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

Ab initio investigation of excited state charge transfer pathways in differently capped bithiophene cages

The electronic excitations of conformationally constrained bithiophene cage systems as previously investigated by Lewis et al. (J. Am. Chem. Soc. 143, 18548 (2021)) are revisited, employing the correlated ab initio Scaled Opposite-Spin Algebraic Diagrammatic Construction Second Order electronic structure method. Quantitative descriptors are determined to assess the extent of charge transfer between the bithiophene moieties and the capping domains, represented by either phenyl or triazine groups. The investigation substantiates intrinsic differences in the photophysical behavior of these two structural variants and reveals the presence of lower-energy excited states characterized by noteworthy charge transfer contributions in the triazine cage system. The manifestation of this charge transfer character is discernible even at the Franck-Condon geometry, persisting throughout the relaxation of the excited state. By examining isolated monomer building blocks, we confirm the existence of analogous charge transfer contributions in their excitations. Employing this methodological approach facilitates the prospective identification of potential wall/cap chromophore pairs, wherein charge transfer pathways can be accessed within the energetically favorable regime.

Earth Mover's Charge Transfer Distance: A General and Robust Approach for Describing Excited State Locality

A novel approach for assessing the extent of electron displacement in optical transitions is proposed by implementing the Earth Mover's Distance (EMD) method, which quantifies the spatial dissimilarity between ground and excited state electron density distributions. In contrast to previous descriptors, this index provides a representative and intuitively understandable distance under a robust and computationally efficient scheme for all possible forms of locality, even in the most difficult to dissect topological cases. The theoretical differences among the existing indices and our method are first illustrated with the help of a simplified model system, followed by a benchmarking of several partial atomic charge models using experimentally relevant push-pull compounds with diverse symmetries. These same molecules are finally employed to further demonstrate the principal advantages of the EMD index and its capabilities in rationalizing charge transfer phenomena.

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.

Earth Mover's Distance as a Metric to Evaluate the Extent of Charge Transfer in Excitations Using Discretized Real-Space Densities

This paper presents a novel theoretical measure, μEMD, based on the earth mover's distance (EMD), for quantifying the density shift caused by electronic excitations in molecules. As input, the EMD metric uses only the discretized ground- and excited-state electron densities in real space, rendering it compatible with almost all electronic structure methods used to calculate excited states. The EMD metric is compared against other popular theoretical metrics for describing the extent of electron-hole separation in a wide range of excited states (valence, Rydberg, charge transfer, etc.). The results showcase the EMD metric's effectiveness across all excitation types and suggest that it is useful as an additional tool to characterize electronic excitations. The study also reveals that μEMD can function as a promising diagnostic tool for predicting the failure of pure exchange-correlation functionals. Specifically, we show statistical relationships among the functional-driven errors, the exact exchange content within the functional, and the magnitude of μEMD values.

The inverted singlet-triplet gap: a vanishing myth?

Molecules with an inverted singlet-triplet gap (STG) between the first excited singlet and triplet states, for example, heptazine, have recently been reported and gained substantial attention since they violate the famous Hund's rule. Utilizing state-of-the-art high-level ab initio methods, the singlet-triplet gap vanishes and approaches zero from below whatever is improved in the theoretical description of the molecules: the basis set or the level of electron correlation. Seemingly, the phenomenon of inverted singlet-triplet gaps tends to vanish the closer we observe.

Photovoltaic properties of novel reactive azobenzoquinolines: experimental and theoretical investigations

