Compartmental modeling of reversible intermolecular two-state excited-state processes coupled with rotational diffusion or with added quencher

Analysis of related time-resolved fluorescence measurements can possibly lead to the determination of the kinetic parameters of excited-state processes. A deterministic identifiability analysis on an error-free fluorescence decay data surface has to be executed to verify whether the parameters of a particular model can be determined and may point to the minimal experimental conditions under which this will become possible. In this work, similarity transformation is chosen as an identifiability analysis approach because it also gives the explicit relationships between the true and alternative model parameters. Results are presented for two kinetic models of a reversible intermolecular two-state excited-state process in isotropic environments: (a) with coupled species-dependent rotational diffusion described by Brownian reorientation and (b) with added quencher. For model a, both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation in the latter, are considered. The fluorescence delta-response functions I(parallel)(t) and I(perpendicular)(t), for fluorescence polarized respectively parallel and perpendicular to the electric vector of linearly polarized excitation, are used to define the sum S(t) = I( parallel)(t) + 2 I( perpendicular)(t) and the difference D(t) = I(parallel)(t) - I(perpendicular)(t) function. The identifiability analysis is carried out using the S(t) and D(t) functions. The analysis involving S(t) shows that two physically acceptable possible solutions for the overall rate constants of the excited-state process exist. Inclusion of information from polarized fluorescence measurements on the rotational kinetic behavior contained in D(t) results in the unique set of rate constants and rotational diffusion coefficients when the rotational diffusion coefficients are different. For model b, it is shown that addition of quencher plays formally the same role as rotational diffusion as far as the identification is concerned. When the quenching rate constants are different, the rate constants of a reversible intermolecular two-state excited-state process with added quencher can be uniquely determined.     

Identifiability analysis of models for reversible intermolecular two-state excited-state processes coupled with species-dependent rotational diffusion monitored by time-resolved fluorescence depolarization

A deterministic identifiability analysis of the kinetic model for a reversible intermolecular two-state excited-state process with species-dependent rotational diffusion described by Brownian reorientation is presented. The cases of both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation on interconversion in the latter case, are specifically considered. The identifiability analysis is carried out in terms of compartmental modeling based on the S(t) identical with I( parallel)(t)+2I( perpendicular)(t) and D(t) identical with I( parallel)(t)-I( perpendicular)(t) functions, where I( parallel)(t) and I( perpendicular)(t) are the delta-response functions for fluorescence, polarized, respectively, parallel and perpendicular to the electric vector of linearly polarized excitation. It is shown that, from polarized time-resolved fluorescence data collected at two concentrations of coreactant and three appropriately chosen emission wavelengths, (a) a unique set of rate constants for the overall excited-state process is always obtained by making use of polarized measurements and (b) the rotational diffusion constants and geometrical factors associated with the different anisotropy decay components can be uniquely determined and assigned to each species. The geometrical factors are determined by the absorption and emission transitions in the two rotating species. For spherical rotors, these factors depend directly on the relative orientations of the transition moments, while for cylindrically symmetric rotors they depend on the orientations with respect to each other and to the symmetry axis.     

Compartmental modeling of the fluorescence anisotropy decay of a cylindrically symmetric brownian rotor: Identifiability analysis.

We present the results of the deterministic identifiability analysis based on similarity transformation for models of one-state excited-state events of cylindrically symmetric rotors in isotropic environments undergoing rotational diffusion described by Brownian reorientation. Such an analysis on error-free time-resolved fluorescence (anisotropy) data can reveal whether the parameters of the considered model can be determined. The fluorescence delta-response functions I(parallel)(t) and I(perpendicular)(t), for fluorescence polarized respectively parallel and perpendicular to the electric vector of linearly polarized excitation, are used to construct, in convenient matrix form, expressions of the sum S(t) = I(parallel)(t) + 2I(perpendicular)(t), the difference D(t) = I(parallel)(t) - I(perpendicular)(t), and the time-resolved fluorescence anisotropy r(t) = D(t)/S(t). The identifiability analysis of r(t) demonstrates that the rotational diffusion coefficients D(parallel) and D(perpendicular) for rotation respectively about and perpendicular to the symmetry axis can be uniquely resolved. However, the polar and azimuthal angles defining the absorption and emission transition moments in the molecular reference frame are not individually identifiable. Nevertheless, the difference between the polar angles of these transition moments is uniquely determined.     

