Chalcogen atom effect on the intersystem crossing kinetic constant of oxygen- and sulfur disubstituted heteroporphyrins

The modulation of the photophysical properties of di-substituted porphyrin rings upon the oxygen and sulfur-for-nitrogen replacement has been investigated at density functional theory (DFT) and its time-dependent formulation (TDDFT). The considered properties range from structural behaviors and excitation energies to spin-orbit coupling (SOC) and nonradiative intersystem kinetic constants. Results show that the SOC strongly increase upon chalcogen substitution and, accordingly, the computed nonradiative kinetic constant also indicate an efficient singlet-triplet intersystem crossing in the sulfur containing macrocycle. The presented results indicate an alternative way to properly modulate the porphyrin's crucial properties for their use in photodynamic therapy, without resorting to the use of heavy atoms.

Molecular phosphorescence enhancement by the plasmon field of metal nanoparticles

A theoretical model is proposed that allows the estimation of the quantum yield of phosphorescence of dye molecules in the vicinity of plasmonic nanoparticles. For this purpose, the rate constants of the radiative and nonradiative intramolecular transitions for rhodamine 123 (Rh123) and brominated rhodamine (Rh123-2Br) dyes have been calculated. The plasmon effect of Ag nanoparticles on various types of luminescence processes has been studied both theoretically and experimentally. We show that in the presence of a plasmonic nanoparticle, the efficiency of the immediate and delayed fluorescence increases significantly. The phosphorescence rate of the rhodamine dyes also increases near plasmonic nanoparticles. The long-lived luminescence i.e., delayed fluorescence and phosphorescence is more enhanced for Rh123-2Br than for Rh123. The largest phosphorescence quantum yield is obtained when the dye molecule is at a distance of 4-6 nm from the nanoparticle surface. Our results can be used in the design of plasmon-enhancing nanostructures for light-emitting media, organic light-emitting diodes, photovoltaic devices, and catalysts for activation of molecular oxygen.

Manipulation of Nonradiative Process Based on the Aggregation Microenvironment to Customize Excited-State Energy Conversion

ConspectusNonradiative processes with the determined role in excited-state energy conversion, such as internal conversion (IC), vibrational relaxation (VR), intersystem crossing (ISC), and energy or electron transfer (ET or eT), have exerted a crucial effect on biological functions in nature. Inspired by these, nonradiative process manipulation has been extensively utilized to develop organic functional materials in the fields of energy and biomedicine. Therefore, comprehensive knowledge and effective manipulation of sophisticated nonradiative processes for achieving high-efficiency excited-state energy conversion are quintessential. So far, many strategies focused on molecular engineering have demonstrated tremendous potential in manipulating nonradiative processes to tailor excited-state energy conversion. Besides, molecular aggregation considerably affects nonradiative processes due to their ultrasensitivity, thus providing us with another essential approach to manipulating nonradiative processes, such as the famous aggregation-induced emission. However, the weak interactions established upon aggregation, namely, the aggregation microenvironment (AME), possess hierarchical, dynamic, and systemic characteristics and are extremely complicated to elucidate. Revealing the relationship between the AME and nonradiative process and employing it to customize excited-state energy conversion would greatly promote advanced materials in energy utilization, biomedicine, etc., but remain a huge challenge. Our group has devoted much effort to achieving this goal.In this Account, we focus on our recent developments in nonradiative process manipulation based on AME. First, we provide insight into the effect of the AME on nonradiative process in terms of its steric effect and electronic regulation, illustrating the possibility of nonradiative process manipulation through AME modulation. Second, the distinct enhanced steric effect is established by crystallization and heterogeneous polymerization to conduct crystallization-induced reversal from dark to bright excited states and dynamic hardening-triggered nonradiative process suppression for highly efficient luminescence. Meanwhile, promoting the ISC process and stabilizing the triplet state are also manipulated by the crystal and polymer matrix to induce room-temperature phosphorescence. Furthermore, the strategies employed to exploit nonradiative processes for photothermy and photosensitization are reviewed. For photothermal conversion, besides the weakened steric effect with promoted molecular motions, a new strategy involving the introduction of diradicals upon aggregation to narrow the energy band gap and enhance intermolecular interactions is put forward to facilitate IC and VR for high-efficiency photothermal conversion. For photosensitization, both the enhanced steric effect from the rigid matrix and the effective electronic regulation from the electron-rich microenvironment are demonstrated to facilitate ISC, ET, and eT for superior photosensitization. Finally, we explore the existing challenges and future directions of nonradiative process manipulation by AME modulation for customized excited-state energy conversion. We hope that this Account will be of wide interest to readers from different disciplines.

Visible-Light Activation of Diorganyl Bis(pyridylimino) Isoindolide Aluminum(III) Complexes and Their Organometallic Radical Reactivity

We report on the synthesis and characterization of a series of (mostly) air-stable diorganyl bis(pyridylimino) isoindolide (BPI) aluminum complexes and their chemistry upon visible-light excitation. The redox non-innocent BPI pincer ligand allows for efficient charge transfer homolytic processes of the title compounds. This makes them a universal platform for the generation of carbon-centered radicals. The photo-induced homolytic cleavage of the Al-C bonds was investigated by means of stationary and transient UV/Vis spectroscopy, spin trapping experiments, as well as EPR and NMR spectroscopy. The experimental findings were supported by quantum chemical calculations. Reactivity studies enabled the utilization of the aluminum complexes as reactants in tin-free Giese-type reactions and carbonyl alkylations under ambient conditions, which both indicated radical-polar crossover behavior. A deeper understanding of the physical fundamentals and photochemical process was provided, furnishing in turn a new strategy to control the reactivity of bench-stable aluminum organometallics.