In this work, synthesis, characterization, DFT, TD-DFT study of some novel reactive azobenzoquinoline dye structures to elucidate their photovoltaic properties. The azobenzoquinoline compounds were experimentally synthesized through a series of reaction routes starting from acenaphthene to obtained aminododecylnaphthalimide and finally coupled with diazonium salts to get the desired azobenzoquinoline. Azo dye synthesized differ in the number of alkyl chains designated as (AR1, AR2, AR3, and AR4) which were experimentally analyzed using FT-IR and NMR spectroscopic methods. The synthesized structures were modelled for computational investigation using density functional theory (DFT) and time-dependent density functional theory (TD-DFT) combined with B3LYP and 6-31+G(d) basis set level of theory. The results showed that the HOMO-LUMO energy gap was steady at approximately 2.8 eV as the alkyl chain increases, which has been proven to be within the material energy gap limit for application in photovoltaic. The highest intramolecular natural bond orbital (NBO) for the studied compounds is 27.60, 55.06, 55.06, and 55.04 kcal/mol for AR1, AR2, AR3, and AR4 respectively and the donor and acceptor interacting orbitals for the highest stabilization energy (E (2)) are LP(1)N 18 and π*C 16−O 19 respectively. The photovoltaic properties in terms of light-harvesting efficiency (LHE), Short circuit current density (J SC), Gibbs free energy of injection (ΔG inj), open-circuit voltage (V OC) and Gibbs free energy of regeneration (ΔG reg) were evaluated to be within the required limit for DSSC design. Overall, the obtained theoretical photovoltaic results were compared with other experimental and computational findings, thus, are in excellent agreement for organic solar cell design.

Absorption behavior of doxorubicin hydrochloride in visible region in different environments: a combined experimental and computational study

The experimental absorption measurements in the interval 350-600 nm (Vis), molecular dynamics simulations, quantum-mechanics calculations and an advanced molecular treatment of simulation data are here combined to provide a complete picture of the absorption behavior in the visible portion of the electromagnetic spectrum of the doxorubicin hydrochloride (DX) molecule in different environments. By such an approach, we have shown that it is possible to characterize the effect of the environment on the DX absorption behavior - including the vibronic contributions - as well as to interpret such differences in terms of molecular electronic excited states, which are found to be strongly influenced by the environment.

Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

The performance of the most recent density functionals is assessed for charge-transfer (CT) excitations using comprehensive intra- and intermolecular CT benchmark sets with high-quality reference values. For this comparison, the state-of-the-art range-separated (RS) and long-range-corrected (LC) double hybrid (DH) approaches are selected, and global DH and LC hybrid functionals are also inspected. The correct long-range behavior of the exchange–correlation (XC) energy is extensively studied, and various CT descriptors are compared as well. Our results show that the most robust performance is attained by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types of CT excitations with outstanding accuracy. Furthermore, concerning the intramolecular transitions, unexpectedly excellent results are obtained for most of the global DHs, but their limitations are also demonstrated for bimolecular complexes. Despite the outstanding performance of the LC-DH methods for common intramolecular excitations, serious deficiencies are pointed out for intermolecular CT transitions, and the wrong long-range behavior of the XC energy is revealed. The application of LC hybrids to such transitions is not recommended in any respect.

Influence of N-introduction in pentacene on the electronic structure and excited electronic states

N-Heteropolycyclic aromatic compounds are promising organic semiconductors for applications in field effect transistors and solar cells. Thereby the electronic structure of organic/metal interfaces and thin films is essential for the performance of organic-molecule-based devices. Here, we studied the structural and the electronic properties of 6,7,12,13-tetraazapentacene (TAP) adsorbed on Au(111) using vibrational and electronic high-resolution electron energy loss spectroscopy in combination with state-of-the-art quantum chemical calculations. In the mono- and multilayer TAP adsorbs in a planar adsorption geometry with the molecular backbone oriented parallel to the gold substrate. The energies of the lowest excited electronic singlet states (S) as well as the triplet state (T) are assigned. The optical gap (S₀ → S₁ transition) is found to be 1.6 eV and the T₁ energy 1.2 eV. In addition, thorough comparison to previously studied pentacene (PEN) and 6,13-diazapentacene (6,13-DAP) is made explaining in detail the influence of nitrogen substitution on the electronic structure and in particular on the intensity of the α-band in the UV/vis absorption spectrum. In the series PEN, 6,13-DAP, and TAP, the α-band (S₀ → S₂ transition) gains significantly in intensity due to individual effects of the introduced nitrogen atoms on the orbital energies.

