Double-quantum Spectra Research Articles

Double-quantum spectroscopy of dense atomic vapors: Interplay between Doppler and self-broadenings.

In this article, we present a simulation study of the linear and nonlinear spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus on double quantum spectroscopy, which directly probes dipole-dipole interactions. By explicitly including thermal velocity, we show that temperature has an important impact on the self-broadening mechanisms of the linear and nonlinear spectra. We also provide analytical expressions for the response functions in the short time limit using the two-body approximation, which shows that double quantum spectroscopy for atomic vapors directly probes the transition amplitude of the electronic excitation between two atoms. We also propose an expression for the double quantum spectrum that includes the effect of Doppler broadening, and we discuss the effect of density on the spectrum. We show that when Doppler broadening is negligible compared to self-broadening, the double quantum spectrum scales with the atomic density, while when Doppler broadening dominates, it scales as the square of the density.

Low-power synchronous helical pulse sequences for large anisotropic interactions in MAS NMR: Double-quantum excitation of 14N.

We develop a theoretical framework for a class of pulse sequences in the nuclear magnetic resonance (NMR) of rotating solids, which are applicable to nuclear spins with anisotropic interactions substantially larger than the spinning frequency, under conditions where the radiofrequency amplitude is smaller than or comparable to the spinning frequency. The treatment is based on average Hamiltonian theory and allows us to derive pulse sequences with well-defined relationships between the pulse parameters and spinning frequency for exciting specific coherences without the need for any detailed calculations. This framework is applied to the excitation of double-quantum spectra of 14N and is used both to evaluate the existing low-power pulse schemes and to predict the new ones, which we present here. It is shown that these sequences can be designed to be γ-encoded and therefore allow the acquisition of sideband-free spectra. It is also shown how these new double-quantum excitation sequences are incorporated into heteronuclear correlation NMR, such as 1H-14N dipolar double-quantum heteronuclear multiple-quantum correlation spectroscopy. The new experiments are evaluated both with numerical simulations and experiments on glycine and N-acetylvaline, which represent cases with "moderate" and "large" quadrupolar interactions, respectively. The analyzed pulse sequences perform well for the case of a "moderate" quadrupolar interaction, however poorly with a "large" quadrupolar interaction, for which future work on pulse sequence development is necessary.

Small angle double quantum spectroscopy (SAQS NMR)

A new experiment for recording double quantum spectra is introduced. The 2D DQ NMR experiment yields phase sensitive spectra with double quantum frequencies in F1. The appearance of remote peaks is vastly suppressed by using a small flip angle double quantum excitation and reconversion. Pulse sequences and phase sensitive processing are discussed. The complexity of the SQ antiphase magnetization given in larger proton spin networks could be reduced by using the option of band selective decoupling during the preparation period. In addition, an ACCORDION element is applied by incrementing the J evolution delay in concert with the t1 period. With this the excitation of double quantum coherence over a wider range of J values is achieved. A broadband homodecoupled version of the DQ experiment is proposed, where correlation peaks with singlet response at F2 chemical shifts and double quantum frequencies in F1 are obtained. We call this experiment Small Angle double Quantum Spectroscopy SAQS NMR.

Low-power broadband solid-state MAS NMR of 14N.

We propose two broadband pulse schemes for 14N solid-state magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) that achieves (i) complete population inversion and (ii) efficient excitation of the double-quantum spectrum using low-power single-sideband-selective pulses. We give a comprehensive theoretical description of both schemes using a common framework that is based on the jolting-frame formalism of Caravatti et al. [J. Magn. Reson. 55, 88 (1983)]. This formalism is used to determine for the first time that we can obtain complete population inversion of 14N under low-power conditions, which we do here using single-sideband-selective adiabatic pulses. It is then used to predict that double-quantum coherences can be excited using low-power single-sideband-selective pulses. We then proceed to design a new experimental scheme for double-quantum excitation. The final double-quantum excitation pulse scheme is easily incorporated into other NMR experiments, as demonstrated here for double quantum-single quantum 14N correlation spectroscopy, and 1H-14N dipolar heteronuclear multiple-quantum correlation experiments. These pulses and irradiation schemes are evaluated numerically using simulations on single crystals and full powders, as well as experimentally on ammonium oxalate ((NH4)2C2O4) at moderate MAS and glycine at ultra-fast MAS. The performance of these new NMR methods is found to be very high, with population inversion efficiencies of 100% and double-quantum excitation efficiencies of 30%-50%, which are hitherto unprecedented for the low radiofrequency field amplitudes, up to the spinning frequency, that are used here.