Ultrafast structural rearrangements in the MLCT excited state for copper(I) bis-phenanthrolines in solution

Ultrafast excited-state structural dynamics of [Cu(I)(dmp)(2)](+) (dmp = 2,9-dimethyl-1,10-phenanthroline) have been studied to identify structural origins of transient spectroscopic changes during the photoinduced metal-to-ligand charge-transfer (MLCT) transition that induces an electronic configuration change from Cu(I) (3d(10)) to Cu(II) (3d(9)). This study has important connections with the flattening of the Franck-Condon state tetrahedral geometry and the ligation of Cu(II)* with the solvent observed in the thermally equilibrated MLCT state by our previous laser-initiated time-resolved X-ray absorption spectroscopy (LITR-XAS) results. To better understand the structural photodynamics of Cu(I) complexes, we have studied both [Cu(I)(dmp)(2)](+) and [Cu(I)(dpp)(2)](+) (dpp = 2,9-diphenyl-1,10-phenanthroline) in solvents with different dielectric constants, viscosities, and thermal diffusivities by transient absorption spectroscopy. The observed spectral dynamics suggest that a solvent-independent inner-sphere relaxation process is occurring despite the large amplitude motions due to the flattening of the tetrahedral coordinated geometry. The singlet fluorescence dynamics of photoexcited [Cu(I)(dmp)(2)](+) were measured in the coordinating solvent acetonitrile, using the fluorescence upconversion method at different emission wavelengths. At the bluest emission wavelengths, a prompt fluorescence lifetime of 77 fs is attributed to the excited-state deactivation processes due to the internal conversion and intersystem crossing at the Franck-Condon state geometry. The differentiation between the prompt fluorescence lifetime with the tetrahedral Franck-Condon geometry and that with the flattened tetrahedral geometry uncovers an unexpected ultrafast flattening process in the MLCT state of [Cu(I)(dmp)(2)](+). These results provide guidance for future X-ray structural studies on ultrafast time scale, as well as for synthesis toward its applications in solar energy conversion.     

Controllability and observability of the photophysical system of intermolecular two-state excited-state processes

In this report, we focus on the consequences of controllability and observability on the number of distinct exponential terms in the fluorescence decay and on the identifiability analysis of the photophysical model of intermolecular two-state excited-state processes. Controllability and observability prove to be useful concepts in photophysics for exploring methodically the conditions under which intermolecular two-state excited-state processes lead to single-exponential fluorescence delta-response functions. A detailed discussion on the distinction of the possible origins of monoexponential fluorescence decays is presented. We also show that the similarity transformation approach to identifiability leads to erroneous conclusions concerning which model parameters can be identified if this photophysical system is not controllable or not observable. The results obtained for this relatively simple photophysical system can be extended in a systematic way to more complicated photophysical models.     

Absorption and emission study of 2',7'-difluorofluorescein and its excited-state buffer-mediated proton exchange reactions

