Integral characteristics of vibronic-spin-orbit interactions in a phosphorus-containing analogue of the fluorene molecule

The strengths (P ₀₀ ^s )² and F _VSO ² of the transitions from the triplet sublevels s = z, y, and x of the electronic state ³A″ of the phenyldibenzophosphole (DB(P-Ph)) molecule are calculated taking into account the intramolecular spin-orbit (SO) and joint vibronic-spin-orbit (VSO) interactions. The contributions to the vibronic transition strengths from the SO interactions in different structural elements of the molecule (the C atoms of the dibenzene framework, the P atom, and the Ph substituent) are determined. The effect of the nonplanar nuclear configuration of the DB(P-Ph) molecule on the values of F _VSO ^s is investigated. The radiative deactivation rate constants of the k _rad ^s triplet sublevels T ^s are estimated. It is found that the vibrations of the A′(B₁) symmetry in the fine-structure phosphorescence spectrum of DB(P-Ph) occur due to both the SO coupling exclusively in the P atom and the T ^x → S₀ transition (the x axis is perpendicular to the planar dibenzene framework of the molecule) with a high (preferential) population of this triplet sublevel.     

Quenching of ππ* triplet states of vaporous polycyclic aromatic compounds by oxygen

The oxygen quenching rate constants k _T ^O2 of the triplet state T ₁ of vapors of polycyclic aromatic hydrocarbons (PAHs) with strongly different oxidation potentials 0.44 eV < E _OX < 1.61 eV and energies of the triplet levels 14800 cm^?1 < E _T < 24500 cm^?1 (anthracene, 2-aminoanthracene, 9-nitroanthracene, chrysene, phenanthrene, fluoranthene, and carbazole) are estimated from the measured dependences of the decay rates and intensities of delayed fluorescence on the oxygen pressure P _O2. It is found that the rate constants k _T ^O2 vary from 4 × 10³ (9-nitroanthracene) to 4 × 10⁵ s^?1 Torr^?1 (2-aminoanthracene) and increase with decreasing oxidation potentials E _OX of PAHs. The rate constants k _T ^O2 for vapors and solutions are compared. The dependences of k _T ^O2 on the free energy of two intermolecular processes, namely, triplet energy transfer to oxygen and electron transfer, are analyzed. It is shown that the rate constants k _T ^O2 increase with decreasing electron transfer free energy, which proves that, along with energy transfer, charge-transfer interactions contribute to the quenching of the triplet states of PAH vapors.     

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.     

The effect of the nonplanarity of heterocyclic analogues of fluorene with the phosphorus atom on spin-orbit interactions

The transition dipole moments P ₀₀ ^S for the transitions from the sublevels s=z,y, and x of the triplet electronic states ³ A″, which are caused by intramolecular spin-orbit (SO) interactions, are calculated. The calculation is carried out for molecules of heterocyclic analogues of fluorene containing phosphorus and nitrogen (namely, the groups P-H, P-C₆H₅, and N-H). The influence that the planar and nonplanar models of the molecules, as well as the substituents ?C₆H₅ and ?H at the heteroatom (HA), exert on the values of (P ₀₀ ^S )² and on the directions of the corresponding vectors is considered. The values of the component \(k_{SO^ \sim } \sum _s (P_{00}^s )^2 \) of the radiative deactivation rate constant of the T ₁ state are calculated. It is ascertained that, in the series of molecules with HA = N, O, P, and S, both the calculated values of k _SO and those experimentally determined from an analysis of the intensity distribution in fine-structure phosphorescence spectra vary little, whereas the constant of the SO coupling in the heteroatom ?_HA increases substantially along this series. The reason for the weak influence of ?_HA on values of k _SO—common for both planar and nonplanar molecules—is found.     

Nonradiative <Emphasis Type="Italic">S-T</Emphasis> intersystem crossing in α and β chlorine derivatives of naphthalene

The rate constants K _ST ^s of nonradiative S ₁ ? T ₁ ^s transitions to triplet sublevels s in molecules of chlorine derivatives of naphthalene (1,4-dichloro- and monosubstituted α-chloro- and β-chloronaphthalene) have been calculated within the model of vibronically induced spin-orbit (VISO) couplings. The contribution of the spin-orbit couplings in Cl atoms and carbon framework of the molecule to VISO couplings is determined. A dependence of the heavy-atom effect on the constant K _ST ^s in relation to the type of sublevel T ^s and α and β positions of chlorine in the molecule is established and explained.     

