Solvatochromic effect on photophysical properties of Quinoxalin-2(1H)-one and 3-Benzylquinoxalin-2(1H)-one

Quinoxalin-2(1H)-one and its derived 3-Benzylquinoxalin-2(1H)-one were synthesized and characterized by UV–visible spectroscopy. The changes displayed by the photophysical properties of these molecules in different solvents can be explained in terms of a sum of dielectric polarity and hydrogen bonding effects taking part in the stabilisation of the structure. 3-Benzylquinoxalin-2(1H)-one exhibits two fluorescence emission bands (F _a and F _n) in very polar solvents and one band (F _n) in low polar solvents. These bands are assigned on the basis of the absorption and emission solvent effect. The abnormal fluorescence (F _a) observed in very polar solvents is attributed to an intermolecular interaction between solute and solvent molecules in the excited state (exciplex formation).     

Quantum-Chemical Simulation of the Solvent Effect on Spontaneous Emission of Singlet Oxygen

A molecular simulation of the solvent effect on radiative rate constant k _r of singlet oxygen is carried out. This study included a search for the most probable conformations of the complexes of molecules of singlet oxygen and ten solvents and calculation of dipole moments M of transitions a¹Δ _g –b¹Σ _g ⁺ (M _a–b ) and a¹Δ _g –X³Σ _g ^- (M _a–X ) of the oxygen molecule for them. Averaging of M _a–b by conformations, taking into account the probability of their formation for complexes without atoms with a large atomic number (Cl, S), yields values that, as a rule, correlate well with the behavior of k _r in the experiment. Taking into account the possibility of decreasing the distance (compared to equilibrium) between molecules in a collision complex at room temperature made it possible to achieve satisfactory agreement of the calculated and experimental data also for complexes with CCl₄, C₂Cl₄, and CS₂. The obtained data indicate that a number of factors affect k _r . The correlation of k _r with molecular polarizability in a number of cases is due, on the one hand, to its effect on the strength of dispersion interactions in the complex and, on the other hand, to the fact that it to some extent reflects the position of the upper filled orbitals of the solvent molecule. Both factors affect the degree of mixing of the π orbitals of the singlet oxygen molecule with the orbitals of the solvent molecule, which, as was found earlier, facilitates the activation of the a¹Δ _g –b¹Σ _g ⁺ transition and the borrowing of its intensity by the a¹Δ _g –X³Σ _g ^- transition.     

β-Phosphorus Hyperfine Coupling Constant in Nitroxides: Conformational Effects in 6-Membered Ring Nitroxides

Recently, we reported a significant solvent effect on the phosphorus hyperfine coupling constant a _P in β-phosphorylated 6-membered ring nitroxides (?a _P = 24 G in Org. Biomol. Chem. 2015). Thus, it led us to investigate the effect of solvent for several 6-membered ring nitroxides. Although smaller than mentioned above, a change of 5–7 G in a _P with the polarity of solvent was still observed for these nitroxides. As for other β-phosphorylated nitroxides, a _N increases with the polarity/polarizability π* and the Hydrogen Bond Donating α properties of the solvent whereas a _P exhibits the reverse trends. The change of a _P with the solvent depends a lot on a subtle interplay between the destabilizing steric hindrance due to the bulkiness of the substituents and the stabilizing hyperconjugation interactions SOMO → σ*_C–P between the anti-bonding orbitals of the C–P bond and the SOMO.     

Beiträge zur Fluoreszenz und Energieübertragung in reinen Lösungsmitteln und flüssigen Mischsystemen organischer Szintillatoren

The intensity and the decay time of pure solvents and mixtures of two different solvents with and without fluorescent molecules have been investigated by way of excitation with electron beams and ultraviolet light. In the solutions Anthracene/Benzene and o-o-Diphenol/Benzene the characteristic transfer constanta=1/τ _t ·c has been determined in two different ways. The investigation of the intensity and the decay time of a solution with two solvents in dependence of the ratio of the components at constant concentration of the fluorescent molecules leads to the conclusion, that the energy transfer from solvent to solute via other solvent molecules is insignificant.     