Absorption Spectra and the Electronic Structure of Gallic Acid in Water at Different pH: Experimental Data and Theoretical Cluster Models

Gallic acid (GA) has been characterized in terms of its optical properties in aqueous solutions at varying pH in experiments and in theoretical calculations by analyzing the protonated and deprotonated forms of GA. This work is part of a series of studies of the optical properties of different carboxylic acids in aqueous media. The experimental electronic spectra of GA exhibit two strong well-separated absorption peaks (B- and C-bands), which agree with previous studies. However, in the current study, an additional well-defined low-energy shoulder band (A-band) in the optical spectra of GA was identified. It is likely that the A-band occurs for other carboxylic acids in solution, but because it can overlap with the B-band, it is difficult to discern. The theoretical calculations based on density functional theory were used to simulate the optical absorption spectra of GA in water at different pH to prove the existence of this newly found shoulder band and to describe and characterize the full experimental optical spectra of GA. Different cluster models were tested: (i) all water molecules are coordinated near the carboxy-group and (ii) additional water molecules near the hydroxy-groups of the phenyl ring were included. In this study, we found that both the polarizable continuum model (dielectric property of a medium) and neighboring water molecules (hydrogen-bonding) play significant roles in the optical spectrum. The results showed that only an extended cluster model with water molecules near carboxy- and hydroxy-groups together with the polarizable continuum model allowed us to fully reproduce the experimental data and capture all three absorption bands (A, B, and C). The oscillator strengths of the absorption bands were obtained from the experimental data and compared with theoretical results. Additionally, our work provides a detailed interpretation of the pH effects observed in the experimental absorption spectra.

The role of excited-state character, structural relaxation, and symmetry breaking in enabling delayed fluorescence activity in push-pull chromophores

Thermally activated delayed fluorescence (TADF) is a current promising route for generating highly efficient light-emitting devices. However, the design process of new chromophores is hampered by the complicated underlying photophysics. In this work, four closely related donor-π-acceptor-π-donor systems are investigated, two of which were synthesised previously, with the aim of elucidating their varying effectiveness for TADF. We outline that the frontier orbitals are insufficient for discriminating between the molecules. Subsequently, a detailed analysis of the excited states at a correlated ab initio level highlights the presence of a number of closely spaced singlet and triplet states of varying character. Results from five density functionals are compared against this reference revealing dramatic changes in, both, excited state energies and wavefunctions following variations in the amount of Hartree-Fock exchange included. Excited-state minima are optimised in solution showing the crucial role of structural variations and symmetry breaking for producing a strongly emissive S₁ state. The adiabatic singlet-triplet gaps thus obtained depend strongly on the range separation parameter used in the hybrid density functional calculations. More generally, this work highlights intricate differences present between singlet and triplet excited state wavefunctions and the challenges in describing them accurately.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Learning the Exciton Properties of Azo-dyes

The ab initio determination of electronic excited state (ES) properties is the cornerstone of theoretical photochemistry. Yet, traditional ES methods become impractical when applied to fairly large molecules, or when used on thousands of systems. Machine learning (ML) techniques have demonstrated their accuracy at retrieving ES properties of large molecular databases at a reduced computational cost. For these applications, nonlinear algorithms tend to be specialized in targeting individual properties. Learning fundamental quantum objects potentially represents a more efficient, yet complex, alternative as a variety of molecular properties could be extracted through postprocessing. Herein, we report a general framework able to learn three fundamental objects: the hole and particle densities, as well as the transition density. We demonstrate the advantages of targeting those outputs and apply our predictions to obtain properties, including the state character and the exciton topological descriptors, for the two bands (nπ* and ππ*) of 3427 azoheteroarene photoswitches.

Deciphering excited state properties utilizing algebraic diagrammatic construction schemes of decreasing order

Excited state properties are difficult to trace back to the common molecular orbital picture when the excited state wavefunction is a linear combination of two or more Slater determinants. Here, a theoretical methodology is introduced based on the algebraic diagrammatic construction scheme for the polarization propagator (ADC(n)) that allows to make this connection and to eventually derive structure-function relationships. The usefulness of this approach is demonstrated by an analysis of the transition dipole moments of the low-lying 1B_3u and 2B_3u states of anthracene and (1,4,5,8)-tetraazaanthracene.

