Electronic Polarization in Organic Crystals: A Comparative Study of Induced Dipoles and Intramolecular Charge Redistribution Schemes

Efficient and Accurate Estimation of Electronic Polarization Energies for Organic Semiconductors: An Embedding Charge Quantum Mechanics/Continuum Dielectric Model

Electronic polarization plays a pivotal role in determining the molecular energy levels of organic semiconductors (OSCs) in the condensed phase. However, accurate estimation of the electronic polarization energy is a challenging task due to the intricate imbalance between the precision and efficiency. In this work, we have developed an embedding charge quantum mechanics/continuum dielectric (EC-QM/CD) model, which enables quantitative evaluation of the ionization potential (IP), electron affinity (EA), and polarization energy in both crystalline and amorphous solids for OSCs. The benchmark calculations on both p-type OSCs of oligoacenes and n-type OSCs of A-D-A small-molecule acceptors show that the values of IP, EA, and polarization energy obtained by EC-QM/CD are in good accordance with the experimental measurements or the results by high-precision methods, while the computational costs are substantially reduced. Given its balance between the accuracy and efficiency, the EC-QM/CD model exhibits considerable potential to broaden the applications in the field of OSCs, for instance, high-throughput screening by using solid-state energy levels or polarization energies as critical descriptors.

The C1s core levels of polycyclic aromatic hydrocarbons and styrenic polymers: A first-principles study

Understanding core level shifts in aromatic compounds is crucial for the correct interpretation of x-ray photoelectron spectroscopy (XPS) of polycyclic aromatic hydrocarbons (PAHs), including acenes, as well as of styrenic polymers, which are increasingly relevant for the microelectronic industry, among other applications. The effect of delocalization through π aromatic systems on the stabilization of valence molecular orbitals has been widely investigated in the past. However, little has been reported on the impact on the deeper C1s core energy levels. In this work, we use first-principles calculations at the level of many body perturbation theory to compute the C1s binding energies of several aromatic systems. We report a C1s red shift in PAHs and acenes of increasing size, both in the gas phase and in the molecular crystal. C1s red shifts are also calculated for stacked benzene and naphthalene pairs at decreasing intermolecular distances. A C1s red shift is in addition found between oligomers of poly(p-hydroxystyrene) and polystyrene of increasing length, which we attribute to ring-ring interactions between the side-chains. The predicted shifts are larger than common instrumental errors and could, therefore, be detected in XPS experiments.

Disentangling the multiorbital contributions of excitons by photoemission exciton tomography

Excitons are realizations of a correlated many-particle wave function, specifically consisting of electrons and holes in an entangled state. Excitons occur widely in semiconductors and are dominant excitations in semiconducting organic and low-dimensional quantum materials. To efficiently harness the strong optical response and high tuneability of excitons in optoelectronics and in energy-transformation processes, access to the full wavefunction of the entangled state is critical, but has so far not been feasible. Here, we show how time-resolved photoemission momentum microscopy can be used to gain access to the entangled wavefunction and to unravel the exciton's multiorbital electron and hole contributions. For the prototypical organic semiconductor buckminsterfullerene (C60), we exemplify the capabilities of exciton tomography and achieve unprecedented access to key properties of the entangled exciton state including localization, charge-transfer character, and ultrafast exciton formation and relaxation dynamics.

Peak Broadening in Photoelectron Spectroscopy of Amorphous Polymers: The Leading Role of the Electrostatic Landscape

The broadening in photoelectron spectra of polymers can be attributed to several factors, such as light source spread, spectrometer resolution, the finite lifetime of the hole state, and solid-state effects. Here, for the first time, we set up a computational protocol to assess the peak broadening induced for both core and valence levels by solid-state effects in four amorphous polymers by using a combination of density functional theory, many-body perturbation theory, and classical polarizable embedding. We show that intrinsic local inhomogeneities in the electrostatic environment induce a Gaussian broadening of 0.2-0.7 eV in the binding energies of both core and semivalence electrons, corresponding to a full width at half-maximum (FWHM) of 0.5-1.7 eV for the investigated systems. The induced broadening is larger in acrylate-based than in styrene-based polymers, revealing the crucial role of polar groups in controlling the roughness of the electrostatic landscape in the solid matrix.

