On the theoretical prediction of fluorescence rates from first principles using the path integral approach

Theoretical insights into dopamine photochemistry adsorbed on graphene-type nanostructures

The equilibrium geometry structures and light absorption properties of the dopamine (DA) and dopamine-o-quinone (DAQ) adsorbed on the graphene surface have been investigated using the ground state and linear-response time-dependent density functional theories. Two types of graphene systems were considered, a rectangular form of hexagonal lattice with optimized C-C bond length as the model system for graphene nanoparticles (GrNP) and a similar system but with fixed C-C bond length (1.42 Å) as the model system for graphene 2D sheet (GrS). The analysis of the vertical excitations showed that three types of electronic transitions are possible, namely, localized on graphene, localized on the DA or DAQ, and charge transfer (CT). In the case of the graphene-DA complex, the charge transfer excitations were characterized by the molecule-to-surface (MSCT) character, whereas the graphene-DAQ was characterized by the reverse, i.e. surface-to-molecule (SMCT). The difference between the two cases is given by the presence of an energetically low-lying unoccupied orbital (LUMO+1) that allows charge transfer from the surface to the molecule in the case of DAQ. However, it was also shown that the fingerprints of excited electronic states associated with the adsorbed molecules cannot be seen in the spectrum, as they are mostly suppressed by the characteristic spectral shape of graphene.

Environmentally Driven Symmetry Breaking Quenches Dual Fluorescence in Proflavine

Nonadiabatic couplings between several electronic excited states are ubiquitous in many organic chromophores and can significantly influence optical properties. A recent experimental study demonstrated that the proflavine molecule exhibits surprising dual fluorescence in the gas phase, which is suppressed in polar solvent environments. Here, we uncover the origin of this phenomenon by parametrizing a linear-vibronic coupling Hamiltonian from spectral densities of system-bath coupling constructed along molecular dynamics trajectories, fully accounting for interactions with the condensed-phase environment. The finite-temperature absorption, steady-state emission, and time-resolved emission spectra are then computed using powerful, numerically exact tensor network approaches. We find that the dual fluorescence in vacuum is driven by a single well-defined coupling mode but is quenched in solution due to dynamic solvent-driven symmetry breaking that mixes the two low-lying electronic states. We expect the computational framework developed here to be widely applicable to the study of non-Condon effects in complex condensed-phase environments.

Shedding light on thermally-activated delayed fluorescence

Thermally activated delayed fluorescence (TADF) is a hot research topic in view of its impressive applications in a wide variety of fields from organic LEDs to photodynamic therapy and metal-free photocatalysis. TADF is a rare and fragile phenomenon that requires a delicate equilibrium between tiny singlet-triplet gaps, sizable spin-orbit couplings, conformational flexibility and a balanced contribution of charge transfer and local excited states. To make the picture more complex, this precarious equilibrium is non-trivially affected by the interaction of the TADF dye with its local environment. The concurrent optimization of the dye and of the embedding medium is therefore of paramount importance to boost practical applications of TADF. Towards this aim, refined theoretical and computational approaches must be cleverly exploited, paying attention to the reliability of adopted approximations. In this perspective, we will address some of the most important issues in the field. Specifically, we will critically review theoretical and computational approaches to TADF rates, highlighting the limits of widespread approaches. Environmental effects on the TADF photophysics are discussed in detail, focusing on the major role played by dielectric and conformational disorder in liquid solutions and amorphous matrices.

Central Ring Puckering Enhances the Stokes Shift of Xanthene Dyes

Small-molecule dyes are generally designed based on well-understood electronic effects. However, steric hindrance can promote excited-state geometric relaxation, increasing the difference between the positions of absorption and emission bands (the Stokes shift). Accordingly, we hypothesized that sterically induced central ring puckering in xanthene dyes could be used to systematically increase their Stokes shift. Through a combined experimental/quantum-chemical approach, we screened a group of (9-acylimino)-pyronin dyes with a perturbed central ring geometry. Our results showed that an atom with sp3 hybridization in position 10 of (9-acylimino)-pyronins induces central ring puckering and facilitates excited-state geometric relaxation, thereby markedly enhancing their Stokes shifts (by up to ~2000 cm-1). Thus, we prepared fluorescent (9-acylimino)-pyronin pH sensors, which showed a Stokes shift disparity between acid and base forms of up to ~8700 cm-1. Moreover, the concept of ring puckering-enhanced Stokes shift can be applied to a wide range of xanthene analogues found in the literature. Therefore, central ring puckering may be reliably used as a strategy for enhancing Stokes shifts in the rational design of dyes.

Suppression of Dexter transfer by covalent encapsulation for efficient matrix-free narrowband deep blue hyperfluorescent OLEDs

Hyperfluorescence shows great promise for the next generation of commercially feasible blue organic light-emitting diodes, for which eliminating the Dexter transfer to terminal emitter triplet states is key to efficiency and stability. Current devices rely on high-gap matrices to prevent Dexter transfer, which unfortunately leads to overly complex devices from a fabrication standpoint. Here we introduce a molecular design where ultranarrowband blue emitters are covalently encapsulated by insulating alkylene straps. Organic light-emitting diodes with simple emissive layers consisting of pristine thermally activated delayed fluorescence hosts doped with encapsulated terminal emitters exhibit negligible external quantum efficiency drops compared with non-doped devices, enabling a maximum external quantum efficiency of 21.5%. To explain the high efficiency in the absence of high-gap matrices, we turn to transient absorption spectroscopy. It is directly observed that Dexter transfer from a pristine thermally activated delayed fluorescence sensitizer host can be substantially reduced by an encapsulated terminal emitter, opening the door to highly efficient 'matrix-free' blue hyperfluorescence.