2',7'-Difluorofluorescein (Oregon Green 488) is a new fluorescein-based dye, which has found many applications, above all in biochemistry and neurosciences, and its use has become very popular in the last years. In recent years, we have been investigating the excited-state proton exchange reactions of fluorescein and the effect of suitable proton acceptors and donors which promote these reactions. The excited-state proton transfer reactions may appreciably influence the fluorescence results when using these dyes. We present steady-state emission evidence that acetate buffer species promote an excited-state proton transfer between neutral, monoanionic, and dianionic forms of 2',7'-difluorofluorescein. The time course of the excited species in this reaction was characterized through time-resolved fluorescence measurements, and the kinetics of the reaction was solved by using the global compartmental analysis. A previous identifiability study on the compartmental system set the conditions to design the fluorescence decay surface. This is the first experimental system, studied within this kinetic model, solved under identifiability conditions through global compartmental analysis. The recovered rate constant values for deactivation were 2.94 x 10(8) s(-1) for the monoanion and 2.47 x 10(8) s(-1) for the dianion, whereas the rate constant values of the buffer-mediated excited-state reaction were 9.70 x 10(8) and 1.79 x 10(8) M(-1) s(-1) for the deprotonation and protonation, respectively. With these values, a pK(a) = 4.02 was obtained. In this work, we additionally provide an absorption study, including acid-base equilibria, determination of ground-state pK(a) values (1.02, 3.61, and 4.69), and recovery of molar absorption coefficients of every prototropic species, including absorption and NMR evidence for the existence of three tautomers in neutral species. Steady-state emission spectra of 2',7'-difluorofluorescein in aqueous solution are also described, where the strong photoacid behavior of the cation is noteworthy.     

Substituent effects on the rate constants for the photo-Claisen rearrangement of allyl aryl ethers

The photochemistry of 11 substituted allyl 4-X- and 3-X-aryl ethers 3 (ArOCH2-CH=CH2) has been examined in both methanol and cyclohexane as solvents. The ethers react by the photo-Claisen rearrangement to give allyl substituted phenols as the major primary photoproducts, as expected from the well-established radical pair mechanism. The excited singlet state properties (absorption spectra, fluorescence spectra, fluorescence quantum yields, and singlet lifetimes) were compared with a parallel set of unreactive 4-X- and 3-X-anisoles 4. The excited-state properties of three substituted 4-X-aryl 4-(1-butenyl) ethers 14 (ArOCH2CH2-CH=CH2) were also examined. The model compounds 4 and the reactive allyl ethers 3 have essentially identical rate constants for the excited-state processes with the exception of, the rate constant for homolytic cleavage from S(1) of the allyl ethers to give the radical pair. The difference between the fluorescence quantum yields and/or singlet lifetimes for 3 and 4 were used to obtain values of for all of the allyl ethers. These values exhibit a large substituent effect, spanning almost 2 orders of magnitude with electron-donating groups (CH3O, CH3) accelerating the reaction and electron-withdrawing ones (CN, CF3) slowing it down. The parallel range of rate constants observed in both methanol and cyclohexane indicates that ion pairs are not important intermediates in these rearrangements. Quantum yields of reaction (Phi(r)) for several of the more reactive ethers demonstrate that neither these values nor rate constants of reaction derived from them are reliable measures of the actual excited-state process. In fact, the values are significantly lower than the ones, indicating that the radical pairs undergo recombination to generate starting material. Finally, the rate constants were found to parallel a trend for the change in bond dissociation energy (deltaBDE) for the O-C (allyl) bond of the allyl ethers, indicating that other possible substituent effects are of minor importance.     

2',7'-Difluorofluorescein excited-state proton reactions: correlation between time-resolved emission and steady-state fluorescence intensity

The presence of excited-state buffer-mediated proton exchange reactions influences the steady-state fluorescence signals from dyes in solution. Since biomolecules in general have some chemical groups that can act as proton acceptors/donors and are usually dissolved in buffer solutions which can also behave as appropriate proton acceptors/donors, the excited-state proton exchange reactions may result in distorted steady-state fluorescence signals. In a previous paper (J. Phys. Chem. A 2005, 109, 734-747), we evaluated kinetic and other pertinent parameters for the excited-state proton reactions of the prototropic forms of 2',7'-difluorofluorescein (Oregon Green 488, OG488), recording a fluorescence decay surface at different pH values and acetate buffer concentrations, analyzed by means of global compartmental analysis. In this article we use the rate constants and the corrected pre-exponential factors from the previously recorded fluorescence decay traces to simulate the decay times and associated pre-exponentials at different acetate buffer concentrations and constant pH and compare these theoretically calculated values with new experimental data. We also calculate the steady-state fluorescence intensity vs pH and vs acetate buffer concentration (at constant pH) and compare these calculated emission values with the experimental data previously published. The agreement between the experimental and simulated data is excellent.     

