Excitons in conjugated polymers: Wavefunctions, symmetries, and quantum numbers

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.

Mastering morphology of non-fullerene acceptors towards long-term stable organic solar cells

Despite the rapid progress of organic solar cells based on non-fullerene acceptors, simultaneously achieving high power conversion efficiency and long-term stability for commercialization requires sustainable research effort. Here, we demonstrate stable devices by integrating a wide bandgap electron-donating polymer (namely PTzBI-dF) and two acceptors (namely L8BO and Y6) that feature similar structures yet different thermal and morphological properties. The organic solar cell based on PTzBI-dF:L8BO:Y6 could achieve a promising efficiency of 18.26% in the conventional device structure. In the inverted structure, excellent long-term thermal stability over 1400 h under 85 °C continuous heating is obtained. The improved performance can be ascribed to suppressed charge recombination along with appropriate charge transport. We find that the morphological features in terms of crystalline coherence length of fresh and aged films can be gradually regulated by the weight ratio of L8BO:Y6. Additionally, the occurrence of melting point decrease and reduced enthalpy in PTzBI-dF:L8BO:Y6 films could prohibit the amorphous phase to cluster, and consequently overcome the energetic traps accumulation aroused by thermal stress, which is a critical issue in high efficiency non-fullerene acceptors-based devices. This work provides insight into understanding non-fullerene acceptors-based organic solar cells for improved efficiency and stability.

Understanding the Microstructure Formation of Polymer Films by Spontaneous Solution Spreading Coating with a High-Throughput Engineering Platform

An important step of the great achievement of organic solar cells in power conversion efficiency is the development of low-band gap polymer donors, PBDB-T derivatives, which present interesting aggregation effects dominating the device performance. The aggregation of polymers can be manipulated by a series of variables from a materials design and processing conditions perspective; however, optimization of film quality is a time- and energy-consuming work. Here, we introduce a robot-based high-throughput platform (HTP) that is offering automated film preparation and optical spectroscopy thin-film characterization in combination with an analysis algorithm. PM6 films are prepared by the so-called spontaneous film spreading (SFS) process, where a polymer solution is coated on a water surface. Automated acquisition of UV/Vis and photoluminescence (PL) spectra and automated extraction of morphological features is coupled to Gaussian Process Regression to exploit available experimental evidence for morphology optimization but also for hypothesis formulation and testing with respect to the underlying physical principles. The integrated spectral modeling workflow yields quantitative microstructure information by distinguishing amorphous from ordered phases and assesses the extension of amorphous versus the ordered domains. This research provides an easy to use methodology to analyze the exciton coherence length in conjugated semiconductors and will allow to optimize exciton splitting in thin film organic semiconductor layers as a function of processing.

Exciton Diffusion in Highly-Ordered One Dimensional Conjugated Polymers: Effects of Back-Bone Torsion, Electronic Symmetry, Phonons and Annihilation

Many optoelectronic devices based on organic materials require rapid and long-range singlet exciton transport. Key factors controlling exciton transport include material structure, exciton-phonon coupling and electronic state symmetry. Here, we employ femtosecond transient absorption microscopy to study the influence of these parameters on exciton transport in one-dimensional conjugated polymers. We find that excitons with 2¹A_g^- symmetry and a planar backbone exhibit a significantly higher diffusion coefficient (34 ± 10 cm² s^-1) compared to excitons with 1¹B_u⁺ symmetry (7 ± 6 cm² s^-1) with a twisted backbone. We also find that exciton transport in the 2¹A_g^- state occurs without exciton-exciton annihilation. Both 2¹A_g^- and 1¹B_u⁺ states are found to exhibit subdiffusive behavior. Ab initio GW-BSE calculations reveal that this is due to the comparable strengths of the exciton-phonon interaction and exciton coupling. Our results demonstrate the link between electronic state symmetry, backbone torsion and phonons in exciton transport in π-conjugated polymers.

Toward an understanding of electronic excitation energies beyond the molecular orbital picture

Can we gain an intuitive understanding of excitation energies beyond the molecular picture?

