Dephasing of spin echoes by multiple heteronuclear dipolar interactions in rotational echo double resonance NMR experiments

The application of rotational echo double resonance (REDOR) nuclear magnetic resonance (NMR) for accurate distance measurements has thus far been largely restricted to isolated heteronuclear two-spin systems. In the present paper, the informational content of REDOR curves is explored for systems characterized by multi-spin interactions. To this end, numerical REDOR simulations are presented for cases in which single observe spins S are dipolarly coupled to groups of spins I in distinct geometries. To develop the utility of REDOR for characterizing dipolar couplings in unknown and/or ill-defined geometries, the validity ranges and systematic errors of certain analytical approximations are studied. In the limit of short dipolar evolution times where 0 < deltaS/S0 < or = 0.2 to 0.3, the REDOR difference signal intensity increases approximately proportional to the square of the dipolar evolution time. Here, the curvature depends simply on the second moment M2 characterizing the overall strength of the heterodipolar coupling, irrespective of specific molecular geometries. Fitting experimental REDOR data in this manner produces slight systematic underestimates of M2. However, these errors tend to be counterbalanced by additional systematic errors made by neglecting weak couplings to more remote spins and distribution effects caused by disorder. Based on these findings, the results suggest a convenient method of obtaining site-resolved second moment information in disordered materials.     

Time displacement rotational echo double resonance: heteronuclear dipolar recoupling with suppression of homonuclear interaction under fast magic-angle spinning

We have developed a novel variant of REDOR which is applicable to multiple-spin systems without proton decoupling. The pulse sequence is constructed based on a systematic time displacement of the pi pulses of the conventional REDOR sequence. This so-called time displacement REDOR (td-REDOR) is insensitive to the effect of homonuclear dipole-dipole interaction when the higher order effects are negligible. The validity of td-REDOR has been verified experimentally by the P-31{C-13} measurements on glyphosate at a spinning frequency of 25 kHz. The experimental dephasing curve is in favorable agreement with the simulation data without considering the homonuclear dipole-dipole interactions.     

Transfer of rotational population in CO by IR laser double resonance

A double resonance experiment on CO using two CO lasers (pump on v = 1 → 0, probe on v = 2 → 1) is described. Molecular diffusion has to be considered to reduce the data. The total rotational relaxation rate constant for J = 10 is found to be 1.25 ± 0.15 s^-1 torr^-1. Population transfer seems to proceed for $\text{2}\text{3}$ by |ΔJ| = 1 and for $\text{1}\text{3}\text{by |ΔJ| =2}$.     

Conversion electron measurements and determination of rotational parameters in 177Lu and 177Hf

We discuss the possibility whether superheavy elements can be produced in Nature by the astrophysical rapid neutron capture process. To this end we have performed fully dynamical network r-process calculations assuming an environment with neutron-to-seed ratio large enough to produce superheavy nuclei. Our calculations include two sets of nuclear masses and fission barriers and include all possible fission channels and the associated fission yield distributions. Our calculations produce superheavy nuclei with $\ensuremath A\approx 300$ that however decay on time scales of days.     

Magnetic resonance T21 measurements of the normal human lung in vivo with ultra-short echo times

The objective of this study was to measure T₂1 values of the normal human lung in vivo during breathhold using a rapid gradient-echo sequence with ultra-short echo times (TE). A sagittal slice of the right lung was imaged in six volunteers with various TE ranging from 0.5 ms to 5 ms using a clinical 1.5 Tesla MR scanner. T₂1 values were calculated in a region of interest in the dependent and non-dependent lung. In the dependent lung, T₂1 values of 1.1 ms ± 0.15 ms were measured, and in the non-dependent lung, 0.86 ms ± 0.11 (p < 0.01). T₂1 measurements of the normal human lung during breathhold are feasible with a clinical MR unit. The short T₂1 values require the use of very short TE times (<2.5 ms) in gradient-echo sequences to obtain adequate signal intensity from lung tissue.     

Nuclear magnetic resonance measurements and the energy band structure of PtSn

Nuclear magnetic resonance measurements of the Knight shift and spin-lattice relaxation time for ¹⁹⁵Pt and ¹¹⁹Sn in PtSn are reported. The energy band structure as determined by the relativistic orthogonalized plane wave method is also presented. The band model developed has holes in the Pt d-band but does not have a large density of states associated therewith.     