Two-dimensional double-quantum spectroscopy: peak shapes as a sensitive probe of carrier interactions in quantum wells

We identify carrier scattering at densities below which it has previously been observed in semiconductor quantum wells. These effects are evident in the peakshapes of 2D double-quantum spectra, which change as a function of excitation density. At high excitation densities ($\geq 10^{9}$ carriers/,cm$^{-2}$) we observe untilted peaks similar to those reported in previous experiments. At low excitation densities (<$10^{8}$ carriers cm$^{-2}$) we observe narrower, tilted peaks. Using a simple simulation, we show that tilted peak-shapes are expected in double-quantum spectra when inhomogeneous broadening is much larger than homogeneous broadening, and that fast pure-decoherence of the double-quantum coherence can obscure this peak tilt. These results show that carrier interactions are important at lower densities than previously expected, and that the `natural' double-quantum peakshapes are hidden by carrier interactions at the excitation densities typically used. Furthermore, these results demonstrate that analysis of 2D peak-shapes in double-quantum spectroscopy provides an incisive tool for identifying interactions at low excitation density.

Theoretical Aspects of Dynamic Nuclear Polarization in the Solid State: The Influence of High Radical Concentrations on the Solid Effect and Cross Effect Mechanisms

Dynamic nuclear polarization (DNP) is used to enhance signals in NMR and MRI experiments. During these experiments microwave (MW) irradiation mediates transfer of spin polarization from unpaired electrons to their neighboring nuclei. Solid state DNP is typically applied to samples containing high concentrations (i.e. 10–40 mM) of stable radicals that are dissolved in glass forming solvents together with molecules of interest. Three DNP mechanisms can be responsible for enhancing the NMR signals: the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Recently, numerical simulations were performed to describe the SE and CE mechanisms in model systems composed of several nuclei and one or two electrons. It was shown that the presence of core nuclei, close to DNP active electrons, can result in a decrease of the nuclear polarization, due to broadening of the double quantum (DQ) and zero quantum (ZQ) spectra. In this publication we consider samples with high radical concentrations, exhibiting broad inhomogeneous EPR line-shapes and slow electron cross-relaxation rates, where the TM mechanism is not the main source for the signal enhancements. In this case most of the electrons in the sample are not affected by the MW field applied at a discrete frequency. Numerical simulations are performed on spin systems composed of several electrons and nuclei in an effort to examine the role of the DNP inactive electrons. Here we show that these electrons also broaden the DQ and ZQ spectra, but that they hardly cause any loss to the DNP enhanced nuclear polarization due to their spin-lattice relaxation mechanism. Their presence can also prevent some of the polarization losses due to the core nuclei.

A software framework for analysing solid-state MAS NMR data.

Solid-state magic-angle-spinning (MAS) NMR of proteins has undergone many rapid methodological developments in recent years, enabling detailed studies of protein structure, function and dynamics. Software development, however, has not kept pace with these advances and data analysis is mostly performed using tools developed for solution NMR which do not directly address solid-state specific issues. Here we present additions to the CcpNmr Analysis software package which enable easier identification of spinning side bands, straightforward analysis of double quantum spectra, automatic consideration of non-uniform labelling schemes, as well as extension of other existing features to the needs of solid-state MAS data. To underpin this, we have updated and extended the CCPN data model and experiment descriptions to include transfer types and nomenclature appropriate for solid-state NMR experiments, as well as a set of experiment prototypes covering the experiments commonly employed by solid-sate MAS protein NMR spectroscopists. This work not only improves solid-state MAS NMR data analysis but provides a platform for anyone who uses the CCPN data model for programming, data transfer, or data archival involving solid-state MAS NMR data.Electronic supplementary materialThe online version of this article (doi:10.1007/s10858-011-9569-2) contains supplementary material, which is available to authorized users.

Complete 1H resonance assignment of β-maltose from 1H–1H DQ-SQ CRAMPS and 1H (DQ-DUMBO)–13C SQ refocused INEPT 2D solid-state NMR spectra and first principles GIPAW calculations

A disaccharide is a challenging case for high-resolution (1)H solid-state NMR because of the 24 distinct protons (14 aliphatic and 10 OH) having (1)H chemical shifts that all fall within a narrow range of approximately 3 to 7 ppm. High-resolution (1)H (500 MHz) double-quantum (DQ) combined rotation and multiple pulse sequence (CRAMPS) solid-state NMR spectra of beta-maltose monohydrate are presented. (1)H-(1)H DQ-SQ CRAMPS spectra are presented together with (1)H (DQ)-(13)C correlation spectra obtained with a new pulse sequence that correlates a high-resolution (1)H DQ dimension with a (13)C single quantum (SQ) dimension using the refocused INEPT pulse-sequence element to transfer magnetization via one-bond (13)C-(1)H J couplings. Compared to the observation of only a single broad peak in a (1)H DQ spectrum recorded at 30 kHz magic-angle spinning (MAS), the use of DUMBO (1)H homonuclear decoupling in the (1)H DQ CRAMPS experiment allows the resolution of distinct DQ correlation peaks which, in combination with first-principles chemical shift calculations based on the GIPAW (Gauge Including Projector Augmented Waves) plane-wave pseudopotential approach, enables the assignment of the (1)H resonances to the 24 distinct protons. We believe this to be the first experimental solid-state NMR determination of the hydroxyl OH (1)H chemical shifts for a simple sugar. Variable-temperature (1)H-(1)H DQ CRAMPS spectra reveal small increases in the (1)H chemical shifts of the OH resonances upon decreasing the temperature from 348 K to 248 K.