Electronic structure and fluorescent properties of malononitrile-based merocyanines with positive and negative solvatochromism

The behavior of the positions and shapes of the fluorescence bands of di-, tetra-, and hexamethine merocyanine dyes with 3H-indolyliden (dyes 1–3) and benzoimidazolyliden (dyes 4–6) as electron-donating substituents and malononitrile as an electron-accepting substituent is studied by the method of moments in solvents of different polarity. The solvatofluorochromic shifts have been found to be smaller than the solvatochromic shifts not only for negatively solvatochromic merocyanines 4–6, but also for dyes 1–3 whose solvatochromism is positive. For dyes 4–6, cases of a change of the sign of solvatofluorochromism with respect to the sign of solvatochromism are revealed. These nontrivial effects are accounted for by transitions between the polyene and polymethine electronic structures of merocyanines in the fluorescence state S ₁ that occur with increasing medium polarity. In contrast to the absorption spectra of merocyanines 1–3, an increase in the chain length results in an increase in the vinylene shifts in the fluorescence spectra of these dyes, as well as in a decrease in the deviations and in the narrowing of the bands. This is explained by the fact that the electronic structure of these merocyanines in the S ₁ state is closer to that of the ideal polymethine (the cyanine limit) than in the S ₀ state. The fluorescence bands of merocyanines 4–6 are observed to be broader compared to the absorption bands. This broadening is caused by a change in the relation between intermolecular and vibronic interactions during absorption and emission of light. The interactions of these types have a decisive effect on the behavior of the Stokes shifts and fluorescence quantum yields of merocyanines 1–6.     

Nonradiative deactivation of the lowest triplet state of naphthalene and its hydroxy derivatives at 77 K

The validity of an inductive resonance theory of energy transfer from the T ₁→S ₀ transition dipole to overtone vibrations of molecular groups containing H and D atoms is experimentally tested for a series of compounds whose conjugation systems are similar in size. To this end, by using kinetic, spectral, and luminescent methods (measurements of the phosphorescence decay times, phosphorescence spectra, ratios between the quantum yields of phosphorescence and fluorescence at 77 K, total quantum yields of fluorescence at 293 K, and ratios between the quantum yields of fluorescence at 293 and 77 K), the deactivation processes of the lowest excited T ₁ and S ₁ states of seven emitting centers (naphthalene, its hydroxy and dihydroxy derivatives, and their monoanions) in solutions in ethanol-h ₆, ethanol-d ₆, and their 2: 1 mixtures with diethyl ether are studied. For all the compounds studied, the rate constants k _r of the radiative T ₁→S ₀ transition and the changes in the overlap integrals of the spectra of phosphorescence and absorption of overtones of CH stretching vibrations are determined. The rate constants of energy transfer k _dd(CH) from the T ₁→S ₀ transition dipole to the stretching vibrations of the CH bonds are calculated without regard for the changes in the localization and orientation of this transition dipole in the compounds under study. The contribution of an individual CH group k _nr(CH) to the total rate constant of nonradiative deactivation of the T ₁ state averaged over the CH groups of the naphthalene ring system is ascertained. A good correlation between the changes in the constants k _nr(CH) and k _dd(CH) in the series of the hydroxy derivatives of naphthalene is found, which is indicative of the inductive resonance mechanism of the energy degradation of the T ₁ state. The deviations from proportionality between the changes in these constants upon passing from naphthalene to its hydroxy derivatives, which correlate with a marked increase in the radiative constant k _nr of the hydroxy derivatives in comparison with naphthalene, indicate changes in the strength and localization of the T ₁→S ₀ transition dipole moment and in its orientation with respect to the plane of the molecule that occur due to introduction of a heteroatom, oxygen, whose lone pair of electrons enters into conjugation with the πelectrons of the naphthalene ring system.     