The effect of the heteroatom on the radiative deactivation of the lowest triplet state in heterocyclic analogues of fluorene

The vibronic transition strengths F _VSO ^s for the transitions from the spin sublevels s of the triplet state T₁ to the energy levels of the nontotally symmetric vibrations of dibenzothiophene (DB(S)) are calculated. For a series of heterocyclic analogues of fluorene (DB(S) and previously studied carbazole, dibenzofuran, and phenyldibenzophosphole), the regular features of the effect of the valence state of the heteroatom and of the spin-orbit interactions in individual atomic groups of the molecule are revealed. The factors affecting changes in the radiative deactivation rate constant of the T₁ state of the molecules studied are established. The intensity distribution of the vibronic lines in the Herzberg-Teller component of the fine structure phosphorescence spectrum of phenyldibenzophosphole is calculated taking into account different populations of the triplet sublevels.     

Ordering of the lowest tungsten carbide W<Subscript>2</Subscript>C

Atomic-vacancy ordering of the lowest tungsten carbide W₂C with the basis hexagonal structure of the L’3 type is analyzed by neutron and x-ray diffraction studies. It is found that the trigonal phase ?-W₂C (space group \(P\bar 3\) 1m) is the only ordered phase in the temperature range from ～2700 to 1370 K. The disorder-order phase transition channel associated with the formation of the trigonal ?-W₂C phase is found to include three superstructure vectors k ₁₅ ⁽¹⁾ , k ₁₅ ⁽²⁾ , and k ₁₇ ⁽¹⁾ of two stars {k ₁₅} and {k ₁₇}. The distribution function of the carbon atoms in the trigonal ?-W₂C superstructure is calculated.     

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.     

Formation of the incommensurate ordered phase in TaC<Subscript>y</Subscript> carbide

Structural neutron diffraction studies indicate that only one ordered phase arises after the disorder-order transition in nonstoichiometric cubic tantalum carbide TaC_y. This phase arises in the composition range y = 0.79–0.89 due to long-term annealing with a decrease in temperature from 1600 to 300 K. It is incommensurate in the [1–11]_B1 direction, but it is close to commensurate M₆C₅ structures (C2/m and P3₁ space groups) in mutual arrangement of atoms and vacancies in nonmetallic (1–11)_B1 planes. The disorder-order transition channel that is associated with the formation of the incommensurate superstructure in TaC_y carbide includes two arms k ₅ ⁽⁶⁾ ≈ 0.473b₂ and k ₅ ⁽⁵⁾ = ?k ₅ ⁽⁶⁾ of the {k₅} star and arms of the {k₄} and {k₃} stars. The translation period of the incommensurate phase in the [1–11]_B1 direction is 8.9–9.1 nm, which is larger than that in the commensurate phase M₆C₅ by a factor of about 18.     

The Structure of Radiative Tunnel Recombination Sites in Emulsion Microcrystals of AgBr(I)

To identify the structure of emissive tunnel recombination sites in the emulsion microcrystals of silver bromide AgBr(I) with iodine contaminations and to determine the role of an emulsion medium in their formation, the temperature dependence of the luminescence spectra in the range from 77 to 120 K, the kinetics of the growth of the maximum luminescence intensity value at λ ≈ 560 nm, and the luminescence flash spectrum stimulated by the infrared light are investigated. Two types of the AgBr_{1 – x}(I _x ) (x = 0.03) microcrystals—namely, obtained in an aqueous solution and on a gelatin substrate—are used in the studies. It is established that the emissive tunnel recombination sites with a luminescence maximum at λ ≈ 560 nm in AgBr_{1 – x}(I _x ) (x = 0.03) are the {(I _a ^- I _a ^- )Ag _i ⁺ } donor–acceptor complexes with the I _a ^- iodine ions located in neighbor anionic sites of the AgBr(I) crystal lattice, next to which the Ag _i ⁺ interstitial silver ion is positioned. With an increase in the temperature, the {(I _a ^- I _a ^- )Ag _i ⁺ } sites undergo structural transformation into the {(I _a ^- I _a ^- )Ag_in⁺} sites, where n = 2, 3, …. Moreover, the {(I _a ^- I _a ^- )Ag _in ⁺ } sites (n = 2) after the capture of an electron and hole also provide the tunnel recombination with a luminescence maximum at λ ≈ 720 nm. The influence of an emulsion medium consists in that gelatin interacts with the surface electron-localization sites, i.e., the interstitial silver ions Ag _in ⁺ , n = 1, 2, and forms the complexes {Ag _in ⁰ G⁺} (n = 1, 2) with them. The latter are deeper electron traps with a small capture cross section as compared to the Ag _in ⁺ sites (n = 1, 2) and that manifest themselves in that the kinetics of the luminescence growth in AgBr(I) to a stationary level at λ ≈ 560 nm is characterized by the presence of “flash firing.” At the same time, the luminescence flash stimulated by IR light, for which the Ag _in ⁺ (n = 1, 2) electron-localization sites are responsible, is absent. It is supposed that the electrons localized on the {Ag _in ⁺ G⁺} complexes (n = 2) retain the capability for emissive tunnel recombination with holes localized on paired iodine sites with a luminescence maximum at λ ≈ 750 nm.     