Embelin's Versatile Photochemistry Makes It a Potent Photosensitizer for Photodynamic Therapy

Embelin, a natural product isolated from Embelia ribes, is a promising small-molecular drug for photodynamic anticancer therapy. Using modern quantum chemical methodology, embelin is shown to possess a versatile photochemistry comprising the capability of singlet oxygen generation, excited-state proton transfer, and oxidation. In particular, the detailed molecular mechanisms of singlet oxygen generation and proton transfer upon excitation are studied in great detail. While excited-state proton transfer can damage the protein itself, it also mediates intersystem crossing along its reaction pathway, thus facilitating singlet oxygen generation. When embelin is bound to proteins, all these processes can lead to protein damage and the desired phototoxicity.

Improved Description of Charge-Transfer Potential Energy Surfaces via Spin-Component-Scaled CC2 and ADC(2) Methods

The molecular level understanding of electronic transport properties depends on the reliable theoretical description of charge-transfer (CT)-type electronic states. In this paper, the performance of spin-component-scaled variants of the popular CC2 and ADC(2) methods is evaluated for CT states, following benchmark strategies of earlier studies that revealed a compromised accuracy of the unmodified models. In addition to statistics on the accuracy of vertical excitation energies at equilibrium and infinite separation of bimolecular complexes, potential energy surfaces of the ammonia-fluorine complex are also reported. The results show the capability of spin-component-scaled approaches to reduce the large errors of their regular counterparts to a significant extent, outperforming even the coupled-cluster single and double method in many cases. The cost-effective scaled-opposite-spin variants are found to provide a remarkably good agreement with the CCSDT-3 reference data, thereby being recommended methods of choice in the study of charge-transfer states.

Influence of the crystal packing in singlet fission: one step beyond the gas phase approximation

Singlet fission (SF), a multiexciton generation process, has been proposed as an alternative to enhance the performance of solar cells. The gas phase dimer model has shown its utility to study this process, but it does not always cover all the physics and the effect of the surrounding atoms has to be included in such cases. In this contribution, we explore the influence of crystal packing on the electronic couplings, and on the so-called exciton descriptors and electron–hole correlation plots. We have studied three tetracene dimers extracted from the crystal structure, as well as several dimers and trimers of the α and β polymorphs of 1,3-diphenylisobenzofuran (DPBF). These polymorphs show different SF yields. Our results highlight that the character of the excited states of tetracene depends on both the mutual disposition of molecules and inclusion of the environment. The latter does however not change significantly the interpretation of the SF mechanism in the studied systems. For DPBF, we establish how the excited state analysis is able to pinpoint differences between the polymorphs. We observe strongly bound correlated excitons in the β polymorph which might hinder the formation of the ¹TT state and, consequently, explain its low SF yield.

Singlet fission (SF), a multiexciton generation process, has been proposed as an alternative to enhance the performance of solar cells.

A New Benchmark Set for Excitation Energy of Charge Transfer States: Systematic Investigation of Coupled Cluster Type Methods

The numerous existing publications on benchmarking quantum chemistry methods for excited states rarely include Charge Transfer (CT) states, although many interesting phenomena in, e.g., biochemistry and material physics involve the transfer of electrons between fragments of the system. Therefore, it is timely to test the accuracy of quantum chemical methods for CT states, as well. In this study we first propose a new benchmark set consisting of dimers having low-energy CT states. On this set, the vertical excitation energy has been calculated with Coupled Cluster methods including triple excitations (CC3, CCSDT-3, CCSD(T)(a)*), as well as with methods including full or approximate doubles (CCSD, STEOM-CCSD, CC2, ADC(2), EOM-CCSD(2)). The results show that the popular CC2 and ADC(2) methods are much less accurate for CT states than for valence states. On the other hand, EOM-CCSD seems to have similar systematic overestimation of the excitation energies for both types of states. Among the triples methods the novel EOM-CCSD(T)(a)* method including noniterative triple excitations is found to stand out with its consistently good performance for all types of states, delivering essentially EOM-CCSDT quality results.

