Role of Geometric Distortion and Polarization in Localizing Electronic Excitations in Conjugated Polymers

Small Polarons in Two-Dimensional Pnictogens: A First-Principles Study

We report the first-principles study of small polarons in the most stable two-dimensional pnictogen allotropes: blue and black phosphorene and arsenene. While both cations and anions of small hydrogen-passivated clusters show charge localization and local lattice distortions, only the hole polaron in the blue allotrope is stable in the infinite size cluster limit. The adiabatic polaron relaxation energy is found to be 0.1 eV for phosphorene and 0.15 eV for arsenene. The polaron is localized on lone-pair orbitals with half of the extra charge distributed among 13 atoms. In the blue phosphorene, these orbitals form the valence band's top with a relatively flat band dispersion. However, in the black phosphorene, lone-pair orbitals hybridize with bonding orbitals, which explains the difference in hole localization strength between the two topologically equivalent allotropes. The polaron's adiabatic barriers for motion are small compared to the most strongly coupled phonon frequency, implying the polaron barrierless motion.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Let Digons be Bygones: The Fate of Excitons in Curved π-Systems

We explore the diverse origins of unpolarized absorption and emission of molecular polygons consisting of π-conjugated oligomer chains held in a bent geometry by strain controlled at the vertex units. For this purpose, we make use of atomistic nonadiabatic excited-state molecular dynamics simulations of a bichromophore molecular polygon (digon) with bent chromophore chains. Both structural and photoexcited dynamics were found to affect polarization features. Bending strain induces exciton localization on individual chromophore units of the conjugated chains. The latter display different transition dipole moment orientations, a feature not present in the linear oligomer counterparts. In addition, bending makes exciton localization very sensitive to molecular distortions induced by thermal fluctuations. The excited-state dynamics reveals an ultrafast intramolecular energy redistribution that spreads the exciton equally among spatially separated chromophore fragments within the molecular system. As a result, digons become virtually unpolarized absorbers and emitters, in agreement with recent experimental studies on the single-molecule level.

Evaluating the electronic structure of formal LnII ions in LnII(C5H4SiMe3)31- using XANES spectroscopy and DFT calculations

The isolation of [K(2.2.2-cryptand)][Ln(C5H4SiMe3)3], formally containing LnII, for all lanthanides (excluding Pm) was surprising given that +2 oxidation states are typically regarded as inaccessible for most 4f-elements. Herein, X-ray absorption near-edge spectroscopy (XANES), ground-state density functional theory (DFT), and transition dipole moment calculations are used to investigate the possibility that Ln(C5H4SiMe3)31- (Ln = Pr, Nd, Sm, Gd, Tb, Dy, Y, Ho, Er, Tm, Yb and Lu) compounds represented molecular LnII complexes. Results from the ground-state DFT calculations were supported by additional calculations that utilized complete-active-space multi-configuration approach with second-order perturbation theoretical correction (CASPT2). Through comparisons with standards, Ln(C5H4SiMe3)31- (Ln = Sm, Tm, Yb, Lu, Y) are determined to contain 4f6 5d0 (SmII), 4f13 5d0 (TmII), 4f14 5d0 (YbII), 4f14 5d1 (LuII), and 4d1 (YII) electronic configurations. Additionally, our results suggest that Ln(C5H4SiMe3)31- (Ln = Pr, Nd, Gd, Tb, Dy, Ho, and Er) also contain LnII ions, but with 4f n 5d1 configurations (not 4f n+1 5d0). In these 4f n 5d1 complexes, the C3h-symmetric ligand environment provides a highly shielded 5d-orbital of a' symmetry that made the 4f n 5d1 electronic configurations lower in energy than the more typical 4f n+1 5d0 configuration.

The correspondence between the conformational and chromophoric properties of amorphous conjugated polymers in mesoscale condensed systems