Experimental and computational studies of the optical properties of 2,5,8-tris(phenylthiolato)heptazine with an inverted singlet-triplet gap

Photophysical properties of the three-fold symmetric 2,5,8-tris(phenylthiolato)heptazine molecule (1) are studied from combined experimental and computational viewpoints. The intense blue photoemission of 1 in the solid state and in toluene solution is proposed to have a fluorescent origin on the basis of a relatively short emission lifetime and no detectable triplet decay. Calculations at correlated ab initio levels of theory also show that 1 has a large inverted singlet-triplet (IST) gap, a non-vanishing spin-orbit coupling matrix element between the first excited singlet and triplet states, and a fast intersystem crossing rate constant that leads to singlet population from the higher-lying triplet state. The IST gap implies that the first excited singlet state is the lowest excited one, agreeing with the measured fluorescent behaviour of 1. IST gaps are also obtained for the oxygen-containing (2) and selenium-containing (3) analogues of 1 at the ADC(2) level of theory, but not for the tellurium one (4). Calculations of the magnetically induced current density demonstrate that the heptazine core of 1 is globally non-aromatic due to the alternation of carbon and nitrogen atoms along its external rim.

Intramolecular rate-constant calculations based on the correlation function using temperature dependent quantum Green's functions

A theoretical method for calculating rate constants for internal conversion (IC), intersystem crossing (ISC) and radiative (R) electronic transitions is presented. The employed method uses temperature-dependent quantum Green's functions, which give the opportunity to consider almost any nth-order polynomial perturbation operator and the influence of external electromagnetic fields on the rate constants. The rate constants of the IC, ISC and R processes are calculated for two important indocyanine molecules namely indocyanine green (ICG) and heptamethine cyanine (IR808) at the Franck-Condon level using the temperature-dependent quantum Green's function approach. Calculations at the time-dependent density functional theory level with the MN15 functional show that ICG and IR808 have only one triplet state below the S1 state. The main deactivation channel of the S1 state is the IC process with a large (kIC(S1 → S0)) rate constant of ∼109-1011 s-1. The estimated quantum yield of fluorescence (φfl) is ∼0.001-0.24 for the two studied molecules, which agrees rather well with experimental values. Thus, the present approach enables calculations of the three kinds of rate constants and the quantum yield of fluorescence using the same computational methodology.

Internal conversion induced by external electric and magnetic fields

We have developed a new methodology for calculating contributions to the rate constants (kIC) of internal conversion that are induced by external electric (kIC-E) or magnetic (kIC-M) fields. The influence of the external electric and magnetic fields on the kIC was estimated for seven representative molecules. We show that the kIC-E contribution calculated at a field strength of 1011 V m-1 is generally as large as the kIC rate constant in the absence of the external field. For indocyanine green, azaoxa[8]circulene, and pyromitene 567, the kIC-E contribution is as large as kIC already at a field strength of 109 V m-1. Such electric-field strengths occur for example in plasmonic studies and in strong laser-field experiments. The induced effect on the kIC rate constant should be accounted for in calculations of photophysical properties of molecules involved in such experiments. The induced effect of an external magnetic field on kIC can be neglected in experiments on Earth because the magnetic contribution becomes significant only at very strong magnetic fields of 104-105 T that cannot be achieved on Earth. However, the magnetic effect on the rate constant of internal conversion can be important in astrophysical studies, where extremely strong magnetic fields occur near neutron stars and white dwarfs.

Prediction of fluorescence quantum yields using the extended thawed Gaussian approximation

Spontaneous emission and internal conversion rates are calculated within harmonic approximations and compared to the results obtained within the semi-classical extended thawed Gaussian approximation (ETGA). This is the first application of the ETGA in the calculation of internal conversion and emission rates for real molecular systems, namely, formaldehyde, fluorobenzene, azulene, and a dicyano-squaraine dye. The viability of the models as black-box tools for prediction of spontaneous emission and internal conversion rates is assessed. All calculations were done using a consistent protocol in order to investigate how different methods perform without previous experimental knowledge using density functional theory (DFT) and time-dependent DFT (TD-DFT) with B3LYP, PBE0, ωB97XD, and CAM-B3LYP functionals. Contrasting the results with experimental data shows that there are further improvements required before theoretical predictions of emission and internal conversion rates can be used as reliable indicators for the photo-luminescence properties of molecules. We find that the ETGA performs rather similar to the vertical harmonical model. Including anharmonicities in the calculation of internal conversion rates has a moderate effect on the quantitative results in the studied systems. The emission rates are fairly stable with respect to computational parameters, but the internal conversion rate reveals itself to be highly dependent on the choice of the spectral line shape function, particularly the width of the Lorentzian function, associated with homogeneous broadening.

Fantastical excited state optimized structures and where to find them

The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima and saddle points. Always implicit in using this machinery is the fact that an excited state PES only exists within the realm of the Born-Oppenheimer approximation, where the nuclear and electronic degrees of freedom separate. This work demonstrates through ab initio calculations and simple nonadiabatic dynamics that some excited state minimum structures are fantastical: they appear to exist as stable configurations only as a consequence of the PES construct, rather than being physically observable. Each fantastical structure exhibits an unphysically high predicted harmonic frequency and associated force constant. This fact can serve as a valuable diagnostic of when an optimized excited state structure is non-observable. The origin of this phenomenon can be attributed to the coupling between different electronic states. As PESs approach one another, the upper surface can form a minimum that is very close to a near-touching point. The force constant, evaluated at this minimum, relates to the strength of the electronic coupling rather than to any characteristic excited state vibration. Nonadiabatic dynamics results using a Landau-Zener model illustrate that fantastical excited state structures have extremely short lifetimes on the order of a few femtoseconds. Their appearance in a calculation signals the presence of a nearby conical intersection through which the system will rapidly cross to a lower surface.

