Anomalous pulse angle dependence of the single and double quantum echoes in a photoinduced spin-correlated coupled radical pair

In this work the response of a spin-correlated coupled radical pair to the sequence flash-t-P _ζ-τ-P _2ζ-T is investigated. For the theoretical analysis, the density operator formalism is used. Analytical expressions are derived for the electron spin single (SQ ESE) and double-quantum echoes (DQ ESE) as a function of pulse flip angle and singlet-triplet mixing angle. To illustrate the theoretical results, computer simulations are presented. In the limit of weak coupling, the “out-of-phase” SQ ESE is shown to be of a pure two-spin order having the maximal amplitude for the flip angle of 65.9°. The echo following the Hahn sequence vanishes in the same limit. This confirms the theoretical result already presented in the literature. However, the more general analysis shows that outside the weak coupling approximation the Hahn echo is of purely one-spin order, whereas the echo following the flash-t-P _ζ-τ-P _2ζ-t sequence has its maximal amplitude for the flip angle of 75° and the singlet-triplet mixing angle of 27°. The “in-phase” single- and double-quantum echoes are shown to vanish due to averaging out, within the electron spin resonance spectrometer deadtime, of contributions modulated with the sum and difference of the zero-quantum beat frequency and the frequency due to the spin-spin interaction within the pair. The calculated out-of-phase DQ ESE signal is inverted with respect to the out-of-phase SQ ESE and has only the half of its amplitude. The DQ ESE vanishes for the Hahn sequence. The echo has maximal amplitude in the weak-coupling limit for the flip angle of 65.9°. In contradiction to the analytical result previously published, the out-of-phase DQ ESE does not vanish for long τ and large zero-quantum-beat frequency.     

乙腈-水和乙二醇-水均相溶液中光诱导杜醌激发三重态与色氨酸、酪氨酸的氢原子转移反应

本文用激光闪光光解技术研究了光诱导生物醌杜醌激发三重态(³DQ^*)和色氨酸(Trp)与酪氨酸(Tyr)在乙腈-水(MeCN-H₂O)及乙二醇-水(EG-H₂O)均相溶液中的光化学反应,分析了反应的机理,并基于Stern-Volmer方法测量了反应速率常数. 光解DQ体系可以生成³DQ^*,³DQ^*与Trp、Tyr发生的氢原子转移反应占主导地位. 对于DQ/Trp/MeCN-H₂O和DQ/Trp/EG-H₂O溶液,³DQ^*与Trp反应生成杜醌中性自由基DQH^·、以碳为中心的色氨酸中性自由基Trp^·/NH和以氮为中心的色氨酸中性自由基Trp/N^·. 对于DQ/Tyr/MeCN-H₂O和DQ/Tyr/EG-H₂O溶液,³DQ^*与Tyr反应生成DQH^·和酪氨酸中性自由基Tyr/O^·. ³DQ^*与Trp、Tyr的氢原子转移反应速率常数都在10⁹ L·mol^-1·s^-1量级,反应近似受扩散控制. MeCN/H₂O均相溶液中³DQ^*与Trp、Tyr的反应速率常数要明显高于EG/H₂O均相溶液中的反应速率常数,这与Stokes-Einstein方程定性一致.     

Viscosity Effect Study on Quenching of Photoinduced Excited Triplet Duroquinone by TEMPO

ABSTRACT

Quenching dynamics of excited quinone molecules are given much attention in photochemistry and biochemistry. In order to study the viscosity effect on the quenching of triplet excited state of duroquinone (³DQ?) by stable radical, 2,2,6,6-tetramethylpiperidinyloxyl (TEMPO), this study measured chemically induced dynamic electron polarization (CIDEP) spectra and transient absorptive spectra in various solvents. The solvents used were ethylene glycol, 1,2-propanol and their mixtures with different ratio in volume. The Stern-Volmer plot was obtained form CIDEP spectra of photolysis of DQ with different TEMPO concentrations. Combining the slope of the Stern-Volmer plot with lifetime of ³DQ?, determined from the ³DQ? transient absorbance decay curve, the quenching rate constants of ³DQ? by TEMPO were calculated in each solvent. The results indicate that the quenching rate constant is viscosity-dependent, and that it decreases linearly with the increase in solvent viscosity in the range used in our experiment.     

