Hole hopping in dimers of N,N′ di(1-naphthyl)-N,N′-diphenyl-4,4′-diamine (α-NPD): a theoretical study

Krysko I.D., Freidzon A.Y., Bagaturyants A.A.

The intramolecular localization and migration of a triplet exciton in the N,N′-di(1-naphthyl)-N,N′-diphenyl-(1,1′-biphenyl)-4,4′-diamine (α-NPD) molecule is studied by the XMCQDPT/CASSCF method. En...

Ji D., Li T., Liu J., Amirjalayer S., Zhong M., Zhang Z., Huang X., Wei Z., Dong H., Hu W., Fuchs H.

With the fast development of organic electronics, organic semiconductors have been extensively studied for various optoelectronic applications, among which organic phototransistors recently emerged as one of the most promising light signal detectors. However, it is still a big challenge to endow organic phototransistors with both high mobility and high light-sensitivity because the low mobility of most organic photoresponsive materials limits the efficiency of transporting and collecting charge carriers. We herein report band-like charge transport in vacuum-deposited small-molecule thin films for organic phototransistor arrays which can be operated at very low dark currents (~10−12 A). Both high mobility and excellent optical figures of merit including photosensitivity, photoresponsivity and detectivity are achieved, wherein, unprecedentedly, a detectivity greater than 1017 cm Hz1/2 W−1 is obtained. All these key parameters are superior to state-of-the-art organic phototransistors, implying a great potential in optoelectronic applications. The potential of organic phototransistors to surpass silicon-based devices is limited by the low carrier mobility of organic photoresponsive materials. Here, Ji et al. report high performance organic phototransistors featuring vacuum-deposited small-molecule films with band-like charge transport.

Lischka H., Nachtigallová D., Aquino A.J., Szalay P.G., Plasser F., Machado F.B., Barbatti M.

Understanding the properties of electronically excited states is a challenging task that becomes increasingly important for numerous applications in chemistry, molecular physics, molecular biology, and materials science. A substantial impact is exerted by the fascinating progress in time-resolved spectroscopy, which leads to a strongly growing demand for theoretical methods to describe the characteristic features of excited states accurately. Whereas for electronic ground state problems of stable molecules the quantum chemical methodology is now so well developed that informed nonexperts can use it efficiently, the situation is entirely different concerning the investigation of excited states. This review is devoted to a specific class of approaches, usually denoted as multireference (MR) methods, the generality of which is needed for solving many spectroscopic or photodynamical problems. However, the understanding and proper application of these MR methods is often found to be difficult due to their complexity and their computational cost. The purpose of this review is to provide an overview of the most important facts about the different theoretical approaches available and to present by means of a collection of characteristic examples useful information, which can guide the reader in performing their own applications.

Giannini S., Carof A., Blumberger J.

The mechanism of charge transport (CT) in a 1D atomistic model of an organic semiconductor is investigated using surface hopping nonadiabatic molecular dynamics. The simulations benefit from a newly implemented state tracking algorithm that accounts for trivial surface crossings and from a projection algorithm that removes decoherence correction-induced artificial long-range charge transfer. The CT mechanism changes from slow hopping of a fully localized charge to fast diffusion of a polaron delocalized over several molecules as electronic coupling between the molecules exceeds the critical threshold V ≥ λ/2 (λ is the reorganization energy). With increasing temperature, the polaron becomes more localized and the mobility exhibits a "band-like" power law decay due to increased site energy and electronic coupling fluctuations (local and nonlocal electron-phonon coupling). Thus, reducing both types of electron-phonon coupling while retaining high mean electronic couplings should be part of the strategy toward discovery of new organics with high room-temperature mobilities.

Oberhofer H., Reuter K., Blumberger J.

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

Massé A., Friederich P., Symalla F., Liu F., Meded V., Coehoorn R., Wenzel W., Bobbert P.A.

In this study, we investigate on the basis of ab initio calculations how the morphology, molecular on-site energies, reorganization energies, and charge transfer integral distribution affect the hopping charge transport and the exciton formation process in disordered organic semiconductors. We focus on three materials applied frequently in organic light-emitting diodes: $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{NPD}$, TCTA, and Spiro-DPVBi. Spatially correlated disorder and, more importantly, superexchange contributions to the transfer integrals, are found to give rise to a significant increase of the electric field dependence of the electron and hole mobility. Furthermore, a material-specific correlation is found between the HOMO and LUMO energy on each specific molecular site. For $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{NPD}$ and TCTA, we find a positive correlation between the HOMO and LUMO energies, dominated by a Coulombic contribution to the energies. In contrast, Spiro-DPVBi shows a negative correlation, dominated by a conformational contribution. The size and sign of this correlation have a strong influence on the exciton formation rate.