Fluorescence quenching of naphthols by Cu2+ in micelles

Effect of the micelles of anionic, cationic and non-ionic surfactants on the fluorescence quenching of 1- and 2-naphthols has been studied in the presence of copper ion. The excited state lifetime, dynamic and static quenching constants for these systems have been determined. Fluorescence quenching in water and SDS micelle is due to the collision of the fluorophore with the quencher with a small static component. The negatively charged naphtholate ions in the excited state are quenched with significantly higher rates than the neutral naphthol molecules, which are located further inside the mesophase. CTAB micelle is less effective than the SDS micelle for fluorescence quenching. The effect of CTAB on water-assisted excited-state deprotonation has been investigated in the presence of ZnSO₄. For TX-100 micelle there is negligible quenching even at higher concentration of the quencher.     

Spectroscopic and photophysical properties of hexanuclear rhenium(III) chalcogenide clusters

The electronic, vibrational, and excited-state properties of hexanuclear rhenium(III) chalcogenide clusters based on the [Re(6)(mu(3)-Q)(8)](2+) (Q = S, Se) core have been investigated by spectroscopic and theoretical methods. Ultraviolet or visible excitation of [Re(6)Q(8)](2+) clusters produces luminescence with ranges in maxima of 12 500-15 100 cm(-)(1), emission quantum yields of 1-24%, and emission lifetimes of 2.6-22.4 microseconds. Nonradiative decay rate constants and the luminescence maxima follow the trend predicted by the energy gap law (EGL). Examination of 24 clusters in solution and 14 in the solid phase establish that exocluster ligands engender the observed EGL behavior; clusters with oxygen- or nitrogen-based apical ligands achieve maximal quantum yields and the longest lifetimes. The excited-state decay mechanism was investigated by applying nonradiative decay models to temperature-dependent emission experiments. Solid-state Raman spectra were recorded to identify vibrational contributions to excited-state deactivation; spectral assignments were enabled by normal coordinate analysis afforded from Hartree-Fock and DFT calculations. Excited-state decay is interpreted with a model where normal modes largely centered on the [Re(6)Q(8)](2+) core induce nonradiative relaxation. Hartree-Fock and DFT calculations of the electronic structure of the hexarhenium family of compounds support such a model. These experimental and theoretical studies of [Re(6)Q(8)](2+) luminescence provide a framework for elaborating a variety of luminescence-based applications of the largest series of isoelectronic clusters yet discovered.     

Compartmental analysis in photophysics: fluorescence decay kinetics and identifiability analysis of a model for successive complexation

The triple-exponential fluorescence delta-response function is derived for the photophysical model of successive complexation between ligand and analyte. Initially, a complex with 1:1 stoichiometry between ligand and analyte is formed. Further binding leads to a complex with two analyte molecules per ligand molecule. We show that this model is uniquely identifiable. This means that all deactivation and exchange rate constants in the excited state and all spectral parameters associated with photoexcitation and fluorescence emission can be uniquely determined. The issues of controllability and observability are discussed for this photophysical system. The conditions, under which a non-controllable or non-observable system is obtained, are described.     

Another look at magic-angle-detected fluorescence and emission anisotropy decays in fluorescence microscopy

It is shown that in contrast to a traditional fluorescence spectroscopy with the parallel beams of light, in which the kinetic fluorescence decays are collected at the so-called magic-angle of thetamag=54.7 degrees, in the fluorescence microscopy, the value of the magic-angle depends on the numerical aperture (NA) of a microscope objective and on the refractive index (n) of an immersion liquid used. Two methods enabling the determination of the magic-angle values corresponding to different values of NA/n, are discussed. It is shown that thetamag changes from a value of 54.7 degrees at the NA/n-->0, to a value of 45 degrees with NA/n-->1. Also in contrast to a traditional fluorescence spectroscopy, in the fluorescence microscopy the term I parallel(t)+2I perpendicular (t) does not represent the total fluorescence intensity Itot(t), because the resulting fluorescence decay I parallel(t)+2I perpendicular (t) is contributed by the dynamic evolution of excited fluorophores. A correctly defined total fluorescence intensity solely represents the kinetic evolution of excited fluorophores, and in the fluorescence microscopy it equals Itot(t)=3Imag(t), where Imag(t) represents the fluorescence intensity detected at thetamag corresponding to a particular NA/n value. If the correct (true) decay of Itot(t) is substituted into the denominator in the expression for the emission anisotropy r(t), r(t) is a (multi)exponential function of time and it accounts for the high-aperture excitation-detection conditions.     