For π-conjugated polymers, the notion of spectroscopic units or "chromophores" provides illuminating insights into the experimentally observed absorption/emission spectra and the mechanisms of energy/charge transfer. To date, however, no statistical analysis has revealed a direct correspondence between chromophoric and conformational properties-with the latter being fundamental to polymer semiconductors. Herein, we propose a "persistence length" calculation to re-evaluate chain conformation over a full conjugation length. The mesoscale condensed systems of MEH-PPV and MEH-PPV/C₆₀ hybrid (system size ∼10 × 10 × 10 nm³) are utilized as two prototypical model systems, along with a full range of segmental lengths (2-20-mer) and five lowest singlet excited states to hint at the generality of the features presented. We demonstrate, for the first time, that two properly re-defined conformational factors that characterize chain folding and planarity, respectively, capture excellently the population distribution of chromophores in both systems investigated. In contrast, the conventional strategy of utilizing two adjacent monomer units to characterize (local) chain conformation results in only an inconspicuous correlation between the two, as previously reported. It is further shown that chain folding-and not chain planarity-is more relevant in capturing the associated oscillator strength for the first excited state, where the transient dipole moments are known to align with the chain conformation, although the corresponding excitation energy and exciton size seem relatively unaffected. The observed effects of C₆₀ on the MEH-PPV adsorption spectra also agree with recent experimental trends. Overall, the present findings are expected to aid future multiscale computer simulations and spectroscopy-data interpretations for polymer semiconductors and their hybrid systems.

Electronic Delocalization, Vibrational Dynamics, and Energy Transfer in Organic Chromophores

The efficiency of materials developed for solar energy and technological applications depends on the interplay between molecular architecture and light-induced electronic energy redistribution. The spatial localization of electronic excitations is very sensitive to molecular distortions. Vibrational nuclear motions can couple to electronic dynamics driving changes in localization. The electronic energy transfer among multiple chromophores arises from several distinct mechanisms that can give rise to experimentally measured signals. Atomistic simulations of coupled electron-vibrational dynamics can help uncover the nuclear motions directing energy flow. Through careful analysis of excited state wave function evolution and a useful fragmenting of multichromophore systems, through-bond transport and exciton hopping (through-space) mechanisms can be distinguished. Such insights are crucial in the interpretation of fluorescence anisotropy measurements and can aid materials design. This Perspective highlights the interconnected vibrational and electronic motions at the foundation of nonadiabatic dynamics where nuclear motions, including torsional rotations and bond vibrations, drive electronic transitions.

Relating Chromophoric and Structural Disorder in Conjugated Polymers

The optoelectronic properties of amorphous conjugated polymers are sensitive to the details of the conformational disorder, and spectroscopy provides the means for structural characterization of the fragments of the chain that interact with light-"chromophores". A faithful interpretation of spectroscopic conformational signatures, however, presents a theoretical challenge. Here we investigate the relationship between the ground-state optical gaps, the properties of the excited states, and the structural features of chromophores of a single molecule poly(3-hexyl)-thiophene (P3HT) using quantum-classical atomistic simulations. Our results demonstrate that chromophoric disorder arises through the interplay between excited-state delocalization and electron-hole polarization, controlled by the torsional disorder introduced by side chains. Within this conceptual framework, we predict and explain the counterintuitive spectral behavior of P3HT, a red-shifted absorption, despite shortening of chromophores, with increasing temperature. This discussion introduces the concept of disorder-induced separation of charges in amorphous conjugated polymers.

Molecular dynamics and charge transport in organic semiconductors: a classical approach to modeling electron transfer

Organic photovoltaics (OPVs) are a promising carbon-neutral energy conversion technology, with recent improvements pushing power conversion efficiencies over 10%. A major factor limiting OPV performance is inefficiency of charge transport in organic semiconducting materials (OSCs). Due to strong coupling with lattice degrees of freedom, the charges form polarons, localized quasi-particles comprised of charges dressed with phonons. These polarons can be conceptualized as pseudo-atoms with a greater effective mass than a bare charge. We propose that due to this increased mass, polarons can be modeled with Langevin molecular dynamics (LMD), a classical approach with a computational cost much lower than most quantum mechanical methods. Here we present LMD simulations of charge transfer between a pair of fullerene molecules, which commonly serve as electron acceptors in OSCs. We find transfer rates consistent with experimental measurements of charge mobility, suggesting that this method may provide quantitative predictions of efficiency when used to simulate materials on the device scale. Our approach also offers information that is not captured in the overall transfer rate or mobility: in the simulation data, we observe exactly when and why intermolecular transfer events occur. In addition, we demonstrate that these simulations can shed light on the properties of polarons in OSCs. Much remains to be learned about these quasi-particles, and there are no widely accepted methods for calculating properties such as effective mass and friction. Our model offers a promising approach to exploring mass and friction as well as providing insight into the details of polaron transport in OSCs.

