Triplet excitons in (TEA) (TCNQ)2

We report the results of EPR studies on the ionic-radical salt (TEA)⁺ (TCNQ)₂^- composed of an oganic free radical anion and a diamagnetic cation. Between about 40 and 80 K this crystal exhibits the triplet exciton EPR spectrum characteristic of an alternating chain of spins. The triplet spin Hamiltonian parameters are |D| = 44 ± 2 G and |E| = 5.5 ± 1 G. The directions of the zero field splitting principal axes are determined through single crystal rotation studies at 55 K and related to the crystal structure.     

Magnetic-field dependent optically detected ESR in the photoexcited triplet states of bridged Zr(IV) metallocenes

We report on the magnetic-field-dependent optically detected magnetic resonance (ODMR) spectra for polycrystalline samples of the bridged Zr(IV) metallocenes, Me₂Si<(Cp₂)ZrCl₂ ( (dimethylsilylbis(cyclopentadienyl)zirconium-dichloride) and Me₂C<(Cp₂)ZrCl₂ (iso-propylidenebis(cyclopentadienyl)zirconium-dichloride). ODMR spectra at zero magnetic field were recorded by frequency sweeping a microwave source from 0.1 to 10 GHz with the sample contained in a microwave helix. ODMR spectra at finite magnetic fields were recorded with the sample contained in either a helix or a slotted-tube resonator with a fixed microwave frequency and sweeping the magnetic field. For all experiments, the sample and microwave probes were contained in an immersion dewar cryostat, and the temperature was held at about 2 K. All three zero field ODMR transitions (2|E|, and |D| − |E| and |D|+|E|) were observed in the frequency-swept ODMR spectra recorded at zero and small magnetic fields. The zero-field frequency-swept spectra allowed the determination ofD andE values uniquely. For frequency-swept small-field ODMR spectra recorded at successively higher magnetic fields, each of the ODMR line intensities was observed to increase with increasing magnetic field. This intensity increase was observed for all three ODMR lines, reflecting an increase in the total intensity rather than simply a change in the polarization of the triplet sublevels. The latter would result in a change in the relative intensities of the ODMR lines but would not change simultaneously the intensities of all three lines. The ODMR line intensities increase in proportion toB ⁿ, wheren<1. This field dependence is weaker than the expected proportionalB ² dependence from the Zeeman effect, which likely originates from the magnetic field dependence of the spin relaxation rates between the triplet sublevels. Magnetic-field-swept ODMR spectra recorded at fixed microwave frequencies in the X-band frequency range (9.8 GHz) do not show all three expected classic Pake powder pattern line shape profiles, exhibited by the molecules with their magneticZ, Y, andX axes parallel to the external magnetic field. In particular, the intensity for molecular magneticY-axes parallel to the external magnetic field is completely suppressed. In addition, an external magnetic field dependence in field-swept ODMR spectra was observed, which results in a linear decrease of the ODMR intensity with increasing strength of the external magnetic field over and above that would be expected in a polycrystalline spectrum. The data are analyzed by simulation of the continuous-wave ESR spectrum with the eigenvalues and eigenvectors of the spin Hamiltonian matrix characterizing the triplet state exhibiting the ODMR spectrum, in conjunction with homotopy, as a function of the orientations of the magnetic axes of the various molecules in a polycrystalline sample. This approach is useful to interpret the experimentally observed ODMR transition frequencies andg-values but does not take the amplitudes in the ODMR spectrum. The corrections required to modify the continuous-wave ESR spectral amplitudes that reproduce the observed ODMR amplitudes are effects associated with the ODMR processes.     

Symmetry enforced gauge invariance of nuclear magnetic shielding constants

E.S.R. experiments performed at 1·3 K by optical detection are reported for the photo-excited triplet state of palladiumporphin in a single crystal of n-octane, and the observation of a level anticrossing signal is described.

In the crystal the orbital degeneracy of the ³ E _u state of the free molecule is lifted by the crystal field and in n-octane the energy difference between the two orbital components |x> and |y> is found to be 58 ± 2 cm^-1. The spinorbit coupling (SOC) and the orbital Zeeman interaction couple the triplet manifolds of |x> and |y>, and for a proper understanding of the magnetic properties of these states it is necessary to work in the basis of the six spin-orbit functions deriving from the ³ E _u state of the free molecule. It is shown that either of the two triplet states can be described by an effective spin hamiltonian of the common form and expressions for the zero-field parameters D and E and the principal values of the g tensor are given. The experimental values of the parameters in the lowest triplet state are D = -24·38 ± 0·03 GHz, |E| = 320 ± 60 MHz, g _‖ = 1·677 ± 0·001 and g _⊥ = 1·989 ± 0·002. The matrix element of the SOC connecting the |x> and |y> triplet manifolds amounts to qZ = 15 ± 3 cm^-1 and the vibronic orbital angular momentum (in units of ?) in the ³ E _u state of the free molecule to qΛ = 1·5 ± 0·3. A tentative value of 0·63 for the orbital reduction factor q is obtained by comparison with a theoretical estimate of Λ. The value of q is indicative of weak Jahn-Teller coupling.     

