Polarization of phosphorescence transitions and probabilities of intramolecular nonradiative deactivation of the lowest triplet state of aromatic molecules

This study continues the experimental testing of the validity of the inductive resonance theory of dipole-dipole energy transfer from the T ₁→S ₀ transition dipole to stretching vibrations of intramolecular CH bonds of naphthalene and its hydroxy derivatives. To this end, in the series of compounds under study, the range of variation of the geometrical parameter [Φ(CH)]² of the Förster theory, which accounts for the mutual orientation of the energy donor and acceptor, is estimated. Preliminarily, the angles between the transition dipole moments of the radiative and absorptive electronic transitions (T ₁→S ₀ and S ₀→S ₁; T ₁→S ₀ and S ₀→S ₂; S ₁→S ₀ and S ₀ →S ₁; and S ₁→S ₀ and S ₀→S ₂) are measured at 77 K by the method of polarization photoselection. From the polarization measurements, the angles between the phosphorescence transition dipole moment and the plane of a molecule are determined. It was found that, upon passage from naphthalene to its β derivatives, the orientation of the dipole moment of the radiative T ₁→S ₀ transition relative to the plane of a molecule markedly changes, with the in-plane component of the dipole moment being increased by an order of magnitude. The experimentally determined rate constants of nonradiative deactivation of the T ₁ state averaged over the CH groups of the naphthalene ring system, k _nr(CH), are compared with the rate constants [Φ(CH)]² of the inductive resonance energy transfer from the dipole of the T ₁→S ₀ transition to the dipole of the CH vibrations polarized in the plane of a molecule, calculated with regard to the orientational factor [Φ(CH)]². This comparison showed that, in the series of compounds under study, a change in the orientation of the dipole moment of the radiative T ₁→S ₀ transition relative to the plane of a molecule does not affect the rate of the nonradiative T ₁?S ₀ transition. This inference is confirmed by the absence of a correlation between the rate constants k _dd(CH) calculated by us (with regard to [Φ(CH)]²) and the well-known rate constants k _nr(CH) of individual sublevels of the T ₁ state measured at T≤1.35 K for a number of organic molecules. The possible sources of discrepancy between the experimental data that k _nr(CH) is independent of [Φ(CH)]² and the predictions of the theory are considered. A conclusion is made that the electronic-vibrational energy transfer between electric dipoles is the most probable mechanism of the T ₁?S ₀ transitions, but the rate constant of the dipole-dipole energy transfer upon interaction of the electronic and vibrational dipoles in a molecule does not depend on their orientations.     

Spin-orbit interactions in heterocyclic analogues of fluorene

For carbazole, dibenzofuran, and dibenzothiophene—heterocyclic analogues of fluorene containing N-H, O, and S groups, respectively—the transition dipole moments P ₀₀ ⁱ for the transitions ³ B ₂→S ₀ and ³ A ₁→S ₀ from the sublevels i=z, y, x of the triplet electronic ππ* states, which are caused by intramolecular spin-orbit (SO) interactions, are calculated. The effect that the SO coupling between the S ₀ state and highest triplet states has on the calculation results is considered. The effects exerted on the value of P ₀₀ ⁱ by such specific features of the molecular structure as the position of a heteroatom on the symmetry axis, its valence, and different constants of SO coupling in heteroatoms are discussed. The reason for the weak influence of the quantity ?_HA on the rate constant of radiative deactivation of the lowest T state is ascertained.     

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.     

A nonradiative intersystem crossing <Emphasis Type="Italic">S</Emphasis>(ππ*) ↝ <Emphasis Type="Italic">T</Emphasis>(ππ*) transition in dibenzo-<Emphasis Type="Italic">p</Emphasis>-dioxin

The probability of the nonradiative S-T intersystem crossing in dibenzo-p-dioxin is theoretically studied using a model for the vibronically induced spin-orbit coupling between electronic states and taking into account all out-of-plane vibrational modes. Several symmetry variants for the lowest S ₁(ππ*) singlet state are considered. In the case of g symmetry of this state, a provision is made for the possibility of its vibronic coupling with the nearest dipole-active singlet ¹ B _2u ππ* state. The rate constants K _ST of the S ₁ ? T(ππ*) transitions to the T ₁(³ B _3g ) state are estimated taking into account several intermediate triplet T _m (ππ*) states of g and u symmetry. For different symmetry types of the S ₁ state, the effect of K _ST on the fluorescence quantum yield ?_fl is discussed. The ¹ B _3g symmetry state is found to be the lowest S ₁ state. It is found that the main contribution to K _ST is made by the S ₁(¹ B _3g ) ? T ₄(³ A _g ) transition.     