Charge delocalization characteristics of regioregular high mobility polymers

Controlling the regioregularity among the structural units of narrow bandgap conjugated polymer backbones has led to improvements in optoelectronic properties, for example in the mobilities observed in field effect transistor devices. To investigate how the regioregularity affects quantities relevant to hole transport, regioregular and regiorandom oligomers representative of polymeric structures were studied using density functional theory. Several structural and electronic characteristics of the oligomers were compared, including chain planarity, cation spin density, excess charges on molecular units and internal reorganizational energy. The main difference between the regioregular and regiorandom oligomers is found to be the conjugated backbone planarity, while the reorganizational energies calculated are quite similar across the molecular family. This work constitutes the first step on understanding the complex interplay of atomistic changes and an oligomer backbone structure toward modeling the charge transport properties.

Polaron Stabilization by Cooperative Lattice Distortion and Cation Rotations in Hybrid Perovskite Materials

Solution-processed organometallic perovskites have rapidly developed into a top candidate for the active layer of photovoltaic devices. Despite the remarkable progress associated with perovskite materials, many questions about the fundamental photophysical processes taking place in these devices, remain open. High on the list of unexplained phenomena are very modest mobilities despite low charge carrier effective masses. Moreover, experiments elucidate unique degradation of photocurrent affecting stable operation of perovskite solar cells. These puzzles suggest that, while ionic hybrid perovskite devices may have efficiencies on par with conventional Si and GaAs devices, they exhibit more complicated charge transport phenomena. Here we report the results from an in-depth computational study of small polaron formation, electronic structure, charge density, and reorganization energies using both periodic boundary conditions and isolated structures. Using the hybrid density functional theory, we found that volumetric strain in a CsPbI3 cluster creates a polaron with binding energy of around 300 and 900 meV for holes and electrons, respectively. In the MAPbI3 (MA = CH3NH3) cluster, both volumetric strain and MA reorientation effects lead to larger binding energies at around 600 and 1300 meV for holes and electrons, respectively. Such large reorganization energies suggest appearance of small polarons in organometallic perovskite materials. The fact that both volumetric lattice strain and MA molecular rotational degrees of freedom can cooperate to create and stabilize polarons indicates that in order to mitigate this problem, formamidinium (FA = HC(NH2)2) and cesium (Cs) based crystals and alloys, are potentially better materials for solar cell and other optoelectronic applications.

The Optical Signature of Charges in Conjugated Polymers

Electrical charge flowing through organic semiconductors drives many of today's mobile phone displays and television screens, suggesting an internally consistent model of charge-carrier properties in these materials to have manifested. In conjugated polymers, charges give rise to additional absorption of light at wavelengths longer than those absorbed by the electrically neutral species. These characteristic absorption bands are universally being related to the emergence of localized energy levels shifted into the forbidden gap of organic semiconductors due to local relaxation of the molecular geometry. However, the traditional view on these energy levels and their occupation is incompatible with expected changes in electron removal and addition energies upon charging molecules. Here, I demonstrate that local Coulomb repulsion, as captured by nonempirically optimized electronic-structure calculations, restores compatibility and suggests a different origin of the charge-induced optical transitions. These results challenge a widely accepted and long-established picture, but an improved understanding of charge carriers in molecular materials promises a more targeted development of organic and hybrid organic/inorganic (opto-)electronic devices.

Self-Trapping of Charge Carriers in Semiconducting Carbon Nanotubes: Structural Analysis

The spatial extent of charged electronic states in semiconducting carbon nanotubes with indices (6,5) and (7,6) was evaluated using density functional theory. It was observed that electrons and holes self-trap along the nanotube axis on length scales of about 4 and 8 nm, respectively, which localize cations and anions on comparable length scales. Self-trapping is accompanied by local structural distortions showing periodic bond-length alternation. The average lengthening (shortening) of the bonds for anions (cations) is expected to shift the G-mode frequency to lower (higher) values. The smaller-diameter nanotube has reduced structural relaxation due to higher carbon-carbon bond strain. The reorganization energy due to charge-induced deformations in both nanotubes is found to be in the 30-60 meV range. Our results represent the first theoretical simulation of self-trapping of charge carriers in semiconducting nanotubes, and agree with available experimental data.

Singlet and triplet excitons and charge polarons in cycloparaphenylenes: a density functional theory study

Upon excitation, electron–phonon coupling leads to spatial localization of the electronic wavefunction and distortion of molecular geometry.