Theoretical Evaluation of Fluorinated Resazurin Derivatives for In Vivo Applications

Primarily owing to the pronounced fluorescence exhibited by its reduced form, resazurin (also known as alamarBlue®) is widely employed as a redox sensor to assess cell viability in in vitrostudies. In an effort to broaden its applicability for in vivo studies, molecular adjustments are necessary to align optical properties with the near-infrared imaging window while preserving redox properties. This study delves into the theoretical characterisation of a set of fluorinated resazurin derivatives proposed by Kachur et al., 2015 examining the influence of fluorination on structural and electrochemical properties. Assuming that the conductor-like polarisable continuum model mimics the solvent effect, the density functional level of theory combining M06-2X/6-311G* was used to calculate the redox potentials. Furthermore, (TD-)DFT calculations were performed with PBE0/def2-TZVP to evaluate nucleophilic characteristics, transition states for fluorination, relative energies, and fluorescence spectra. With the aim of exploring the potential of resazurin fluorinated derivatives as redox sensors tailored for in vivo applications, acid-base properties and partition coefficients were calculated. The theoretical characterisation has demonstrated its potential for designing novel molecules based on fundamental principles.

Benzazole-Based ESIPT Fluorophores: Proton Transfer from the Chalcogen Perspective. A Combined Theoretical and Experimental Study

In this study, we present a comprehensive photophysical investigation of ESIPT-reactive benzazole derivatives in both solution and the solid state. These derivatives incorporate different chalcogen atoms (O, S, and Se) into their structures, and we explore how these variations impact their electronic properties in both ground and excited states. Changes in the UV-Vis absorption and fluorescence emission spectra were analyzed and correlated with the chalcogen atom and solvent polarity. In general, the spectral band of the benzazole derivative containing selenium was redshifted in both the ground and excited states compared to that of its oxygen and sulfur counterparts. Furthermore, we observed that the solvent played a distinctive role in influencing the ESIPT process within these compounds, underscoring once again the significant influence of the chalcogen atom on their photophysical behavior. Theoretical calculations provided a deeper understanding of the molecular dynamics, electronic structures, and photophysical properties of these compounds. These calculations highlighted the effect of chalcogen atoms on the molecular geometry, absorption and emission characteristics, and intramolecular hydrogen bonding, revealing intricate details of the ESIPT mechanism. The integration of experimental and computational data offers a detailed view of the structural and electronic factors governing the photophysical behavior of benzazole derivatives.

Taming the third order cumulant approximation to linear optical spectroscopy

The second order cumulant method offers a promising pathway to predicting optical properties in condensed phase systems. It allows for the computation of linear absorption spectra from excitation energy fluctuations sampled along molecular dynamics (MD) trajectories, fully accounting for vibronic effects, direct solute-solvent interactions, and environmental polarization effects. However, the second order cumulant approximation only guarantees accurate line shapes for energy gap fluctuations obeying Gaussian statistics. A third order correction has recently been derived but often yields unphysical spectra or divergent line shapes for moderately non-Gaussian fluctuations due to the neglect of higher order terms in the cumulant expansion. In this work, we develop a corrected cumulant approach, where the collective effect of neglected higher order contributions is approximately accounted for through a dampening factor applied to the third order cumulant term. We show that this dampening factor can be expressed as a function of the skewness and kurtosis of energy gap fluctuations and can be parameterized from a large set of randomly sampled model Hamiltonians for which exact spectral line shapes are known. This approach is shown to systematically remove unphysical contributions in the form of negative absorbances from cumulant spectra in both model Hamiltonians and condensed phase systems sampled from MD and dramatically improves over the second order cumulant method in describing systems exhibiting Duschinsky mode mixing effects. We successfully apply the approach to the coumarin-153 dye in toluene, obtaining excellent agreement with experiment.

A theoretical spectroscopy study of the photoluminescence properties of narrow band Eu2+-doped phosphors containing multiple candidate doping centers. Prediction of an unprecedented narrow band red phosphor

We have previously presented a computational protocol that is based on an embedded cluster model and operates in the framework of TD-DFT in conjunction with the excited state dynamics (ESD) approach. The protocol is able to predict the experimental absorption and emission spectral shapes of Eu2+-doped phosphors. In this work, the applicability domain of the above protocol is expanded to Eu2+-doped phosphors bearing multiple candidate Eu doping centers. It will be demonstrated that this protocol provides full control of the parameter space that describes the emission process. The stability of Eu doping at various centers is explored through local energy decomposition (LED) analysis of DLPNO-CCSD(T) energies. This enables further development of the understanding of the electronic structure of the targeted phosphors, the diverse interactions between Eu and the local environment, and their impact on Eu doping probability, and control of the emission properties. Hence, it can be employed to systematically improve deficiencies of existing phosphor materials, defined by the presence of various intensity emission bands at undesired frequencies, towards classes of candidate Eu2+-doped phosphors with desired narrow band red emission. For this purpose, the chosen study set consists of three UCr4C4-based narrow-band phosphors, namely the known alkali lithosilicates RbNa[Li3SiO4]2:Eu2+ (RNLSO2), RbNa3[Li3SiO4]4:Eu2+ (RNLSO) and their isotypic nitridolithoaluminate phosphors consisting of CaBa[LiAl3N4]2:Eu2+ (CBLA2) and the proposed Ca3Ba[LiAl3N4]4:Eu2+ (CBLA), respectively. The theoretical analysis presented in this work led us to propose a modification of the CBLA2 phosphor that should have improved and unprecedented narrow band red emission properties. Finally, we believe that the analysis presented here is important for the future rational design of novel Eu2+-doped phosphor materials, with a wide range of applications in science and technology.

Beyond the Condon limit: Condensed phase optical spectra from atomistic simulations

While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed phase spectroscopy remains a fundamental challenge. We derive a Gaussian theory to predict and analyze condensed phase optical spectra beyond the Condon limit. Our theory introduces novel quantities that encode how nuclear motions modulate the energy gap and transition dipole of electronic transitions in the form of spectral densities. By formulating the theory through a statistical framework of thermal averages and fluctuations, we circumvent the limitations of widely used microscopically harmonic theories, allowing us to tackle systems with generally anharmonic atomistic interactions and non-Condon fluctuations of arbitrary strength. We show how to calculate these spectral densities using first-principles simulations, capturing realistic molecular interactions and incorporating finite-temperature, disorder, and dynamical effects. Our theory accurately predicts the spectra of systems known to exhibit strong non-Condon effects (phenolate in various solvents) and reveals distinct mechanisms for electronic peak splitting: timescale separation of modes that tune non-Condon effects and spectral interference from correlated energy gap and transition dipole fluctuations. We further introduce analysis tools to identify how intramolecular vibrations, solute-solvent interactions, and environmental polarization effects impact dark transitions. Moreover, we prove an upper bound on the strength of cross correlated energy gap and transition dipole fluctuations, thereby elucidating a simple condition that a system must follow for our theory to accurately predict its spectrum.