EPR and optical absorption studies of Cr ions in potassium sodium dl-tartrate tetrahydrate

EPR spectra of Cr³⁺ ions doped in potassium sodium dl-tartrate tetrahydrate single crystals are recorded at 77 K. The spin Hamiltonian and zero field parameters g, |D| and |E| are measured from the resonance lines obtained at various rotations of the magnetic field. The values obtained are: g_x=1.9257±0.0002, g_y=1.9720±0.0002, g_z=2.0102±0.0002, |D|=313±2 (×10⁻⁴) cm⁻¹ and |E|=101±2 (×10⁻⁴) cm⁻¹. From the results of EPR study, the site symmetry of Cr³⁺ ion in the crystal is discussed. The optical absorption at room temperature is also studied. From the observed band positions, the crystal field splitting parameter (D_q) and the Racah inter-electronic repulsion parameters (B and C) are evaluated. The bonding parameters are obtained by correlating optical and EPR data and the nature of bonding in the crystal is discussed.     

Zero-field optical detected magnetic resonance of [70]-fullerene

The phosphorescence spectrum of [70]-fullerene in a glassy toluene matrix has been investigated at 77, 4.2 and 1.2 K. At 77 K, only one decay time (47.0 ms) has been observed while at 4.2 and 1.2 K two decay times (46.7, 5.6 ms and 46.6, 24.2 ms, respectively) were recorded. The zero field splitting parameters |D|=0.00489(25) cm^?1 and |E|=0.00135(7) cm^?1 were measured at 1.2 K using a pulsed ODMR technique.     

Application of commercially available fluorophores as triplet spin probes in EPR spectroscopy

ABSTRACT

In recent years, photoexcited molecular triplet states became increasingly popular in magnetic resonance, e.g. as spin probes to measure distances relative to other electron-paramagnetic species or as moieties that transfer light-generated electron–spin polarisation of the triplet state to surrounding magnetic nuclei. In this study, the triplet states of three commercially available dyes, Erythrosin B, Rose Bengal and Atto Thio 12, all typically utilised as fluorophores in optical spectroscopies and microscopies, are investigated in aqueous solutions by using transient absorption spectroscopy and transient electron paramagnetic resonance (EPR). From these methods, the triplet-state lifetimes as well as their zero-field splitting parameters, D and E, which reflect the electronic structures of the triplet state wavefunctions, were obtained. Atto Thio 12 exhibits much smaller D and E values as compared to Rose Bengal and Erythrosin B. On the basis of density functional theory calculations of the triplets’ energy splittings at zero magnetic field, these findings were rationalised. As a proof of concept for applications, the triplet-state properties of Atto Thio 12 bound to an aptamer were also determined and the results are discussed.     

Effect of solvent nature on spin exchange in rigid nitroxide biradicals

Intramolecular electron spin exchange as a function of temperature and solvent viscosity and polarity has been studied by X-band electron paramagnetic resonance (EPR) spectroscopy in two rigid nitroxide biradicals existing in one spatial conformation only. Temperature variations of the isotropic hyperfine splitting constanta and exchange integral value |J/a| were measured from EPR spectra and subsequently analyzed. The interaction of polar solvent molecules with >N-O fragments of nitroxide groups led to a slight decrease of the |J/a| value with the increase of temperatureT. In contrast, the interaction of polar solvent molecules with functional groups inside the bridge resulted in a noticeable increase of |J/a| vs.T. In the last case, a coverse relationship between the values of |J/a| and the hyperfine splitting constanta has been observed for solvents with different polarity.     

Theoretical study of spin-singlet contributions to zero-field splitting of a 3d6 ion in a trigonal ligand field and applications to Fe2+ in FeSiF6 · 6H2O and FeCO3

The complete energy matrix (210 × 210) for d⁶(d⁴) configuration ions in a trigonal ligand field is constructed. The energy levels and zero-field splitting parameters in ferrous fluosilicate and ferrous carbonate are studied. The contributions of spin singlets to zero-field splitting parameters in a trigonal ligand field are investigated for the first time. The calculation results indicate that the spin-singlet contribution to second-order zero-field splitting parameter D is negligible, but the contributions to fourth-order zero-field splitting parameter a ? F cannot be neglected. Moreover, it is found that the stronger the trigonal ligand field, the larger are the spin-singlet contributions to the zero-field splitting parameters.     