Mechanism of Enhanced Triplet-Triplet Upconversion in Organic Molecules

We use time-dependent density functional theory (TDDFT) to investigate the mechanism of efficient triplet-triplet upconversion (TTU) in certain organic materials. In particular, we focus on materials where some singlets are generated in a two-step spin-nonconserving process (T1 + T1 → T2 → S1). For this mechanism to contribute significantly, the intersystem crossing (ISC) from the high-lying triplet to the singlet (T2 → S1) must outcompete the internal conversion (IC) to the low-lying triplet (T2 → T1). By considering multiple families of materials, we show that the T2 → S1 ISC can be enhanced in a number of ways: the substitution of electron-donating (ED) and electron-withdrawing (EW) groups at appropriate positions; the substitution of bulky groups that distort the molecular geometry; and the substitution of heavy atoms that enhance the spin-orbit coupling (SOC). In the first two cases, the enhancements are consistent with El-Sayed's rule in that rapid T2 → S1 ISC requires significant differences in the characters of the S1 and the T2 wavefunctions. Together, these effects enable a wide tunability of T2 → S1 ISC rates over at least 5 orders of magnitude. Meanwhile, the T2 → T1 IC is inhibited in these systems due to the large T2 - T1 energy gap >0.5 eV, which entails a high energy barrier to the T2 → T1 IC and the prediction of a slow rate regardless of the substituents or the presence of heavy atoms. In this way, tuning the T2 → S1 ISC appears to provide an effective strategy to achieve systematic improvement of TTU materials.

Influence of plasmons on the luminescence properties of solvatochromic merocyanine dyes with different solvatochromism

The effect of localized surface plasmon resonance (LSPR) of a system consisting of a highly dipolar merocyanine dye and a silver nanoparticle (NP) was studied experimentally and theoretically. A theoretical model for estimating the fluorescence quantum yield (φfl) using quantum chemical calculations of intramolecular and intermolecular electronic transition rate constants was developed. Calculations show that the main deactivation channels of the lowest excited singlet state of the studied merocyanines are internal conversion (kIC(S1 → S0)) and fluorescence (kr(S1 → S0)). The intersystem-crossing transition has a low probability due to the large energy difference between the singlet and triplet levels. In the presence of plasmonic NPs, the fluorescence quantum yield is increased by a factor of two according to both experiment and computations. The calculated values of φfl, when considering changes in kr(S1 → S0) and the energy-transfer rate constant (ktransfer) from the dye to the NP was also twice as large at distances of 6-8 nm between the NP and the dye molecule. We also found that the LSPR effect can be increased or decreased depending on the value of the dielectric constant (εm) of the environment.

Theoretical and Experimental Investigation of the Electronic Propensity Rule: A Linear Relationship between Radiative and Nonradiative Decay Rates of Molecules

The electronic propensity rule, which suggests a proportional relationship between radiative and nonradiative electronic coupling elements in fluorescent molecules, has been postulated for some time. Despite its potential significance, the rule has not been rigorously derived and experimentally validated. In this work, we draw upon the theoretical framework established by Schuurmans et al. for the relation between the radiative and nonradiative electronic coupling elements of the rare earth metal in the crystal at low temperature and extend their approach to the fluorescent molecules under external electric field perturbation at a fixed energy gap and varied temperatures, with a further single-electron approximation (Schuurmans, M. F. H., et al. Physica B & C 1984, 123, 131-155). We obtained a linear relation between the radiative decay rates and nonradiative decay rates for internal conversion, which is verified by experimental data from two types of dextran-dye complexes and the light-harvesting antenna complex in photosynthetic bacteria.

Calculation of Excited State Internal Conversion Rate Constant Using the One-Effective Mode Marcus-Jortner-Levich Theory

In this article, the one-effective mode Marcus-Jortner-Levich (MJL) theory and the classical Marcus theory for electron transfer were applied to estimate the internal conversion rate constant, k_IC, of organic molecules and a Ru-based complex, all belonging to the Marcus inverted region. For this, the reorganization energy was calculated using the minimum energy conical intersection point to account for more vibrational levels, correcting the density of states. The results showed good agreement with experimental and theoretically determined k_IC, with a small overestimation by the Marcus theory. Also, molecules less dependent on the solvent effects, like benzophenone, presented better results than molecules with an expressive dependence, like 1-aminonaphthalene. Moreover, the results suggest that each molecule possesses unique normal modes leading to the excited state deactivation that does not necessarily match the X-H bond stretching, as previously suggested.

Internal conversion rate constant calculations considering Duschinsky, anharmonic and Herzberg-Teller effects

A novel method for calculating rate constants for internal conversion (k_IC) that simultaneously accounts for Duschinsky, anharmonic and Herzberg-Teller effects has been developed and implemented. This method has been applied to robust planar molecules like tetraoxa[8]circulene (4B), free-base porphyrin (H2P) and pyrometene (PM567) with small Duschinsky rotation (i.e. with almost identical normal coordinates in the ground and excited states) and to poly[n]fluorenes (P[n]F) (n = 2-14) with a substantial Duschinsky rotation. The obtained results show that the Duschinsky effect is large in the harmonic approximation, whereas it is in general much smaller in the anharmonic approximation. The Duschinsky effect is found to be large for high frequency vibrational modes with energies of ∼3300 cm^-1 such as the X-H (X = C, N and O) stretching modes that mix in the S₁ → S₀ electronic transition. However, even in this case, the increase in k_IC due to the Duschinsky effect does not exceed one order of magnitude. The calculations show that anharmonic contributions to k_IC are larger than Herzberg-Teller contributions which in turn are larger than contributions from the Duschinsky effect ANH > HT > Du. We also show that an approximation, where only X-H bonds are considered in the k_IC calculation, is accurate even for P[n]F (n = 2-14).

