The line-dipole approximation for the evaluation of the exciton transfer integral, $J$, between conjugated polymer chains is rigorously justified. Using this approximation, as well as the plane-wave approximation for the exciton center-of-mass wavefunction, it is shown analytically that $J \sim L$ when the chain lengths are smaller than the separation between them, or $J\sim L^{-1}$ when the chain lengths are larger than their separation, where $L$ is the polymer length. Scaling relations are also obtained numerically for the more realistic standing-wave approximation for the exciton center-of-mass wavefunction, where it is found that for chain lengths larger than their separation $J \sim L^{-1.8}$ or $J \sim L^{-2}$, for parallel or collinear chains, respectively. These results have important implications for the photo-physics of conjugated polymers and self-assembled molecular systems, as the Davydov splitting in aggregates and the Förster transfer rate for exciton migration decreases with chain lengths larger than their separation. This latter result has obvious deleterious consequences for the performance of polymer photovoltaic devices.
This is a review of exciton dynamics in conjugated polymers. Exciton dynamics encompass multiple time and length scales. Ultrafast femtosecond processes are intrachain and involve a quantum mechanical correlation of the exciton and nuclear degrees of freedom. In contrast, post-picosecond processes involve the incoherent Forster transfer of excitons between polymer chains. Exciton dynamics is also strongly determined by the spatial and temporal disorder that is ubiquitous in conjugated polymers. Since excitons are delocalized over hundreds of atoms, a theoretical understanding of these processe…
The scattering and recombination processes between two triplet excitons in conjugated polymers are investigated by using a nonadiabatic evolution method, based on an extended Su-Schrieffer-Heeger model including interchain interactions. Due to the interchain coupling, the electron and/or hole in the two triplet excitons can exchange. The results show that the recombination induces the formation of singlet excitons, excited polarons and biexcitons. Moreover, we also find the yields of these products, which can contribute to the emission, increase with the interchain coupling strength, in good a…
This paper presents a possible explanation for the enhanced singlet exciton yield in light emitting polymers. We propose a theory of electron-hole recombination via inter-molecular inter-conversion from inter-molecular weakly bound polaron pairs (or charge-transfer excitons) to intra-molecular excitons. This theory is applicable to parallel polymer chains. A crucial aspect of the theory is that both the intra-molecular and inter-molecular excitons are effective-particles, which are described by both a relative-particle wavefunction and a center-of-mass wavefunction. This implies two electronic…
The cross-over from coherent to incoherent exciton transport in disordered polymer films is studied by computationally solving a modified form of the Redfield equation for the exciton density matrix. This theory models quantum mechanical (ballistic) and incoherent (diffusive) transport as limiting cases. It also reproduces Forster transport for certain parameter regimes. Using model parameters appropriate to polymer thin films it is shown that short-time quantum mechanical coherence increases the exciton diffusion length. It also causes rapid initial energy relaxation and larger line widths. T…
We report on large-scale simulations of intrachain exciton dynamics in poly(para-phenylene vinylene). Our coarse-grained model describes Frenkel exciton coupling to both fast, quantized C-C bond vibrations and slow, classical torsional modes. We also incorporate system-bath interactions. The dynamics are simulated using the Time Evolution Block Decimation method, which avoids the failures of the Ehrenfest approximation to describe decoherence processes and nonadiabatic interstate conversion. System-bath interactions are modeled using quantum trajectories and Lindblad quantum jump operators. We…
Attachment of chemical substituents (such as polar moieties) constitutes an efficient and convenient way to modify physical and chemical properties of conjugated polymers and oligomers. Associated modifications in the molecular electronic states can be comprehensively described by examining scattering of excitons in the polymer's backbone at the scattering center representing the chemical substituent. Here, we implement effective tight-binding models as a tool to examine the analytical properties of the exciton scattering matrices in semi-infinite polymer chains with substitutions. We demonstr…
The photophysics of $π$-conjugated polymers has been of considerable interest over the last three decades because of their organic semiconductor properties. Primary photoexcitations, Frenkel excitons, can be probed optically by means of numerous linear spectroscopies, providing a wealth of information on the the strength of excitonic coupling, the exciton coherence length, and on the nature of the disordered energy landscape. Nonetheless, there are intrinsic limitations in the information that can be obtained with linear spectroscopy compared to non-linear coherent techniques. Examples of this…
