Observer-selective double electron-electron-spin resonance, a pulse sequence to improve orientation selection

By pulsed double electron-electron resonance (DEER), distances between spin labels in disordered systems up to 8 nm can be measured. In addition, the relative orientation of the interacting radicals can be determined, provided that the bandwidth of the pulses is sufficiently small. On the other hand, the bandwidth has to exceed the dipolar interaction considerably, because otherwise the DEER modulations become distorted and the modulation depth decreases, making distance determination impossible. Therefore, small bandwidths, i.e. long pulses, place a lower limit on the distance that can be determined. Two new pulse sequences, observer-selective DEER (os-DEER) and dead-time free os-DEER, are introduced that make it possible to use long observer pulses with bandwidths that are smaller than the dipolar interaction. The new pulse sequences do not suffer from the distortions caused by the limited bandwidth of the observer pulses, as demonstrated by measurements on a nitroxide biradical. With observer pulses of 140 ns, i.e., significantly longer than the 32 ns used in the conventional DEER sequence, a dipolar interaction of 7.8 MHz has been measured.     

MAS NMR with and without double-quantum filtration at and near the n=0 rotational resonance condition

Spectral lineshapes of MAS NMR spectra of dipolar (re)coupled spin pairs exhibiting considerable chemical shielding anisotropies at and near the so-called n=0 rotational resonance (R2) condition are considered. The n=0 R2 condition is found to be not extremely sharp. Anisotropic interaction parameters such as chemical shielding tensor orientations and the magnitude of the dipolar coupling constant remain sensitively encoded in such lineshapes even when differences in isotropic chemical shielding values of up to 400 Hz (corresponding to ca. half the size of the dipolar coupling constant) are present. Additional double-quantum filtration (DQF) may enhance the sensitivity of spectral lineshapes to anisotropic interaction parameters for even larger differences in isotropic chemical shielding values. The dependence of the DQF efficiency on spin-system parameters as well as on external parameters (Larmor and MAS frequencies) is investigated. Away from R2 conditions a trend to lower DQF efficiencies is found whereas some spin-system parameters are more sensitively encoded in the corresponding spectral lineshapes. Our study is based on numerical simulations, with the known parameters of the 31P spin pair in Na4P2O7.10H2O representing our model case.     

Asymmetric line broadening in the electron resonance spectra of biradicals

At high temperatures the dominant relaxation process which determines the linewidths in the electron resonance spectra of flexible biradicals is modulation of the scalar electron-electron exchange interaction. In systems of high viscosity, the modulation of the exchange interaction is often quenched, and the rotational modulation of the anisotropic magnetic interactions now constitutes the principal relaxation mechanism. In this paper we derive a theoretical expression for the broadening which results from this relaxation process. The applications of the theory to the determination of molecular configurations, electron-electron separations and the sign of the exchange interaction are illustrated by comparison with the electron resonance spectrum of bis(2,2,6,6-tetramethyl-piperidinol-1-oxyl)carbonate. The theory is also of value in understanding the spectra of partially immobilized biradical spin labels.     

Double-quantum filtered MAS NMR in the presence of chemical shielding anisotropies and direct dipolar and J couplings

Double-quantum filtered MAS NMR spectra of an isolated homonuclear spin-1/2 pair are considered, at and away from rotational resonance conditions. The pulse sequence used is the solid-state NMR equivalent of double-quantum filtered COSY, known from solution-state NMR. The 119Sn spin pair in [(chex3Sn)2S] is characterized by a difference in isotropic chemical shielding smaller than the two chemical shielding anisotropies and by direct dipolar and isotropic J-coupling constants of similar magnitudes. At rotational resonance, one-dimensional double-quantum filtered 119Sn lineshapes yield the relative orientation of the two 119Sn chemical shielding tensors. Good double-quantum filtration efficiencies are found at and away from rotational resonance conditions, despite the presence of large chemical shielding anisotropies. Numerical simulations illustrate the interplay of the direct dipolar and J-coupling pathways and identify the latter as the main pathway even at rotational resonance conditions.     