Computational Investigation of Substituent Effects on the Alcohol + Carbonyl Channel of Peroxy Radical Self- and Cross-Reactions

Organic peroxy radicals (RO₂) are key intermediates in atmospheric chemistry and can undergo a large variety of both uni- and bimolecular reactions. One of the least understood reaction classes of RO₂ are their self- and cross-reactions: RO₂ + R'O₂. In our previous work, we have investigated how RO₂ + R'O₂ reactions can lead to the formation of ROOR' accretion products through intersystem crossings and subsequent recombination of a triplet intermediate complex ³(RO···OR'). Accretion products can potentially have very low saturation vapor pressures, and may therefore participate in the formation of aerosol particles. In this work, we investigate the competing H-shift channel, which leads to the formation of more volatile carbonyl and alcohol products. This is one of the main, and sometimes the dominant, RO₂ + R'O₂ reaction channels for small RO₂. We investigate how substituents (R and R' groups) affect the H-shift barriers and rates for a set of ³(RO···OR') complexes. The variation in barrier heights and rates is found to be surprisingly small, and most computed H-shift rates are fast: around 10⁸-10⁹ s^-1. We find that the barrier height is affected by three competing factors: (1) the weakening of the breaking C-H bond due to interactions with adjacent functional groups; (2) the overall binding energy of the ³(RO···OR'), which tends to increase the barrier height; and (3) the thermodynamic stability of the reaction products. We also calculated intersystem crossing rate coefficients (ISC) for the same systems and found that most of them were of the same order of magnitude as the H-shift rates. This suggests that both studied channels are competitive for small and medium-sized RO₂. However, for complex enough R or R' groups, the binding energy effect may render the H-shift channel uncompetitive with intersystem crossings (and thus ROOR' formation), as the rate of the latter, while variable, seems to be largely independent of system size. This may help explain the experimental observation that accretion product formation becomes highly effective for large and multifunctional RO₂.

Internal conversion rates from the extended thawed Gaussian approximation: Theory and validation

The theoretical prediction of the rates of nonradiative processes in molecules is fundamental in assessing their emissive properties. In this context, global harmonic models have been widely used to simulate vibronic spectra as well as internal conversion rates and to predict photoluminescence quantum yields. However, these simplified models suffer from the limitations that are inherent to the harmonic approximation and can have a severe effect on the calculated internal conversion rates. Therefore, the development of more accurate semiclassical methods is highly desirable. Here, we introduce a procedure for the calculation of nonradiative rates in the framework of the time-dependent semi-classical Extended Thawed Gaussian Approximation (ETGA). We systematically investigate the performance of the ETGA method by comparing it to the adiabatic and vertical harmonic methods, which belong to the class of widely used global harmonic models. Its performance is tested in potentials that cannot be treated adequately by global harmonic models, beginning with Morse potentials of varying anharmonicity followed by a double well potential. The calculated radiative and nonradiative internal conversion rates are compared to reference values based on exact quantum dynamics. We find that the ETGA has the capability to predict internal conversion rates in anharmonic systems with an appreciable energy gap, whereas the global harmonic models prove to be insufficient.

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

Gold(i)-containing light-emitting molecules with an inverted singlet–triplet gap†

Delayed fluorescence from molecules with an inverted singlet–triplet gap (DFIST) is the consequence of the unusual reverse order of the lowest excited singlet (S₁) and triplet (T₁) states of thermally activated delayed fluorescence (TADF) emitters. Heptazine (1,3,4,6,7,9,9b-heptaazaphenalene) derivatives have an inverted singlet–triplet gap thanks to the combination of multiple resonance (MR) effects and a significant double excitation character. Here, we study computationally the effect of gold(i) metalation and coordination on the optical properties of heptazine (molecule 4) and the phosphine-functionalized 2,5,8-tris(dimethylphosphino)heptazine derivatives (molecules 1–3). Ab initio calculations at the approximate second-order coupled cluster (CC2) and extended multiconfigurational quasi degenerate perturbation theory at the second order (XMC-QDPT2) levels show that molecules 1–4 have an inverted singlet–triplet gap due to the alternating spatial localization of the electron and hole of the exciton in the heptazine core. A non-vanishing one-electron spin–orbit coupling operator matrix element between T₁ and and a fast S₁ ← T₁ intersystem crossing rate constant (k_ISC) calculated at the XMC-QDPT2(12,12) level of theory for molecule 4 suggest that this new family of complexes may be the first organometallic DFIST emitters reported.

Substitution with gold(i)-containing moieties results in non-vanishing oscillator strengths and spin–orbit coupling leading to fast intersystem crossing in light-emitting heptazine derivates with an inverted singlet–triplet gap.

Spectroscopic characterization and assessment of microbiological potential of 1,3,4-thiadiazole derivative showing ESIPT dual fluorescence enhanced by aggregation effects

In the presented study, advanced experimental techniques, including electronic absorption and fluorescence spectroscopies [with Resonance Light Scattering (RLS)], measurements of fluorescence lifetimes in the frequency domain, calculations of dipole moment fluctuations, quantum yields, and radiative and non-radiative transfer constants, were used to characterize a selected analogue from the group of 1,3,4-thiadiazole, namely: 4-[5-(naphthalen-1-ylmethyl)-1,3,4-thiadiazol-2-yl]benzene-1,3-diol (NTBD), intrinsically capable to demonstrate enol → keto excited-states intramolecular proton transfer (ESIPT) effects. The results of spectroscopic analyses conducted in solvent media as well as selected mixtures were complemented by considering biological properties of the derivative in question, particularly in terms of its potential microbiological activity. The compound demonstrated a dual fluorescence effect in non-polar solvents, e.g. chloroform and DMSO/H₂O mixtures, while in polar solvents only a single emission maximum was detected. In the studied systems, ESIPT effects were indeed observed, as was the associated phenomenon of dual fluorescence, and, as demonstrated for the DMSO: H₂O mixtures, the same could be relatively easily induced by aggregation effects related to aggregation-induced emission (AIE). Subsequently conducted quantum-chemical (TD-)DFT calculations supported further possibility of ESIPT effects. The following article provides a comprehensive description of the spectroscopic and biological properties of the analyzed 1,3,4-thiadiazole derivatives, highlighting its potential applicability as a very good fluorescence probes as well as a compound capable of high microbiological activity.