Fluorescence and picosecond induced absorption from the lowest singlet excited states of quercetin in solutions and polymer films

The spectroscopic and photophysical properties of the biologically important plant antioxidant quercetin in organic solvents, polymer films of polyvinyl alcohol, and a buffer solution at pH 7.0 are studied by stationary luminescence and femtosecond laser spectroscopy at room temperature and 77 K. The large magnitude of the dipole moment of the quercetin molecule in the excited Franck–Condon state μ _e ^FC = 52.8 C m indicates the dipolar nature of quercetin in this excited state. The transient induced absorption spectra S ₁→S _n in all solvents are characterized by a short-wave band at λ _abs ^max = 460 nm with exponential decay times in the range of 10.0–20.0 ps. In the entire spectral range at times of >100 ps, no residual induced absorption was observed that could be attributed to the triplet–triplet transitions Т ₁ → Т _k in quercetin. In polar solvents, two-band fluorescence was also recorded at room temperature, which is due to the luminescence of the initial enol form of quercetin (~415 nm) and its keto form with a transferred proton (550 nm). The short-wave band is absent in nonpolar 2-methyltetrahydrofuran (2-MTHF). The spectra of fluorescence and fluorescence excitation exhibit a low dependence on the wavelength of excitation and detection, which may be related to the solvation and conformational changes in the quercetin molecule. Decreasing the temperature of a glassy-like freezing quercetin solution in ethanol and 2-MTHF to 77 K leads to a strong increase in the intensity (by a factor of ~100) of both bands. The energy circuits for the proton transfer process are proposed depending on the polarity of the medium. The main channel for the exchange of electronic excitation energy in the quercetin molecule at room temperature is the internal conversion S ₁ ? S ₀, induced by the state with a proton transfer.     

Density functional study of $$\hbox {AgScO}_2$$: Electronic and optical properties

Dielectric relaxation studies of binary (jk) polar mixtures of tetrahydrofuran with N-methyl acetamide, N,N-dimethyl acetamide, N-methyl formamide and N,N-dimethyl formamide dissolved in benzene(i) for different weight fractions (w _{j k} ’s) of the polar solutes and mole fractions (x _j ’s) of tetrahydrofuran at 25 ^°C are attempted by measuring the conductivity of the solution under 9.90 GHz electric field using Debye theory. The estimated relaxation time (τ _{j k} ’s) and dipole moment (μ _{j k} ’s) agree well with the reported values signifying the validity of the proposed methods. Structural and associational aspects are predicted from the plot of τ _{j k} and μ _{j k} against x _j of tetrahydrofuran to arrive at solute–solute (dimer) molecular association upto x _j =0.3 of tetrahydrofuran and thereafter solute–solvent (monomer) molecular association upto x _j =1.0 for all systems except tetrahydrofuran + N,N-dimethyl acetamide.     

Fluorescence quenching of vaporous polycyclic aromatic hydrocarbons by oxygen

The fluorescence quenching by oxygen of vapors of nine polycyclic aromatic hydrocarbons with strongly different oxidation potentials 0.44 eV < E _ox < 1.61 eV (anthracene, 9-methylanthracene, 2-aminoanthracene, 9,10-dibromanthracene, pyrene, chrysene, phenanthrene, fluoranthene, and carbazole) is studied. From the dependences of the fluorescence decay rates and intensities on the oxygen pressure P _O2, the quenching rate constants k _S ^O2 for the excited singlet states S ₁ and the fraction f _S ^O2 of the S ₁ states quenched by oxygen are estimated. At P _O2 = 5 Torr, the k _S ^O2 constants vary from 1.2 × 10⁷ to 3.0 × 10⁵ s^?1 Torr^?1, while the fraction of the quenched excited singlet states changes from 0.1 (fluoranthene) to 0.7 (chrysene) and 0.8 (pyrene). The dependences of k _S ^O2 on the photophysical and electron-donor characteristics of the fluorescing compounds are analyzed. It is shown that, in the gas phase of anthracene and its derivatives, the magnitudes of k _S ^O2 are limited by the rate constants of gas-kinetic collisions k _gk and do not depend on the electron-donor characteristics of fluorophores, while the fraction of quenched states f _S ^O2 changes with the oxidation potential. For compounds with k _S ^O2 < k gk, both the rate constants k _S ^O2 and the fraction of quenched states f _S ^O2 depend on the E _ox of sensitizers, which demonstrates an important role played by the charge-transfer interactions in quenching of the S ₁ states. The dependence of the rate constants k _S ^O2 on the free energy of electron transfer ΔG _et is considered.     