OH rotational temperature and number density measurements in high-pressure laminar flames using double phase-conjugate four-wave mixing

OH number densities and rotational temperatures up to 9 bar have been measured using double-phase-conjugate four-wave mixing (DPCFWM) in flat laminar premixed methane/air flames. By phase conjugating the backward pump to the forward pump with a phase-conjugate mirror conventional degenerate four-wave mixing (DFWM) becomes DPCFWM and quantitative measurements of OH radicals and OH rotational temperatures in flames at high pressure are possible. Our results show that conventional DFWM with a standard mirror is a low-biased measurement at high pressure primarly due to a fluctuating interaction volume which results from large fluctuating density gradients at the edge of the flame and from flame movement. A comparison is made between a laser-saturated fluorescence technique, conventional DFWM, and DPCFWM at 1, 5 and 9 bar.     

A simple procedure for secondary extinction corrections in crystal structure determination

The purpose of this contribution is to present a simple method of estimating the extinction coefficient of examined crystal and to perform the extinction corrections based on Zachariasen's approach Acta Cryst.16 (1963), 1139. Its advantage in comparison with the hitherto used procedures is briefly mentioned.     

Distance determination in human ubiquitin by pulsed double electron-electron resonance and double quantum coherence ESR methods

Recently, distance measurements by pulsed ESR (electron spin resonance) have been obtained using pulsed DEER (double electron-electron resonance) and DQC (double quantum coherence) in SDSL (site directed spin labeling) proteins. These methods can observe long range dipole interactions (15-80A). We applied these methods to human ubiquitin proteins. The distance between the 20th and the 35th cysteine was estimated in doubly spin labeled human ubiquitin. Pulsed DEER requires two microwave sources. However, a phase cycle is not usually required in this method. On the other hand, DQC-ESR at X-band ( approximately 9GHz) can acquire a large echo signal by using pulses of short duration and high power, but this method has an ESEEM (electron spin echo envelope modulation) problem. We used a commercial pulsed ESR spectrometer and compared these two methods.     

The rotational resonance Raman spectrum of nitrogen dioxide and the determination of electronic state symmetry from resonance Raman selection rules

The pure rotational Raman spectrum of nitrogen dioxide has been observed and shown to be consistent with existing determinations of molecular parameters. Upon observation at 600 Torr pressure and 0.4 cm⁻¹ resolution a well-defined rotational spectrum is obtained. This spectrum is overlaid with a number of fluorescence lines. The fluorescence lines are separated from the Raman spectrum by a comparison of Stokes and anti-Stokes branches of the rotational spectrum. Out of seven strong fluorescence lines seen with 5145 Å excitation, five probably are identifiable with vibration-rotation fluorescence progressions observed by Abe.The most striking feature of these observations is the potential use of the resonance Raman effect for the analysis of complicated electronic spectra. When this rotational spectrum is observed with excitation by 5309 Å or 5145 Å excitation, the Raman spectrum follows a-axis selection rules and the Q-branches are in the noise level or barely out of it. However, at 4880 Å the ΔK = 2Q-branches become a major feature of a spectrum, indicating that an appreciable part of the absorption at this wavelength is occurring through the operation of b- or c-axis selection rules. These findings are consistent with present notions of a ²B₂ excited state dominating absorption at longer wavelengths, while at shorter wavelengths a ²B₁ excited state becomes important. Given a tunable laser, one could map the relative importance of these two possible selection rules for NO₂ without any theoretical analysis more sophisticated than that presented in this paper.A simplified statement of the selection rules for resonance rotational Raman spectra of asymmetric tops has been developed in the course of this investigation. No attempt has been made to refine the rotational parameters of NO₂ since all of the lines seen areunresolved multiplets. Our data should be regarded as a search spectrum preliminary to investigation on a high resolution instrument.     