Spin-Orbit Coupling Calculation Combined with the Reference Interaction Site Model Self-Consistent Field Explicitly Including Constrained Spatial Electron Density Distribution

Studying the radiative and non-radiative decay processes of molecules in a solution is an important issue in the design of organic and functional molecules. Theoretical approaches have great potential for revealing this decay process through computation of various parameters, such as the energy surfaces at the excited state and spin-orbit coupling (SOC). The development of quantum chemical programs has enabled the calculation of SOC values to become popular for the gas phase. However, SOC calculations in solution have some difficulties that need to be overcome. In the present study, the authors combined the SOC calculations with the reference interaction site model self-consistent field explicitly including constrained spatial electron density distribution. To validate the reliability of our method, the decay process of dimethylaminobenzonitrile in cyclohexane and acetonitrile was studied. By computing the SOC values in both solution systems, the authors were able to investigate the decay process at the atomistic level. Furthermore, a natural transition orbital analysis and the measurement of the decomposed SOC values were found to provide a clear understanding of intersystem crossing.

The Energy Gap Law at Work: Emission Yield and Rate Fluctuations of Single NIR Emitters

Internal conversion (IC) often is the dominating relaxation pathway in NIR emitters, lowering their fluorescence quantum yield. Here, we investigate dibenzoterrylene (DBT) by bulk and single molecule spectroscopy. With increasing solvent polarity, the S₁-S₀ energy gap decreases leading to a decrease of the fluorescence quantum yield and an increase of the IC rate in full accordance with the energy gap law. Making use of the unexpectedly strong fluorescence solvatochromism of this aromatic hydrocarbon, the validity of the energy gap law could also be demonstrated at the single molecule level. The S₁-S₀ energy gap not only controls the fluorescence lifetime and quantum yield of single molecules but also dictates how these quantities develop during spectral fluctuations. Our results open new avenues into unexplored single molecule photophysics and appear as a promising tool for nanoscale probing of dynamic heterogeneities.

Imaging Fluorescence Blinking of a Mitochondrial Localization Probe: Cellular Localization Probes Turned into Multifunctional Sensors

Mitochondrial membranes and their microenvironments directly influence and reflect cellular metabolic states but are difficult to probe on site in live cells. Here, we demonstrate a strategy, showing how the widely used mitochondrial membrane localization fluorophore 10-nonyl acridine orange (NAO) can be transformed into a multifunctional probe of membrane microenvironments by monitoring its blinking kinetics. By transient state (TRAST) studies of NAO in small unilamellar vesicles (SUVs), together with computational simulations, we found that NAO exhibits prominent reversible singlet-triplet state transitions and can act as a light-induced Lewis acid forming a red-emissive doublet radical. The resulting blinking kinetics are highly environment-sensitive, specifically reflecting local membrane oxygen concentrations, redox conditions, membrane charge, fluidity, and lipid compositions. Here, not only cardiolipin concentration but also the cardiolipin acyl chain composition was found to strongly influence the NAO blinking kinetics. The blinking kinetics also reflect hydroxyl ion-dependent transitions to and from the fluorophore doublet radical, closely coupled to the proton-transfer events in the membranes, local pH, and two- and three-dimensional buffering properties on and above the membranes. Following the SUV studies, we show by TRAST imaging that the fluorescence blinking properties of NAO can be imaged in live cells in a spatially resolved manner. Generally, the demonstrated blinking imaging strategy can transform existing fluorophore markers into multiparametric sensors reflecting conditions of large biological relevance, which are difficult to retrieve by other means. This opens additional possibilities for fundamental membrane studies in lipid vesicles and live cells.

Exciton Dynamics of a Diketo-Pyrrolopyrrole Core for All Low-Lying Electronic Excited States Using Density Functional Theory-Based Methods

Ab initio treatments of interexcited state internal conversion (IC) are more often than not missing from exciton dynamic descriptions, because of their inherent complexity. Here, we define "interexcited state IC" as a same-spin nonradiative transition between states i and j, where i ≠ j ≠ 0. Competing directly with multiexciton processes such as singlet fission or triplet photoupconversion, inclusion of this mechanism in the narrative of molecular photophysics would allow for strategic synthesis of chromophores for more efficient photon-harvesting applications. Herein, we present a robust formalism which can model these rates using density functional theory (DFT)-based methods within the Franck-Condon and Herzberg-Teller regime. Using an unsubstituted diketo-pyrrolopyrrole (DPP) core as a case study, we illustrate the exciton dynamics along the first four excited states for both singlet and triplet manifolds, showing ultrafast same-spin transfer mechanisms due to all excited states, excluding the first triplet level, being in close energetic proximity (within 0.8 eV of each other). The resulting electron same-spin rates outcompete the electron spin-flipping intersystem crossing (ISC) rates, with excitons firmly obeying Kasha's rule as they cascade down from the high-lying excited states toward the lower states. Furthermore, we calculated that only the first singlet excited state displayed a reasonable probability of triplet exciton generation, of ∼40%, with a near-zero chance of the exciton reverting to the singlet manifold once the electron-hole pair are of parallel spin.

Effect of the iodine atom position on the phosphorescence of BODIPY derivatives: a combined computational and experimental study

A new BODIPY derivative (o-I-BDP) containing an iodine atom in the ortho position of the meso-linked phenyl group was prepared. Photophysical and electrochemical properties of the molecule were compared to previously reported iodo BODIPY derivatives, as well as to the non-iodinated analog. While in the case of derivatives featuring iodine substituents in the BODIPY core, efficient population of the triplet state is accompanied by a substantial positive shift of the reduction potential compared to pristine BODIPY, o-I-BDP displays phosphorescence and simultaneously maintains the electrochemical properties of unsubstituted BODIPYs. A theoretical investigation was settled to analyze results and rationalize the influence of iodine position on electronic and photophysical properties, with the purpose of preparing a fully organic phosphorescent BODIPY derivative. TD-DFT and spin-orbit coupling calculations shed light on the subtle effects played by the introduction of iodine atom in different positions of BODIPY.

The combination of skeleton-engineering and periphery-engineering: a design strategy for organic doublet emitters

A series of radicals based on tris(2,4,6-trichlorophenyl)methyl (TTM) were theoretically designed and evaluated by combining skeleton-engineering and periphery-engineering strategies.