Separation of the ortho and para NMR signals in solid deuterium via DQ filtering

Double quantum (DQ) filtering is shown to lead to an effective separation of the NMR signals from the para (I = 1) and ortho (I = 2) molecules in solid deuterium. The separation is achieved by the pulse sequence 90_φ^°–t_pr–90_φ^°–t_ev–90_x^°–t, where the phase-cycled first two pulses create the DQ coherence. Two components are observed after the third pulse; the para signal shows the maximum at a short time t while the ortho signal reaches the maximum at a longer t. The observed signal can be expressed as ∑_I [F_I(t_pr − t) − F_I(t_pr + t)], where F_I(t) is a proper fitting function for the free induction signal of the para and ortho molecules (with I = 1 or 2, respectively). Numerical fits to experimental data at 4.2 and 2 K show that this method can be used to determine the ratio F₁(0)/F₂(0) and thus, because the initial value F_I(0) is proportional to the respective magnetization before the pulse sequence, the ortho and para concentrations in solid deuterium.     

Practical comparison of sensitivity and resolution between STMAS and MQMAS for Al

An experimental comparison of sensitivity and resolution of satellite transition (ST) MAS and multiple quantum (MQ) MAS was performed for ²⁷Al (I = 5/2) using several pulse sequences with a z-filter and SPAM, and two inorganic samples of kaolin (Al₂Si₂O₅(OH)₄) and glass (43.1CaO–12.5Al₂O₃–44.4SiO₂). Six pulse sequences of STMAS (double-quantum filter-soft pulse added mixing = DQF-SPAM, double-quantum filter = DQF, double-quantum = DQ) and MQMAS (3QMAS-z-filter = 3Qz, 3QMAS-SPAM = 3Q-SPAM, 5QMAS-z-filter = 5Qz) are employed. All experiments have been conducted utilizing a static field of 16.4 T (700 MHz for ¹H) and a rotor spinning frequency of 20 kHz. Dependence of S/N ratios as a function of radio frequency (r.f.) field strengths indicates that strong r.f. fields are essential to obtain a better S/N ratio in all experiments. High sensitivity is obtained in the following order: DQF-SPAM, DQF, DQ, 3QSPAM, and 3Qz, although the degree of sensitivity enhancement given by STMAS for glass is slightly smaller than that for kaolin. This might be due to the different excitation and conversion efficiencies of ST and MQ coherences as a function C_q values because quadrupolar interaction of the glass are widely distributed, or to motional broadening caused by framework flexibility in the structure of glass. With respect to resolution, the full widths at half maximum (FWHM) of F₁ projections of DQF-STMAS and 3QMAS spectra for kaolin are found to be comparable, which agrees with a simulated result reported in a literature. For glass, the STMAS possess slightly wider line widths than 3QMAS. However, because such a difference in line widths of STMAS and 3QMAS spectra is substantially small, we have concluded that STMAS and 3QMAS have comparable resolution for crystalline and non-crystalline materials.     

High-Resolution H NMR Spectroscopy in the Solid State: Very Fast Sample Rotation and Multiple-Quantum Coherences

In the past few years, solid-state ¹H NMR spectroscopy under fast magic-angle spinning (MAS) has developed into a versatile tool for elucidating structure and dynamics. Dipolar multiple-quantum (MQ), in particular double-quantum (DQ), MAS spectroscopy has been applied to a variety of materials and provided unique insight, e.g., into the structure of hydrogen-bonded systems. This review intends to present solid-state ¹H DQ and MQ MAS spectroscopy in a systematic fashion with a particular emphasis on methodological aspects, followed by an overview of applications.     