Effect of the orbital structure and symmetry of electronic states on nonradiative <Emphasis Type="Italic">S-T</Emphasis> intersystem crossing: Dibenzofuran

The nonradiative S-T intersystem crossing S ₁(ππ*) ? T ₁(ππ*) in dibenzofuran (DB(O)) molecules has been theoretically investigated within the model of vibronically induced spin-orbit (VISO) coupling of electronic states, where the vibronic perturbation takes into account all out-of-plane vibrational modes of a molecule. It is established that the S-T intersystem crossing S ₁(¹ A ₁) ? T ₁(³ B ₂) involves also the intermediate (T _m )T ₂(³ A ₁) and T ₃(³ B ₂) triplet states. The calculated rate constant K _ST = (4.5–4.7) × 10⁷s^?1 of the nonradiative transition is in agreement with the known experimental data. The manifestation of approximate (belonging to the D _2h group) symmetry of singlet and triplet molecular states in VISO couplings has been studied. An effect of the heavy (oxygen) atom of a DB(O) molecule on K _ST is established.     

Fine-structure phosphorescence and radiative deactivation of the lowest triplet states in the most toxic dioxins

The transition dipole moments for the transition T₁(ππ*) → S₀ to vibrational energy levels of the nontotally symmetric vibrational modes of 2,3,7,8-tetrachloro-and 1,2,3,7,8-pentachlorodibenzo-p-dioxins are calculated. The interpretation of the fine-structure phosphorescence spectrum of the first of these compounds is refined, and the radiative deactivation rate constants for the s sublevels of the lowest triplet state T₁ are estimated. For a number of polychlorinated compounds, the effect of chlorine atoms occupying the α and β positions in a molecule on the T^s → S₀ transition dipole moments is discussed.     

Exact expressions for the energy current and stress tensor operators in many-particle systems

For some purposes in statistical physics, such as, for example, the calculation of various transport coefficients, it is necessary to have expressions for the energy current operatorS and stress tensor operatorT _lm . In this work it is shown that by using a simple identity, exact expressions forS andT _lm which satisfy the conservation laws for the energy density? and momentum densityP, respectively, exist.S andT _lm can each be written as a sum of two parts,S=S ^(A) +S ^(B) T _lm =T _lm ^(A) +T _lm ^(B) . The “A” part is the ordinary convective or kinetic part while the “B” part is shown to be expressible as a gradient and hence its homogeneous component vanishes identically. The expressions are compared with approximate forms found in the literature. The operators are Fourier analyzed and written in terms of the field operators in the second quantization formalism.     

Estimating of CP-violation in <Emphasis Type="Italic">B</Emphasis><Superscript>0</Superscript>→ψ(2<Emphasis Type="Italic">S</Emphasis>)π<Superscript>0</Superscript> decay

I present estimates of CP-violating asymmetries in the non-leptonic charmonium two-body B⁰→ψ(2S)π⁰ decay and the same decays of B⁺→ψ(2S)π⁺ and B⁺→ψ(2S)K⁺ These estimates are based on QCD and improved QCD factorization approach making use of next-to-leading order (NLO) contributions. The CP-violating asymmetry for B⁰→ψ(2S)π⁰ decay is not available, according to the same calculations, it is expected if it can be measured in the future its value will be S_ψ(2S)π0(B⁰ → ψ(2S)π⁰)= 0.662 ± 0.197 and C_ψ(2S)π0(B⁰ → ψ(2S)π⁰)= 0.024 ± 0.007.     