Correlation between photophysical parameters and gold-gold distances in gold(I) (4-pyridyl)ethynyl complexes

The systematic analysis of the luminescence of a series of alkynyl gold derivatives with general formulas [(diphos)(AuC≡Cpy)(2)] (diphosphane =2,2'-bis(diphenylphosphanyl)propane or dppip (1), bis(diphenylphosphanyl)acetylene or dppa (2), 1,2-bis(diphenylphosphanyl)ethane or dppe (3) and 1,4-bis(diphenylphosphanyl)butane or dppb, (4), has shown a straightforward correlation between the Au(I)···Au(I) distance and the emission quantum yields and decaytimes. The analysis of the decaytimes, quantum yields and thus, the corresponding calculated rate constants demonstrated the existence of a correlation between Au(I)···Au(I) distance and the radiative rate constant for the deactivation of the emissive triplet states. It was concluded that the increased emission of these compounds results from the increase in spin-orbit coupling that favors the spin forbidden transition to the singlet ground state.     

Investigations of the EPR parameters for Sm3+ ions in KY3F10 and LiYF4 crystals

In this paper, we calculate the EPR parameters (g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) of rare earth ion Sm3+ in fluoride crystals KY3F10 and LiYF4 from the perturbation formulas of EPR parameters for a 4f5 ion in tetragonal symmetry. In these formulas, the crystal-field J-mixing of the first and second excited-state multiplets 6H(7/2) and 6H(9/2) into the ground state multiplet 6H(5/2), the mixtures among the states with the same J value via spin-orbit coupling interaction and the interactions between the ground Kramers doublet Gammagamma and the same irreducible representation as Gammagamma in other 11 Kramers doublets Gammax within 6HJ (J=5/2, 7/2, 9/2) states via crystal-field and orbital angular momentum (or hyperfine structure) are considered. The calculated results (which are in agreement with the observed values) are discussed.     

Defect model and EPR parameters for the tetragonal Yb3+ center in KTaO3 crystal

The defect model of the tetragonal Yb3+ (at K+ site) center in KTaO3 crystal is suggested, i.e., Yb3+ ion does not occupy the ideal K+ site, but is displaced by an amount DeltaZ along one of 100 axes because of the much smaller ionic radius of Yb3+ compared with that of the replaced K+. Based on the defect model, the EPR parameters (g factors g(parallel), g(perpendicular) and hyperfine structure constants 171A parallel, 171A perpendicular, 173A parallel, 173A perpendicular) are calculated by diagonalizing the 14 x 14 complete energy matrix. The calculated values are in agreement with the observed values and the off-center displacement DeltaZ (approximately 0.2 angstroms) is estimated from the calculations. These results are discussed.     

Photophysics of reduced silicon tetraphenylporphyrin

The contrasting photophysical properties of two silicon (IV) tetraphenylporphyrins, Si(TPP)(py)2 and Si(TPP)Cl2, have been investigated using static absorption and fluorescence spectroscopy and ultrafast transient absorption measurements. The parent Si(TPP)Cl2, in which the porphyrin macrocycle has its normal 2- oxidation state, has a fluorescence yield of 0.027, and a lifetime of 1.8 ns for the lowest excited singlet state. In marked contrast, the reduced, anti-aromatic complex Si(TPP)(py)2, with the macrocycle in the 4- oxidation state, has an extremely low fluorescence yield (< or =0.0004) and a 750-fold shorter excited-state lifetime (2.4 ps) in the same solvent (pyridine). The rapid deactivation of photoexcited Si(TPP)(py)2 to the ground state is likely associated with its ruffled structure and the presence of low-energy excited states in its electronic manifold.     