Optical devices fabricated using conjugated polymer systems give rise to singlet exciton yields which are high compared to the statistically predicted estimate of 25% obtained using simple recombination schemes. In this study we evaluate the singlet exciton yield in conjugated polymers systems by fitting to a model that incorporates the Pauli exclusion principle. The rate equations which describe the exciton dynamics include quantum dynamical components (both density and spin-dependent) which arise during the spin-allowed conversion of composite intra-molecular excitons into loosely bound char…
We investigate the effect of exciton coupling on the optical absorption spectrum of polymer molecules under conditions of strong inhomogeneous broadening. We demonstrate that the dependence of the maximum in the rescaled absorption spectrum on the number of monomers is determined by the average monomer excitation energies and their resonant coupling and insensitive to the inhomogeneous broadening. Thus the absorption spectrum can be used to determine optical interactions between monomers. The results are applied to the absorption spectra of poly-A poly-T DNA hairpins and used to interpret the …
We report on high-dimensional quantum dynamical simulations of torsion-induced exciton migration in a single-chain oligothiophene segment comprising twenty repeat units, using a first-principles parametrized Frenkel J-aggregate Hamiltonian. Starting from an initial inter-ring torsional defect, these simulations provide evidence of an ultrafast two-time scale process at low temperatures, involving exciton-polaron formation within tens of femtoseconds, followed by torsional relaxation on a ~300 femtosecond time scale. The second step is the driving force for exciton migration, as initial conjuga…
The reported enhanced singlet-exciton yields in light-emitting polymers over the statistical limit of 25% has attracted wide experimental and theoretical attention. Most theoretical estimates of the singlet-exciton yield depend crucially on estimates of the inter-system crossing rates induced by spin-orbit coupling. In this paper we use the experimentally determined phosphorescent life-time and energy of the lowest-lying triplet state, as well as calculated values of Huang-Rhys factors to estimate the spin-orbit matrix element and inter-system crossing time between the lowest-lying singlet and…
Many optoelectronic devices based on organic materials require rapid and long-range singlet exciton transport. Key factors that control the transport of singlet excitons includes the electronic structure of the material, disorder and exciton-phonon coupling. An important parameter whose influence on exciton transport has not been explored is the symmetry of the singlet electronic state (S1). Here, we employ femtosecond transient absorption spectroscopy and microscopy to reveal the relationship between the symmetry of S1 and exciton transport in highly aligned, near-disorder free, one-dimension…
Copolymers such as PCDTBT (poly(N-9'-heptadecanyl-2,7-carbazole-alt-5,5-(4',7'-di-2-thienyl- 2',1',3'-benzothiadiazole))) are commonly employed as donor material in bulk heterojunction solar cells. Recently, chemical defects such as homocouplings have been shown to form at the material synthesis stage, strongly reducing the short circuit current in organic photovoltaics. Here we show that both, low molecular weight and homocoupling defects reduce the short circuit current of solar cells because of limited exciton diffusion. We propose a model that unites and explains the influence of both chem…
The exciton relaxation dynamics of photoexcited electronic states in poly($p$-phenylenevinylene) (PPV) are theoretically investigated within a coarse-grained model, in which both the exciton and nuclear degrees of freedom are treated quantum mechanically. The Frenkel-Holstein Hamiltonian is used to describe the strong exciton-phonon coupling present in the system, while external damping of the internal nuclear degrees of freedom are accounted for by a Lindblad master equation. Numerically, the dynamics are computed using the time evolving block decimation (TEBD) and quantum jump trajectory tec…
Motivated by an experiment in which the singlet-triplet gap in triphenylene based copolymers was effectively tuned, we used time dependent density functional theory (TDDFT) to reproduce the main results. By means of conventional and long-range corrected exchange correlation functionals, the luminescence energies and the exciton localization were calculated for a triphenylene homopolymer and several different copolymers. The phosphorescence energy of the pure triphenylene chain is predicted accurately by means of the optimally tuned long-range corrected LC-PBE functional and slightly less accur…
Charge-transfer (CT) exciton effects are investigated for the optical absorption spectra of crosslinked C60 systems by using the intermediate exciton theory. We consider the C60-dimers, and the two (and three) molecule systems of the C60-polymers. We use a tight-binding model with long-range Coulomb interactions among electrons, and the model is treated by the Hartree-Fock approximation followed by the single-excitation configuration interaction method. We discuss the variations in the optical spectra by changing the conjugation parameter between molecules. We find that the total CT-component …
A hot-exciton is usually the initial elementary excitation product of the solid phase, particularly in low dimensional photonic materials, which is a bottle-neck to all subsequent processes. Measurement of hot-exciton emission (HExEm) is a great challenge due to fast EK relaxation and thus very weak transient emission. Here we report the first unambiguous observation of femtosecond HExEm from thin films of a model quasi-one-dimensional π-conjugated organic rigid-rod quantum nanowire, MeLPPP (methyl-substituted ladder-type poly(para-phenylenes), by using femtosecond time-resolved fluorescence s…