HYSCORE and DEER with an upgraded 95GHz pulse EPR spectrometer

The set-up of a new microwave bridge for a 95 GHz pulse EPR spectrometer is described. The virtues of the bridge are its simple and flexible design and its relatively high output power (0.7 W) that generates pi pulses of 25 ns and a microwave field, B(1)=0.71 mT. Such a high B(1) enhances considerably the sensitivity of high field double electron-electron resonance (DEER) measurements for distance determination, as we demonstrate on a nitroxide biradical with an interspin distance of 3.6 nm. Moreover, it allowed us to carry out HYSCORE (hyperfine sublevel-correlation) experiments at 95 GHz, observing nuclear modulation frequencies of 14N and 17O as high as 40 MHz. This opens a new window for the observation of relatively large hyperfine couplings, yet not resolved in the EPR spectrum, that are difficult to observe with HYSCORE carried out at conventional X-band frequencies. The correlations provided by the HYSCORE spectra are most important for signal assignment, and the improved resolution due to the two dimensional character of the experiment provides 14N quadrupolar splittings.     

Absorption Lineshapes in Two-Dimensional Electron Spin Resonance and the Effects of Slow Motions in Complex Fluids

A methodology for obtaining pure absorption two-dimensional electron spin resonance spectra is presented for the case of large inhomogeneous broadening and/or slow motions. For slow motions, the spectra consist of “complex Lorentzians” superimposed with complex weighting factors, presenting a challenge to obtaining absorption spectra. It is shown how absorption-type spectra can be recovered for the two-pulse COSY and SECSY experiments in such cases. For three-pulse 2D ELDOR experiments, absorption lineshapes can be obtained for the autopeaks, whereas the cross peaks would be of mixed-mode character, in general. However, for practical cases the dispersive components in the cross peaks will be relatively small. Theoretical and experimental absorption spectra are provided to illustrate the method and to show the improved resolution obtained from absorption lineshapes. In particular, the variation in linewidths across a SECSY spectrum, which is a key component in elucidating motional dynamics, is clearly rendered in the pure absorption mode. A convenient method for introducing the necessary phase corrections for the slow-motional spectra is also provided.     

Carbon-13 lineshapes in solid-state NMR of labeled compounds. Effects of coherent CSA-dipolar cross-correlation

The experimental lineshapes of the carboxyl and methyl carbon resonances of fully 13C enriched L-Alanine are studied in detail at different MAS frequencies and decoupling field strengths. Complex lineshapes at intermediate spinning speeds were explained by the joint effect of off rotational resonance and coherent CSA-dipolar cross-correlation. Whereas off rotational-resonance effects lead to complex lineshapes due to a splitting of some energy levels, coherent CSA-dipolar cross-correlation introduces either a differential intensity and/or a differential broadening of the lines of the J-multiplet. The conditions which lead to such effects are explained and experimentally verified. Additional simulations show that these effects can be expected over a wide range of static magnetic fields and are not restricted to L-Alanine.     

Spinning-frequency-dependent narrowband RF-driven dipolar recoupling

Dipolar recoupling techniques of homonuclear spin pairs are commonly used for distance or orientation measurements in solids. Accurate measurements are interfered with by broadening mechanisms. In this publication narrowband RF-driven dipolar recoupling magnetization exchange experiments are performed as a function of the spinning frequency to reduce the effect of zero-quantum T(2) relaxation. To enhance the exchange of magnetization between the coupled spins, a fixed number of rotor-synchronous pi-pulses are applied at spinning frequencies approaching the rotational resonance (R(2)) conditions. The analysis of the powder averaged dipolar decay curves of the spin magnetizations as a function of the spinning frequency provides a quantitative measure of the dipolar coupling. An effective Hamiltonian for this experiment is derived, taking into account all chemical shift parameters of the spins. The length of the nbRFDR mixing time and the number of rotor cycles per pi-pulse are optimized by numerical simulations for sensitive probing of the dipolar coupling strength. The zero-quantum T(2) relaxation time can easily be taken into account in the data analysis, because the overall exchange time is almost constant in these experiments. Spinning-frequency-dependent nbRFDR experiments near the m = 1 and m = 2 R(2) condition are shown for doubly (13)C-labeled hydroxybutyric acid. Copyright 2000 Academic Press.     