Density-based descriptors and exciton analyses for visualizing and understanding the electronic structure of excited states

Analysis and interpretation of the electronic structure of excited electronic states are prerequisites for developing a fundamental understanding of photochemistry and optical properties of molecular systems and an everyday task for a computational photochemist. Hence, wavefunction-based and density-based analysis tools have been devised over the last decades, and most recently also a family of quantitative exciton-wavefunction based descriptors has been developed. While the latter represent the main focus of this perspective, they are also discussed in the context of other existing analysis methods. Exciton analysis bridges the gap between the physically intuitive exciton picture and complex quantum-chemical wavefunctions by yielding insightful quantitative descriptors like exciton size, hole and electron size, electron-hole distance and exciton correlation. Thereby, not only a comprehensive characterization of the electronic structure is provided, but moreover, the formalism is automatizable and thus also optimally suited for benchmarking excited-state electronic structure methods.

Energetics of exciton binding and dissociation in polythiophenes: a tight binding approach

A tight-binding exciton model that describes the continuum from the bound exciton to the free hole and electron polarons in conjugated polymer chains is introduced and applied to polythiophenes.

Universal Exciton Size in Organic Polymers is Determined by Nonlocal Orbital Exchange in Time-Dependent Density Functional Theory

The exciton size of the lowest singlet excited state in a diverse set of organic π-conjugated polymers is studied and found to be a universal, system-independent quantity of approximately 7 Å in the single-chain picture. With time-dependent density functional theory (TDDFT), its value as well as the overall description of the exciton is almost exclusively governed by the amount of nonlocal orbital exchange. This is traced back to the lack of the Coulomb attraction between the electron and hole quasiparticles in pure TDDFT, which is reintroduced only with the admixture of nonlocal orbital exchange.

One-dimensional hydrogen atom

The theory of the one-dimensional (1D) hydrogen atom was initiated by a 1952 paper but, after more than 60 years, it remains a topic of debate and controversy. The aim here is a critique of the current status of the theory and its relation to relevant experiments. A 1959 solution of the Schrödinger equation by the use of a cut-off at x = a to remove the singularity at the origin in the 1/| x | form of the potential is clarified and a mistaken approximation is identified. The singular atom is not found in the real world but the theory with cut-off has been applied successfully to a range of four practical three-dimensional systems confined towards one dimension, particularly their observed large increases in ground state binding energy. The true 1D atom is in principle restored when the short distance a tends to zero but it is sometimes claimed that the solutions obtained by the limiting procedure differ from those obtained by solution of the basic Schrödinger equation without any cut-off in the potential. The treatment of the singularity by a limiting procedure for applications to practical systems is endorsed.

New tools for the systematic analysis and visualization of electronic excitations. I. Formalism

A variety of density matrix based methods for the analysis and visualization of electronic excitations are discussed and their implementation within the framework of the algebraic diagrammatic construction of the polarization propagator is reported. Their mathematical expressions are given and an extensive phenomenological discussion is provided to aid the interpretation of the results. Starting from several standard procedures, e.g., population analysis, natural orbital decomposition, and density plotting, we proceed to more advanced concepts of natural transition orbitals and attachment/detachment densities. In addition, special focus is laid on information coded in the transition density matrix and its phenomenological analysis in terms of an electron-hole picture. Taking advantage of both the orbital and real space representations of the density matrices, the physical information in these analysis methods is outlined, and similarities and differences between the approaches are highlighted. Moreover, new analysis tools for excited states are introduced including state averaged natural transition orbitals, which give a compact description of a number of states simultaneously, and natural difference orbitals (defined as the eigenvectors of the difference density matrix), which reveal details about orbital relaxation effects.

Exciton localization in disordered poly(3-hexylthiophene)

Singlet exciton localization in conformationally disordered poly(3-hexylthiophene) (P3HT) is investigated via configuration interaction (singles) calculations of the Pariser-Parr-Pople model. The P3HT structures are generated by molecular dynamics simulations. The lowest-lying excitons are spatially localized, space filling, and nonoverlapping. These define spectroscopic segments or chromophores. The strong conformational disorder in P3HT causes breaks in the pi-conjugation. Depending on the relative values of the disorder-induced localization length and the distances between the pi-conjugation breaks, these breaks sometimes serve to pin the low-lying localized excitons. The exciton confinement also causes a local spectrum of low-lying exciton states. Coulomb-induced intra- or interchain interactions between spectroscopic segments in close spatial proximity can delocalize an exciton across these segments, in principle causing phase coherent transition dipole moments.