Modeling the Fluorescence Quantum Yields of Aromatic Compounds: Benchmarking the Machinery to Compute Intersystem Crossing Rates

The from-first-principles calculation of fluorescence quantum yields (FQYs) and lifetimes of organic dyes remains very challenging. In this article, we extensively test the machinery to calculate FQYs. Specifically, we perform an extensive analysis on the parameters influencing the intersystem crossing (ISC), internal conversion (IC), and fluorescence rate constants calculations. The impact of (i) the electronic structure (chosen exchange-correlation functional and spin-orbit Hamiltonian), (ii) the vibronic parameters (coordinate system, broadening function, and dipole expansion), and (iii) the excited-state kinetic models are systematically assessed for a series of seven rigid aromatic molecules. Our studies provide more insights into the choice of parameters and the expected accuracy for the computational protocols aiming to deliver FQY values. Some challenges are highlighted, such as, on the one hand, the difficulty to benchmark against the experimental nonradiative rate constants, for which the separation between the IC and ISC contributions is often not provided in the literature and, on the other hand, the need to go beyond the harmonic approximation for the calculation of the IC rates.

How is the Observation of High-Order Overtones and Combinations Elucidated by the Charge-Transfer Mechanism in SERS?

The charge-transfer chemical mechanism is responsible for altering the molecular spectral pattern and providing valuable insights into the properties of adsorbates. The impact of charge transfer becomes more pronounced in SERS spectra when CT states can gain intensity through vibronic coupling with high-intensity excitations. Experimental SERS spectra of diamino molecules, such as 4,4'-diaminostilbene (DAS) and 4,4'-diaminotolane (DAT), featuring bright CT transitions, have been compared to dipyridyl compounds, such as 1,2-bis(4-pyridyl) ethylene (BPE) and 1,2-di(4-pyridyl) acetylene (DPA), characterized by nearly dark CT excitations. This comparison aims to elucidate the effect of CT transitions on the presence of overtones and combination bands. We explain this distinction using Albrecht's formalism for resonance Raman spectroscopy within the framework of path integral time-dependent density functional theory considering the Herzberg-Teller corrections. It is worth noting that the energy gap between the highest occupied metallic orbital and the lowest unoccupied molecular orbital in diamino derivatives is noticeably smaller than in compounds featuring two pyridyl rings. The high-intensity SERS-CT spectra for diamino derivatives, primarily driven by the Albrecht A term, were acquired and used to elucidate the experimental observation of high-order modes with a significant Huang-Rhys factor. Conversely, the absolute intensity of SERS-CT for dipyridyl compounds is at least 106 times smaller than that for diamines, and the C term makes a significant contribution, explaining the silent overtones.

First-Principles Calculations of Excited-State Decay Rate Constants in Organic Fluorophores

In this Perspective, we discuss recent advances made to evaluate from first-principles the excited-state decay rate constants of organic fluorophores, focusing on the so-called static strategy. In this strategy, one essentially takes advantage of Fermi's golden rule (FGR) to evaluate rate constants at key points of the potential energy surfaces, a procedure that can be refined in a variety of ways. In this way, the radiative rate constant can be straightforwardly obtained by integrating the fluorescence line shape, itself determined from vibronic calculations. Likewise, FGR allows for a consistent calculation of the internal conversion (related to the non-adiabatic couplings) in the weak-coupling regime and intersystem crossing rates, therefore giving access to estimates of the emission yields when no complex photophysical phenomenon is at play. Beyond outlining the underlying theories, we summarize here the results of benchmarks performed for various types of rates, highlighting that both the quality of the vibronic calculations and the accuracy of the relative energies are crucial to reaching semiquantitative estimates. Finally, we illustrate the successes and challenges in determining the fluorescence quantum yields using a series of organic fluorophores.

Resonance Raman spectra and excited state properties of methyl viologen and its radical cation from time-dependent density functional theory

Time-dependent density functional theory (TDDFT) was applied to gain insights into the electronic and vibrational spectroscopic properties of an important electron transport mediator, methyl viologen (MV2+ ). An organic dication, MV2+ has numerous applications in electrochemistry that include energy conversion and storage, environmental remediation, and chemical sensing and electrosynthesis. MV2+ is easily reduced by a single electron transfer to form a radical cation species (MV•+ ), which has an intense UV-visible absorption near 600 nm. The redox properties of the MV2+ /MV•+ couple and light-sensitivity of MV•+ have made the system appealing for photo-electrochemical energy conversion (e.g., solar hydrogen generation from water) and the study of photo-induced charge transfer processes through electronic absorption and resonance Raman spectroscopic measurements. The reported work applies leading TDDFT approaches to investigate the electronic and vibrational spectroscopic properties of MV2+ and MV•+ . Using a conventional hybrid exchange functional (B3-LYP) and a long-range corrected hybrid exchange functional (ωB97X-D3), including with a conductor-like polarizable continuum model to account for solvation, the electronic absorption and resonance Raman spectra predicted are in good agreement with experiment. Also analyzed are the charge transfer character and natural transition orbitals derived from the TDDFT vertical excitations calculated. The findings and models developed further the understanding of the electronic properties of viologens and related organic redox mediators important in renewable energy applications and serve as a reference for guiding the interpretation of electronic absorption and Raman spectra of the ions.