Site connectivities in silver borophosphate glasses: new results from 11B{31P} and 31P{11B} rotational echo double resonance NMR spectroscopy

Local and medium range order in the glass system 50Ag2O-50[(B2O3)x-(P2O5)(1-x)] (x=0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6) have been investigated by high-resolution solid state nuclear magnetic resonance (NMR) techniques. The detailed local site distribution has been derived from deconvolution analysis of the 11B and 31P magic-angle spinning (MAS) NMR signals. Quantitative information regarding the extent of boron-oxygen-phosphorus connectivity has been obtained on the basis of 11B[31P} and 31P{11B} rotational echo double resonance experiments. Incorporation of borate into silver metaphosphate glasses produces four-coordinate BO4/2- sites, which crosslink the metaphosphate chains, resulting in a significant increase in the glass transition temperature. Furthermore, the presence of borate favors the disproportionation of P(2) chain-like units into P(1) and P(3) sites, an effect not observed in binary alkali phosphate glasses. Finally, borate incorporation beyond x=0.3 results in the formation of neutral BO3/2 units, indicating some net charge transfer from the borate to the phosphate network former species. This latter result corresponds to the general metal ion scavenging effect observed for phosphate species in other mixed network former glass systems. In the present system, the effect is relatively moderate, however, suggesting that anionic BO4/2- groups are stabilized by the interaction with the phosphate groups.     

The inter molecular potential of NH+ 4-Ar II. Calculations and experimental measurements for the rotational structure of the v 3 band

The mid-infrared spectrum of the v ₃,(t ₂) transition of the NH⁺ ₄-Ar complex has been recorded at rotational resolution using photofragmentation spectroscopy. The spectrum is divided into perpendicular and parallel subbands corresponding to transitions between different hindered internal rotor states. The P and R branches of the strongest perpendicular subbands are rotationally resolved providing rotational and centrifugal distortion constants. The widths of individual rotational lines are limited by the laser bandwidth of 0.02 cm^?1, giving a lower limit of 250 ps for the lifetime of the excited states. Effective intermolecular separations for each internal rotor state are determined from its rotational constant, after correction for the contribution due to Coriolis coupling between the internal and total rotational angular momenta. The absolute energies, rotational and distortion constants for the first few intermolecular bending and stretching levels of the ground intramolecular vibrational state are determined in a numerical solution to the rotation-intermolecular vibration Hamiltonian, employing a three-dimensional ab initio intermolecular potential. The results are compared with the experimental constants in order to assess the accuracy of the calculated potential. The relative energy levels from this calculation are also compared with those from a two-dimensional representation of the potential energy surface (‘fixed-R’ model) in order to judge directly the influence of the radial dependence of the potential.     

Gas temperature determination from the unresolved rotational structure of vibronic bands of diatomic molecules

Journal of Applied Spectroscopy -     

Dipolar coupling information in multispin systems: application of a compensated REDOR NMR approach to inorganic phosphates. Rotational echo double resonance

An experimental strategy has been developed for measuring multiple dipole-dipole interactions in inorganic compounds using the technique of rotational echo double resonance (REDOR) NMR. Geometry-independent information about the dipole couplings between the observe nuclear species S (arbitrary quantum number) and the heteronuclear species I (spin-12) can be conveniently obtained from the experimental curve of DeltaS/S(0) versus dipolar evolution time by limiting the analysis to the initial data range 0 < delta S/S(0) < 0.30. Numerical simulations have been carried out on a three-spin system of type SI(2) in order to assess the effect of the I-I homonuclear dipole-dipole coupling and the influence of experimental imperfections such as finite pulse length and misadjustments of the 180 degrees pulses applied to the I-spin species. The simulations show further that within the initial data range the effects of such misadjustments can be internally compensated by a modified sequence having an additional 180 degrees pulse on the I channel in the middle of the dipolar evolution periods. Experimental (27)Al?(31)P? REDOR results on the multispin systems Al(PO(3))(3), AlPO(4), [AlPO(4)](12)(C(3)H(7))(4)NF, and Na(3)PO(4) confirm the general utility of this approach. Thus, for applications to unknown systems the compensation strategy obviates calibration procedures with model compounds.     