TheoDORE: A toolbox for a detailed and automated analysis of electronic excited state computations

The advent of ever more powerful excited-state electronic structure methods has led to a tremendous increase in the predictive power of computation, but it has also rendered the analysis of these computations much more challenging and time-consuming. TheoDORE tackles this problem through providing tools for post-processing excited-state computations, which automate repetitive tasks and provide rigorous and reproducible descriptors. Interfaces are available for ten different quantum chemistry codes and a range of excited-state methods implemented therein. This article provides an overview of three popular functionalities within TheoDORE, a fragment-based analysis for assigning state character, the computation of exciton sizes for measuring charge transfer, and the natural transition orbitals used not only for visualization but also for quantifying multiconfigurational character. Using the examples of an organic push-pull chromophore and a transition metal complex, it is shown how these tools can be used for a rigorous and automated assignment of excited-state character. In the case of a conjugated polymer, we venture beyond the limits of the traditional molecular orbital picture to uncover spatial correlation effects using electron-hole correlation plots and conditional densities.

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?

Absorption spectra of benzoic acid in water at different pH and in the presence of salts: insights from the integration of experimental data and theoretical cluster models

The absorption spectra of molecular organic chromophores in aqueous media are of considerable importance in environmental chemistry. In this work, the UV-vis spectra of benzoic acid (BA), the simplest aromatic carboxylic acid, in aqueous solutions at varying pH and in the presence of salts are measured experimentally. The solutions of different pH provide insights into the contributions from both the non-dissociated acid molecule and the deprotonated anionic species. The microscopic interpretation of these spectra is then provided by quantum chemical calculations for small cluster models of benzoic species (benzoic acid and benzoate anion) with water molecules. Calculations of the UV-vis absorbance spectra are then carried out for different clusters such as C6H5COOH·(H2O)n and C6H5COO-·(H2O)n, where n = 0-8. The following main conclusions from these calculations and the comparison to experimental results can be made: (i) the small water cluster yields good quantitative agreement with observed solution experiments; (ii) the main peak position is found to be very similar at different levels of theory and is in excellent agreement with the experimental value, however, a weaker feature about 1 eV to lower energy (red shift) of the main peak is correctly reproduced only by using high level of theory, such as Algebraic Diagrammatic Construction (ADC); (iii) dissociation of the BA into ions is found to occur with a minimum of water molecules of n = 8; (iv) the deprotonation of BA has an influence on the computed spectrum and the energetics of the lowest energy electronic transitions; (v) the effect of the water on the spectra is much larger for the deprotonated species than for the non-dissociated acid. It was found that to reproduce experimental spectrum at pH 8.0, additional continuum representation for the extended solvent environment must be included in combination with explicit solvent molecules (n ≥ 3); (vi) salts (NaCl and CaCl2) have minimal effect on the absorption spectrum and; (vii) experimental results showed that B-band of neutral BA is not sensitive to the solvent effects whereas the effect of the water on the C-band is significant. The water effects blue-shift this band up to ∼0.2 eV. Overall, the results demonstrate the ability to further our understanding of the microscopic interpretation of the electronic structure and absorption spectra of BA in aqueous media through calculations restricted to small cluster models.

Investigating the character of excited states in TiO2 nanoparticles from topological descriptors: implications for photocatalysis

Excited state topological descriptors based on the attachment/detachment one-electron charge density are used to investigate the centroids of photoactive TiO₂ nanoclusters and nanoparticles.

Electron transfer in photoexcited pyrrole dimers

Following on from previous experimental and theoretical work [Neville et al., Nat. Commun. 7, 11357 (2016)], we report the results of a combined electronic structure theory and quantum dynamics study of the excited state dynamics of the pyrrole dimer following excitation to its first two excited states. Employing an exciton-based analysis of the Ã(π3s/σ^*) and B̃(π3s/3p/σ^*) states, we identify an excited-state electron transfer pathway involving the coupling of the Ã(π3s/σ^*) and B̃(π3s/3p/σ^*) states and driven by N-H dissociation in the B̃(π3s/3p/σ^*) state. This electron transfer mechanism is found to be mediated by vibronic coupling of the B̃ state, which has a mixed π3s/3p Rydberg character at the Franck-Condon point, to a high-lying charge transfer state of the πσ^* character by the N-H stretch coordinate. Motivated by these results, quantum dynamics simulations of the excited-state dynamics of the pyrrole dimer are performed using the multiconfigurational time-dependent Hartree method and a newly developed model Hamiltonian. It is predicted that the newly identified electron transfer pathway will be open following excitation to both the Ã(π3s/σ^*) and B̃(π3s/3p/σ^*) states and may be the dominant relaxation pathway in the latter case.