New Hybrid Compound Candidate as Photothermal Agent Based on DPP Derivatives and Toluidine Blue: A Theoretical Perspective

In this article, the synthesis of a new hybrid compound, candidate as photothermal agent, is proposed, based on TDPP (3,6-di(thiophene-2-yl)-2,5-dihydropyrrolo[3,4-c]pyrrole-1,4-dione) and toluidine blue. Electronic structure calculations at the DFT, TD-DFT and CCSD level of theories were performed to obtain ground and excited states molecular structures, photophysical properties and absorption spectrum of the hybrid and the starting compounds. Additionally, ADMET calculations were performed to predict the pharmacokinetic, metabolic and toxicity properties of the proposed compound. The results showed that the proposed compound is a strong candidate for photothermal agent since (1) it absorbs close to the near-infrared region, (2) it has low fluorescence and intersystem crossing rate constants, (3) it has accessible conical intersection with low energy barrier, (4) the compound shows lower toxicity than the well know compound toluidine blue, which is used in photodynamic therapy, (5) the compound does not show carcinogenic potential, and (6) it obeys the Lipinski's rule of five, used as a reference for the design of new pharmaceuticals.

Polarizing agents beyond pentacene for efficient triplet dynamic nuclear polarization in glass matrices

Triplet dynamic nuclear polarization (triplet-DNP) is a technique that can obtain high nuclear polarization under moderate conditions. However, in order to obtain practically useful polarization, large single crystals doped with a polarizing agent must be strictly oriented with respect to the magnetic field to sharpen the electron spin resonance (ESR) spectra, which is a fatal problem that prevents its application to truly useful biomolecular targets. Instead of this conventional physical approach of controlling crystal orientation, here, we propose a chemical approach, i.e., molecular design of polarizing agents; pentacene molecules, the most typical triplet-DNP polarizing agent, are modified so as to make the triplet electron distribution wider and more isotropic without loss of the triplet polarization. The thiophene-modified pentacene exhibits a sharper and stronger ESR spectrum than the parent pentacene, and state-of-the-art quantum chemical calculations revealed that the direction of the spin polarization is altered by the modification with thiophene moieties and the size of D and E parameters are reduced from parent pentacene due to the partial delocalization of spin densities on the thiophene moieties. The triplet-DNP with the new polarizing agent successfully exceeds the previous highest 1H polarization of glassy materials by a factor of 5. This demonstrates the feasibility of a polarizing agent that can surpass pentacene, the best polarizing agent for more than 30 y since triplet-DNP was first reported, in the unoriented state. This work provides a pathway toward practically useful high nuclear polarization of various biomolecules by triplet-DNP.

Extensive Analysis of the Parameters Influencing Radiative Rates Obtained through Vibronic Calculations

Defining a theoretical model systematically delivering accurate ab initio predictions of the fluorescence quantum yields of organic dyes is highly desirable for designing improved fluorophores in a systematic rather than trial-and-error way. To this end, the first required step is to obtain reliable radiative rates (kr), as low kr typically precludes effective emission. In the present contribution, using a series of 10 substituted phenyls with known experimental kr, we analyze the impact of the computational protocol on the kr determined through the thermal vibration correlation function (TVCF) approach on the basis of time-dependent density functional theory (TD-DFT) calculations of the energies, structures, and vibrational parameters. Both the electronic structure (selected exchange-correlation functional, application or not of the Tamm-Dancoff approximation) and the vibronic parameters (line-shape formalism, coordinate system, potential energy surface model, and dipole expansion) are tackled. Considering all possible combinations yields more than 3500 cases, allowing to extract statistically-relevant information regarding the impact of each computational parameter on the magnitude of the estimated kr. It turns out that the selected vibronic model can have a significant impact on the computed kr, especially the potential energy surface model. This effect is of the same order of magnitude as the difference noted between B3LYP and CAM-B3LYP estimates. For the treated compounds, all evaluated functionals do deliver reasonable trends, fitting the experimental values.

Rhenium(I) Complexes with Sulfur-Bridged Dipyridyl Ligands: Structural, Photophysical, and Computational Studies

A series of six new rhenium(I) tricarbonyl complexes [Re(CO)3(N-N)Br] bearing sulfur-bridged dipyridyl (N-N) ligands with three different oxidation states (sulfide (S), sulfoxide (SO), and sulfone (SO2)) are described. Spectroscopic studies show that changing the oxidation state of the ligands influences the photophysical properties of the complexes, with complexes 3 and 6 containing the sulfone ligand exhibiting a lower energy MLCT absorption band tailing into the visible region. Solution-state emission measurements show that these complexes exhibit readily tunable emission energies from 480 to 610 nm, depending on the oxidation state of the sulfur bridge and the presence of substituents on the pyridyl rings. Solid-state emission measurements show that the emission is significantly red-shifted upon oxidation of the sulfur bridge to sulfone with enhanced photoluminescence quantum yield.

Bismuth Infrared Star: Being at a Glance

Bismuth polycations have garnered significant attention from researchers due to their extraordinary and counter-intuitive structures and stoichiometries. Despite extensive experimental and theoretical investigations, understanding of the bonding in such clusters remains insufficient. An AdNDP bonding analysis was conducted to elucidate the bonding characteristics using both homoatomic and heteroatomic bismuth clusters with various stoichiometries. Analysis of the calculated nucleus-independent chemical shift data confirmed the aromatic nature of these species. Universal bonding patterns were identified that can be applied to a range of homoatomic and heteroatomic bismuth clusters. Additionally, calculations of absorbance and fluorescence spectra were performed to gain insights into the near-infrared emission and establish a potential correlation between absorbance and the identified bonding patterns.

Rigidized 3-aminocoumarins as fluorescent probes for strongly acidic environments and rapid yeast vacuolar lumen staining: mechanism and application

Coumarins remain one of the most important groups of fluorescent bio-probes, thanks to their high quantum yields, moderate photostability, efficient cell permeation and low (cyto)toxicity. Herein, we introduce new 3-aminocoumarins as turn-on pH probes under strongly acidic conditions and for indicators capable of significantly improving yeast vacuolar lumen staining compared to the commercial CMAC derivatives. We present the details of the on-off switching mechanism revealed by the TD-DFT and ab initio calculations complemented by a Franck-Condon analysis of the probes' emission profiles.