Many-body GW calculations with very large scale polarizable environments made affordable: A fully ab initio QM/QM approach

We present a many-body GW formalism for quantum subsystems embedded in discrete polarizable environments containing up to several hundred thousand atoms described at a fully ab initio random phase approximation level. Our approach is based on a fragment approximation in the construction of the Green's function and independent-electron susceptibilities. Further, the environing fragments susceptibility matrices are reduced to a minimal but accurate representation preserving low order polarizability tensors through a constrained minimization scheme. This approach dramatically reduces the cost associated with inverting the Dyson equation for the screened Coulomb potential W, while preserving the description of short to long-range screening effects. The efficiency and accuracy of the present scheme is exemplified in the paradigmatic cases of fullerene bulk, surface, subsurface, and slabs with varying number of layers.

Solvent Effects on Ultrafast Charge Transfer Population: Insights from the Quantum Dynamics of Guanine-Cytosine in Chloroform

We study the ultrafast photoactivated dynamics of the hydrogen bonded dimer Guanine-Cytosine in chloroform solution, focusing on the population of the Guanine→Cytosine charge transfer state (GC-CT), an important elementary process for the photophysics and photochemistry of nucleic acids. We integrate a quantum dynamics propagation scheme, based on a linear vibronic model parameterized through time dependent density functional theory calculations, with four different solvation models, either implicit or explicit. On average, after 50 fs, 30∼40 % of the bright excited state population has been transferred to GC-CT. This process is thus fast and effective, especially when transferring from the Guanine bright excited states, in line with the available experimental studies. Independent of the adopted solvation model, the population of GC-CT is however disfavoured in solution with respect to the gas phase. We show that dynamical solvation effects are responsible for this puzzling result and assess the different chemical-physical effects modulating the population of CT states on the ultrafast time-scale. We also propose some simple analyses to predict how solvent can affect the population transfer between bright and CT states, showing that the effect of the solute/solvent electrostatic interactions on the energy of the CT state can provide a rather reliable indication of its possible population.

Doping-Induced Dielectric Catastrophe Prompts Free-Carrier Release in Organic Semiconductors

The control over material properties attainable through molecular doping is essential to many technological applications of organic semiconductors, such as organic light-emitting diodes or thermoelectrics. These excitonic semiconductors typically reach the degenerate limit only at impurity concentrations of 5-10%, a phenomenon that has been put in relation with the strong Coulomb binding between charge carriers and ionized dopants, and whose comprehension remained elusive so far. This study proposes a general mechanism for the release of carriers at finite doping in terms of collective screening phenomena. A multiscale model for the dielectric properties of doped organic semiconductor is set up by combining first principles and microelectrostatic calculations. The results predict a large nonlinear enhancement of the dielectric constant (tenfold at 8% load) as the system approaches a dielectric instability (catastrophe) upon increasing doping. This can be attributed to the presence of highly polarizable host-dopant complexes, plus a nontrivial leading contribution from dipolar interactions in the disordered and heterogeneous system. The enhanced screening in the material drastically reduces the (free) energy barriers for electron-hole separation, rationalizing the possibility for thermal charge release. The proposed mechanism is consistent with conductivity data and sets the basis for achieving higher conductivities at lower doping loads.

Strongly Bound Excitons in Metal-Organic Framework MOF-5: A Many-Body Perturbation Theory Study

During the past years, one of the most iconic metal-organic frameworks (MOFs), MOF-5, has been characterized as a semiconductor by theory and experiments. Here we employ the GW many-body perturbation theory in conjunction with the Bethe-Salpeter equation to compute the electronic structure and optical properties of this MOF. The GW calculations show that MOF-5 is a wide-band-gap insulator with a fundamental gap of ∼8 eV. The strong excitonic effects, arising from highly localized states and low screening, result in an optical gap of 4.5 eV and in an optical absorption spectrum in excellent agreement with experiments. The origin of the incorrect conclusion reported by past studies and the implication of this result are also discussed.

Fate of Low-Lying Charge-Transfer Excited States in a Donor:Acceptor Blend with a Large Energy Offset

In an effort to gain a comprehensive picture of the interfacial states in bulk heterojunction solar cells, we provide a combined experimental-theoretical analysis of the energetics and dynamics of low-lying electronic charge-transfer (CT) states in donor:acceptor blends with a large frontier orbital energy offset. By varying the blend composition and temperature, we unravel the static and dynamic contributions to the disordered density of states (DOS) of the CT-state manifold and assess their recombination to the ground state. Namely, we find that static disorder (conformational and electrostatic) shapes the CT DOS and that fast nonradiative recombination crops the low-energy tail of the distribution probed by external quantum efficiency (EQE) measurements (thereby largely contributing to voltage losses). Our results then question the standard practice of extracting microscopic parameters such as exciton energy and energetic disorder from EQE.