Unified Framework for Photophysical Rate Calculations in TADF Molecules

One of the challenges in organic light-emitting diodes research is finding ways to increase device efficiency by making use of the triplet excitons that are inevitably generated in the process of electroluminescence. One way to do so is by thermally activated delayed fluorescence (TADF), a process in which triplet excitons undergo upconversion to singlet states, allowing them to relax radiatively. The discovery of this phenomenon has ensued a quest for new materials that are able to effectively take advantage of this mechanism. From a theoretical standpoint, this requires the capacity to estimate the rates of the various processes involved in the photophysics of candidate molecules, such as intersystem crossing, reverse intersystem crossing, fluorescence, and phosphorescence. Here, we present a method that is able to, within a single framework, compute all of these rates and predict the photophysics of new molecules. We apply the method to two TADF molecules and show that results compare favorably with other theoretical approaches and experimental results. Finally, we use a kinetic model to show how the calculated rates act in concert to produce different photophysical behavior.

Modeling radiative and non-radiative pathways at both the Franck-Condon and Herzberg-Teller approximation level

Here, we present a concise model that can predict the photoluminescent properties of a given compound from first principles, both within and beyond the Franck-Condon approximation. The formalism required to compute fluorescence, Internal Conversion (IC), and Inter-System Crossing (ISC) is discussed. The IC mechanism, in particular, is a difficult pathway to compute due to difficulties associated with the computation of required bosonic configurations and non-adiabatic coupling elements. Here, we offer a discussion and breakdown on how to model these pathways at the Density Functional Theory (DFT) level with respect to its computational implementation, strengths, and current limitations. The model is then used to compute the photoluminescent quantum yield (PLQY) of a number of small but important compounds: anthracene, tetracene, pentacene, diketo-pyrrolo-pyrrole (DPP), and Perylene Diimide (PDI) within a polarizable continuum model. Rate constants for fluorescence, IC, and ISC compare well for the most part with respect to experiment, despite triplet energies being overestimated to a degree. The resulting PLQYs are promising with respect to the level of theory being DFT. While we obtained a positive result for PDI within the Franck-Condon limit, the other systems require a second order correction. Recomputing quantum yields with Herzberg-Teller terms yields PLQYs of 0.19, 0.08, 0.04, 0.70, and 0.99 for anthracene, tetracene, pentacene, DPP, and PDI, respectively. Based on these results, we are confident that the presented methodology is sound with respect to the level of quantum chemistry and presents an important stepping stone in the search for a tool to predict the properties of larger coupled systems.

Donor-acceptor-acceptor-type near-infrared fluorophores that contain dithienophosphole oxide and boryl groups: effect of the boryl group on the nonradiative decay

The use of donor-π-acceptor (D-π-A) skeletons is an effective strategy for the design of fluorophores with red-shifted emission. In particular, the use of amino and boryl moieties as the electron-donating and -accepting groups, respectively, can produce dyes that exhibit high fluorescence and solvatochromism. Herein, we introduce a dithienophosphole P-oxide scaffold as an acceptor-spacer to produce a boryl- and amino-substituted donor-acceptor-acceptor (D-A-A) π-system. The thus obtained fluorophores exhibit emission in the near-infrared (NIR) region, while maintaining high fluorescence quantum yields even in polar solvents (e.g. λ _em = 704 nm and Φ _F = 0.69 in CH₃CN). A comparison of these compounds with their formyl- or cyano-substituted counterparts demonstrated the importance of the boryl group for generating intense emission. The differences among these electron-accepting substituents were examined in detail using theoretical calculations, which revealed the crucial role of the boryl group in lowering the nonradiative decay rate constant by decreasing the non-adiabatic coupling in the internal conversion process. The D-A-A framework was further fine-tuned to improve the photostability. One of these D-A-A dyes was successfully used in bioimaging to visualize the blood vessels of Japanese medaka larvae and mouse brain.

Fast estimation of the internal conversion rate constant in photophysical applications

An efficient method for estimating non-adiabatic coupling matrix elements (NACME) and rate constants for internal conversion (k_IC) is presented. The method, based on Plotnikov's theory, requires only calculations of the electronic wave functions and the corresponding electronic excitation energies. Computationally expensive calculations of the derivatives of the electronic wave function with respect to the nuclear coordinates are avoided. When the main accepting modes of the electronic excitation energy are X-H vibrations, the present method can be used for estimating the efficiency of the energy transfer between donor and acceptor molecules. It can also be used in studies of the influence of hydrogen bonding or solvent effect on fluorescence quenching, in studies of vibronic effects of TADF (thermally activated delayed fluorescence) emitters, and for calculating k_IC. Here, k_IC and NACME are calculated for free-base porhyrin, magnesium porphyrin, azulene, naphthalene, pyrene and fluorenone interacting with a solvent molecule. Reverse k_IC and NACME are further calculated for the T₁→ T₂ transition of dibenzothiophene-S,S-dioxide (PTZ-DBTO2), which is used in TADF applications. Finally, we estimate the efficiency of the energy transfer between two large porphyrinoid dimers.

Efficient enumeration of bosonic configurations with applications to the calculation of non-radiative rates

This work presents algorithms for the efficient enumeration of configuration spaces following Boltzmann-like statistics, with example applications to the calculation of non-radiative rates, and an open-source implementation. Configuration spaces are found in several areas of physics, particularly wherever there are energy levels that possess variable occupations. In bosonic systems, where there are no upper limits on the occupation of each level, enumeration of all possible configurations is an exceptionally hard problem. We look at the case where the levels need to be filled to satisfy an energy criterion, for example, a target excitation energy, which is a type of knapsack problem as found in combinatorics. We present analyses of the density of configuration spaces in arbitrary dimensions and how particular forms of kernel can be used to envelope the important regions. In this way, we arrive at three new algorithms for enumeration of such spaces that are several orders of magnitude more efficient than the naive brute force approach. Finally, we show how these can be applied to the particular case of internal conversion rates in a selection of molecules and discuss how a stochastic approach can, in principle, reduce the computational complexity to polynomial time.