Origin of intersystem crossing in highly distorted organic molecules: a case study with red light-absorbing N,N,O,O-boron-chelated Bodipys

To explore the relationship between the twisted π-conjugation framework of aromatic chromophores and the efficacy of intersystem crossing (ISC), we have studied a N,N,O,O-boron-chelated Bodipy derivative possessing a severely distorted molecular structure. Surprisingly, this chromophore is highly fluorescent, showing inefficient ISC (singlet oxygen quantum yield, Φ_Δ = 12%). These features differ from those of helical aromatic hydrocarbons, where the twisted framework promotes ISC. We attribute the inefficient ISC to a large singlet-triplet energy gap (ΔE_S1/T1 = 0.61 eV). This postulate is tested by critical examination of a distorted Bodipy having an anthryl unit at the meso-position, for which Φ_Δ is increased to 40%. The improved ISC yield is rationalized by the presence of a T₂ state, localized on the anthryl unit, with energy close to that of the S₁ state. The electron spin polarization phase pattern of the triplet state is (e, e, e, a, a, a), with the T_z sublevel of the T₁ state overpopulated. The small zero-field splitting D parameter (-1470 MHz) indicates that the electron spin density is delocalized over the twisted framework. It is concluded that twisting of π-conjugation framework does not necessarily induce ISC, but S₁/T_n energy matching may be a generic feature for increasing ISC for a new-generation of heavy atom-free triplet photosensitizers.

Cost-Effective Simulations of Vibrationally-Resolved Absorption Spectra of Fluorophores with Machine-Learning-Based Inhomogeneous Broadening

The results of electronic and vibrational structure simulations are an invaluable support for interpreting experimental absorption/emission spectra, which stimulates the development of reliable and cost-effective computational protocols. In this work, we contribute to these efforts and propose an efficient first-principle protocol for simulating vibrationally-resolved absorption spectra, including nonempirical estimations of the inhomogeneous broadening. To this end, we analyze three key aspects: (i) a metric-based selection of density functional approximation (DFA) so to benefit from the computational efficiency of time-dependent density function theory (TD-DFT) while safeguarding the accuracy of the vibrationally-resolved spectra, (ii) an assessment of two vibrational structure schemes (vertical gradient and adiabatic Hessian) to compute the Franck-Condon factors, and (iii) the use of machine learning to speed up nonempirical estimations of the inhomogeneous broadening. In more detail, we predict the absorption band shapes for a set of 20 medium-sized fluorescent dyes, focusing on the bright ππ^★ S₀ → S₁ transition and using experimental results as references. We demonstrate that, for the studied 20-dye set which includes structures with large structural variability, the preselection of DFAs based on an easily accessible metric ensures accurate band shapes with respect to the reference approach and that range-separated functionals show the best performance when combined with the vertical gradient model. As far as band widths are concerned, we propose a new machine-learning-based approach for determining the inhomogeneous broadening induced by the solvent microenvironment. This approach is shown to be very robust offering inhomogeneous broadenings with errors as small as 2 cm^-1 with respect to genuine electronic-structure calculations, with a total CPU time reduced by 98%.

Interactions of Sodium Salicylate with β-Cyclodextrin and an Anionic Resorcin[4]arene: Mutual Diffusion Coefficients and Computational Study

The interaction between sodium salicylate (NaSal) and the two macrocycles 5,11,17,23-tetrakissulfonatomethylene-2,8,14,20-tetra(ethyl)resorcinarene (Na₄EtRA) and β-cyclodextrin (β-CD) has been studied by the determination of ternary mutual diffusion coefficients, and spectroscopic and computational techniques. The results obtained by the Job method suggest that the complex formation is given in a 1:1 ratio for all systems. The mutual diffusion coefficients and the computational experiments have shown that the β-CD-NaSal system presents an inclusion process, whereas the Na₄EtRA-NaSal system forms an outer-side complex. This fact is also in line with the results obtained from the computational experiments, where the calculated solvation free energy has been found to be more negative for the Na₄EtRA-NaSal complex because of the partial entry of the drug inside the Na₄EtRA cavity.

Intermolecular-Type Conical Intersections in Benzene Dimer

The equilibrium and conical intersection geometries of the benzene dimer were computed in the framework of the conventional, linear-response time-dependent and spin-flipped time-dependent density functional theories (known as DFT, TDDFT and SF-TDDFT) as well as using the multiconfigurational complete active space self-consistent field (CASSCF) method considering the minimally augmented def2-TZVPP and the 6-31G(d,p) basis sets. It was found that the stacking distance between the benzene monomers decreases by about 0.5 Å in the first electronic excited state, due to the stronger intermolecular interaction energy, bringing the two monomers closer together. Intermolecular-type conical intersection (CI) geometries can be formed between the two benzene molecules, when (i) both monomer rings show planar deformation and (ii) weaker (approximately 1.6-1.8 Å long) C-C bonds are formed between the two monomers, with parallel and antiparallel orientation with respect to the monomer. These intermolecular-type CIs look energetically more favorable than dimeric CIs containing only one deformed monomer. The validity of the dimer-type CI geometries obtained by SF-TDDFT was confirmed by the CASSCF method. The nudged elastic band method used for finding the optimal relaxation path has confirmed both the accessibility of these intermolecular-type CIs and the possibility of the radiationless deactivation of the electronic excited states through these CI geometries. Although not as energetically favorable as the previous two CI geometries, there are other CI geometries characterized by the relative rotation of monomers at different angles around a vertical C-C axis.

A Materials Acceleration Platform for Organic Laser Discovery

Conventional materials discovery is a laborious and time-consuming process that can take decades from initial conception of the material to commercialization. Recent developments in materials acceleration platforms promise to accelerate materials discovery using automation of experiments coupled with machine learning. However, most of the automation efforts in chemistry focus on synthesis and compound identification, with integrated target property characterization receiving less attention. In this work, an automated platform is introduced for the discovery of molecules as gain mediums for organic semiconductor lasers, a problem that has been challenging for conventional approaches. This platform encompasses automated lego-like synthesis, product identification, and optical characterization that can be executed in a fully integrated end-to-end fashion. Using this workflow to screen organic laser candidates, discovered eight potential candidates for organic lasers is discovered. The lasing threshold of four molecules in thin-film devices and find two molecules with state-of-the-art performance is tested. These promising results show the potential of automated synthesis and screening for accelerated materials development.