DeerAnalysis2006—a comprehensive software package for analyzing pulsed ELDOR data

Pulsed electron-electron double resonance techniques such as the four-pulse double electron-electron resonance experiment measure a dipolar evolution function of the sample. For a sample consisting of spin-carrying nanoobjects, this function is the product of a form factor, corresponding to the internal structure of the nanoobject, and a background factor, corresponding to the distribution of nanoobjects in space. The form factor contains information on the spin-to-spin distance distribution within the nanoobject and on the average number of spins per nanoobject, while the background factor depends on constraints, such as a confinement of the nanoobjects to a two-dimensional layer. Separation of the dipolar evolution function into these two contributions and extraction of the spin-to-spin distance distribution require numerically stable mathematical algorithms that can handle data for different classes of samples, e.g., spin-labelled biomacromolecules and synthetic materials. Furthermore, experimental imperfections such as the limited excitation bandwidth of microwave pulses need to be considered. The software package DeerAnalysis2006 provides access to a comprehensive set of tools for such data analysis within a common user interface. This interface allows for several tests of the reliability and precision of the extracted information. User-supplied models for the spin-to-spin distance distribution within a certain class of nanoobjects can be added to an existing library and be fitted with a universal algorithm.     

Visualization of distance distribution from pulsed double electron-electron resonance data

Double electron-electron resonance (DEER), also known as pulsed electron-electron double resonance (PELDOR), is a time-domain electron paramagnetic resonance method that can measure the weak dipole-dipole interactions between unpaired electrons. DEER has been applied to discrete pairs of free radicals in biological macromolecules and to clusters containing small numbers of free radicals in polymers and irradiated materials. The goal of such work is to determine the distance or distribution of distances between radicals, which is an underdetermined problem. That is, the spectrum of dipolar interactions can be readily calculated for any distribution of free radicals, but there are many, quite different distributions of radicals that could produce the same experimental dipolar spectrum. This paper describes two methods that are useful for approximating the distance distributions for the large subset of cases in which the mutual orientations of the free radicals are uncorrelated and the width of the distribution is more than a few percent of its mean. The first method relies on a coordinate transformation and is parameter-free, while the second is based on iterative least-squares with Tikhonov regularization. Both methods are useful in DEER studies of spin-labeled biomolecules containing more than two labels.     

Practical Methods for Solid-State NMR Distance Measurements on Large Biomolecules: Constant-Time Rotational Resonance

Simple modifications of the rotational resonance experiment substantially reduce the total experimental time needed to measure weak homonuclear dipolar couplings, a critical factor for achieving routine internuclear distance measurements in large biomolecular systems. These modifications also address several problems cited in the literature. Here we introduce a constant-time rotational resonance experiment that eliminates the need for control spectra to correct for effects from variable RF heating, particularly critical for accurate long-distance measurements. This reduces the total number of experiments needed by as much as a factor of 2. Other improvements incorporated include achieving selective inversion with a delay rather than a weak pulse (P. R. Costa et al., J. Am. Chem. Soc. 119, 10487-10493, 1997), which we observe results in the elimination of oscillations in peak intensities for short mixing time points. This reduces the total experiment time in two ways. First, there is no longer a need to average different "zero"-time points (S. O. Smith et al., Biochemistry 33, 6334-6341, 1994) to correct for intensity variations. Second, short-mixing-time lineshape differences observed in large membrane-bound proteins only appear with the weak-pulse inversion and not when using the delay inversion. Consistent lineshapes between short and long mixing times permit the use of a single spectrum for subtraction of natural abundance background signals from all labeled-protein time points. Elimination of these effects improves the accuracy and efficiency of rotational resonance internuclear distance measurements.     

