an intermediate step before the electron and hole are completely separated. The observed highly efficient dissociation of this Coulombically bound state raises the question on the dissociation mechanism. Here, we show that the observed high quantum yields of charge carrier generation and CT state dissociation are due to extended (and consequently weakly bound) CT states visible in absorption and emission spectra and first-principles calculations. Identifying a new geminate-pair loss mechanism via donor excimers, we find that the hole on the small-molecule donor is not localized on a single molecule and charge separation is correlated with the energetic offset between excimer and CT states. Thus, the charges upon interface charge transfer and even in the case of back-transfer and recombination are less localized than commonly assumed.

Full-dimensional multilayer multiconfigurational time-dependent Hartree study of electron transfer dynamics in the anthracene/C60 complex

Electron transfer at the donor-acceptor heterojunctions plays a critical role in the photoinduced process during the solar energy conversion in organic photovoltaic materials. We theoretically investigate the electron transfer process in the anthracene/C60 donor-acceptor complex by using quantum dynamics calculations. The electron-transfer model Hamiltonian with full dimensionality was built by quantum-chemical calculations. The quantum dynamics calculations were performed using the multiconfigurational time-dependent Hartree (MCTDH) theory and multilayer (ML) MCTDH methods. The latter approach (ML-MCTDH) allows us to conduct the comprehensive study on the quantum evolution of the full-dimensional electron-transfer model including 4 electronic states and 246 vibrational degrees of freedom. Our quantum dynamics calculations exhibit the ultrafast anthracene → C60 charge transfer process because of the strong coupling between excitonic and charge transfer states. This work demonstrates that the ML-MCTDH is a very powerful method to treat the quantum evolution of complex systems.

Charge Separation and Recombination at Polymer-Fullerene Heterojunctions: Delocalization and Hybridization Effects

We address charge separation and recombination in polymer/fullerene solar cells with a multiscale modeling built from accurate atomistic inputs and accounting for disorder, interface electrostatics and genuine quantum effects on equal footings. Our results show that bound localized charge transfer states at the interface coexist with a large majority of thermally accessible delocalized space-separated states that can be also reached by direct photoexcitation, thanks to their strong hybridization with singlet polymer excitons. These findings reconcile the recent experimental reports of ultrafast exciton separation ("hot" process) with the evidence that high quantum yields do not require excess electronic or vibrational energy ("cold" process), and show that delocalization, by shifting the density of charge transfer states toward larger effective electron-hole radii, may reduce energy losses through charge recombination.

Concurrent Effects of Delocalization and Internal Conversion Tune Charge Separation at Regioregular Polythiophene-Fullerene Heterojunctions

Quantum-dynamical simulations are used to investigate the interplay of exciton delocalization and vibronically induced internal conversion processes in the elementary charge separation steps at regioregular donor-acceptor heterojunctions. Ultrafast internal conversion leads to efficient deexcitation within the excitonic and charge transfer manifolds, thus modifying the charge separation dynamics. We address a model donor-acceptor junction representative of regioregular P3HT-PCBM, using high-dimensional quantum dynamics simulations by multiconfigurational methods. While partial trapping into an interfacial charge separated state occurs, long-range charge-separated states are accessed as previously demonstrated in the work of Tamura and Burghardt [J. Am. Chem. Soc. 2013, 135, 16364]. For an H-aggregate type, stacked donor species, the initial bright state undergoes ultrafast internal conversion within the excitonic manifold, creating multiple charge transfer pathways before reaching the lowest-energy dark exciton, which is uncoupled from the charge transfer manifold. This process profoundly affects the charge separation mechanism and efficiency. For small energetic offsets between the interfacial excitonic and charge transfer states, a delocalized initial bright state proves less prone to electron-hole capture by the interfacial trap than a localized, vibronic wavepacket close to the interface. For both delocalized and localized initial states, a comparable yield of free carriers is obtained, which is found to be optimal for energetic offsets of the order of the Coulomb barrier to charge separation. Interfacial trapping is significantly reduced as the barrier height decreases with fullerene aggregation. Despite the high-dimensional nature of the system, charge separation is an ultrafast coherent quantum process exhibiting oscillatory features as observed in recent experiments.

Non-fullerene acceptors: exciton dissociation with PTCDA versus C60

Extensive development of new polymer and small molecule donors has helped produce a steady increase in the efficiency of organic photovoltaic (OPV) devices.