Re-examining the electronic structure of fluorescent tetra-silver clusters in zeolites

In the present study, we have examined the electronic structures related to the fluorescence properties of small Ag42+ complexes encapsulated in zeolites. We find that interaction between Ag42+ and coordinated water molecules, which was previously proposed to be the origin of fluorescence, may not be a sufficient condition by itself. Refinement of the previously used all-silicon-cage model to include framework Al atoms leads to an asymmetric environment, and this alters the electronic structure in favor of fluorescence. We have further examined the substitution of the H2O ligands by NH3, H2S, PH3, CO and CS. Among these systems, Ag42+ binds most strongly to NH3 but the energetics for the H2S and PH3 complexes is also reasonable. The energy of the fluorescent light is related to the energy of the lowest-energy triplet state, and these energies for the H2O, NH3, H2S and PH3 systems span the range of ∼2-3 eV, i.e., roughly the visible range. Thus, the use of different ligands appears to be an attractive means for tailoring the luminescence properties.

Deciphering the unusual fluorescence in weakly coupled bis-nitro-pyrrolo[3,2-b]pyrroles

Electron-deficient π-conjugated functional dyes lie at the heart of organic optoelectronics. Adding nitro groups to aromatic compounds usually quenches their fluorescence via inter-system crossing (ISC) or internal conversion (IC). While strong electronic coupling of the nitro groups with the dyes ensures the benefits from these electron-withdrawing substituents, it also leads to fluorescence quenching. Here, we demonstrate how such electronic coupling affects the photophysics of acceptor-donor-acceptor fluorescent dyes, with nitrophenyl acceptors and a pyrrolo[3,2-b]pyrrole donor. The position of the nitro groups and the donor-acceptor distance strongly affect the fluorescence properties of the bis-nitrotetraphenylpyrrolopyrroles. Concurrently, increasing solvent polarity quenches the emission that recovers upon solidifying the media. Intramolecular charge transfer (CT) and molecular dynamics, therefore, govern the fluorescence of these nitro-aromatics. While balanced donor-acceptor coupling ensures fast radiative deactivation and slow ISC essential for large fluorescence quantum yields, vibronic borrowing accounts for medium dependent IC via back CT. These mechanistic paradigms set important design principles for molecular photonics and electronics.

The non-adiabatic exciton transfer in tetrathiafulvalene chains: a theoretical study of signal transmission in a molecular logic system

Using an exciton as a carrier was examined as a possible solution to the problem of signal transmission between molecular logic gates. A tetrathiafulvalene chain was chosen as a model for a molecular logic system and its distinct logic states were described as excitons located at certain tetrathiafulvalene units. The parameters of the exciton transfer between the units of the chain were studied. The transfer rate between the two adjacent units was calculated using the Plotnikov-Bixon-Jortner theory basing on molecular parameters calculated using TD-DFT. The order of electronic states was studied at the MCQDPT and TD-DFT levels of theory. It was found that certain functional groups in the chain can make exciton transfer faster than its recombination. The exciton can effectively carry a signal through the chain, which in turn can be enlarged and modified.

Fluorescence Quantum Yields in Complex Environments from QM-MM TDDFT Simulations: The Case of Indole in Different Solvents

Fluorescence is commonly exploited to probe microscopic properties. An important example is tryptophan in protein environments, where variations in fluorescence quantum yield, and in absorption and emission maxima, are used as indicators of changes in the environment. Modeling the fluorescence quantum yield requires the determination of both radiative and nonradiative decay constants, both on the potential energy surface of the excited fluorophore. Furthermore, the inclusion of complex environments implies their accurate representation as well as extensive configurational sampling. In this work, we present and test various methodologies based on time-dependent density functional theory (TDDFT) and quantum mechanics/molecular mechanics (QM/MM) dynamics that take all of these requirements into account to provide a quantitative prediction of the effect of the environment on the fluorescence quantum yield of indole, a tryptophan fluorophore. This investigation paves the way for applications to the realistic spectroscopic characterization of the local protein environment of tryptophan from computer simulations.

The influence of spin-orbit coupling, Duschinsky rotation and displacement vector on the rate of intersystem crossing of benzophenone and its fused analog fluorenone: a time dependent correlation function based approach

To understand the effect of structural rigidity or flexibility on the intersystem crossing rate, herein we have adopted a time dependent correlation function based approach, an appropriate method for a harmonic oscillator under Condon approximation. Following this technique, we have developed generalized codes for calculating the rate of intersystem crossing (ISC) both at 0 K and at finite temperature. Since the rate of ISC is a measurable quantity, we have separated the real and imaginary parts of the complex correlation function carefully and eliminated the imaginary part by exploiting the odd nature of this function. Using this simplified method, we have calculated the ISC rate constant (kISC) of two molecules, namely, benzophenone and its fused analog, fluorenone. The calculations clearly elucidate that kISC of benzophenone is 103 times larger compared to that of fluorenone. Interestingly, our analyses reveal that the combined effect of spin-orbit coupling and the number of normal modes could increase the rate of ISC of benzophenone by three orders in comparison to that of fluorenone. Furthermore, the Duschinsky rotation matrix (J) and displacement vectors (D) could influence the rate of ISC by one order each, indicating that the overall rate of ISC of benzophenone could have been 105 times higher than that of fluorenone if the latter two factors, namely, J and D have practically no impact on the rate of ISC of fluorenone. However, it has been found that albeit J can't alter the rate of ISC of fluorenone, D indeed can change the rate by two orders, thereby keeping the overall ratio of the rate of ISC of benzophenone and fluorenone as 103. The present study elucidates that none of the above mentioned factors alone can explain the relative rate of ISC of the studied systems; rather a complex interplay between all these factors makes the rate of ISC of benzophenone 103 times higher than that of fluorenone.