Enhanced effect of magnetic field gradients using multiple quantum NMR spectroscopy applied to self-diffusion coefficient measurement

NMR spectroscopy can be used to measure molecular self-diffusion coefficients using a modified spin-echo pulse sequence known as the longitudinal eddy current delay (LED) method which incorporates pulsed magnetic field gradients. The effect of such gradients on multiple quantum coherences is investigated and shown to be of benefit for the measurement of diffusion coefficients using modest gradient strengths. The multiple quantum coherences involved in the spin operator 8I _x I _y I _y S _y of a weakly coupled SI₃ spin system (¹³CH₃ at natural abundance, in alanine in this case) were studied. The multiple quantum coherences included the quadruple-quantum (QQ) order of (3I + S), double-quantum (DQ) order of (3I - S) and (3I + S), and zero-quantum (ZQ) order of (I - S) with effective magnetogyric ratios of (3γ_H + γ_C), (3γ_H - γ_C), (γ_H + γ_C) and (γ_H - γ_C) respectively. The results show that the use of higher level quantum coherences for diffusion coefficient measurement can have the practical effect of significantly enhancing the gradient strength and this is important for slowly diffusing species.     

Distribution effects on 1H double-quantum MAS NMR spectra

The effect of a distribution in the (1)H-(1)H dipolar coupling on (1)H double-quantum (DQ) magic angle spinning (MAS) nuclear magnetic resonance (NMR) spinning sideband patterns is considered. In disordered or amorphous materials a distribution in the magnitude of the (1)H-(1)H dipolar coupling is a realistic possibility. Simulations of the (1)H DQ MAS NMR spinning sideband spectra were performed with the two-spin approximation. These simulations reveal that a dipolar coupling distribution can greatly affect the DQ spectral shape and behavior of the DQ build-up. The spectral line shapes are quantified by measurement of the relative intensities of the DQ sidebands. These variations in the (1)H DQ NMR spectra are evaluated as a function of the width of the dipolar coupling distribution. As an example, the experimental DQ spinning sideband spectrum for a hydrated polyoxoniobate containing 15 H(2)O molecules per hexaniobate cluster, are better simulated with a distribution of dipolar couplings opposed to a single coupling constant.     

A high level computational study of the CH4/CF4 dimer: how does it compare with the CH4/CH4 and CF4/CF4 dimers?

The interaction within the methane–methane (CH₄/CH₄), perfluoromethane–perfluoromethane (CF₄/CF₄) methane–perfluoromethane dimers (CH₄/CF₄) was calculated using the Hartree–Fock (HF) method, multiple orders of Møller–Plesset perturbation theory [MP2, MP3, MP4(DQ), MP4(SDQ), MP4(SDTQ)], and coupled cluster theory [CCSD, CCSD(T)], as well as the PW91, B97D, and M06-2X density functional theory (DFT) functionals. The basis sets of Dunning and coworkers (aug-cc-pVxZ, x?=?D, T, Q), Krishnan and coworkers [6-311++G(d,p), 6-311++G(2d,2p)], and Tsuzuki and coworkers [aug(df, pd)-6-311G(d,p)] were used. Basis set superposition error (BSSE) was corrected via the counterpoise method in all cases. Interaction energies obtained with the MP2 method do not fit with the experimental finding that the methane–perfluoromethane system phase separates at 94.5?K. It was not until the CCSD(T) method was considered that the interaction energy of the methane–perfluoromethane dimer (?0.69?kcal?mol^?1) was found to be intermediate between the methane (?0.51?kcal?mol^?1) and perfluoromethane (?0.78?kcal?mol^?1) dimers. This suggests that a perfluoromethane molecule interacts preferentially with another perfluoromethane (by about 0.09?kcal?mol^?1) than with a methane molecule. At temperatures much lower than the CH₄/CF₄ critical solution temperature of 94.5?K, this energy difference becomes significant and leads perfluoromethane molecules to associate with themselves, forming a phase separation. The DFT functionals yielded erratic results for the three dimers. Further development of DFT is needed in order to model dispersion interactions in hydrocarbon/perfluorocarbon systems.     