Electron-Hole Correlation as Unambiguous and Universal Classification for the Nature of Low-Lying ππ* States of Nitrogen Heterocycles

The ¹L_a and ¹L_b classification of electronically excited states of cata-condensed hydrocarbons proposed by Platt in 1949 ( Platt , J. R. J. Chem. Phys. 1949 , 17 , 484 ) is challenged by investigating a series of N-heteronaphthalenes and comparison of their low-lying ππ* excited states to those of naphthalene. The breakdown of Platt's classification scheme for N-heterocycles is highlighted, and a reliable and versatile alternative using exciton analyses is presented. The strength of electron-hole correlation turns out to be the most reliable distinguishing feature, and thus, an alternative nomenclature of ¹L_w (weakly correlated) and ¹L_s (strongly correlated) is proposed. Furthermore, fundamental guidelines for their property modulation through N-atom substitution patterns are discussed.

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.

Dynamics of benzene excimer formation from the parallel-displaced dimer

Excimers play a key role in a variety of excited-state processes, such as exciton trapping, fluorescence quenching, and singlet-fission. The dynamics of benzene excimer formation in the first 2 ps after S₁ excitation from the parallel-displaced geometry of the benzene dimer is reported here. It was simulated via nonadiabatic surface-hopping dynamics using the second-order algebraic diagrammatic construction (ADC(2)). After excitation, the benzene rings take ∼0.5-1.0 ps to approach each other in a parallel-stacked structure of the S₁ minimum and stay in the excimer region for ∼0.1-0.4 ps before leaving due to excess vibrational energy. The S₁-S₂ gap widens considerably while the rings visit the excimer region in the potential energy surface. Our work provides detailed insight into correlations between nuclear and electronic structure in the excimer and shows that decreased ring distance goes along with enhanced charge transfer and that fast exciton transfer happens between the rings, leading to the equal probability of finding the exciton in each ring after around 1.0 ps.

Dipole-Induced Transition Orbitals: A Novel Tool for Investigating Optical Transitions in Extended Systems

Optical absorption spectra for nanostructures and solids can be obtained from the macroscopic dielectric function within the random phase approximation. While experimental spectra can be reproduced with good accuracy, important properties, such as the charge-transfer character associated with a particular transition, are not retrievable. This contribution presents a computationally inexpensive method for the analysis of optical and excitonic properties for extended systems based on solely their electronic ground-state structure. We formulate a perturbative orbital transformation theory based on dipole-induced transition moments between orbitals, which yields correlated pairs of particle and hole functions. To demonstrate the potency of this new transformation formalism, we investigate the nature of excitations in inorganic molecular complexes and in extended systems. With our method, it is possible to extract mechanistic insights from the transitions observed in the optical spectrum, without requiring explicit calculation of the many-electron excited states.

Discrete and continuum modeling of solvent effects in a twisted intramolecular charge transfer system: The 4-N,N-dimethylaminobenzonitrile (DMABN) molecule