[2.2]Paracyclophane: theoretical study of its lower excited states and of the zero-field splitting parameters D

The lower excited singlet and triplet states and the zero-field splitting parameters D of [2.2]paracyclophane are studied within a semiempirical π theory which takes into account overlap effects between the two benzene rings, transanular and through-bond interaction via the methylene bridges. Whereas the singlet energies depend strongly on the through-bond interaction and the mutual polarization of σ core and π system this is not the case for the energies and zero-field splitting parameters D of the two lowest triplet states. The deformations of the benzene rings in [2.2]paracyclophane lead only to a small decrease of the excitation energies of about 0·2 eV. The D parameter can be written as a sum D = D_A + D_B + D_AB with the intrasubunit contributions D_A and D_B of the conjugated subunits A and B of the phane and an intersubunit term D_AB . We demonstrate that the deformations reduce the intrasubunit terms D_A and D_B and that they are crucial for the decrease of the D values of [2.2]paracyclophane with respect to p-xylene. The difference between the D values of the first and second triplet states is governed by the intersubunit term D_AB which has a different sign in the two states. However, this difference does not depend markedly on the transanular interaction. A further reduction of D_A and D_B in the first triplet state only is caused by transanular interaction by means of symmetrical charge-transfer terms in the wavefunction.     

An E.S.R. study of the triplet dianions of 1,3,5-triphenylbenzene and 2,4,6-triphenyl-sym-triazine

Upon prolonged alkali reduction in ethereal solvents 1,3,5-triphenylbenzene (Tpb), 2,4,6-triphenyl-sym-triazine (Tpt) and 2,4,6-tritolyl-sym-triazine (Ttt) can be reduced to their dinegative ions. Dissolved in rigid solvent matrices these ions produce E.S.R. spectra which are characteristic for randomly oriented triplet systems. Hückel and SCF MO calculations indicate that these dianions have a twofold degenerate lowest anti-bonding level.

Although the ions Tpb^2- and Tpt^2- are iso-electronic their magnetic properties prove to be strikingly different. While Tpb^2- has a triplet ground state irrespective of solvent, counter ion and temperature, Tpt^2- (and also Ttt^2-) has a singlet ground state with a thermally accessible triplet state in solvents with poorly solvating properties and has a triplet ground state in better solvating media. Furthermore, the zero field splitting parameters D and E of the lowest triplet states of Tpt^2- and Ttt^2- are markedly different from those obtained from Tpb^2-. The former show a considerably larger D value than Tpb^2- and, in contrast to Tpb^2-, the ions Tpt^2- and Ttt^2- have a non-zero E value in poorly solvating solvents, pointing to a non-trigonal spin distribution of the triplet systems.

An explanation of the observed differences is given in terms of current MO theories. The results suggest that in the case of Tpt^2- and Ttt^2- the association with the counter ions even in strongly solvating solvents is very strong.     

Superhyperfine interactions and covalency contribution to axial zero field splitting for |MnF6|4− complexes in fluorides

An approximate L.C.A.O.-M.O. calculation based upon the one-electron ionic hamiltonian initially derived by Sugano and Shulman, gives satisfactory agreement with measurements of superhyperfine interactions at the ligand shell and outer shell nuclei, for Mn²⁺ in AMF₃ crystals, when one takes into account an external crystal potential acting on the |MnF₆|^4? complex. The results obtained for cubic symmetry are extrapolated to an independent bond model in order to discuss the covalency contribution to axial zero field splitting.     

Heat capacity of MnBr2·4H2O near the antiferromagnetic transition temperature

Heat capacity of MnBr₂·4H₂O has been measured in the critical region around the Neel temperature. The data can be fitted, over a restricted range of |t|⩽10⁻², to the asymptotic power law. The critical exponents and the amplitudesA andA′ are not consistent with any theoretic predictions. However when scaling constraints are imposed, their values agree with the parameters of Ising model. Corrections to scaling are necessary to extend the range of the fit to |t|>10⁻². The correction terms are asymmetric giving −1·15±0·25 as the ratio of the amplitudes of the lowest order correction terms,D andD′ above and belowT _c. This value is in agreement with the recent predictions of the renormalisation group theory.     