Antiferromagnetic Resonance in GdB<Subscript>6</Subscript>

The electron spin resonance has been measured for the first time both in the paramagnetic phase of the metallic GdB₆ antiferromagnet (T_N = 15.5K) and in the antiferromagnetic state (T < T_N). In the paramagnetic phase below T* ~ 70 K, the material is found to exhibit a pronounced increase in the resonance linewidth and a shift in the g-factor, which is proportional to the linewidth Δg(T) ~ ΔH(T). Such behavior is not characteristic of antiferromagnetic metals and seems to be due to the effects related to displacements of Gd³⁺ ions from the centrosymmetric positions in the boron cage. The transition to the antiferromagnetic phase is accompanied by an abrupt change in the position of resonance (from μ₀H₀ ≈ 1.9 T to μ₀H₀ ≈ 3.9 T at ν = 60 GHz), after which a smooth evolution of the spectrum occurs, resulting eventually in the formation of the spectrum consisting of four resonance lines. The magnetic field dependence of the frequency of the resonant modes ω₀(H₀) obtained in the range of 28–69 GHz is well interpreted within the model of ESR in an antiferromagnet with the easy anisotropy axis ω/γ = (H ₀ ² +2H_AH_E)^1/2, where H_E is the exchange field and H_A is the anisotropy field. This provides an estimate for the anisotropy field, H_A ≈ 800 Oe. This value can result from the dipole?dipole interaction related to the mutual displacement of Gd³⁺ ions, which occurs at the antiferromagnetic transition.     

Zerfallsschema und Matrixelemente für denβ-Übergang Ag110m→Cd110

Theβ decay Ag^110m→Cd¹¹⁰ has been investigated with a double lens spectrometer and aβ-γ circular-polarization correlation setup. The shape of the 6⁺→6⁺ β spectrum withE ₀=529 keV was found to be allowed, in disagreement with earlier work. The constantA of theβ-γ circular-polarization correlation was measured to beA=0·07±0·02. This implies a ratioX of Fermi to Gamow-Teller contribution to the decay ofX ₁=?0·02±0·03 orX ₂=?10·3 _?4·1 ^+2·3 . Qualitative shell model considerations favor the valueX ₁. Additional information is given for the disintegration schemes of Ag^110m and Ag¹¹⁰.     

Anomalous temperature dependence of magnetic relaxation in YBa<Subscript>2</Subscript>Cu<Subscript>2</Subscript>O<Subscript>7 − δ</Subscript> oxygen-deficient single crystals

The dependence of the magnetization relaxation rate S = ?d lnM/dlnt on temperature T is measured in YBa₂Cu₃O_{7 ? δ} samples with various oxygen concentrations. It is found that the S(T) curve changes qualitatively when oxygen deficit δ exceeds the threshold value δ_th = 0.37. For δ < δ_th (T _c > 60 K, where T _c is the superconducting transition temperature), function S(T) has the well-known peak at T/T _c = 0.4. For δ > δ_th (at T _c < 51 K), this peak transforms into a plateau and a new sharp peak appears at T/T _c = 0.1. The threshold value δ_th of the oxygen deficit corresponds to the transition of the sample from the disordered state into the ordered state of oxygen vacancies. We consider the change in the shape of the S(T) curve as a macroscopic manifestation of this transition.     

Some Features in the behavior of the density of superconducting condensate in superconductors

The correlation between the density ρ_s(T→0) of superconducting condensate and the superconducting transition temperature T _c in underdoped HTSC systems is considered. It is shown that the linear relation between ρ_s(0) and T _c observed in some experiments can easily be interpreted in the framework of the conventional Bardeen-Cooper-Schrieffer (BCS) model without invoking any exotic superconductivity models.     

Spectral manifestations of <Emphasis Type="Italic">d</Emphasis>-π exchange and charge transfer interactions in Cu(II) porphyrins

New absorption bands due to spin-forbidden transitions from the ground state to excited triplet states are found at 295 K in the near-IR absorption spectra of a number of Cu(II) complexes of octaethylporphyrin (OEP) that differ in the nature, number, and position of their side substituents. The frequency distribution, number, and nature of these transitions are analyzed using computer decomposition of complex contours into Gaussian components and additional data from the phosphorescence and phosphorescence excitation spectra (295-77 K). The d-π exchange integrals, determining the energy splitting ΔE = E(²T₁)–E(⁴T₁) in the compounds under study, are calculated on the basis of the experimental data obtained. It is shown that, in addition to the formally spin-allowed ²S₀ → ²T₁ transition (λ_max = 833 nm), the absorption spectrum of the nonplanar CuOETPP molecule at 295 K exhibits the low-intensity spin-forbidden ²S₀ → ⁴T₁ transition (λ_max = 937 nm). For this compound at 77 K, phosphorescence from the ⁴T₁ state is observed (λ_max = 955 nm), with a quantum yield equal to ?_Ph = 0.0015 and a decay time amounting to τ_Ph = 190 ns. For the CuOEP-Ph(o-NO₂) molecule, which contains the electron-acceptor nitro group, direct absorption from the ground state S₀ to a charge transfer (CT) state (λ_max = 845 nm) is observed at 295 K. The extinction coefficient of this absorption and the energy of the CT state are determined.     