Liu F., Massé A., Friederich P., Symalla F., Nitsche R., Wenzel W., Coehoorn R., Bobbert P.A.

We present an ab initio modeling study of steady-state and time-dependent charge transport in hole-only devices of the amorphous molecular semiconductor α–NPD [N,N′-Di(1–naphthyl)-N,N′-diphenyl-(1,1′-biphenyl)-4,4′-diamine]. The study is based on the microscopic information obtained from atomistic simulations of the morphology and density functional theory calculations of the molecular hole energies, reorganization energies, and transfer integrals. Using stochastic approaches, the microscopic information obtained in simulation boxes at a length scale of ∼10 nm is expanded and employed in one-dimensional (1D) and three-dimensional (3D) master-equation modeling of the charge transport at the device scale of ∼100 nm. Without any fit parameter, predicted current density-voltage and impedance spectroscopy data obtained with the 3D modeling are in very good agreement with measured data on devices with different α-NPD layer thicknesses in a wide range of temperatures, bias voltages, and frequencies. Similarly good results are obtained with the computationally much more efficient 1D modeling after optimizing a hopping prefactor.

Freidzon A.Y., Safonov A.A., Bagaturyants A.A.

The multireference XMCQDPT2/CASSCF method is used to get insight into the charge transport mechanism of bis(10-hydroxybenzo[h]quinolinato)beryllium (Bebq2) and to explain some features of its light absorption and emission in monomeric and dimeric forms. Energy profiles corresponding to electron and hole hopping in Bebq2 monomer and in three close-packed dimers that can occur in the solid phase are calculated. Our calculation revealed that charges and excitons could be either localized on individual ligands or delocalized over a pair of stacking ligands in dimers. Delocalized hole states serve as deep charge traps hindering hole transport. On the other hand, the electron states are localized, and hopping electron transport can take place with low barriers. The excited states of dimers exhibit exciton splitting. In some dimers, the transition dipole moment arrangement is unfavorable for luminescence. Therefore, our calculations explain why Bebq2 is an electron transporter (hole blocker) and why regular pack...

Wang L., Prezhdo O.V., Beljonne D.

This perspective summaries recent progresses of using mean field and surface hopping mixed quantum-classical dynamics for charge transport in organics.

Shuai Z., Geng H., Xu W., Liao Y., André J.

This review introduces the development and application of a multiscale approach to assess the charge mobility for organic semiconductors, which combines quantum chemistry, Kinetic Monte Carlo (KMC), and molecular dynamics (MD) simulations. This approach is especially applicable in describing a large class of organic semiconductors with intermolecular electronic coupling (V) much less than intramolecular charge reorganization energy (λ), a situation where the band description fails obviously. The charge transport is modeled as successive charge hopping from one molecule to another. We highlight the quantum nuclear tunneling effect in the charge transfer, beyond the semiclassical Marcus theory. Such an effect is essential for interpreting the "paradoxical" experimental finding that optical measurement indicated "local charge" while electrical measurement indicated "bandlike". Coupled MD and KMC simulations demonstrated that the dynamic disorder caused by intermolecular vibration has negligible effect on the carrier mobility. We further apply the approach for molecular design of n-type materials and for rationalization of experimental results. The charge reorganization energy is analyzed through decomposition into internal coordinates relaxation, so that chemical structure contributions to the intramolecular electron-phonon interaction are revealed and give helpful indication to reduce the charge reorganization energy.

Granovsky A.A.

The distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 11A′ – 21A′ conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 11A1 to 21A1 electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems.

Troisi A.

The theories developed since the fifties to describe charge transport in molecular crystals proved to be inadequate for the most promising classes of high mobility molecular semiconductors identified in the recent years, including for example pentacene and rubrene. After reviewing at an elementary level the classical theories, which still provide the language for the understanding of charge transport in these systems, this tutorial review outlines the recent experimental and computational evidence that prompted the development of new theories of charge transport in molecular crystals. A critical discussion will illustrate how very rarely it is possible to assume a charge hopping mechanism for high mobility organic crystals at any temperature. Recent models based on the effect of non-local electron-phonon coupling, dynamic disorder, coexistence of localized and delocalized states are reviewed. Additionally, a few more recent avenues of theoretical investigation, including the study of defect states, are discussed.

Ortmann F., Bechstedt F., Hannewald K.

van Mensfoort S.L., Shabro V., de Vries R.J., Janssen R.A., Coehoorn R.