The 4-N,N-dimethylaminobenzonitrile (DMABN) molecule is a prototypical system displaying twisted intramolecular (TICT) charge transfer effects. The ground and the first four electronic excited states (S₁-S₄) in gas phase and upon solvation were studied. Charge transfer values as function of the torsion angle between the donor group (dimethylamine) and the acceptor moiety (benzonitrile) were explicitly computed. Potential energy curves were also obtained. The algebraic diagrammatic construction method at the second-order [ADC(2)] ab initio wave function was employed. Three solvents of increased polarities (benzene, DMSO and water) were investigated using discrete (average solvent electrostatic configuration - ASEC) and continuum (conductor-like screening model - COSMO) models. The results for the S₃ and S₄ excited states and the S₁-S₄ charge transfer curves were not previously available in the literature. Electronic gas phase and solvent vertical spectra are in good agreement with previous theoretical and experimental results. In the twisted (90°) geometry the optical oscillator strengths have negligible values even for the S₂ bright state. Potential energy curves show two distinct pairs of curves intersecting at decreasing angles or not crossing in the more polar solvents. Charge transfer and electric dipole values allowed the rationalization of these results. The former effects are mostly independent of the solvent model and polarity. Although COSMO and ASEC solvent models mostly lead to similar results, there is an important difference: some crossings of the excitation energy curves appear only in the ASEC solvation model, which has important implications to the photochemistry of DMABN.

Real and Imaginary Excitons: Making Sense of Resonance Wave Functions by Using Reduced State and Transition Density Matrices

Within non-Hermitian quantum mechanics, metastable electronic states can be represented by isolated L²-integrable complex-valued wave functions with complex energies. An analysis scheme of the real and imaginary parts of resonance wave functions by using reduced transition density matrices and natural transition orbitals is presented. While the real parts of excitons describe changes in the electron density corresponding to the bound part of the resonance, the imaginary excitons can be interpreted as virtual states facilitating one-electron decay into the continuum. The different nature of real and imaginary excitons is revealed by exciton descriptors, in particular hole-particle separation and their correlation. Singular values and respective participation ratios quantify the extent of collectivity of the excitation and a number of distinct decay channels. The utility of the new tool is illustrated by the analysis of bound and metastable excited states of cyanopolyyne anions.

Modeling TADF in organic emitters requires a careful consideration of the environment and going beyond the Franck-Condon approximation

The origin of the thermally-activated delayed fluorescence (TADF) of three organic emitters is investigated, focusing on the nature of the lowest excited states, their transition properties, as well as the role of the environment. For this purpose, the algebraic-diagrammatic construction for the polarization propagator at second order of perturbation theory [ADC(2)], time-dependent density-functional theory in the Tamm-Dancoff approximation (TDA) and unrestricted Kohn-Sham DFT in combination with the maximum-overlap method (ΔDFT) are employed. The influence of the dielectric environment is rigorously included using different variants of the polarizable continuum model. The calculations reveal the lowest excited singlet and triplet states of all studied emitters to be dominated by charge-transfer (CT) character already in the most apolar environment corresponding to cyclo-hexane. The dielectric stabilization entails a drastic reduction of the singlet-triplet gaps, increasing the calculated TADF rates by several orders of magnitude. Another ingredient for accurate TADF rates is hidden in the excited-state potential-energy surfaces along the donor-acceptor twisting angle. A presence of large, shallow plateaus in apolar environments causes the transition properties to be governed by thermal fluctuations rather than the minimum-energy geometries. This leads to a large increase of the oscillator strengths, as well as a breakdown of the Franck-Condon approximation. The last ingredient is a small but significant spin-orbit coupling (SOC) between the singlet and triplet CT states, which is traced back to a delocalization of the excitation hole or excited electron of the triplet CT state. Taking into account all of these effects, a reasonable agreement with experimental TADF and fluorescence lifetimes is obtained. For this, it proves to be sufficient to consider only the lowest lying singlet and triplet excited states.

Theoretical Modeling of Singlet Fission

Singlet fission is a photophysical reaction in which a singlet excited electronic state splits into two spin-triplet states. Singlet fission was discovered more than 50 years ago, but the interest in this process has gained a lot of momentum in the past decade due to its potential as a way to boost solar cell efficiencies. This review presents and discusses the most recent advances with respect to the theoretical and computational studies on the singlet fission phenomenon. The work revisits important aspects regarding electronic states involved in the process, the evaluation of fission rates and interstate couplings, the study of the excited state dynamics in singlet fission, and the advances in the design and characterization of singlet fission compounds and materials such as molecular dimers, polymers, or extended structures. Finally, the review tries to pinpoint some aspects that need further improvement and proposes future lines of research for theoretical and computational chemists and physicists in order to further push the understanding and applicability of singlet fission.