High-frequency EPR of Cr<Superscript>2+</Superscript> ions in CdGa<Subscript>2</Subscript>S<Subscript>4</Subscript>

High-frequency broad-band (65–240 GHz) EPR is used to study impurity centers of bivalent chromium in a CdGa₂S₄ crystal. It is found that the EPR spectra correspond to tetragonal symmetry. The spin Hamiltonian H = βB · g · S + B ₂ ⁰ O ₂ ⁰ + B ₄ ⁰ O ₄ ⁰ + B ₄ ⁴ O ₄ ⁴ with the parameters B ₂ ⁰ =23659±2 MHz, B ₄ ⁰ =1.9±1 MHz, |B ₄ ⁴ |=54.2±2 MHz, g_‖=1.93±0.02, and g_⊥=1.99±0.02 is used to describe the observed spectra. It is concluded that chromium ions occupy one of the tetrahedrally coordinated cation positions.     

Nuclear magnetic relaxation of spin<Emphasis Type="Italic">I</Emphasis>=1/2 scalar coupled to a quadrupolar nucleus in the presence of cross-correlation effects

The rigorous treatment of relaxation for the dipolar-multipolarAX spin system (I=1/2,S>1/2) in the presence of the dipolarI-S coupling, anisotropy chemical shift and quadrupolar interaction ofS spin is proposed. The calculations of the spin evolution under the relaxation Hamiltonian are based on the second-order time-dependent perturbation theory and are carried out in the operator representation. For this task the double commutator identities of the type [[I _±S _z ⁿ ,A _q ^μp ]A _?q ^μp ] and [[I _zS _z ⁿ ,A _q ^μp ]A _?q ^μp. ] are derived. The fist-order differential equations for the evolution of longitudinal two-spin orderI _zS _z ⁿ , z=magnetization ofS spinS _z ⁿ and coherences <I _±S _z ⁿ > in the spin systemIS with scalar coupling between spin 1/2 and quadrupolar spinS>1/2 were obtained. These equations are used to get equations for the evolutions of each component of the multiplet structure of spinI. The imaginary part of the cross-correlation spectral density function and indirect spin-spin coupling Hamiltonian are taken into account. Equations for the longitudinal components of theI spin spectrum in the presence of cross-correlation effects were obtained also. Longitudinal and transverse relaxation times and cross-relaxation times in the presence of cross-correlation D-CSA, Q-CSA, Q-D were analyzed.     

Spectroscopy of the <Stack><Subscript>Λ</Subscript><Superscript>7</Superscript></Stack>He nucleus in a three-cluster model

The _Λ ⁷ He hypernucleus is considered within the _Λ ⁵ He + n + n cluster model. The hyperon—nucleon interaction is described by a one-boson-exchange potential that is constructed on the basis of the NSC97f model. Phenomenological potentials are used to describe the αΛ and αN interactions. For the _Λ ⁵ Hen interaction, use is made of the folding-model potential. The calculations of the hyperon binding energy in the ground state of the _Λ ⁷ He hypernucleus on the basis of Faddeev equations in configuration space yield a result (5.35 MeV) that agrees well with preliminary experimental data (5.4 MeV). The problem of calculating the hyperon binding energy within the three-body approach is discussed. In calculating the energy spectrum of _Λ ⁷ He, use is made of a version of the method of analytic continuation in the coupling constant. Low-lying excited states of this nucleus can be classified as an analog of the corresponding states of the ⁶He nucleus with allowance for the clustering of the _Λ ⁵ He+n+n system in the ⁶He(J ^π)+Λ(s) form.     

Probabilities of forbidden magnetic-dipole transitions in the hydrogen atom and hydrogen-like ions

Explicit formulasfor strongly forbidden magnetic-dipole transitiions between states njl and n′jl in the hydrogen atom and light hydrogen-like ions are derived. The expressions for transition probabilities are presented in the form W _{n′jl; njl} ^(M1) = D _n′n ^lj αm _e (αZ)¹⁰ (in relativistic units), where m _e is the electron mass, α is the fine-structure constant, and Z is the nuclear charge; the constants D _n′n ^lj are presented in an analytical form. Before now, only the D ₂₁ ^01/2 coefficient corresponding to the 1s _1/2–2s _1/2 transition was known in explicit form. The results obtained can be used in designing an experiment on parity violation in the hydrogen atom.     