In this paper the hole mobility in the amorphous small molecule material N,N′-bis(1-naphthyl)-N,N′-diphenyl-1,1′-biphenyl-4,4′-diamine (α-NPD), which is frequently used in organic light-emitting diodes, is studied. From an analysis of the temperature and layer thickness dependence of the steady-state current density in sandwich-type α-NPD-based hole-only devices, it is found that a conventional mobility model assuming a Poole–Frenkel type field dependence and neglecting the carrier density dependence is not appropriate. Consistent descriptions with equal quality are obtained within the framework of two forms of the Gaussian disorder model (GDM and CDM), within which the presence of energetic disorder is described by a Gaussian density of states and within which spatial correlations between the site energies are absent or are included, respectively. Both models contain a carrier density dependence of the mobility. Based on a comparison of the site densities as obtained from both models with the molecular density, we argue that the analysis provides evidence for the presence of correlated disorder.

Wen S., Li A., Song J., Deng W., Han K., Goddard W.A.

We report a simple first-principles-based simulation model (combining quantum mechanics with Marcus-Hush theory) that provides the quantitative structural relationships between angular resolution anisotropic hole mobility and molecular structures and packing. We validate that this model correctly predicts the anisotropic hole mobilities of ruberene, pentacene, tetracene, 5,11-dichlorotetracene (DCT), and hexathiapentacene (HTP), leading to results in good agreement with experiment.

Koudjina S., Kumar V., Tripathi A., Atohoun G., Gbenou J., Chetti P.

ABSTRACTThe optoelectronic and charge transfer integral properties of N,N′‐di(1‐naphthyl)‐N,N′‐diphenyl‐4,4′‐diamine (α‐NPD) organic light‐emitting diode (OLED) in amorphous and crystalline structures is studied based on the Marcus–Levitch–Jortner theory and quantum chemistry calculations. The charge transfer integral simulations have been investigated through hole‐hopping regime from molecule‐to‐molecule in dimers molecules and are determined by frontier molecular orbitals (FMOs) for hole and electron transport. Quantum approaches with TD/DFT and DFT have been used to describe the most relevant electronic transitions of α‐NPD, which present character in harmony with the solvent states. Furthermore, the obtained results reveal that geometric deformations have been relied to naphthalene form and benzene rings in α‐NPD structures, and the charge transfer integral in amorphous state shows and , and in the crystalline state, it shows and . Comparing the transfer integrals average of hole/electron in the both amorphous and crystalline states, a higher value of hole transfer is explored in the amorphous form. The charge transfer transition obtained from FMO states and density of states (DOS), as well as reorganization energies values, indicates that α‐NPD would be an effective organic electronic hole transport material.

Alkhudhayr E.A., Sirbu D., Fsadni M., Vella B., Muhammad B.T., Waddell P.G., Probert M.R., Penfold T.J., Hallam T., Gibson E.A., Docampo P.

Wakahara T., Nagaoka K., Hirata C., Miyazawa K., Fujii K., Matsushita Y., Ito O., Takagi M., Shimazaki T., Tachikawa M., Wada Y., Yagyu S., Liu Y., Nakajima Y., Tsukagoshi K.

The one-dimensional porphyrin chains in the cocrystal play a very important role in the hole transport properties of C70/porphyrin nanoribbons.

Freidzon A., Dubinets N., Bagaturyants A.

The photogeneration of charges in bulk heterojunction organic photovoltaics is of crucial importance in the mechanism of charge separation. This results in the formation of both locally excited and charge-transfer exciplex states. While the former states are prone to radiative or nonradiative recombination, the latter ones can have a sufficiently long lifetime. In this work, the formation of charge-transfer exciplex states in pairs of PC61BM (acceptor) with different oligothiophenes (donors) is studied theoretically using density functional theory. The ground and excited states of three oligothiophene-PC61BM complexes are studied. It is found that the intensively absorbing state is localized on the oligothiophene. Another excited state is localized on PC61BM, being characterized by only slight absorption. The charge-transfer (CT) excited state of the complex lies either below or slightly higher than the locally excited (LE) states. The latter case is unfavorable for charge separation. Criteria for the efficient formation of charge-transfer exciplexes are found, and the possibility of oligothiophene modification to facilitate the formation of such exciplexes is explored. Shifting the donor absorption to the near IR, which is important for organic solar cells, is another goal of oligothiophene modification. A modified oligothiophene satisfying these two criteria is proposed. The structure and radiative lifetimes of the LE and CT states and also the binding energy of the CT states with respect to their dissociation into a radical cation and a radical anion are calculated. It is demonstrated that the lifetime of the CT exciplexes is sufficiently long to accomplish charge separation.

Freidzon A.Y., Bagaturyants A.A., Burdakov Y.V., Nikitenko V.R., Postnikov V.A.