Electronic Excited States in Amorphous MEH-PPV Polymers from Large-Scale First Principles Calculations

Visualizing and characterizing excited states from time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and semi-quantitative accuracy in many contexts, even if there are well recognized limitations. This Perspective describes various ways in which excited states from TD-DFT calculations can be visualized and analyzed, both qualitatively and quantitatively. This includes not just orbitals and densities but also well-defined statistical measures of electron-hole separation and of Frenkel-type exciton delocalization. Emphasis is placed on mathematical connections between methods that have often been discussed separately. Particular attention is paid to charge-transfer diagnostics, which provide indicators of when TD-DFT may not be trustworthy due to its categorical failure to describe long-range electron transfer. Measures of exciton size and charge separation that are directly connected to the underlying transition density are recommended over more ad hoc metrics for quantifying charge-transfer character.

Transfer learning with graph neural networks for optoelectronic properties of conjugated oligomers

Despite the remarkable progress of machine learning (ML) techniques in chemistry, modeling the optoelectronic properties of long conjugated oligomers and polymers with ML remains challenging due to the difficulty in obtaining sufficient training data. Here, we use transfer learning to address the data scarcity issue by pre-training graph neural networks using data from short oligomers. With only a few hundred training data, we are able to achieve an average error of about 0.1 eV for the excited-state energy of oligothiophenes against time-dependent density functional theory (TDDFT) calculations. We show that the success of our transfer learning approach relies on the relative locality of low-lying electronic excitations in long conjugated oligomers. Finally, we demonstrate the transferability of our approach by modeling the lowest-lying excited-state energies of poly(3-hexylthiophene) in its single-crystal and solution phases using the transfer learning models trained with the data of gas-phase oligothiophenes. The transfer learning predicted excited-state energy distributions agree quantitatively with TDDFT calculations and capture some important qualitative features observed in experimental absorption spectra.

Implications of relaxation dynamics of collapsed conjugated polymeric nanoparticles for light-harvesting applications

The mechanism of the formation of nanoparticles (collapsed state) from the extended state of polymers and their ultrafast excited state relaxation dynamics are illustrated.

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.

Origin of the Excited-State Absorption Spectrum of Polythiophene

The excited states of conjugated polymers play a central role in their applications in organic solar photovoltaics. The delocalized excited states of conjugated polymers are short-lived (τ < 40 fs) but are imperative in the photovoltaic properties of these materials. Photoexcitation of poly(3-hexylthiophene) (P3HT) induces an excited-state absorption band, but the transitions that are involved are not well understood. In this work, calculations have been performed on P3HT analogues using nonlinear response time-dependent density functional theory to show that an increase in the oligomer length correlates with the dominance of the S₁ → S₃ transition. Furthermore, the predicted transition energy shows an excellent agreement with experiment. The calculations also yielded results on intramolecular charge transfer in P3HT due to the S₁ → S₃ transition, providing insight into the mechanism of exciton dissociation to form charge carriers.

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.

Development of a Novel Index for Analysis of Electronically Excited States

Concerning the major factors in the context of excited states analyses, namely charge centroids of the orbitals involved in the excitations, the distance between orbital centroids, and overlap integrals, a new metric-the Ω index-is proposed to assign the character and optical properties of electronically excited states. Using several molecules from different classes and also a well-studied standard database for time-dependent density functional theory (TD-DFT) studies as benchmark criteria, accountability of the developed index is numerically assessed for local, charge transfer, and Rydberg excitations. It is shown that the nature of excited states can be discriminated using the Ω index, where its superior performance for those situations in which the previous descriptors were not helpful is also unveiled. Relationships are also examined between the Ω index and optical properties of some molecules under study in the framework of the sum-over-state approach. It is observed that there are correlations between the proposed index and computed hyperpolarizabilities based on the sum-over-state scheme. These findings offer the possibility of estimating excited-state properties of large systems from simple descriptors without explicitly performing calculations of high-order response functions.

Communication: Exciton analysis in time-dependent density functional theory: How functionals shape excited-state characters

Excited-state descriptors based on the one-particle transition density matrix referring to the exciton picture have been implemented for time-dependent density functional theory. State characters such as local, extended ππ(∗), Rydberg, or charge transfer can be intuitively classified by simple comparison of these descriptors. Strong effects of the choice of the exchange-correlation kernel on the physical nature of excited states can be found and decomposed in detail leading to a new perspective on functional performance and the design of new functionals.