A theoretical perspective on the accuracy of rotational resonance (R 2)-based distance measurements in solid-state NMR

The application of solid-state NMR methodology for bio-molecular structure determination requires the measurement of constraints in the form of ¹³C–¹³C and ¹³C–¹⁵N distances, torsion angles and, in some cases, correlation of the anisotropic interactions. Since the availability of structurally important constraints in the solid state is limited due to lack of sufficient spectral resolution, the accuracy of the measured constraints become vital in studies relating the three-dimensional structure of proteins to its biological functions. Consequently, the theoretical methods employed to quantify the experimental data become important. To accentuate this aspect, we re-examine analytical two-spin models currently employed in the estimation of ¹³C–¹³C distances based on the rotational resonance (R ²) phenomenon. Although the error bars for the estimated distances tend to be in the range 0.5–1.0 Å, R ² experiments are routinely employed in a variety of systems ranging from simple peptides to more complex amyloidogenic proteins. In this article we address this aspect by highlighting the systematic errors introduced by analytical models employing phenomenological damping terms to describe multi-spin effects. Specifically, the spin dynamics in R ² experiments is described using Floquet theory employing two different operator formalisms. The systematic errors introduced by the phenomenological damping terms and their limitations are elucidated in two analytical models and analysed by comparing the results with rigorous numerical simulations.     

On the determination of the reduced rotational operator for polyatomic molecules

Irreducible tensorial sets are used for constructing the reduced rotational Hamiltonian of the molecule, i.e., for obtaining the Hamiltonian with independent rotational, centrifugal distortion, and resonance parameters. General formulas are obtained which allow one to do this, and are valid for molecules of any symmetry. As an illustration of the general results, molecules of T_d symmetry are considered.     

The rotational spectrum of the X 2Σ+ state of the SrF radical using laser microwave optical double resonance

The pure rotational spectrum of the $\text{X}{}^2\text{Σ}{}^{\mathrm{+}}$ state of the gaseous SrF radical has been measured using microwave optical double resonance (MODR) techniques. The analysis fully confirms the recent dye laser excitation spectrum and rotational assignment of the $\text{B}{}^2\text{Σ}{}^{\mathrm{+}}\text{-X}{}^2\text{Σ}{}^{\mathrm{+}}$ system. Transitions were measured in both the v″ = 0 and v″ = 1 states to give values of B_e″ = 0.250533 cm^?1, α_e″ = 1.546 × 10^?3 cm^?1 and γ″ (spin-rotation) = 2.49 × 10^?3 cm^?1. General qualitative features of MODR in ²Σ⁺ states are treated and suggested improvements for obtaining experimental hyperfine constants are discussed. The more precise ground state constants are merged with the B-X optical analysis to obtain a more accurate set of constants for both states.     

W态纠缠实现双腔远程控制原子的非经典特性

考虑将双模纠缠相干光场的两模场同时分别注入两个腔中,初态处于W态的三体纠缠二能级原子中的两个分别在这两个腔内,并且都与光场发生共振相互作用,经腔QED演化之后,对纠缠相干光场进行光子探测和对纠缠原子进行选择性测量,通过操纵相互作用的时间和光场的参数可控制W态中处于腔外的第三个原子的非经典效应,如粒子数布居差的崩塌一回复现象和偶极压缩现象,从而实现了更强地远程控制原子的非经典特性.     

2H[19F] REDOR for distance measurements in biological solids using a double resonance spectrometer

A new approach for distance measurements in biological solids employing 2H[19F] rotational echo double resonance was developed and validated on 2H,19F-D-alanine and an imidazopyridine based inhibitor of the gastric H+/K+-ATPase. The 2H-19F double resonance experiments presented here were performed without 1H decoupling using a double resonance NMR spectrometer. In this way, it was possible to benefit from the relatively longer distance range of fluorine without the need of specialized fluorine equipment. A distance of 2.5 +/- 0.3 A was measured in the alanine derivative, indicating a gauche conformation of the two labels. In the case of the imidazopyridine compound a lower distance limit of 5.2 A was determined and is in agreement with an extended conformation of the inhibitor. Several REDOR variants were compared, and their advantages and limitations discussed. Composite fluorine dephasing pulses were found to enhance the frequency bandwidth significantly, and to reduce the dependence of the performance of the experiment on the exact choice of the transmitter frequency.