The electronic properties of macromolecular semiconductor thin films depend profoundly on their solid-state microstructure, which in turn is governed, among other things, by the processing conditions selected and the polymer chemical nature and molecular weight. Specifically, low-molecular-weight materials form crystalline domains of cofacially $π$-stacked molecules, while the usually entangled nature of higher molecular-weight polymers leads to microstructures comprised of molecularly ordered crystallites interconnected by amorphous regions. Here, we examine the interplay between extended exc…
Component of photoexcited states with large spatial extent is investigated for optical absorption spectra of the electroluminescent conjugated polymers by using the intermediate exciton theory. We calculate the ratio of oscillator strengths due to long-range excitons with respect to sum of all the oscillator strengths of the absorption as a function of the monomer number. The oscillator strengths of the long-range excitons in poly(para-phenylene) are smaller than those in poly(para-phenylenevinylene), and those of poly(para-phenylenedivinylene) are larger than those in poly(para-phenylenevinyl…
Ring torsion effects on optical excitation properties in poly(para-phenylene) (PPP) and polyaniline (PAN) are investigated by extending the Shimoi-Abe model [Synth. Met. 78, 219 (1996)]. The model is solved by the intermediate exciton formalism. Long-range excitons are characterized, and the long-range component of the oscillator strengths is calculated. We find that ring torsions affect the long-range excitons in PAN more easily than in PPP, due to the larger torsion angle of PAN and the large number of bonds whose hopping integrals are modulated by torsions. Next, ring torsional disorder eff…
Control of chain length and morphology in combination with single-molecule spectroscopy techniques provide a comprehensive photophysical picture of excited-state losses in the prototypical conjugated polymer poly(3-hexylthiophene) (P3HT). A universal self-quenching mechanism is revealed, based on singlet-triplet exciton annihilation, which accounts for the dramatic loss in fluorescence quantum yield of a single P3HT chain between its solution (unfolded) and bulk-like (folded) state. Triplet excitons fundamentally limit the fluorescence of organic photovoltaic materials, which impacts on the co…
We probe charge photogeneration and subsequent recombination dynamics in neat regioregular poly(3-hexylthiophene) films over six decades in time by means of time-resolved photoluminescence spectroscopy. Exciton dissociation at 10K occurs extrinsically at interfaces between molecularly ordered and disordered domains. Polaron pairs thus produced recombine by tunnelling with distributed rates governed by the distribution of electron-hole radii. Quantum-chemical calculations suggest that hot-exciton dissociation at such interfaces results from a high charge-transfer character.
Exciton-polaritons in organic materials are hybrid states that result from the strong interaction of photons and the bound excitons that these materials host. Organic polaritons hold great interest for optoelectronic applications, however progress towards this end has been impeded by the lack of a first principles approach that quantifies light-matter interactions in these systems, and which would allow the formulation of molecular design rules. Here we develop such a first principles approach, quantifying light-matter interactions. We exemplify our approach by studying variants of the conjuga…
An appealing definition of the term "molecule" arises from consideration of the nature of fluorescence, with discrete molecular entities emitting a stream of single photons. We address the question of how large a molecular object may become by growing deterministic aggregates from single conjugated polymer chains. Even particles containing dozens of individual chains still behave as single quantum emitters due to efficient excitation energy transfer, while the brightness is raised due to the increased absorption cross-section of the suprastructure. Excitation energy can delocalize between indi…
Treated traditionally by the Ehrenfest approximation, dynamics of a one-dimensional molecular crystal model with off-diagonal exciton-phonon coupling is investigated in this work using the Dirac-Frenkel time-dependent variational principle with the multi-D$_2$ {\it Ansatz}. It is shown that the Ehrenfest method is equivalent to our variational method with the single D$_2$ {\it Ansatz}, and with the multi-D$_2$ {\it Ansatz}, the accuracy of our simulated dynamics is significantly enhanced in comparison with the semi-classical Ehrenfest dynamics. The multi-D$_2$ {\it Ansatz} is able to capture n…
An exact real time quantum dynamics preaveraged over imaginary time path integral is formulated for general condensed phase equilibrium ensemble. This formulation results in the well-known centroid dynamics approach upon filtering of centroid constraint, and provides a rigorous framework to understand and analyze a related quantum dynamics approximation method called ring polymer molecular dynamics. The formulation also serves as the basis for developing new kinds of quantum dynamics that utilize the cyclic nature of the imaginary time path integral.