Modeling Spectroscopic Properties of Ni2+ Ions in the Haldane Gap System Y2BaNiO5

Modeling of spin Hamiltonian parameters enables correlation of crystallographic, spectroscopic, and magnetic data for transition ions in crystals. In this paper, based on the crystallographic data and utilizing the point-charge model and superposition model, the crystal field parameters (CFPs) are estimated for Ni²⁺(3d ⁸) ions in the Haldane gap system Y₂BaNiO₅. The CFPs serve as input for the perturbation theory expressions and the crystal field analysis package for microscopic spin Hamiltonian modeling of the zero-field splitting parameters (ZFSPs) D and E. Results of an extensive literature search of the pertinent crystallographic data, experimental ZFSPs, and model parameters are briefly outlined. The modeling aims at verification of the experimental ‘single ion anisotropy’ parameters and explanation of the controversy concerning the maximal rhombic distortion |E/D| ≈1/3 reported for Ni²⁺ ions in Y₂BaNiO₅. The preliminary results call for reanalysis of some magnetic studies of the Haldane gap systems.     

EPR, Optical Absorption and Superposition Model Study of Fe3+-Doped Ammonium Dihydrogen Phosphate Single Crystals

X-band electron paramagnetic resonance (EPR) studies are carried out on Fe³⁺ ions doped in ammonium dihydrogen phosphate (ADP) single crystals at room temperature. The crystal field and spin Hamiltonian parameters are evaluated from the resonance lines obtained at different angular rotations. The obtained values of spin Hamiltonian and zero-field parameters of the Fe³⁺ ion in ADP are: g = 1.994 ± 0.002, |D| = (220 ± 5) × 10^?4 cm^?1 and a = (640 ± 5) × 10^?4 cm^?1. On the basis of EPR data, the site symmetry of the Fe³⁺ ion in the crystal is discussed. The Fe³⁺ ion enters the lattice substitutionally replacing the NH₄ ⁺ sites. The optical absorption of the crystal is also studied at room temperature in the wavelength range of 195–925 nm. The energy values of different orbital levels are calculated. The observed bands are assigned as transitions from the ⁶ A _1g (S) ground state to various excited quartet levels of the Fe³⁺ ion in a cubic crystalline field. From the observed band positions, Racah interelectronic repulsion parameters (B and C), cubic crystal field splitting parameter (D _q ) and Trees correction are calculated. There values are: B = 970, C = 1,923, D _q  = 1,380 cm^?1 and α = 90 cm^?1, respectively. On the basis of EPR and optical data, the nature of bonding in the crystal is discussed. The zero-field splitting (ZFS) parameters are also determined theoretically using B _kq parameters estimated from the superposition model. The values of ZFS parameters thus obtained are |D| = (213 ± 5) × 10^?4 cm^?1 and |E| = (21 ± 5) × 10^?4 cm^?1.     

Zeeman splitting factor of the Er3+ ion in a crystal field

Numerical computations are presented on the energy levels of the Er³⁺ ion in crystalline fields of cubic, trigonal, tetragonal and orthorhombic symmetry. Zeeman splitting factors were obtained from the level splitting in an additional magnetic field. For the quartet Γ₈ states in cubic symmetry the Zeeman effect is described by an effective Hamiltonian ℋ= gμ_BBJ+ uμ_BBJ³ with the parametersg andu calculated for mixed fourth- and sixth-order potentials. For the eight doublets in the lower symmetry of an axial trigonal or tetragonal crystal field the principalg tensor components g_∥ and g_⊥ were calculated. The results of such calculations for a ground-state doublet can exactly account for the experimental data obtained on around 70 erbium centers in various crystalline hosts. However, sometimes different sets of parameters give comparably good results. An empirical rule of constant trace g_∥ + 2g_⊥ is supported by the calculations. In contrast to analytical treatments the effect of the crystalline field can be followed over a continuous range of the crystal field parameters. This allows one to establish relations on the relative signs of tensor components. It is found that the measured trace of tensors |g_∥| + 2|g_⊥| is not always equal to their real trace g_∥ + 2g_⊥. In an exploratory calculation a nonaxial center was simulated in an orthorhombic field, with calculation of the three principal values g_x, g_y and g_z. A good agreement is obtained for the recently reportedg values of an erbium center in silicon.     