杜醌自由基光化学路径的CIDEP研究

用自制的高时间分辨电子自旋共振波谱仪,测量得到了酸性、碱性和胶束环境下的光解杜醌/乙二醇(DQ/EG)溶液瞬态自由基的化学诱导动态电子自旋极化(CIDEP)谱.在光解均相DQ/EG溶液时,观察到了以增强发射的的中性杜半醌自由基(DQH.)的CIDEP信号;在碱性环境下(pH=9)和TX-100胶束环境下光解DQ/EG体系时得到杜醌负离子自由基(DQ-.)的CIDEP信号;在酸性环境下(pH=2.5)光解DQ/EG体系时,出现的又是中性杜半醌自由基(DQH.)的CIDEP信号.实验结果显示,DQH.由3DQ*与EG之间的氢原子转移反应生成,DQ.-由DQH.的去质子化反应生成,反应中伴随着极化转移.     

Above-barrier enhancement of fusion in the 6He + 209Bi nuclear reaction

The fission cross sections for the ⁶He + ²⁰⁹Bi reaction as functions of the ⁶He-beam energy are measured. The experimental excitation functions for the reaction ²⁰⁹Bi(⁶He, 4n)²¹¹ At are also presented. The ⁶He secondary ion beam is obtained on the basis of the extracted-beam transport system of the U400-M accelerator (the Q4DQ spectrometer). A comparison of the experimental data obtained with available results for the ⁶He + ²⁰⁹Bi reaction shows that a pronounced enhancement of the fission cross sections in the above-barrier energy region is observed in the case of the reaction with the ⁶He beam. In order to fit the results of theoretical calculations to the experimental data, it is necessary to reduce the Coulomb barrier by 15% (20%). This corresponds to an increase of 1.5 (1.6) fm in the parameter r ₀ of the nuclear potential.     

Measurement of Magnitude and Sign of Heteronuclear Coupling Constants in Transition Metal Complexes

Sets of specifically tailored E.COSY-type correlation experiments and double-quantum/zero-quantum (DQ/ZQ) experiments are presented which enable the determination of sign and size of small heteronuclear coupling constants across the metal center of transition metal complexes. For the octahedrally coordinated complexes, [Ru(TPM)(H)(CO)(PPh₃)]⁺[BF₄]⁻(1) and [Ir(TPM)(H)(CO)(CO₂CH₃)]⁺[BF₄]⁻(2), 14 of 15 and 15 of 15 possible two-bond scalar coupling constants across the metal center were measured, respectively, using¹⁵N and¹⁵N/¹³C enriched samples (TPM = tris(1-pyrazolyl)methane)). The reduced coupling constants²K_X-M-Y= 4π²²J/(hγ_Xγ_Y) were found to be positive when the coupled nuclei X and Y weretranswith respect to the metal center, and negative when the coupled nuclei were incisposition. The validity of this sign rule was verified forJ_CC,J_NN,J_PN,J_PC,J_CN,J_HP,J_HC, andJ_HNcouplings. Idiosyncracies associated with 2D NMR spectra for the sign determination of coupling constants with¹⁵N which lead to corrections for the signs ofJ_HN,J_PN, andJ_CNcouplings reported previously are discussed.     