Calculation of solid-state NMR lineshapes using contour analysis

Two new methods for calculating lineshapes in solid-state NMR spectra are described. The first method, which we refer to as semi-analytical, allows the rapid calculation of quadrupolar central-transition lineshapes in both static and magic-angle spinning cases. The second method, which is fully numerical, allows the calculation of lineshapes resulting from any combination of interactions, including quadrupolar, dipolar and chemical shift anisotropy, and is not restricted to cases in which the principal axis systems for the different interactions are aligned. Both methods are derived from consideration of the contour lines on a plot of the resonance frequency against the Euler angles, allowing the intensity of the lineshape to be calculated at each frequency. Consequently, highly accurate lineshapes can be calculated more rapidly than previously possible, since only orientations contributing to each specific frequency are considered. For our semi-analytical method, the intensity of each point in the lineshape can be directly calculated in tens of milliseconds on a standard PC. In contrast, established methods can take several hours to calculate the same lineshape.     

Geometry of kinked protein helices from NMR data

Residual dipolar couplings between spin-1/2 and quadrupolar nuclei are often observed and exploited in the magic-angle spinning (MAS) NMR spectra of spin-1/2 nuclei. These orientation-dependent splittings contain information on the dipolar interaction, which can be translated into structural information. The same type of splittings may also be observed for pairs of quadrupolar nuclei, although information is often difficult to extract from the quadrupolar-broadened lineshapes. Here, the complete theory for describing the dipolar coupling between two quadrupolar nuclei in the frequency domain by Hamiltonian diagonalization is given. The theory is developed under MAS and double-rotation (DOR) conditions, and is valid for any spin quantum numbers, quadrupolar coupling constants, asymmetry parameters, and tensor orientations at both nuclei. All terms in the dipolar Hamiltonian become partially secular and contribute to the NMR spectrum. The theory is validated using experimental 11B and 35/37Cl NMR experiments carried out on powdered B-chlorocatecholborane, where both MAS and DOR are used to help separate effects of the quadrupolar interaction from those of the dipolar interaction. It is shown that the lineshapes are sensitive to the quadrupolar coupling constant of both nuclei and to the J coupling (including its sign). From these experiments, the dipolar coupling constant for a heteronuclear spin pair of quadrupolar nuclei may be obtained as well as the sign of the quadrupolar coupling constant of the perturbing nucleus; these are two parameters that are difficult to obtain experimentally otherwise.     

Improved narrowband dipolar recoupling for homonuclear distance measurements in rotating solids

Recovery of the magnetic dipolar interaction between nuclei bearing the same gyromagnetic ratio in rotating solids can be promoted by synchronous rf irradiation. Determination of the dipolar interaction strength can serve as a tool for structural elucidation in polycrystalline powders. Spinning frequency dependent narrow-band (nb) RFDR and SEDRA experiments are utilized as simple techniques for the determination of dipolar interactions between the nuclei in coupled homonuclear spin pairs. The magnetization exchange and coherence dephasing due to a fixed number of rotor-synchronously applied pi-pulses is monitored at spinning frequencies in the vicinity of the rotational resonance (R(2)) conditions. The powder nbRFDR and nbSEDRA decay curves of spin magnetizations and coherences, respectively, as a function of the spinning frequency can be measured and analyzed using simple rate equations providing a quantitative measure of the dipolar coupling. The effects of the phenomenological relaxation parameters in these rate equations are discussed and an improved methodology is suggested for analyzing nbRFDR data for small dipolar couplings. The distance between the labeled nuclei in the 1,3-(13)C(2)-hydroxybutyric acid molecule is rederived using existing nbRFDR results and the new simulation procedure. A nbSEDRA experiment has been performed successfully on a powder sample of singly labeled 1-(13)C-L-leucine measuring the dipolar interaction between the labeled carboxyl carbon and the natural abundant beta-carbon. Both narrowband techniques are employed for the determination of the nuclear distances between the side-chain carbons of leucine and its carbonyl carbon in a tripeptide Leu-Gly-Phe that is singly (13)C-labeled at the leucine carbonyl carbon position.     