Organic semiconductors have the remarkable property that their optical excitation not only generates charge-neutral electron-hole pairs (excitons) but also charge-separated polaron pairs with high yield. The microscopic mechanisms underlying this charge separation have been debated for many years. Here we use ultrafast two-dimensional electronic spectroscopy to study the dynamics of polaron pair formation in a prototypical polymer thin film on a sub-20-fs time scale. We observe multi-period peak oscillations persisting for up to about 1 ps as distinct signatures of vibronic quantum coherence a…
We introduce mapping-variable ring polymer molecular dynamics (MV-RPMD), a model dynamics for the direct simulation of multi-electron processes. An extension of the RPMD idea, this method is based on an exact, imaginary time path-integral representation of the quantum Boltzmann operator using continuous Cartesian variables for both electronic states and nuclear degrees of freedom. We demonstrate the accuracy of the MV-RPMD approach in calculations of real-time, thermal correlation functions for a range of two-state single-mode model systems with different coupling strengths and asymmetries. Fu…
In organic photovoltaics, the mechanism by which free electrons and holes are generated overcoming the Coulomb attraction is a currently much debated topic. To elucidate this mechanism at a molecular level, we carried out a combined electronic structure and quantum dynamical analysis that captures the elementary events from the exciton dissociation to the free carrier generation at polymer/fullerene donor-acceptor heterojunctions. Our calculations show that experimentally observed efficient charge separations can be explained by a combination of two effects: First, the delocalization of charge…
Path-integral-based molecular dynamics (MD) simulations are widely used for the calculation of numerically exact quantum Boltzmann properties and approximate dynamical quantities. A nearly universal feature of MD numerical integration schemes for equations of motion based on imaginary-time path integrals is the use of harmonic normal modes for the exact evolution of the free ring-polymer positions and momenta. In this work, we demonstrate that this standard practice creates numerical artifacts. In the context of conservative (i.e., microcanonical) equations of motion, it leads to numerical ins…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art pa…
The reduced density matrix of excitons coupled to a phonon bath at a finite temperature is studied using the path integral Monte Carlo method. Appropriate choices of estimators and importance sampling schemes are crucial to the performance of the Monte Carlo simulation. We show that by choosing the population-normalized estimator for the reduced density matrix, an efficient and physically-meaningful sampling function can be obtained. In addition, the nonadiabatic phonon probability density is obtained as a byproduct during the sampling procedure. For importance sampling, we adopted the Metropo…
In polymeric semiconductors, charge carriers are polarons, which means that the excess charge deforms the molecular structure of the polymer chain that hosts it. This effect results in distinctive signatures in the vibrational modes of the polymer. We probe polaron photo- generation dynamics at polymer:fullerene heterojunctions by monitoring its time-resolved resonance-Raman spectrum following ultrafast photoexcitation. We conclude that polarons emerge within 200 fs, which is nearly two orders of magnitude faster than exciton localisation in the neat polymer film. Surprisingly, further vibrati…
Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending…
Charges in conjugated polymer materials have a strong impact on the photophysics and their interaction with the primary excited state species has to be taken into account in understanding device properties. Here, we employ single-molecule spectroscopy to unravel the influence of charges on several photoluminescence (PL) observables. The charges are injected either stochastically by a photochemical process, or deterministically in a hole-injection sandwich device configuration. We find that upon charge injection, besides a blue-shift of the PL emission and a shortening of the PL lifetime due to…