Tetranuclear Copper(I) and Silver(I) Pyrazolate Adducts with 1,1'-Dimethyl-2,2'-bibenzimidazole: Influence of Structure on Photophysics

A reaction of a cyclic trinuclear copper(I) or silver(I) pyrazolate complex ([MPz]₃, M = Cu, Ag) with 1,1'-dimethyl-2,2'-bibenzimidazole (L) leads to the formation of tetranuclear adducts decorated by one or two molecules of a diimine ligand, depending on the amount of the ligand added (0.75 or 1.5 equivalents). The coordination of two L molecules stabilizes the formation of a practically idealized tetrahedral four-metal core in the case of a copper-containing complex and a distorted tetrahedron in the case of a Ag analog. In contrast, complexes containing one molecule of diimine possess two types of metals, two- and three-coordinated, forming the significantly distorted central M₄ cores. The diimine ligands are twisted in these complexes with dihedral angles of ca. 50-60°. A TD-DFT analysis demonstrated the preference of a triplet state for the twisted 1,1'-dimethyl-2,2'-bibenzimidazole and a singlet state for the planar geometry. All obtained complexes demonstrated, in a solution, the blue fluorescence of the ligand-centered (LC) nature typical for free diimine. In contrast, a temperature decrease to 77 K stabilized the structure close to that observed in the solid state and activated the triplet states, leading to green phosphorescence at ca. 500 nm. The silver-containing complex Ag₄Pz₄L exhibited dual emission from both the singlet and triplet states, even at room temperature.

The dominant nature of Herzberg-Teller terms in the photophysical description of naphthalene compared to anthracene and tetracene

The first order and second order corrected photoluminescence quantum yields are computed and compared to experiment for naphthalene in this manuscript discussing negative results. Results for anthracene and tetracene are recalled from previous work (Manian et al. in J Chem Phys 155:054108, 2021), and the results for all three polyacenes are juxtaposed to each other. While at the Franck-Condon point, each of the three noted polyacenes were found to possess a quantum yield near unity. Following the consideration of Herzberg-Teller effects, quantum yields stabilised for anthracene and tetracene to 0.19 and 0.08, respectively. Conversely, the second order corrected quantum yield for naphthalene was found to be 0.91. Analysis of this result showed that while the predicted non-radiative pathways correlate well with what should be expected, the approximation used to calculate second order corrected fluorescence, which yielded very positive results for many other molecular systems, here is unable to account for strong second order contributions, resulting in a grossly overestimated rate of fluorescence. However, substitution of an experimental radiative rate results in a quantum yield of 0.33. This work extols the importance of Herzberg-Teller terms in photophysical descriptions of chromophores, and highlights those cases in which a treatment beyond the above approximation is required.

Fluorescence vs. Phosphorescence: Which Scenario Is Preferable in Au(I) Complexes with Benzothiadiazoles?

The photoluminescence of Au(I) complexes is generally characterized by long radiative lifetimes owing to the large spin-orbital coupling constant of the Au(I) ion. Herein, we report three brightly emissive Au(I) coordination compounds, 1, 2a, and 2b, that reveal unexpectedly short emission lifetimes of 10-20 ns. Polymorphs 2a and 2b exclusively exhibit fluorescence, which is quite rare for Au(I) compounds, while compound 1 reveals fluorescence as the major radiative pathway, and a minor contribution of a microsecond-scale component. The fluorescent behaviour for 1-2 is rationalized by means of quantum chemical (TD)-DFT calculations, which reveal the following: (1) S₀-S₁ and S₀-T₁ transitions mainly exhibit an intraligand nature. (2) The calculated spin-orbital coupling (SOC) between the states is small, which is a consequence of overall small metal contribution to the frontier orbitals. (3) The T₁ state features much lower energy than the S₁ state (by ca. 7000 cm^-1), which hinders the SOC between the states. Thus, the S₁ state decays in the form of fluorescence, rather than couples with T₁. In the specific case of complex 1, the potential energy surfaces for the S₁ and T₂ states intersect, while the vibrationally resolved S₁-S₀ and T₂-S₀ calculated radiative transitions show substantial overlap. Thus, the microsecond-scale component for complex 1 can stem from the coupling between the S₁ and T₂ states.

Expanding the Knowledge of the Selective-Sensing Mechanism of Nitro Compounds by Luminescent Terbium Metal-Organic Frameworks through Multiconfigurational ab Initio Calculations

The current research shows that the excited-state dynamics of the antenna ligand, both in the interacting system sensor/analyte and in the sensor without analyte, is a safe tool for elucidating the detection principle of the luminescent lanthanide-based metal-organic framework sensors. In this report the detection principle of the luminescence quenching mechanism in two Tb-based MOFs sensors is elucidated. The first system is a luminescent Tb-MOF [Tb(BTTA)_1.5(H₂O)_4.5]_n (H₂BTTA = 2,5-bis(1H-1,2,4-triazol-1-yl) terephthalic acid) selective to nitrobenzene (NB), labeled as Tb-1. The second system is {[Tb(DPYT)(BPDC)_1/2(NO₃)]·H₂O}_n (DPYT = 2,5-di(pyridin-4-yl) terephthalic acid, BPDC = biphenyl-4,4'-dicarboxylic acid), reported as a selective chemical sensor to nitromethane (NM) in situ, labeled as Tb-2. The luminescence quenching of the MOFs is promoted by intermolecular interactions with the analytes that induce destabilization of the T₁ electronic state of the linker "antenna", altering thus the sensitization pathways of the Tb atoms. This study demonstrates the value of host-guest interaction simulations and the rate constants of the radiative and nonradiative processes in understanding and elucidating the sensing mechanism in Ln-MOF sensors.