Optically detected E.P.R. and low-field ENDOR of triplet benzophenone

The ENDOR spectrum of ¹³C substituted (carbonyl carbon) triplet excited benzophenone was studied at ca. 100 G applied magnetic field by means of optical detection. The benzophenone was substitutionally dissolved in dibromodiphenylether (DDE). The ENDOR transitions and the E.P.R. transitions were studied as a function of applied field direction in the ab and bc crystal planes. The angle ? between the line joining the phenyl group centres and a principal axis of the fine structure tensor was found to be 23·6° ± 0·02° (standard deviation limited to one set of measurements). The principal axes of the ¹³C hyperfine tensor were within experimental error (±10°) coincident with the fine structure axes. The principal values of the hyperfine tensor were found to be : |A_xx /h| = 43·16 ± 1·84, |A_yy /th| = 22·66 ± 2·50, |A_zz /h| = 10·25 ± 1·30 MHz. The low-field ENDOR does not provide an indication of the signs of these tensor elements, so the value of the isotropic coupling constant cannot be measured. Two values of the anisotropic (dipole) hyperfine tensor elements were deduced on the assumption that the transitions frequencies are mainly determined by interactions between the nuclear spin and electron density on the carbonyl carbon atom. These values were (i) A _xx / ^d /h = 17·82, A_yy /h = -22·68, A_zz /h = -15·14 MHz and (ii) A_xx /h = 39·73, A_yy /h = -26·09, A_zz /h = -13·63 MHz. Set (ii) is consistent with recent calculations of the spin density distribution in triplet benzophenone in which the orbital spin densities are 0·64 for the carbonyl carbon π-orbital, 0·17 for the oxygen π-orbital, and 0·88 for the non-bonding orbital on oxygen (all expressed as fractions of one electron).

Isotope effects on the fine structure constants of triplet benzophenone were measured and found to be consistent with the changes occurring in the spin-orbit coupling with the ground state.

The kinetic parameters for the excitation and de-excitation of the triplet substates were deduced from transient ODMR studies of benzophenone in DDE. The T_z spin state is mainly populated (85–88 per cent) and this is also the most strongly radiative state (k_z ^r = 0·88). The steady-state populations of the three triplet levels are similar.     

| m | Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef _|m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off _|m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f _|m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off _|m|(θ) on the positive real |m| axis.     

Comment on Vub from exclusive semileptonic B and D decays

The prospects for determining |V_ub| from exclusive B semileptonic decay are discussed. The double ratio of form factors (f^(B→ρ)/f^(B→K*))/(f^(D→ρ)/f^(D→K*)) is calculated using chiral perturbation theory. Its deviation from unity due to contributions that are non-analytic in the symmetry breaking parameters is very small. Combining experimental data obtainable from , and can lead to a model independent determination of |V_ub| with an uncertainty from theory of about 10%.     

<Emphasis Type="Italic">CP</Emphasis> violation due to multi-Froggatt–Nielsen fields

We study how to incorporate CP violation in the Froggatt–Nielsen (FN) mechanism. To this end, we introduce non-renormalizable interactions with a flavor democratic structure to the fermion mass generation sector. It is found that at least two iso-singlet scalar fields with a discrete symmetry imposed are necessary to generate CP violation due to the appearance of the relative phase between their vacuum expectation values. In the simplest model, the ratios of quark masses and the Cabibbo–Kobayashi–Maskawa (CKM) matrix including the CP violating phase are determined by the CKM element |V_us| and the ratio of two vacuum expectation values of FN fields, R=|R|e^iα (a magnitude and a phase). It is demonstrated how the angles φ_i (i=1,...,3) of the unitarity triangle and the CKM off-diagonal elements |V_ub| and |V_cb| are predicted as a function of |V_us|, |R| and α. Although the predicted value of the CP violating phase does not agree with the experimental data within the simplest model, the basic idea of our scenario would be promising if one wants to construct a more realistic model of flavor and CP violation. PACS 11.30.Er; 12.60.-i     

Fullerene C<Subscript>70</Subscript> Triplet Zero-Field Splitting Parameters Revisited by Light-Induced EPR at Thermal Equilibrium

Continuous-wave (CW) electron paramagnetic resonance (EPR) and echo-detected (ED) EPR spectra of triplet state of fullerene C₇₀ in molecular glasses of decalin, o-terphenyl and toluene, and in polymethylmethacrylate polymer were obtained under continuous light illumination. Temperature was high enough so that the EPR spectra corresponded to thermal equilibrium between the spin sublevels. The comparison of CW EPR and ED EPR data has shown that pseudorotation in the ³C₇₀ frame does not remarkably affect deriving the zero-field splitting (ZFS) D and E parameters from the EPR spectra. ³C₇₀ EPR spectra were simulated at 77 K fairly well using the distribution of the ZFS D and E parameters. These distributions may be caused by the inhomogeneity of the glassy matrix surrounding, which affects the Jahn–Teller distortions of ³C₇₀ molecules (D-strain and E-strain).