Selective Hole-Burning in RIDME Experiment: Dead-Time Free Measurement of Dipolar Modulation

The most common technique used in pulse electron paramagnetic resonance spectroscopy to determine interspin distances in the nanometer range is pulse electron double resonance, while relaxation-induced dipolar modulation enhancement (RIDME) is a promising alternative to this method. In this article we introduced a selective hole-burning technique for RIDME experiment, which allows dead-time free measurement of dipolar modulation without the use of the second microwave frequency or a magnetic field jump. This technique was tested on a short, stable biradical in a frozen solution, and the optimal experimental conditions for the measurement of dipolar modulation were found. Interspin distances in the range of 13 Å ≤ r ≤ 25 Å can be measured by the proposed method.     

Multidimensional spectroscopy

The quantum states produced by non-linear interaction of a coherent uniform radiation field with dipolar matter are evaluated by a time-dependent perturbation expansion of the density matrix. The non-linear terms of the expansion are Fourier transformed to yield multi-dimensional spectra which indicate the connectivities in the underlying energy level diagrams. The spectra can be measured in experiments with multiple resonance, multiple pulse or stochastic excitation. Although the theory presented is of general validity in coherent spectroscopy, emphasis is placed on its application in non-linear N.M.R. spectroscopy. It illustrates particularly well the common basis of double, 2D correlated and multi-dimensional stochastic magnetic resonance.     

Search for singlet-triplet bistability or biradicaloid properties in polycyclic conjugated hydrocarbons: a valence-bond analysis

Two classes of molecules displaying singlet-triplet biradical bistability (i.e. species having significant biradicaloid properties) can be designed as follows. Alternant conjugated polycyclic hydrocarbons with numerous fixed double bonds (double bonds that remain unchanged in all its Kekulé resonance structures), a large number of Dewar resonance structures which measures the corresponding diradical resonance, and a small HOMO-LUMO band gap which measures the ease of thermal spin inversion are candidates for singlet triplet biradical bistability. Chichibabin's hydrocarbon ( 1 ) is an example. In addition, in the search for candidate molecules having singlet triplet bistability, one should also examine polycyclic conjugated systems having nonalternant induced spin frustration. Spin frustrated nonalternant polycyclic conjugated hydrocarbons will display singlet-triplet bistability (biradicaloid properties) and are generated from alternant valence-bond diradicals or Hückel molecular orbital diradicals having classical Kekulé structures by appropriate intramolecular joining of two starred or nonstarred positions with bonds, respectively.     

Quantitative Comparison of REAPDOR and TRAPDOR Experiments by Numerical Simulations and Determination of H–Al Distances in Zeolites

Quantitative H–Al distances in acid sites of two zeolites with MFI and IFR framework topology were obtained by numerical simulation of ¹H{²⁷Al} rotational echo adiabatic passage double resonance (REAPDOR) experiments. A ²⁷Al offset-dependent data set yields for each resolved ¹H NMR line a corresponding nuclear electric quadrupole coupling constant of the neighboring ²⁷Al site. This information is used for analyzing a second data set for on-resonance irradiation, where the dipolar evolution time (number of rotor cycles) was varied, to yield the ¹H–²⁷Al dipolar coupling constant. Numerical simulations indicate that the REAPDOR method does not depend significantly on the polar angles, defining the orientation of the electric field gradient tensor of ²⁷Al with respect to the Al–H dipolar vector. In contrast, the transfer of populations in double resonance sequence is sensitive to these angles, and it can be thus used to measure them.