Improving the Brightness of Pyronin Fluorophore Systems through Quantum-Mechanical Predictions

The pyronin class of fluorophores serves a critical role in numerous imaging applications, particularly involving preferential staining of RNA through base pair intercalation. Despite this important role in molecular staining applications, the same set of century-old pyronins (i.e., pyronin Y (PY) and pyronin B (PB)), which possess relatively low fluorophore brightness, are still predominantly being used due to the lack of methodology for generating enhanced variants. Here, we use TD-DFT calculations of interconversion energies between structures on the S1 surface as a preliminary means to evaluate fluorophore brightness for a proposed set of pyronins containing variable substitution patterns at the 2, 3, 6, and 7 positions. Using a nucleophilic aromatic substitution/hydride addition approach, we synthesized the same set of pyronins and demonstrate that quantum-mechanical computations are useful for predicting fluorophore performance. We produced the brightest series of pyronin fluorophores described to date, which possess considerable gains over PY and PB.

Comparison among several vibronic coupling methods

A comparison of four approaches to account the vibronic coupling in photoabsorption is performed. The methods considered are nuclear ensemble (NE), direct vibronic coupling (DVC), adiabatic Hessian (AH), and vertical gradient (VG). The case study is the symmetry-forbidden [Formula: see text] [Formula: see text]A[Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text]A[Formula: see text] (n [Formula: see text] [Formula: see text]) transition in formaldehyde. Being forbidden in the equilibrium geometry, this transition is entirely induced by vibronic coupling and constitutes an appropriate case to study the performance of different methods. From DVC, it is found that mode 1 (C=O out-of-plane bending) is the most inducing, followed by mode 6 (in-plane C-H asymmetric stretching) and finally by mode 2 (in-plane C-H asymmetric bending). We were able to correlate 17 out of 20 structures obtained from NE with these modes, showing that these two methods, although different in principle, give comparable results. The simulated spectra were obtained for all methods and compared, and each one has its own advantage. In what concerns the transition studied, NE gives the best description of the spectrum, DVC is the only one that easily gives an absolute value for OOS, and AH and VG are the computationally less expensive methods. From the latter two, VG is the less demanding on computational grounds, since it does not require the excited state Hessian.

On the Importance of Well-Defined Thermal Correlation Functions in Simulating Vibronic Spectra

Two difficulties associated with the computations of thermal vibrational correlation functions are discussed. The first one is the lack of a well-behaved expression that is valid at both high-temperature and T → 0 K limits. Specifically, if the partition function and the propagator are considered separately, then thermal vibrational correlation functions may have an indeterminate form 0/0 in the limit T → 0 K. This difficulty is resolved when the partition function and the propagator are jointly considered in the harmonic approximation, which allows a problematic term that emanates from the zero-point energy to be canceled out, thereby producing a thermal correlation function with a determinate form in the T → 0 K limit. The second difficulty is related to the multivaluedness of the vibrational correlation function. We show numerically that an improper selection of branch leads to discontinuities in the computed correlation function and incorrect vibronic spectra. We propose a phase tracking procedure that ensures continuity of both real and imaginary parts of the correlation function to recover the correct spectra. We support our findings by simulating the UV-vis absorption spectra of pentacene at 4 K and benzene at 298 K. Both are found to be in good agreement with their experimental counterparts.

Can domain-based local pair natural orbitals approaches accurately predict phosphorescence energies?

Since the discovery of the peculiar conducting and optical properties of aromatics, many efforts have been made to characterize and predict their phosphorescence. This physical process is exploited in modern Organic Emitting Light Diodes (OLEDs), and it is also one of the processes decreasing the efficiency of Dye-sensitized solar cells (DSSCs). Herein, we propose a computational strategy for the accurate calculation of singlet-triplet gaps of aromatic compounds, which provides results that are in excellent agreement with available experimental data. Our approach relies on the domain-based local pair natural orbital (DLPNO) variant of the "gold standard" CCSD(T) method. The convergence of our results with respect to the key technical parameters of the calculation, such as the basis set used, the approximations employed in the perturbative triples correction, and the dimension of the PNOs space, was thoroughly discussed.

Exploring the excited-state charge transfer fluorescence profile of 7-hydroxycoumarin and 2-methylimidazole - a combined X-ray diffraction and theoretical approach

This study investigated the effect of 2-methylimidazole (2-MIM) addition on the fluorescence of ethyl-7-hydroxy-2-oxo-2H-chromene-3-carboxylate using low-cost density functional theory (DFT) and Time-Dependent DFT calculations on single crystal X-ray geometries of ethyl-7-hydroxy-2-oxo-2H-chromene-3-carboxylate hydrate (1), 2-MIM (2), and the 1 : 1 co-crystal of (1) and (2), (3). At low concentrations (1 : 1-1 : 10) of 2-MIM, the fluorophore shows a decrease in the fluorescence intensity, but at higher concentrations (above 1 : 10) the fluorescence excitation maximum shifted from 354 nm to 405 nm, with a significant emission intensity increase. The changed excitation and emission profile at high concentrations is due to the deprotonation of the coumarin's phenolic group, which was confirmed by the increased shielding of the aromatic protons in the titration ¹H NMR spectra. The experimental fluorescence data between the 1 : 1 and 1 : 10 ratios agreed with the theoretical fluorescence data, with a redshift and decreased intensity when comparing (1) and (3). The data indicated that combining the fluorophore with 2-MIM increased levels of vibronic coupling between 2-MIM and the fluorophore decreasing de-excitation efficiency. These increased vibronic changes were due to charge transfer between the fluorophore and 2-MIM in (3). The subtle movement of the proton, H(5) toward N(2') (0.07 Å) caused a significant decrease in fluorescence due to electron density distribution (EDD) changes. This was identified by comparison of the EDD in the excited (S₁) and ground (S₀) states plotted as an isosurface of EDD difference. For the higher concentrations, an alternative excitation pathway was explored by modifying the crystal geometry of (3) based on ¹H NMR spectroscopy data to resemble excitoplexes. Theses excitoplex geometries reflected the fluorescence profile of the fluorophore with high concentrations of 2-MIM; there were dramatic changes in the theoretical fluorescence pathway, which was 100% vibronic coupling compared to 15.31% in the free fluorophore. At this concentration, the de-excitation pathway causes remodelling of the lactone ring via stretching/breaking the CO bond in the S₁ causing increased fluorescence by movement of the transition dipole moment. These results reflect previous studies, but the methods used are less experimentally and computationally expensive. This study is among the first to explain charge transfer fluorescence using crystalline geometries. This study will be of interest to the fields of crystal engineering and fluorescence spectroscopy.