Influence of the polarity of a medium on the photonics of a merocyanine dye with a high quadratic polarizability

The influence of the polarity of a medium on the spectral and luminescent properties of 2-[(2E,4E)-6-(1,3,3-trimethyl-2,3-dihydro-1H-2-indolyliden)-2,4-hexadienyliden]malononitrile (THDM) in solutions and polymer matrices is studied at room temperature under conditions of steady-state and pulsed laser excitation. A large bathochromic shift of the absorption spectra observed upon an increase in the polarity of a solvent is caused by a strong increase in the molecular dipole moment μ due to a transition of molecules from the ground state (μ_g = 7.6 D) to an excited Franck-Condon state (μ^FC = 33.5 D). Based on the solvatochromic data, the quadratic polarizability was calculated to be β = (3.2 ± 0.6) × 10^?28 esu, which is close to the experimentally determined value β_ex = (3.9 ± 0.2) × 10^?28 esu. A strong narrowing of the fluorescence spectra in comparison with the absorption spectra is observed upon an increase in the solvent polarity. This narrowing is explained by a decrease in the bond length alternation parameter and by weakening of vibronic interactions in the singlet excited state. The dynamic solvatofluorochromism of THDM in the picosecond range is caused by reorientations of molecules of the polar environment occurring during a time period consistent with the dielectric relaxation time of these molecules.     

Aussagen der Theorie von Kraichnan für die isotrope hydromagnetische Turbulenz

The theory ofKraichnan is applied to quasi-stationary isotropic hydromagnetic turbulence. The average infinitesimal-impulse-response functionsg(k, τ), g _m (k, τ) and the time-correlationsr(k, τ), r _m (k, τ) are evaluated by the non-local direct-interaction approximation within the inertial range. For the range of ohmic but no viscous dissipation it is found that the magnetic energy spectrumE _m (k) obeys aE(k)k ^?2-law in accordance with results ofGolitsyn andMoffatt.     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. II. Distributions with Heavy Tails

We study the asymptotic structure of the first K largest eigenvalues λ _k,V and the corresponding eigenfunctions ψ(?;λ _k,V ) of a finite-volume Anderson model (discrete Schrödinger operator) \(\mathcal{H}_{V}= \kappa \Delta_{V}+\xi(\cdot)\) on the multidimensional lattice torus V increasing to the whole of lattice ? ^ν , provided the distribution function F(?) of i.i.d. potential ξ(?) satisfies condition ?log(1?F(t))=o(t ³) and some additional regularity conditions as t→∞. For z∈V, denote by λ ⁰(z) the principal eigenvalue of the “single-peak” Hamiltonian κΔ _V +ξ(z)δ _z in l ²(V), and let \(\lambda^{0}_{k,V}\) be the kth largest value of the sample λ ⁰(?) in V. We first show that the eigenvalues λ _k,V are asymptotically close to \(\lambda^{0}_{k,V}\). We then prove extremal type limit theorems (i.e., Poisson statistics) for the normalized eigenvalues (λ _k,V ?B _V )a _V , where the normalizing constants a _V >0 and B _V are chosen the same as in the corresponding limit theorems for \(\lambda^{0}_{k,V}\). The eigenfunction ψ(?;λ _k,V ) is shown to be asymptotically completely localized (as V↑?) at the sites z _k,V ∈V defined by \(\lambda^{0}(z_{k,V})=\lambda^{0}_{k,V}\). Proofs are based on the finite-rank (in particular, rank one) perturbation arguments for discrete Schrödinger operator when potential peaks are sparse.     

A theoretical investigation of the effect of water on the structure and fluorescence spectra of L-tryptophan

Fluorescence spectra of two long-wavelength electron transitions S₀ ← ¹L_b and S₀ ← ¹L_a in uncharged and zwitterionic forms of L-tryptophan (Trp) in aqueous solution and in the complex of Trp with water molecule were calculated using the Frank–Condon approximation. Geometric parameters of Trp in electronically excited states were determined, and the vibrational structure of vibronic spectra was analyzed. It was shown that the relative position of structural fragments of alanine (R-Ala) and indole (R-In) could have a determining effect on the fluorescence and formation of the vibrational structure of electronic spectra. The increase of the rotation angle between the R-Ala and R-In, which depends on the Trp environment, results in the Trp fluorescence originating only from the singlet excited state ¹L_a.     