First-principles calculations of anharmonic and deuteration effects on the photophysical properties of polyacenes and porphyrinoids

A new method for calculating internal conversion rate constants (k[combining low line]IC), including anharmonic effects and using the Lagrangian multiplier technique, is proposed. The deuteration effect on k[combining low line]IC is investigated for naphthalene, anthracene, free-base porphyrin (H2P) and tetraphenylporphyrin (H2TPP). The results show that anharmonic effects are important when calculating k[combining low line]IC for transitions between electronic states that are energetically separated (ΔE) by more than 20 000-25 000 cm-1. Anharmonic effects are also important when ΔE < 20 000-25 000 cm-1 and when the accepting modes are X-H stretching vibrations with a frequency larger than 2000 cm-1. The calculations show that there is mixing between the S1 and S2 states of naphthalene induced by non-adiabatic interactions. The non-adiabatic interaction matrix element between the S1 and S2 states is 250 cm-1 and 50 cm-1 for the normal and fully deuterated naphthalene structure and this difference significantly affects the estimated fluorescence quantum yield. Besides aromatic hydrocarbons H2P and H2TPP, the k[combining low line]IC rate constant is also calculated for pyrometene (PM567) and tetraoxa[8]circulene (4B) with a detailed analysis of the effect of the vibrational anharmonicity.

Widely Electronically Tunable 2,6-Disubstituted Dithieno[1,4]thiazines-Electron-Rich Fluorophores Up to Intense NIR Emission

2,6-Difunctionalized dithieno[1,4]thiazines were efficiently synthesized by (pseudo)five- or (pseudo)three-component one-pot processes based on lithiation-electrophilic trapping sequences. As supported by structure-property relationships, the thiophene anellation mode predominantly controls the photophysical and electrochemical properties and the electronic structures (as obtained by DFT calculations). From molecular geometries and redox potentials to fluorescence quantum yields in solution, the interaction of the dithieno[1,4]thiazine-core with the substituents causes striking differences within the series of regioisomers. Most interestingly, strong acceptors introduced in anti-anti dithieno[1,4]thiazines nearly induce a planarization of the ground-state geometry and a highly intense NIR fluorescence (ΦF =0.52), whereas an equally substituted syn-syn dithieno[1,4]thiazine exhibits a much stronger folded molecular structure and fluoresces poorly (ΦF =0.01). In essence, electrochemical and photophysical properties of dithieno[1,4]thiazines can be tuned widely and outscore the compared phenothiazine with cathodically shifted oxidation potentials and redshifted and more intense absorption bands.

Comparing Reaction Routes for 3(RO···OR') Intermediates Formed in Peroxy Radical Self- and Cross-Reactions

Organic peroxy radicals (RO₂) are key intermediates in the chemistry of the atmosphere. One of the main sink reactions of RO₂ is the recombination reaction RO₂ + R'O₂, which has three main channels (all with O₂ as a coproduct): (1) R_-H═O + R'OH, (2) RO + R'O, and (3) ROOR'. The RO + R'O "alkoxy" channel promotes radical and oxidant recycling, while the ROOR' "dimer" channel leads to low-volatility products relevant to aerosol processes. The ROOR' channel has only recently been discovered to play a role in the gas phase. Recent computational studies indicate that all of these channels first go through an intermediate complex ¹(RO···³O₂···OR'). Here, ³O₂ is very weakly bound and will likely evaporate from the system, giving a triplet cluster of two alkoxy radicals: ³(RO···OR'). In this study, we systematically investigate the three reaction channels for an atmospherically representative set of RO + R'O radicals formed in the corresponding RO₂ + R'O₂ reaction. First, we systematically sample the possible conformations of the RO···OR' clusters on the triplet potential energy surface. Next, we compute energetic parameters and attempt to estimate reaction rate coefficients for the three channels: evaporation/dissociation to RO + R'O, a hydrogen shift leading to the formation of R'_-H═O + ROH, and "spin-flip" (intersystem crossing) leading to, or at least allowing, the formation of ROOR' dimers. While large uncertainties in the computed energetics prevent a quantitative comparison of reaction rates, all three channels were found to be very fast (with typical rates greater than 10⁶ s^-1). This qualitatively demonstrates that the computationally proposed novel RO₂ + R'O₂ reaction mechanism is compatible with experimental data showing non-negligible branching ratios for all three channels, at least for sufficiently complex RO₂.

Is either direct photolysis or photocatalysed H-shift of peroxyl radicals a competitive pathway in the troposphere?

Peroxyl radicals (RO O . ) are key intermediates in atmospheric chemistry, with relatively long lifetimes compared to most other radical species. In this study, we use multireference quantum chemical methods to investigate whether photolysis can compete with well-established RO O . sink reactions. We assume that the photolysis channel is always RO O . + hν => RO + O(³P). Our results show that the maximal value of the cross-section for this channel is σ = 1.3 × 10^-18 cm² at 240 nm for five atmospherically representative peroxyl radicals: CH₃O O . , C(O)HCH₂O O . , CH₃CH₂O O . , HC(O)O O . and CH₃C(O)O O . . These values agree with experiments to within a factor of 2. The rate constant of photolysis in the troposphere is around 10^-5 s^-1 for all five RO O . . As the lifetime of peroxyl radicals in the troposphere is typically less than 100 s, photolysis is thus not a competitive process. Furthermore, we investigate whether or not electronic excitation to the first excited state (D₁) by infrared radiation can facilitate various H-shift reactions, leading, for example, in the case of CH₃O O . to formation of O . H and CH₂O or HO O . and CH₂ products. While the activation barriers for H-shifts in the D₁ state may be lower than in the ground state (D₀), we find that H-shifts are unlikely to be competitive with decay back to the D₀ state through internal conversion, as this has a rate of the order of 10¹³ s^-1 for all studied systems.

Photophysical properties of the triangular [Au(HNCOH)]3 complex and its dimer

Radiative and non-radiative rate constants have been calculated for cyclic trinuclear gold(i) complexes within the Herzberg–Teller approximation.

Structure, stability and electronic properties of one-dimensional tetrathia- and tetraselena[8]circulene-based materials: a comparative DFT study

Computations reveal how the electronic and optical properties can be controlled in nanostructures.