Stability of Coulomb systems

The stability of m ₁ ⁺ m ₂ ⁺ m ₃ ^? m ₄ ^? Coulomb systems formed by particles of unit charge against dissociation is considered as a function of the particle mass. It is shown that, from the stability of the m ₁ ⁺ m ₂ ⁺ m ₃ ^? three-particle system, it follows that the m ₁ ⁺ m ₂ ⁺ m ₃ ^? m ₄ ^? four-particle system containing an additional particle of mass satisfying the condition m ₄ ^? ? m ₃ ^? is stable. The results of calculations of the stability domain for m ₁ ⁺ m ₂ ⁺ m ₃ ^? systems asymmetric in particle masses are reported. The stability of 39 asymmetric exotic four-particle molecules and mesic molecules against dissociation is established.     

Magnetoresistance of granular YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − δ</Subscript> HTSC in weak magnetic field: Angular dependence

The magnetoresistance of ceramic YBa₂Cu₃O_～6.5 HTSC samples is studied as a function of the mutual orientation of the current I and external magnetic field H _ext at T = 77.3 K in magnetic fields of up to ～500 Oe. It is found that, if the demagnetization factor D is taken into account, the effective critical field of complete penetration of Josephson vortices into weak links H _c2J ^eff does not depend on the mutual orientation of I and H _ext. The lower critical field H _c1A ^eff associated with the beginning of penetration of Abrikosov vortices into superconducting grains increases substantially with the angle between I and H _ext. The strongest variation with the mutual orientation of I and H _ext is exhibited by the critical field of the Bragg glass-vortex glass first-order phase transition H _BG-VG ^eff and by the magnetoresistance jump at this phase transition.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Excitons in monoclinic zinc diphosphide: The <Emphasis Type="Italic">A</Emphasis>-exciton series and Fano effect

The A-exciton series in the absorption spectra of β-ZnP₂ monoclinic zinc diphosphide samples is investigated at different directions of the wave vector and different polarization states of radiation. It is shown that the oscillator strengths determined for the observed transitions are adequately described by the relationship F _n ∝n^?3 characteristic of S-type exciton states. The assumption is made that the A-exciton series is associated with the partially allowed dipole transitions to nS states of the orthoexciton with Γ ₂ ^? (x) symmetry at m _s =0. These states are mixed, to a first approximation, with nS states of the Γ ₂ ^? (z) singlet exciton due to the spin-orbit 2 interaction and are split off by the long-range (nonanalytical) part of the exchange interaction. The Fano antiresonances arise in the absorption spectra at resonances of the A-exciton series when the radiation vector E (or the induction vector D) has a component along the crystallographic axis c. These antiresonances are induced by the configurational interaction of discrete exciton states of the A series with the continuum of the exciton-phonon spectrum due to indirect transitions to the 1S band of the singlet exciton with phonon emission.     

Influence of Pressure on the Intramolecular Spin Exchange in a Short Imidazolium-Nitroxide Biradical

A short-chain imidazoline-type nitroxide biradical R ₅ ^NO –CH=N–N=C(CH₃)–R ₅ ^N , B2, with nitroxide rings R ₅ ^N and R ₅ ^NO as 1-oxyl-2,2,5,5-tetramethyl-3-imidazoline and 1-oxyl-2,2,5,5-tetramethyl-3-N-oxide imidazoline, respectively, has been studied using X-band electron paramagnetic resonance (EPR) spectroscopy in CH₃CN solutions at variable temperature T and pressure P. Changes of the solution viscosity on the intramolecular electron spin exchange in B2 is characterized by calculating the value of the exchange integral |J/a|, where a denotes the ¹⁴N hyperfine splitting (hfs) constant. It is revealed that the intramolecular dynamics in B2 do not follow the Debye–Stokes–Einstein law, while the Arrhenius dependence is fulfilled. Probable reasons of such behavior are discussed.     

Bound-exciton cathodoluminescence in ZnSe crystals and two-phonon resonance

A study has been made of the cathodoluminescence of ZnSe crystals annealed in vacuum [ZnSe(Vac)], in vacuum and, subsequently, in antimony melt [(ZnSe(Vac)(Sb)], or in a zinc melt with subsequent annealing in antimony [ZnSe(Zn)(Sb)]. The emission of all samples contained the I ₁ ^s,d -nLO series. The LO-phonon replicas of the emission line I ₁ ^s observed in ZnSe(Vac) samples are accompanied by single-plasmon satellites. The plasmon energy determining the replica separation is ?ω_p?10 meV. The emission lines of ZnSe(Zn)(Sb) samples have the smallest half-width. We report the first observation of anomalous broadening of the zero-phonon line I ₁ ^s in ZnSe(Vac) samples caused by a high zinc vacancy content. A theory on the shape of the emission spectrum under two-phonon resonance is developed including bound-exciton interaction with mixed plasmon-phonon vibrational modes. It is shown that the splitting of the I ₁ ^d line at T?2 K may originate from resonance exciton-phonon interaction between exciton-impurity complexes.