An exact solution in the theory of fluorescence resonance energy transfer with vibrational relaxation

The elegant expression of Förster that predicts the well-known 1/R⁶ distance (R) dependence of the rate of energy transfer, although widely used, was derived using several approximations. Notable among them is the neglect of the vibrational relaxation in the reactant (donor) and product (acceptor) manifolds. Vibrational relaxation can play an important role when the energy transfer rate is faster than the vibrational relaxation rate. Under such conditions, donor to acceptor energy transfer can occur from the excited vibrational states. This phenomenon is not captured by the usual formulation based on the overlap of donor emission and acceptor absorption spectra. Here, we develop a Green's function-based generalized formalism and obtain an exact solution for the excited state population relaxation and the rate of energy transfer in the presence of vibrational relaxation. We find that the application of the well-known Förster's expression might lead to overestimation of R.

Excitation-Wavelength-Dependent Light-Induced Electron Transfer and Twisted Intramolecular Charge Transfer in N,N-Bis(4'-tert-butylbiphenyl-4-yl)aniline Functionalized Borondipyrromethenes

A series of bis(4'-tert-butylbiphenyl-4-yl)aniline (BBA) functionalized borondipyrromethene (BODIPY) dyads, Dyads 1-3, containing the BBA group tethered to BODIPY moiety either directly or through a phenyl or alkynyl phenyl spacers are synthesized, and the light-mediated charge transfer within the chromophores has been systematically investigated. The crystal structure of Dyad-1 showed a tilt of 44.2° between the BODIPY and BBA molecular planes and intermolecular C-H···π interactions with these moieties. Cyclic voltammetric and computational studies showed that the BBA moiety can act as the electron donor (D) and BODIPY as the electron acceptor (A) and the optical absorption studies revealed that an increase in the conjugation of the linker from Dyad-1 to Dyad-2 resulted in bathochromic shifts. Steady-state fluorescence studies involving photoexcitation of the BBA moiety at 326 nm resulted in the decrease in fluorescence intensity of the BBA, indicating the possibility of sequential occurrence of faster photoinduced energy transfer (PEnT) followed by the photoinduced electron transfer (PET) or solely PET within the dyads, and the driving forces of the charge separation were calculated to be exothermic in all of the employed solvents. Parallel time-resolved fluorescence experiments involving the excitation of BBA moiety also supported the occurrence of charge separation in these dyads. Interestingly, excitation of the BODIPY moiety of Dyad-1 and Dyad-2 at 490 nm in solvents of increasing polarity leads to a red-shifted BODIPY emission with weakened intensity. This spectral behavior indicated the occurrence of emission from the locally excited (LE) state in nonpolar solvents, whereas formation of an LE state followed by the rotation of the chromophores at the D-A bond leads to a low energy twisted intramolecular charge transfer state (TICT), resulting in a charge-separated state BBA^+•-BODIPY^-• in polar solvents. Furthermore, the hydrophobicity studies involving the solutions of dyads in admixtures of polar tetrahydrofuran (THF) and nonpolar hexanes revealed that when the fraction of hexanes in these mixtures is increased, the emission of BODIPY moiety was observed to be blue-shifted and exhibited enhanced intensity supporting the occurrence of TICT in these dyads.

Computational Investigation of Drug Phototoxicity: Photosafety Assessment, Photo-Toxophore Identification, and Machine Learning

One of the most appreciated capabilities of computational toxicology is to support the design of pharmaceuticals with reduced toxicological hazard. To this end, we have strengthened our drug photosafety assessments by applying novel computer models for the anticipation of in vitro phototoxicity and human photosensitization. These models are typically used in pharmaceutical discovery projects as part of the compound toxicity assessments and compound optimization methods. To ensure good data quality and aiming at models with global applicability we separately compiled and curated highly chemically diverse data sets from 3T3 NRU phototoxicity reports (450 compounds) and clinical photosensitization alerts (1419 compounds) which are provided as supplements. The latter data gives rise to a comprehensive list of explanatory fragments for visual guidance, termed phototoxophores, by application of a Bayesian statistics approach. To extend beyond the domain of well sampled fragments we applied machine learning techniques based on explanatory descriptors such as pharmacophoric fingerprints or, more important, accurate electronic energy descriptors. Electronic descriptors were extracted from quantum chemical computations at the density functional theory (DFT) level. Accurate UV/vis spectral absorption descriptors and pharmacophoric fingerprints turned out to be necessary for predictive computer models, which were both derived from Deep Neural Networks but also the simpler Random Decision Forests approach. Model accuracies of 83-85% could typically be reached for diverse test data sets and other company in-house data, while model sensitivity (the capability of correctly detecting toxicants) was even better, reaching 86%-90%. Importantly, a computer model-triggered response-map allowed for graphical/chemical interpretability also in the case of previously unknown phototoxophores. The photosafety models described here are currently applied in a prospective manner for the hazard identification, prioritization, and optimization of newly designed molecules.

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.