Quantum Chemical Studies of Light Harvesting

The design of optimal light-harvesting (supra)molecular systems and materials is one of the most challenging frontiers of science. Theoretical methods and computational models play a fundamental role in this difficult task, as they allow the establishment of structural blueprints inspired by natural photosynthetic organisms that can be applied to the design of novel artificial light-harvesting devices. Among theoretical strategies, the application of quantum chemical tools represents an important reality that has already reached an evident degree of maturity, although it still has to show its real potentials. This Review presents an overview of the state of the art of this strategy, showing the actual fields of applicability but also indicating its current limitations, which need to be solved in future developments.

Charge mobility induced by Brownian fluctuations in π-conjugated polymers in solution

We study the motion of a doped charge in a π-conjugated polymer chain in solution subject to Brownian fluctuations. Specifically, we take poly(para-phenylene) to be our model system where the Brownian fluctuations cause rotational motion of the phenylene rings. The instantaneous torsional fluctuations cause Anderson localization of the charge wavefunction, with the lower-energy spectrum being composed of local ground states and the higher-energy spectrum being composed of quasi-extended states. At low temperatures, additional charge localization occurs via torsional relaxation. The dynamical torsional fluctuations lead to two distinct modes of motion of the charge: adiabatic and non-adiabatic. Adiabatic motion is a 'crawling' motion of the charge along the polymer chain while the charge remains in its local ground state. Non-adiabatic motion is a rapid 'hopping' motion as the charge is excited into higher energy quasi-extended states and travels ballistically along the chain before relaxing into a local ground state. The adiabatic motion dominates at low temperatures, and exhibits a linear temperature dependence and thus a constant zero-field charge mobility. Non-adiabatic motion begins to dominate as the temperature is increased, as the charge is thermally excited into higher energy states. At high temperatures the diffusion constant becomes almost temperature independent, indicating a decrease in the charge mobility with increasing temperature, which we attribute to the charge localization length being a decreasing function of temperature at high temperatures.

Excitons in poly(para phenylene vinylene): a quantum-chemical perspective based on high-level ab initio calculations

Exciton analyses of high-level quantum-chemical computations for poly(paraphenylene vinylene) reveal the nature of the excitonic bands in PPV oligomers.

Statistical analysis of electronic excitation processes: Spatial location, compactness, charge transfer, and electron-hole correlation

We report the development of a set of excited-state analysis tools that are based on the construction of an effective exciton wavefunction and its statistical analysis in terms of spatial multipole moments. This construction does not only enable the quantification of the spatial location and compactness of the individual hole and electron densities but also correlation phenomena can be analyzed, which makes this procedure particularly useful when excitonic or charge-resonance effects are of interest. The methods are first applied to bianthryl with a focus on elucidating charge-resonance interactions. It is shown how these derive from anticorrelations between the electron and hole quasiparticles, and it is discussed how the resulting variations in state characters affect the excited-state absorption spectrum. As a second example, cytosine is chosen. It is illustrated how the various descriptors vary for valence, Rydberg, and core-excited states, and the possibility of using this information for an automatic characterization of state characters is discussed.

Dynamics of the excitonic coupling in organic crystals

We show that the excitonic coupling in molecular crystals undergoes a very large fluctuation at room temperature as a result of the combined thermal motions of the nuclei. This observation dramatically affects the description of exciton transport in organic crystals and any other phenomenon (like singlet fission or exciton dissociation) that originates from an exciton in a molecular crystal or thin film. This unexpected result is due to the predominance of the short-range excitonic coupling mechanisms (exchange, overlap, and charge-transfer mediated) over the Coulombic excitonic coupling for molecules in van der Waals contact. To quantify this effect we develop a procedure to evaluate accurately the short-range excitonic coupling (via a diabatization scheme) along a molecular dynamics trajectory of the representative molecular crystals of anthracene and tetracene.

Tunable spectra and charge transfer process of benzodifurandione-based polymer by sulfur substitution

The ground state geometry, optical and charge transport properties of benzodifurandione-based PPV (BDPPV) have been studied with density functional theory methods.

Rational design of D–A1–D–A2 conjugated polymers with superior spectral coverage

Calculations and experiments elucidate factors governing how D–A₁–D–A₂ polymers offer fundamentally improved spectral coverage via allowed transitions to both acceptor LUMOs.