Proton-Coupled Electron Transfer between 4-Cyanophenol and Photoexcited Rhenium(I) Complexes with Different Protonatable Sites

Two rhenium(I) tricarbonyl diimine complexes, one of them with a 2,2'-bipyrazine (bpz) and a pyridine (py) ligand in addition to the carbonyls ([Re(bpz)(CO)(3)(py)](+)), and one tricarbonyl complex with a 2,2'-bipyridine (bpy) and a 1,4-pyrazine (pz) ligand ([Re(bpy)(CO)(3)(pz)](+)) were synthesized, and their photochemistry with 4-cyanophenol in acetonitrile solution was explored. Metal-to-ligand charge transfer (MLCT) excitation occurs toward the protonatable bpz ligand in the [Re(bpz)(CO)(3)(py)](+) complex while in the [Re(bpy)(CO)(3)(pz)](+) complex the same type of excitation promotes an electron away from the protonatable pz ligand. This study aimed to explore how this difference in electronic excited-state structure affects the rates and the reaction mechanism for photoinduced proton-coupled electron transfer (PCET) between 4-cyanophenol and the two rhenium(I) complexes. Transient absorption spectroscopy provides clear evidence for PCET reaction products, and significant H/D kinetic isotope effects are observed in some of the luminescence quenching experiments. Concerted proton-electron transfer is likely to play an important role in both cases, but a reaction sequence of proton transfer and electron transfer steps cannot be fully excluded for the 4-cyanophenol/[Re(bpz)(CO)(3)(py)](+) reaction couple. Interestingly, the rate constants for bimolecular excited-state quenching are on the same order of magnitude for both rhenium(I) complexes.     

Kinetics and equilibria of proton exchange in the lowest excited singlet states of 8-methoxyquinoline and 8-methoxyquinaldine: analysis of some complex fluorimetric titration curves

The determination of the rate constants for proton exchange in the lowest excited singlet states of 8-methoxyquinoline and 8-methoxyquinaldine from the pH dependences of their fluorescence spectra is complicated by overlap of the spectra of the conjugate acids and bases of both compounds and by the enhancement of 8-methoxyquinoline fluorescence at high pH by a process apparently unrelated to proton exchange. The fluorimetric titration data are analyzed in ways which compensate for these difficulties and the kinetic parameters of excited-state proton exchange determined. Qualitative relationships between the parameters of excited-state proton exchange, electronic structure and steric factors are considered.     

Fine tuning the energetics of excited-state intramolecular proton transfer (ESIPT): white light generation in a single ESIPT system

Using 7-hydroxy-1-indanone as a prototype (I), which exhibits excited-state intramolecular proton transfer (ESIPT), chemical modification has been performed at C(2)-C(3) positions by fusing benzene (molecule II) and naphthalene rings, (molecule III). I undergoes an ultrafast rate of ESIPT, resulting in a unique tautomer emission (λ(max) ～530 nm), whereas excited-state equilibrium is established for both II and III, as supported by the dual emission and the associated relaxation dynamics. The forward ESIPT (normal to proton-transfer tautomer species) rates for II and III are deduced to be (30 ps)(-1) and (22 ps)(-1), respectively, while the backward ESIPT rates are (11 ps)(-1) and (48 ps)(-1). The ESIPT equilibrium constants are thus calculated to be 0.37 and 2.2 for II and III, respectively, giving a corresponding free energy change of 0.59 and -0.47 kcal/mol between normal and tautomer species. For III, normal and tautomer emissions in solid are maximized at 435 and 580 nm, respectively, achieving a white light generation with Commission Internationale de l'Eclairage (CIE) (0.30, 0.27). An organic light-emitting diode based on III is also successfully fabricated with maximum brightness of 665 cd m(-2) at 20 V (885 mA cm(-2)) and the CIE coordinates of (0.26, 0.35). The results provide the proof of concept that the white light generation can be achieved in a single ESIPT system.