Thermodynamic study of compounds of the Nd-Ba-Cu-O system

Standard enthalpies of formation for solid solutions of composition Nd_{1 + x} Ba_{2 ? x} Cu₃O _y (x = 0–0.8, y = 6.65–7.24) from oxides were determined by solution calorimetry. The heat capacity of NdBa₂Cu₃O_6.87 phase was measured in the range 5–320 K by low-temperature adiabatic calorimetry. The absolute entropy S ^o(T), the difference of enthalpies H ^o(T)-H ^o(0 K), and the reduced Gibbs energy Φ^o(T) = S ^o(T)–[H ^o(T)–H ^o(0)]/T were calculated on the basis of smoothed dependence C _p (T) in the 0–320 K range. An assessment was made for the heat capacities and the absolute entropies of solid solutions Nd_1+x Ba_2?x Cu₃O _y . The obtained set of thermodynamic parameters can be used for the calculation of phase equilibria in the Nd-Ba-Cu-O system.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Thermodynamic and dilatometric properties of the dimerized phase of a C<Subscript>60</Subscript> fullerene

This paper reports on the results of complex investigations into the structural, thermodynamic, and dilatometric properties of the C₆₀ dimerized phase prepared under compression of a C₆₀ fullerite at a pressure up to 8 GPa and a temperature of 290 K. It is demonstrated that the dimerized phase has a face-centered cubic structure with a lattice parameter a=14.02±0.05 Å. The dimeric structure of the studied sample is confirmed by x-ray diffraction analysis. According to the dilatometric data, the volume jump observed in the vicinity of the orientational transition for the dimerized phase is estimated to be approximately 30 times less than that for the C₆₀ fullerite. The temperature dependence of the heat capacity of the (C₆₀)₂ crystalline dimer is examined using precision adiabatic vacuum calorimetry under normal pressure in the temperature range from T → 0 K to 340 K. The results obtained are used in the calculations of thermodynamic functions, namely, the heat capacity C _p ⁰ (T), the enthalpy H⁰(T)-H⁰(0), the entropy S⁰(T), and the Gibbs function G⁰(T)-H⁰(0). The fractal dimension D is determined as a function of the heat capacity. The standard entropy of the formation of the (C₆₀)₂ crystalline dimer from a simple compound (graphite) at T=298.15 K and normal pressure is calculated.     

Phase Diagrams of Solid Solutions of Relaxor Ferroelectrics from the Dielectric Spectroscopy Data

The dielectric spectra of Pb(_1–z)Ba _z (Mg_1/3Nb_2/3) _m (Zn_1/3Nb_2/3) _y (Ni_1/3Nb_2/3) _n TixO₃ (x = 0.25–0.4, y = 0.1130–0.0842, m = 0.4844–0.1298, n = 0.1266–0.4726, z = 0–0.15) ceramics with substitution in both A and B crystallographic positions of the perovskite structure are studied. The system demonstrates a transition from the relaxor state to the normal ferroelectric state in both cases: when the concentration of lead titanate grows and the concentration of barium is reduced. On the basis of experimental results, the x–T and z–T phase diagrams are plotted. Despite different crystal chemical reasons of the relaxor state emergence in the investigated solid solutions, their diagrams demonstrate an evident similarity. We have revealed the disappearance of the temperature hysteresis at the transition to the relaxor state in both cases, which has allowed us to make an assumption of the existence of tricritical points on the corresponding diagrams.     