Molecular versus Excitonic Disorder in Individual Artificial Light-Harvesting Systems

Natural light-harvesting antennae employ a dense array of chromophores to optimize energy transport via the formation of delocalized excited states (excitons), which are critically sensitive to spatio-energetic variations of the molecular structure. Identifying the origin and impact of such variations is highly desirable for understanding and predicting functional properties yet hard to achieve due to averaging of many overlapping responses from individual systems. Here, we overcome this problem by measuring the heterogeneity of synthetic analogues of natural antennae-self-assembled molecular nanotubes-by two complementary approaches: single-nanotube photoluminescence spectroscopy and ultrafast 2D correlation. We demonstrate remarkable homogeneity of the nanotube ensemble and reveal that ultrafast (∼50 fs) modulation of the exciton frequencies governs spectral broadening. Using multiscale exciton modeling, we show that the dominance of homogeneous broadening at the exciton level results from exchange narrowing of strong static disorder found for individual molecules within the nanotube. The detailed characterization of static and dynamic disorder at the exciton as well as the molecular level presented here opens new avenues in analyzing and predicting dynamic exciton properties, such as excitation energy transport.

Multiscale modeling of molecular structure and optical properties of complex supramolecular aggregates

Supramolecular aggregates of synthetic dye molecules offer great perspectives to prepare biomimetic functional materials for light-harvesting and energy transport. The design is complicated by the fact that structure–property relationships are hard to establish, because the molecular packing results from a delicate balance of interactions and the excitonic properties that dictate the optics and excited state dynamics, in turn sensitively depend on this packing. Here we show how an iterative multiscale approach combining molecular dynamics and quantum mechanical exciton modeling can be used to obtain accurate insight into the packing of thousands of cyanine dye molecules in a complex double-walled tubular aggregate in close interaction with its solvent environment. Our approach allows us to answer open questions not only on the structure of these prototypical aggregates, but also about their molecular-scale structural and energetic heterogeneity, as well as on the microscopic origin of their photophysical properties. This opens the route to accurate predictions of energy transport and other functional properties.

Multiscale modeling resolves the molecular structure of a synthetic light-harvesting complex, unraveling the microscopic origin of its photophysical properties.

Orientation dependent molecular electrostatics drives efficient charge generation in homojunction organic solar cells

Organic solar cells usually utilise a heterojunction between electron-donating (D) and electron-accepting (A) materials to split excitons into charges. However, the use of D-A blends intrinsically limits the photovoltage and introduces morphological instability. Here, we demonstrate that polycrystalline films of chemically identical molecules offer a promising alternative and show that photoexcitation of α-sexithiophene (α-6T) films results in efficient charge generation. This leads to α-6T based homojunction organic solar cells with an external quantum efficiency reaching up to 44% and an open-circuit voltage of 1.61 V. Morphological, photoemission, and modelling studies show that boundaries between α-6T crystalline domains with different orientations generate an electrostatic landscape with an interfacial energy offset of 0.4 eV, which promotes the formation of hybridised exciton/charge-transfer states at the interface, dissociating efficiently into free charges. Our findings open new avenues for organic solar cell design where material energetics are tuned through molecular electrostatic engineering and mesoscale structural control.

Barrier-Free Charge Separation Enabled by Electronic Polarization in High-Efficiency Non-fullerene Organic Solar Cells

The separation of charge-transfer states into free charges at the donor/acceptor (D/A) interfaces plays a central role in organic solar cells (OSCs). Because of strong Coulomb attraction, the separation mechanisms are elusive, particularly for the high-efficiency non-fullerene (NF) OSCs with low exciton-dissociation driving forces. Here, we demonstrate that the Coulomb barriers can be substantially overcome by electronic polarization for OSCs based on a series of A-D-A acceptors (ITIC, IT-4F, and Y6). In contrast to fullerene-based D/A heterojunctions, the polarization energies for both donor holes and acceptor electrons are remarkably increased from the interfaces to pure regions in the NF heterojunctions because of strong stabilization on electrons but destabilization on holes by electrostatic interactions in the A-D-A acceptors. In particular, upon incorporation of fluorine substituents and electron-poor cores into ITIC, the increased polarization energies can completely compensate for the Coulomb attraction in the IT-4F- and Y6-based heterojunctions, leading to barrierless charge separation.