Three-dimensional lattice Boltzmann method for simulating blood flow in aortic arch

The three-dimensional （3D） lattice Boltzmann models, 3DQ15, 3DQ19 and 3DQ27, under different wall boundary conditions and lattice resolutions have been investigated by simulating Poiseuille flow in a circular cylinder for a wide range of Reynolds numbers. The 3DQ19 model with improved Fillippova and Hanel （FH） curved boundary condition represents a good compromise between computational efficiency and reliability. Blood flow in an aortic arch is then simulated as a typical haemodynamic application. Axial and secondary fluid velocity and effective wall shear stress profiles in a 180° bend are obtained, and the results also demonstrate that the lattice Boltzmann method is suitable for simulating the flow in 3D large-curved vessels.     

Simultaneous spectral editing for gamma-aminobutyric acid and taurine using double quantum coherence transfer

Conventional double quantum (DQ) editing techniques recover resonances of one metabolite at a time and are thus inefficient for monitoring metabolic changes involving several metabolites. A DQ coherence transfer double editing sequence using a dual-band DQ coherence read pulse is described here. The sequence permits simultaneous spectral editing for two metabolites with similar J coupling constants in a single scan. Simultaneous editing for taurine and gamma-aminobutyric acid (GABA) is demonstrated using solution phantoms and rat brain tissue. Selectivity of the double editing sequence for the target metabolites is as good as that achieved using conventional DQ editing which selects each metabolite individually. With experimental parameters of the double editing sequence chosen to optimize GABA editing, the sensitivity for GABA detection is the same as that with GABA editing only, while the sensitivity for taurine detection is decreased slightly compared to that with taurine editing only.     

Off-resonance effects of the radiofrequency pulses used in spectral editing with double-quantum coherence transfer

Spectral editing using gradient selected double-quantum (DQ) coherence transfer is often used for the selective observation of metabolites in vivo. In attempting to optimize the detection sensitivity of a conventional DQ spectral editing sequence, the effects of using radiofrequency (RF) pulses that are not at the resonance frequency of the observed peaks were investigated both theoretically and experimentally. The results show that spectral editing using pulses at the frequency of the observed resonance does not necessarily give the optimal detection sensitivity. At 7 T, the detection sensitivity of lactate observed using a DQ editing method can be increased by up to 30% by setting the RF pulses off resonance at the proper frequency. The results also suggest that slice selective RF pulses used in DQ spectral editing combined with PRESS localization may have slice profiles different from those when the same pulses are used for standard PRESS spatial localization.     

Basic principles of static proton low-resolution spin diffusion NMR in nanophase-separated materials with mobility contrast

We review basic principles of low-resolution proton NMR spin diffusion experiments, relying on mobility differences in nm-sized phases of inhomogeneous organic materials such as block-co- or semicrystalline polymers. They are of use for estimates of domain sizes and insights into nanometric dynamic inhomogeneities. Experimental procedures and limitations of mobility-based signal decomposition/filtering prior to spin diffusion are addressed on the example of as yet unpublished data on semicrystalline poly(ϵ-caprolactone), PCL. Specifically, we discuss technical aspects of the quantitative, dead-time free detection of rigid-domain signals by aid of the magic-sandwich echo (MSE), and magic-and-polarization-echo (MAPE) and double-quantum (DQ) magnetization filters to select rigid and mobile components, respectively. Such filters are of general use in reliable fitting approaches for phase composition determinations. Spin diffusion studies at low field using benchtop instruments are challenged by rather short ¹H T₁ relaxation times, which calls for simulation-based analyses. Applying these, in combination with domain sizes as determined by small-angle X-ray scattering, we have determined spin diffusion coefficients D for PCL (0.34, 0.19 and 0.032 nm²/ms for crystalline, interphase and amorphous parts, respectively). We further address thermal-history effects related to secondary crystallization. Finally, the state of knowledge concerning the connection between D values determined locally at the atomic level, using ¹³C detection and CP- or REDOR-based “¹H hole burning” procedures, and those obtained by calibration experiments, is summarized. Specifically, the non-trivial dependence of D on the magic-angle spinning (MAS) frequency, with a minimum under static and a local maximum under moderate-MAS conditions, is highlighted.     