Dopamine Photochemical Behaviour under UV Irradiation

To understand the photochemical behaviour of the polydopamine polymer in detail, one would also need to know the behaviour of its building blocks. The electronic absorption, as well as the fluorescence emission and excitation spectra of the dopamine were experimentally and theoretically investigated considering time-resolved fluorescence spectroscopy and first-principles quantum theory methods. The shape of the experimental absorption spectra obtained for different dopamine species with standard, zwitterionic, protonated, and deprotonated geometries was interpreted by considering the advanced equation-of-motion coupled-cluster theory of DLPNO-STEOM. Dynamical properties such as fluorescence lifetimes or quantum yield were also experimentally investigated and compared with theoretically predicted transition rates based on Fermi's Golden Rule-like equation. The results show that the photochemical behaviour of dopamine is strongly dependent on the concentration of dopamine, whereas in the case of a high concentration, the zwitterionic form significantly affects the shape of the spectrum. On the other hand, the solvent pH is also a determining factor for the absorption, but especially for the fluorescence spectrum, where at lower pH (5.5), the protonated and, at higher pH (8.0), the deprotonated forms influence the shape of the spectra. Quantum yield measurements showed that, besides the radiative deactivation mechanism characterized by a relatively small QY value, non-radiative deactivation channels are very important in the relaxation process of the electronic excited states of different dopamine species.

Quantum simulations of thermally activated delayed fluorescence in an all-organic emitter

We investigate the prototypical NAI-DMAC thermally activated delayed fluorescence (TADF) emitter in the gas phase- and high-packing fraction limits at finite temperature, by combining first principles molecular dynamics with a quantum thermostat to account for nuclear quantum effects (NQE). We find a weak dependence of the singlet-triplet energy gap (ΔE_ST) on temperature in both the solid and the molecule, and a substantial effect of packing. While the ΔE_ST vanishes in the perfect crystal, it is of the order of ∼0.3 eV in the molecule, with fluctuations ranging from 0.1 to 0.4 eV at 300 K. The transition probability between the HOMOs and LUMOs has a stronger dependence on temperature than the singlet-triplet gap, with a desirable effect for thermally activated fluorescence; such temperature effect is weaker in the condensed phase than in the molecule. Our results on ΔE_ST and oscillator strengths, together with our estimates of direct and reverse intersystem crossing rates, show that optimization of packing and geometrical conformation is critical to increase the efficiency of TADF compounds. Our findings highlight the importance of considering thermal fluctuations and NQE to obtain robust predictions of the electronic properties of NAI-DMAC.

Electronic and Optical Properties of Eu2+-Activated Narrow-Band Phosphors for Phosphor-Converted Light-Emitting Diode Applications: Insights from a Theoretical Spectroscopy Perspective

In this work, we present a computational protocol that is able to predict the experimental absorption and emission spectral shapes of Eu²⁺-doped phosphors. The protocol is based on time-dependent density functional theory and operates in conjunction with an excited-state dynamics approach. It is demonstrated that across the study set consisting of representative examples of nitride, oxo-nitride, and oxide Eu²⁺-doped phosphors, the energy distribution and the band shape of the emission spectrum are related to the nature of the 4f–5d transitions that are probed in the absorption process. Since the 4f orbitals are very nearly nonbonding, the decisive quantity is the covalency of the 5d acceptor orbitals that become populated in the electronically excited state that leads to emission. The stronger the (anti) bonding interaction between the lanthanide and the ligands is in the excited state, the larger will be the excited state distortion. Consequently, the corresponding emission will get broader due to the vibronic progression that is induced by the structural distortion. In addition, the energy separation of the absorption bands that are dominated by states with valence 4f–5d and a metal to ligand charge transfer character defines a measure for the thermal quenching of the studied Eu²⁺-doped phosphors. Based on this analysis, simple descriptors are identified that show a strong correlation with the energy position and bandwidth of the experimental emission bands without the need for elaborate calculations. Overall, we believe that this study serves as an important reference for designing new Eu²⁺-doped phosphors with desired photoluminescence properties.

Comparison of Linear Response Theory, Projected Initial Maximum Overlap Method, and Molecular Dynamics-Based Vibronic Spectra: The Case of Methylene Blue

The simulation of optical spectra is essential to molecular characterization and, in many cases, critical for interpreting experimental spectra. The most common method for simulating vibronic absorption spectra relies on the geometry optimization and computation of normal modes for ground and excited electronic states. In this report, we show that the utilization of such a procedure within an adiabatic linear response (LR) theory framework may lead to state mixings and a breakdown of the Born-Oppenheimer approximation, resulting in a poor description of absorption spectra. In contrast, computing excited states via a self-consistent field method in conjunction with a maximum overlap model produces states that are not subject to such mixings. We show that this latter method produces vibronic spectra much more aligned with vertical gradient and molecular dynamics (MD) trajectory-based approaches. For the methylene blue chromophore, we compare vibronic absorption spectra computed with the following: an adiabatic Hessian approach with LR theory-optimized structures and normal modes, a vertical gradient procedure, the Hessian and normal modes of maximum overlap method-optimized structures, and excitation energy time-correlation functions generated from an MD trajectory. Because of mixing between the bright S₁ and dark S₂ surfaces near the S₁ minimum, computing the adiabatic Hessian with LR theory and time-dependent density functional theory with the B3LYP density functional predicts a large vibronic shoulder for the absorption spectrum that is not present for any of the other methods. Spectral densities are analyzed and we compare the behavior of the key normal mode that in LR theory strongly couples to the optical excitation while showing S₁/S₂ state mixings. Overall, our study provides a note of caution in computing vibronic spectra using the excited-state adiabatic Hessian of LR theory-optimized structures and also showcases three alternatives that are less sensitive to adiabatic state mixing effects.