Self-trapping of excitons, violation of Condon approximation, and efficient fluorescence in conjugated cycloparaphenylenes

Cycloparaphenylenes, the simplest structural unit of armchair carbon nanotubes, have unique optoelectronic properties counterintuitive in the class of conjugated organic materials. Our time-dependent density functional theory study and excited state dynamics simulations of cycloparaphenylene chromophores provide a simple and conceptually appealing physical picture explaining experimentally observed trends in optical properties in this family of molecules. Fully delocalized degenerate second and third excitonic states define linear absorption spectra. Self-trapping of the lowest excitonic state due to electron-phonon coupling leads to the formation of spatially localized excitation in large cycloparaphenylenes within 100 fs. This invalidates the commonly used Condon approximation and breaks optical selection rules, making these materials superior fluorophores. This process does not occur in the small molecules, which remain inefficient emitters. A complex interplay of symmetry, π-conjugation, conformational distortion and bending strain controls all photophysics of cycloparaphenylenes.

Mapping orientational order of charge-probed domains in a semiconducting polymer

Structure-property relationships are of fundamental importance to develop quantitative models describing charge transport in organic semiconductor based electronic devices, which are among the best candidates for future portable and lightweight electronic applications. While microstructural investigations, such as those based on X-rays, electron microscopy, or polarized optical probes, provide necessary information for the rationalization of transport in macromolecular solids, a general model predicting how charge accommodates within structural maps is not yet available. Therefore, techniques capable of directly monitoring how charge is distributed when injected into a polymer film and how it correlates to structural domains can help fill this gap. Supported by density functional theory calculations, here we show that polarized charge modulation microscopy (p-CMM) can unambiguously and selectively map the orientational order of the only conjugated segments that are probed by mobile charge in the few nanometer thick accumulation layer of a high-mobility polymer-based field-effect transistor . Depending on the specific solvent-induced microstructure within the accumulation layer, we show that p-CMM can image charge-probed domains that extend from submicrometer to tens of micrometers size, with markedly different degrees of alignment. Wider and more ordered p-CMM domains are associated with improved carrier mobility, as extracted from device characteristics. This observation evidences the unprecedented opportunity to correlate, directly in a working device, electronic properties with structural information on those conjugated segments involved in charge transport at the buried semiconductor-dielectric interface of a field-effect device.

Exploring photophysical properties of metal-free coumarin sensitizers: an efficient strategy to improve the performance of dye-sensitized solar cells

The five important parameters (φ_LHE,φ_inject,φ_reg,φ_cc,V_oc) for DSSCs are improved by modifying the dyes with electron-deficient units.

Effect of Packing on Formation of Deep Carrier Traps in Amorphous Conjugated Polymers

We theoretically investigate the role of conformational disorder and intermolecular interactions on the localization properties of electronic states, leading to the formation of carrier traps in amorphous aggregates of conjugated polymers. Samples of amorphous conformations of poly(p-phenylene vinylene) (PPV), poly2-methoxy-5-(2-ethyl-hexyloxy)PPV (MEH-PPV), and [poly-(9,9'-dioctyluorene)] (PFO) oligomers are simulated by classical molecular dynamics, while their electronic structure is calculated using first-principles density functional theory. Localization and delocalization properties of molecular orbitals are studied based on the participation ratio analysis, an approach commonly used in inorganic semiconductors. Our simulations confirm that the alkyl side chains insignificantly affect the conformational disorder in amorphous polymers while having a dramatic effect on the intermolecular disorder and packing. The nature of the disorder and its impact on charge-carrier localization in amorphous polymers with alkyl side chains differ drastically from those of disordered polymers without side chains, such as PPVs. Thus, long-range intermolecular interactions and sparse packing are responsible for the formation of multiple, deep, highly localized trap states in amorphous MEH-PPVs and PFOs, while close packing in combination with conformational disorder leads to the trap states distributed mostly near the bandgap edges in PPV aggregates.

Electronically excited states in poly(p-phenylenevinylene): vertical excitations and torsional potentials from high-level ab initio calculations

Ab initio second-order algebraic diagrammatic construction (ADC(2)) calculations using the resolution of the identity (RI) method have been performed on poly-(p-phenylenevinylene) (PPV) oligomers with chain lengths up to eight phenyl rings. Vertical excitation energies for the four lowest π–π* excitations and geometry relaxation effects for the lowest excited state (S₁) are reported. Extrapolation to infinite chain length shows good agreement with analogous data derived from experiment. Analysis of the bond length alternation (BLA) based on the optimized S₁ geometry provides conclusive evidence for the localization of the defect in the center of the oligomer chain. Torsional potentials have been computed for the four excited states investigated and the transition densities divided into fragment contributions have been used to identify excitonic interactions. The present investigation provides benchmark results, which can be used (i) as reference for lower level methods and (ii) give the possibility to parametrize an effective Frenkel exciton Hamiltonian for quantum dynamical simulations of ultrafast exciton transfer dynamics in PPV type systems.