Der Zerfall des Co60m und Zr90m

Co^60m was produced by the reaction Co⁵⁹ (n,γ) Co^60m ; its decay has been investigated by scintillation spectrometers. The half-period has been remeasured yielding a value ofT _1/2=(10·35 ±0·20) min. The isomeric decay mainly leads to the Co⁶⁰ ground state by a (58·6±0·6) keV transition. TheK-conversion coefficientα _K= 41±3 and the total conversion coefficientα=47±3 indicate the transition to beM3 and the spin of Co^60m to be 2⁺. Further Co^60m decays by beta transitions to Ni⁶⁰. The beta component (8·6±1·2)·10^?3%, log ft=7·32 leading to a (2·16±0·02) MeV level has been measured for the first time. A second component (0·24±0·03)%, log ft=7·23 leads to the 1·33 MeV level. The 2·16 MeV level decays to the Ni⁶⁰ ground state mainly by a 0·83–1·33 MeV cascade, in a few cases by a direct transition. The spin of the 2·16 MeV level is 2⁺. Zr^90m was produced by the reaction Zr⁹⁰ (n,n′) Zr^90m . The half-period was measured yielding a value ofT _1/2=(0·83±0·03) sec. Zr^90m decays in the following way: (77±5) % by a direct (2·31±0·02) MeV —E 5 transition to the Zr ground state and (23±5)% by a (132·5±1·5) keV-(2·18±0·03) MeV cascade detected for the first time in the isomeric decay. TheK-conversion coefficient of the 132·5 keV transition isα _k=(2·2±0·3) indicating this transition to beE3 and the spin of the 2·18 MeV level to be 2⁺. The Zr^90m -decay sheme is in accordance with the level sequence of Zr⁹⁰ as measured in the Nb⁹⁰ decay.     

Anomalous thermopower in heavy-fermion compounds CeB<Subscript>6</Subscript>, CeAl<Subscript>3</Subscript>, and CeCu<Subscript>6 − <Emphasis Type="Italic">x</Emphasis></Subscript>Au<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

High-precision measurements of thermopower have been performed in a wide temperature range (2–300 K) for a series of cerium-based heavy-fermion compounds, including CeB₆, CeAl₃, CeCu₆, and substitutional solid solutions of the CeCu_{6 ? x} Au _x system (x = 0.1, 0.2). All compounds exhibit an unusual (logarithmic) asymptotic behavior of the temperature dependence of the Seebeck coefficient: S ∝ ?lnT. In the case of cerium hexaboride, this anomalous behavior of S(T) is accompanied by the appearance of weak-carrier-localization-mode asymptotics in the conductivity (σ(T) ∝ T ^0.39), while the paramagnetic susceptibility χ(T) and the effective mass of charge carriers m _eff(T) vary according to a power law (χ(T), m _eff(T) ∝ T ^?0.8) in the temperature interval T = 10–80 K. This behavior corresponds to renormalization of the density of states at the Fermi level. The observed anomalous behavior of thermopower in CeB₆ and other cerium-based intermetallic compounds is attributed to the formation of heavy fermions (many-body states in the metal matrix) at low temperatures.     

Covalence-induced stabilization of an intermediate-spin state and the magnetic susceptibility of LaCoO<Subscript>3</Subscript>

The energies of terms with spins S = 0, 1, 2 have been found using exact diagnoalization of the multielectron Hamiltonian of a multiband pd model for the CoO₆ cluster. Co (e _g orbital)-O hops, which form the covalent σ bond, are shown to decrease the energy of the state (IS) with an intermediate spin (S = 1) as compared to the energy of the state (LS) with a low spin (S = 0). An analogue of the Tanabe-Sugano diagram that takes into account the covalence of the CoO₆ cluster is constructed. The state with S = 1 is shown to be a ground state at certain model parameters. An increase in temperature is established to decrease the crystal field and, thus, favors the transition of the ground state from LS to IS at T = 100 K and the transition of the IS ground state to a state (HS) with a high spin (S = 2) at T = 550 K. The magnetic susceptibility of LaCoO₃ is calculated with allowance for the LS, IS, and HS states and for the fact that the HS state exhibits threefold orbital degeneracy of the t _2g shell, which results in an effective orbital moment L = 1 and the importance of spin-orbit interaction. The behavior of this magnetic susceptibility agrees well with the experimental x(T) dependence of LaCoO₃.