Singlet exciton fission via an intermolecular charge transfer state in coevaporated pentacene-perfluoropentacene thin films

Singlet exciton fission is a spin-allowed process in organic semiconductors by which one absorbed photon generates two triplet excitons. Theory predicts that singlet fission is mediated by intermolecular charge-transfer states in solid-state materials with appropriate singlet-triplet energy spacing, but direct evidence for the involvement of such states in the process has not been provided yet. Here, we report on the observation of subpicosecond singlet fission in mixed films of pentacene and perfluoropentacene. By combining transient spectroscopy measurements to nonadiabatic quantum-dynamics simulations, we show that direct excitation in the charge-transfer absorption band of the mixed films leads to the formation of triplet excitons, unambiguously proving that they act as intermediate states in the fission process.

Comprehensive modelling study of singlet exciton diffusion in donor-acceptor dyads: when small changes in chemical structure matter

We compare two small π-conjugated donor-bridge-acceptor organic molecules differing mainly in the number of thiophene rings in their bridging motifs (1 ring in 1; 2 rings in 2) with the aim of rationalizing the origin of the enhancement in the singlet exciton diffusion coefficient and length of 1 with respect to 2. By combining force field molecular dynamics and micro electrostatic schemes with time-dependent density functional theory and kinetic Monte Carlo simulations, we dissect the nature of the lowest electronic excitations in amorphous thin films of these molecules and model the transport of singlet excitons across their broadly disordered energy landscapes. In addition to a longer excited-state lifetime associated with a more pronounced intramolecular charge-transfer character, our calculations reveal that singlet excitons in 1 are capable of funneling through long-distance hopping percolation pathways, presumably as a result of the less anisotropic shape of the molecule, which favours long-range 3D transport.

Read between the Molecules: Computational Insights into Organic Semiconductors

The performance and key electronic properties of molecular organic semiconductors are dictated by the interplay between the chemistry of the molecular core and the intermolecular factors of which manipulation has inspired both experimentalists and theorists. This Perspective presents major computational challenges and modern methodological strategies to advance the field. The discussion ranges from insights and design principles at the quantum chemical level, in-depth atomistic modeling based on multiscale protocols, morphological prediction and characterization as well as energy-property maps involving data-driven analysis. A personal overview of the past achievements and future direction is also provided.

Hole Hopping Rates in Organic Semiconductors: A Second-Order Cumulant Approach

Second-order cumulant expansion of the time dependent reduced density matrix has been employed to evaluate hole hopping rates in pentacene, tetracene, picene, and rubrene homodimers. The cumulant expansion is a full quantum mechanical approach, which enables the use of the whole set of nuclear coordinates in computations and the inclusion of both the effects of the equilibrium position displacements and of normal mode mixing upon hole transfer. The time dependent populations predicted by cumulant approach are in good agreement with those obtained by numerical solution of time dependent Schrödinger equation, even for ultrafast processes, where the Fermi Golden Rule fails.

Partial atomic multipoles for internally consistent microelectrostatic calculations

An extension of the extant microelectrostatic methodologies, based on the concept of distributed generalized polarizability matrix derived from the Coupled Perturbed Hartree-Fock (CPHF) equations, is proposed for self-consistent calculation of charge carrier and charge-transfer (CT) state electrostatic energies in molecular solids, including the doped, defected and disordered ones. The CPHF equations are solved only once and the generalized molecular polarizability they yield enables low cost iterations that mutually adjust the molecular electronic distributions and the local electric field in which the molecules are immersed. The approach offers a precise picture of molecular charge densities, accounting for atomic partial multipoles up to order 2, which allows one to reproduce the recently reported large charge-quadrupole contributions to CT state energies in low-symmetry local environments. It is particularly well suited for repetitive calculations for large clusters (up to 300,000 atoms), and may potentially be useful for describing electrostatic solvent effects. © 2017 Wiley Periodicals, Inc.

Combining the GW formalism with the polarizable continuum model: A state-specific non-equilibrium approach

We have implemented the polarizable continuum model within the framework of the many-body Green's function GW formalism for the calculation of electron addition and removal energies in solution. The present formalism includes both ground-state and non-equilibrium polarization effects. In addition, the polarization energies are state-specific, allowing to obtain the bath-induced renormalisation energy of all occupied and virtual energy levels. Our implementation is validated by comparisons with ΔSCF calculations performed at both the density functional theory and coupled-cluster single and double levels for solvated nucleobases. The present study opens the way to GW and Bethe-Salpeter calculations in disordered condensed phases of interest in organic optoelectronics, wet chemistry, and biology.