<Emphasis Type="Italic">nd</Emphasis> scattering at low energies in the two-body potential model

The S-wave phase shift δ(E) for the spin-doublet nd scattering at low energy E is calculated in the framework of the two-body approach. The effective-range-theory formula k cot δ = (1+k²/k ₀ ² )^?1(?1/α+C₂k²+C₄k⁴) is used to obtain approximate analytical results with different potentials. The corresponding coefficients C₂ and C₄ are obtained from our previous calculations of the asymptotic normalization parameter function C _t ² (aκ), where κ is the triton wave number and a is the doublet nd scattering length. The model reasonably describes δ(E), the results being quite sensitive to the choice of the effective nd potential.     

Vibronic-spin-orbit interactions in heterocyclic analogues of fluorene with the N and O heteroatoms

The transition dipole moments P _0n ^s for the transitions from the electronic triplet state ³ B ²(ππ*) to vibrational sublevels of the vibrational out-of-plane modes n of the carbazole and dibenzofuran molecules are calculated. The values of the radiative deactivation rate constant k _rad ^s of the triplet sublevels T ^s are determined along with the components k _SO ^s and k _VSO ^s of this constant, which depend on the intramolecular spin-orbit (SO) and vibronic-spin-orbit (VSO) interaction. It is ascertained that k _rad ^z > k _rad ^y . For different structural units of the molecules (the heteroatom and the carbon atoms of the dibenzene fragment), the effect of the SO coupling on the constant k _VSO～Σ_{s, n} (P _0n ^s )² is studied. A competition between the effects on k _VSO from the SO coupling in the carbon atoms and in the light N and O heteroatoms is revealed. This competition accounts for the weak influence of the heteroatom on this component of the rate constant k _rad in these molecules. It is ascertained that the intensity distribution among the vibronic lines in the phosphorescence spectra of carbazole and dibenzofuran I _0n ～Σs (P _0n ^s )² is different due to the substantially different influence of the N and O heteroatoms on the deactivation of the triplet sublevel T ^y .     

On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v _g is proposed for a wave process with arbitrary dispersion relation ω = ω′(k) + iω″(k). For the monochromatic approximation, a limit expression v _g (k) is obtained. A condition under which v _g (k) takes the form of the Kuzelev–Rukhadze expression [1] dω′(k)/dk is found. In the general case, it appears that v _g (k) is defined not only by the dispersion relation ω(k), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v _g (k) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k′(ω) + ik″(ω) which corresponds to the boundary problem.     

Almost One Bit Violation for the Additivity of the Minimum Output Entropy

In a previous paper, we proved that, in the appropriate asymptotic regime, the limit of the collection of possible eigenvalues of output states of a random quantum channel is a deterministic, compact set K_k,t. We also showed that the set K_k,t is obtained, up to an intersection, as the unit ball of the dual of a free compression norm. In this paper, we identify the maximum of \({\ell^p}\) norms on the set K_k,t and prove that the maximum is attained on a vector of shape (a, b, . . . , b) where a > b. In particular, we compute the precise limit value of the minimum output entropy of a single random quantum channel. As a corollary, we show that for any \({\varepsilon > 0}\), it is possible to obtain a violation for the additivity of the minimum output entropy for an output dimension as low as 183, and that for appropriate choice of parameters, the violation can be as large as \({\log 2 -\varepsilon}\). Conversely, our result implies that, with probability one in the limit, one does not obtain a violation of additivity using conjugate random quantum channels and the Bell state, in dimension 182 and less.     

Branches of zero sound excitations in asymmetric nuclear matter: The dependence on density

Results from calculating zero sound excitations in isospin asymmetric nuclear matter are presented. A polarization operator constructed in the random phase approximations is used in the calculations. Three branches of the complex solutions ω_sτ(k), τ = p,n,np are presented. The type of branch depends on that of the considered branch damping. An imaginary part of the solution corresponds to the damping of collective excitations due to mixing with the background of noninteracting (1) proton particle–hole pairs (ω _sp (k)), (2) neutron particle–hole pairs (ω _sn (k)), and (3) both proton and neutron particle–hole pairs (ω _snp (k)). The behavior of the solutions upon variations in density depends on the value of the asymmetry parameter.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.