Hot and Cold Charge-Transfer Mechanisms in Organic Photovoltaics: Insights into the Excited States of Donor/Acceptor Interfaces

The evolution of the excited-state manifold in organic D/A aggregates (e.g., the prototypical P3HT/PCBM) is investigated through a bottom-up approach via first-principles calculations. We show how the excited-state energies, the charge transfer (CT) states, and the electron-hole density distributions are strongly influenced by the size, the orientation, and the position (i.e., on-top versus on-edge phases) of P3HT/PCBM domains. We discuss how the structural order influences the excited-state electronic structure, providing an atomistic interpretation of the photophysics of organic blends. We show how the simultaneous presence of on-top and on-edge phases does not alter the optical absorption spectrum of the blend but does affect the photophysics. Photovoltaic processes such as (i) the simultaneous charge generation obtained from hot and cold excitations, (ii) the instantaneous and delayed charge separation, and (iii) the pump-push-probe charge generation can be interpreted based on our study.

Molecular Packing Determines Charge Separation in a Liquid Crystalline Bisthiophene-Perylene Diimide Donor-Acceptor Material

Combined electronic structure and quantum dynamical calculations are employed to investigate charge separation in a novel class of covalently bound bisthiophene-perylene diimide type donor-acceptor (DA) co-oligomer aggregates. In an earlier spectroscopic study of this DA system in a smectic liquid crystalline (LC) film, efficient and ultrafast (subpicosecond) initial charge separation was found to be followed by rapid recombination. By comparison, the same DA system in solution exhibits ultrafast resonant energy transfer followed by slower (picosecond scale) charge separation. The present first-principles study explains these contrasting observations, highlighting the role of an efficient intermolecular charge-transfer pathway that results from the molecular packing in the LC phase. Despite the efficiency of this primary charge-transfer step, long-range charge separation is impeded by a comparatively high Coulomb barrier in conjunction with small electron- and hole-transfer integrals. Quantum dynamical calculations are carried out for a fragment-based model Hamiltonian, parametrized by ab initio second-order Algebraic Diagrammatic Construction (ADC(2)) and Time-Dependent Density Functional Theory (TDDFT) electronic structure calculations. Simulations of coherent vibronic quantum dynamics for up to 156 electronic states and 48 modes are performed using the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method. Excellent agreement with experimentally determined charge separation time scales is obtained, and the spatially coherent nature of the dynamics is analyzed.

Controlling charge separation and recombination by chemical design in donor–acceptor dyads

Conjugated donor–acceptor block co-oligomers that self-organize into D–A mesomorphic arrays have raised increasing interest due to their potential applications in organic solar cells.

Calculating X-ray Absorption Spectra of Open-Shell Molecules with the Unrestricted Algebraic-Diagrammatic Construction Scheme for the Polarization Propagator

X-ray absorption spectroscopy (XAS) is a powerful tool that provides information about the electronic structure of molecules via excitation of electrons from the K-shell core region to the unoccupied molecular levels. These high-lying electronic core-excited states can be accurately calculated using the algebraic-diagrammatic construction scheme of second order ADC(2) by applying the core-valence separation (CVS) approximation to the ADC(2) working equations. For the first time, an efficient implementation of an unrestricted CVS-ADC(2) variant CVS-UADC(2) is presented for the calculation of open-shell molecules by treating α and β spins separately from each other. The potential of the CVS-UADC(2) method is demonstrated with a set of small organic radicals by comparison with standard TD-DFT/B3LYP values and experimental data. It turns out that the extended variant CVS-UADC(2)-x, in particular, provides the most accurate results with errors of only 0.1% compared to experimental values. This remarkable agreement justifies the prediction of yet nonrecorded experimental XAS spectra like the one of the anthracene cation. The cation exhibits additional peaks due to the half-filled single-occupied molecular orbital, which may help to distinguish cation from the neutral species.

A simple model for exploring the role of quantum coherence and the environment in excitonic energy transfer

We investigate the role of quantum coherence in modulating the energy transfer rate between two independent energy donors and a single acceptor participating in an excitonic energy transfer process. The energy transfer rate depends explicitly on the nature of the initial coherent superposition state of the two donors and we connect it to the observed absorption profile of the acceptor and the stimulated emission profile of the energy donors. We consider simple models with mesoscopic environments interacting with the donors and the acceptor and compare the expression we obtained for the energy transfer rate with the results of numerical integration.

Distinguishing the Effects of Bond-Length Alternation versus Bond-Order Alternation on the Nonlinear Optical Properties of π-Conjugated Chromophores

Understanding the relationships between the molecular nonlinear optical (NLO) properties and the bond-length alternation (BLA) or π-bond-order alternation (BOA) along the molecular backbone of linear π-conjugated systems has proven widely useful in the development of NLO organic chromophores and materials. Here, we examine model polymethines to elucidate the reliability of these relationships. While BLA is solely a measure of molecular geometric structure, BOA includes information pertaining to the electronic structure. As a result, BLA is found to be a good predictor of NLO properties only when optimized geometries are considered, whereas BOA is more broadly applicable. Proper understanding of the distinction between BLA and BOA is critical when designing computational studies of NLO properties, especially for molecules in complex environments or in nonequilibrium geometries.