Simulating charge transport in organic semiconductors and devices: a review

Charge transport simulation can be a valuable tool to better understand, optimise and design organic transistors (OTFTs), photovoltaics (OPVs), and light-emitting diodes (OLEDs). This review presents an overview of common charge transport and device models; namely drift-diffusion, master equation, mesoscale kinetic Monte Carlo and quantum chemical Monte Carlo, and a discussion of the relative merits of each. This is followed by a review of the application of these models as applied to charge transport in organic semiconductors and devices, highlighting in particular the insights made possible by modelling. The review concludes with an outlook for charge transport modelling in organic electronics.

Evaluation of electronic polarization energy in oligoacene molecular crystals using the solvated supermolecular approach

The solvated supermolecular approach, i.e., block-localized wave function coupled with polarizable continuum model (BLW/PCM), was proposed to calculate molecular ionization potential (IP), electron affinity (EA) in the solid phase, and related electronic polarization.

Electrostatic phenomena in organic semiconductors: fundamentals and implications for photovoltaics

This review summarizes the current understanding of electrostatic phenomena in ordered and disordered organic semiconductors, outlines numerical schemes developed for quantitative evaluation of electrostatic and induction contributions to ionization potentials and electron affinities of organic molecules in a solid state, and illustrates two applications of these techniques: interpretation of photoelectron spectroscopy of thin films and energetics of heterointerfaces in organic solar cells.

Theoretical Study of the Charge-Transfer State Separation within Marcus Theory: The C60-Anthracene Case Study

We study, within Marcus theory, the possibility of the charge-transfer (CT) state splitting at organic interfaces and a subsequent transport of the free charge carriers to the electrodes. As a case study we analyze model anthracene-C60 interfaces. Kinetic Monte Carlo (KMC) simulations on the cold CT state were performed at a range of applied electric fields, and with the fields applied at a range of angles to the interface to simulate the action of the electric field in a bulk heterojunction (BHJ) interface. The results show that the inclusion of polarization in our model increases CT state dissociation and charge collection. The effect of the electric field on CT state splitting and free charge carrier conduction is analyzed in detail with and without polarization. Also, depending on the relative orientation of the anthracene and C60 molecules at the interface, CT state splitting shows different behavior with respect to both applied field strength and applied field angle. The importance of the hot CT in helping the charge carrier dissociation is also analyzed in our scheme.

Combining the Many-Body GW Formalism with Classical Polarizable Models: Insights on the Electronic Structure of Molecular Solids

We present an original hybrid QM/MM scheme merging the many-body Green's function GW formalism with classical discrete polarizable models and its application to the paradigmatic case of a pentacene crystal. Our calculated transport gap is found to be in excellent agreement with reference periodic bulk GW calculations, together with properly parametrized classical microelectrostatic calculations, and with photoionization measurements at crystal surfaces. More importantly, we prove that the gap is insensitive to the partitioning of pentacene molecules in QM and MM subsystems, as a result of the mutual compensation of quantum and classical polarizabilities, clarifying the relation between polarization energy and delocalization. The proposed hybrid method offers a computationally attractive strategy to compute the full spectrum of charged excitations in complex molecular environments, accounting for both QM and MM contributions to the polarization energy, a crucial requirement in the limit of large QM subsystems.

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.

Direct Observation of Entropy-Driven Electron-Hole Pair Separation at an Organic Semiconductor Interface

How an electron-hole pair escapes the Coulomb potential at a donor-acceptor interface has been a key issue in organic photovoltaic research. Recent evidence suggests that long-distance charge separation can occur on ultrafast time scales, yet the underlying mechanism remains unclear. Here we use charge transfer excitons (CTEs) across an organic semiconductor-vacuum interface as a model and show that nascent hot CTEs can spontaneously climb up the Coulomb potential within 100 fs. This process is driven by entropic gain due to the rapid rise in density of states with increasing electron-hole separation. In contrast, the lowest CTE cannot delocalize, but undergoes self-trapping and recombination.

Are hydrogen-bonded charge transfer crystals room temperature ferroelectrics?

We present a theoretical investigation of the anomalous ferroelectricity of mixed-stack charge transfer molecular crystals, based on the Peierls-Hubbard model, and first-principles calculations for its parametrization. This approach is first validated by reproducing the temperature-induced transition and the electronic polarization of TTF-CA, and then applied to a novel series of hydrogen-bonded crystals, for which room temperature ferroelectricity has recently been claimed. Our analysis shows that the hydrogen-bonded systems present a very low degree of charge transfer and hence support a very small polarization. A critical reexamination of experimental data supports our findings, shedding doubts on the ferroelectricity of these systems. More generally, our modeling allows the rationalization of general features of the ferroelectric transition in charge transfer crystals and suggests design principles for materials optimization.