Domain sizes in heterogeneous polymers by spin diffusion using single-quantum and double-quantum dipolar filters

1H spin-diffusion experiments employing a double-quantum (DQ) dipolar filter were performed for the characterization of the microdomain structure of heterogeneous samples. For this purpose the NMR spin-diffusion process was analysed based on a model morphology of three different domains with arbitrary sizes, diffusivities, and filter efficiency. General analytical solutions for z magnetization source and sink were obtained valid for a one-dimensional lamellar morphology in the full range of spin-diffusion times. These solutions of the spin-diffusion equations were used for determining the crystalline, interface, and amorphous domain sizes in polystyrene-poly(ethylene oxide) (PS-PEO) and poly(hydroxyethylmethacrylate)-poly(ethylene oxide) (PHEMA-PEO). The DQ dipolar filter has a good efficiency for PS-PEO but is only partially efficient in filtering the signal of the mobile domains in the PHEMA-PEO diblock copolymer. The domain sizes measured by the DQ filter method are compared to those obtained using the traditional dipolar filter creating z magnetization in the mobile domains.     

A variable order approach to improve differential quadrature accuracy in dynamic analysis

Differential quadrature (DQ) is a numerical technique which can produce highly accurate results by using a considerably small number of grid points. When it is applied to dynamic equations, however, DQ may exhibit dynamic numerical instability. The present paper analyzed the sources of dynamic numerical instability through a simple example, and the main finding is that dynamic stability is dominated by the grid points near and on boundaries. Based on this, we propose a variable order approach which is characterized by applying different DQ schemes to the grid points near boundaries and grid points far away from boundaries. Numerical examples of both linear and non-linear dynamic equations show that the variable order approach presented in this paper may greatly improve dynamic stability, producing convincing results.     

High-resolution 1H NMR spectroscopy in the solid state: very fast sample rotation and multiple-quantum coherences

In the past few years, solid-state 1H NMR spectroscopy under fast magic-angle spinning (MAS) has developed into a versatile tool for elucidating structure and dynamics. Dipolar multiple-quantum (MQ), in particular double-quantum (DQ), MAS spectroscopy has been applied to a variety of materials and provided unique insight, e.g., into the structure of hydrogen-bonded systems. This review intends to present solid-state 1H DQ and MQ MAS spectroscopy in a systematic fashion with a particular emphasis on methodological aspects, followed by an overview of applications.     

Application of the Floquet theory to multiple quantum NMR of dipolar-coupled multi-spin systems under magic angle spinning

A new analytical Liouville-space representation of the time-propagator under magic angle spinning (MAS) is introduced using the formalized quantum Floquet theory. This approach has the advantage that it is applicable to the analysis of any type of NMR experiment where MAS is combined with multiple-pulse excitation. General relationships describing the spectral parameters in multiple-quantum (MQ) MAS spectra are derived in this representation. Their use is illustrated with an application to double-quantum (DQ) NMR spectra of dipolar-coupled multi-spin systems. Corresponding to the separation of the MAS time-propagator into a rotor modulated and a dephasing component, two distinct mechanisms for DQ excitation are identified. One of them exploits the rotor-modulated component to excite DQ coherences through dipolar-recoupling techniques, which are familiar for spin pairs. Analytical expressions of the integral intensities and linewidths in the resulting DQ sideband pattern are derived in the form of power series expansions of the inverse rotor frequency, of which coefficients depend on structural parameters. In a multi-spin system they can most reliably be extracted in the fast spinning regime. The other mechanism exploits the dephasing component, which is characteristic to multi-spin systems only. This is shown to give rise to DQ coherences by free evolution at full rotor periods. The possibility to exploit it for selective excitation of higher order MQ coherences is discussed. In either case, the dephasing component also leads to residual broadening. The main results of the theoretical developments are demonstrated experimentally on adamantane.