Electronic structure of substitutional nitrogen impurity in TiO 2 studied by the β-NMR method

In order to study the local electronic structure of nitrogen impurity in rutile TiO2, we have measured double-quantum NMR spectra of short lived β-emitter 12N(I=1, T 1/2=11 ms) implanted into a rutile single crystal by means of the β-NMR technique. The resonance line obtained at room temperature is well accounted for by the second order shift due to the quadrupole interaction at the oxygen substitutional site. The spectrum at 25 K has shown the other lines than the central diamagnetic line shifted by 10–15 kHz to both sides, which has been already shown in the previous data obtained with a different crystal orientation and an external field. The present results supports the existence of a paramagnetic state formed by the substitutional nitrogen impurities.

Tailoring broadband inversion pulses for MAS Solid state NMR

A simple approach is demonstrated for designing optimised broadband inversion pulses for MAS solid state NMR studies of biological systems. The method involves a two step numerical optimisation procedure and takes into account experimental requirements such as the pulse length, resonance offset range and extent of H(1) inhomogeneity compensation needed. A simulated annealing protocol is used initially to find appropriate values for the parameters that define the well known tanh/tan adiabatic pulse such that a satisfactory spin inversion is achieved with minimum RF field strength. This information is then used in the subsequent stage of refinement where the RF pulse characteristics are further tailored via a local optimisation procedure without imposing any restrictions on the amplitude and frequency modulation profiles. We demonstrate that this approach constitutes a generally applicable tool for obtaining pulses with good inversion characteristics. At moderate MAS frequencies the efficacy of the method is experimentally demonstrated for generating double-quantum NMR spectra via the zero-quantum dipolar recoupling scheme RFDR.

Assigning powders to crystal structures by high-resolution1H–1H double quantum and1H–13C J-INEPT solid-state NMR spectroscopy and first principles computation. A case study of penicillin G

We show how powder samples at natural isotopic abundance can be assigned to crystal structures by using high-resolution proton and carbon-13 solid-state NMR spectra in combination with first principles calculations. Homonuclear proton double-quantum spectra in combination with through-bond proton-carbon HSQC spectra are used to assign the NMR spectra. We then show that the proton chemical shifts can be included in the process of assigning the spectra to a crystal structure using first principles calculations. The method is demonstrated on the K salt of penicillin G.

Two-dimensional solid-state NMR studies of crystalline poly(ethylene oxide): Conformations and chemical shifts

The torsion angles of the OC–CO bonds in crystalline poly(ethylene oxide), PEO, were investigated by solid-state nuclear magnetic resonance (NMR). Two-dimensional double-quantum (DOQSY) spectra indicate that the OC–CO bonds are all gauche with an average torsion angle of ψ=74±4° and a narrow torsion-angle distribution, σ ψ <8°. This is contradictory to the wider range of gauche torsion angles in the distorted helical structure previously proposed based on X-ray fiber diffraction. The low-temperature magic-angle-spinning (MAS) 13C NMR spectrum of unlabeled PEO contains four maxima and several shoulders, over a range of 3.1 ppm. Deconvolution of this spectrum, together with two-dimensional 13C INADEQUATE NMR and exchange MAS spectra, suggests a possible assignment of chemical shifts to the 14 carbons in the 7 2 helical repeat unit. The small line widths of the individual peaks indicate that the helical repeat unit is accurately replicated throughout the crystals. The results show that packing effects or small conformational differences can change chemical shifts by amounts that had previously been ascribed only to trans/ gauche differences.

Double-quantum biased covariance spectroscopy: Application to the 2D INADEQUATE experiment

A novel processing scheme is presented that converts a two-dimensional double-quantum NMR spectrum into a single-quantum correlation spectrum. The covariance-like spectrum is computed from the 2D Fourier transform spectrum by emphasizing contributions that fulfill the double-quantum condition resulting in a symmetric spectrum that is easier to analyze. The method is demonstrated for the 2D INADEQUATE experiment.

Multiple-pulse and magic-angle spinning aided double-quantum proton solid-state NMR spectroscopy

We here report on a high-resolution pulse scheme for double-quantum (DQ) proton NMR spectroscopy in the solid-state. The pulse scheme employs a combination of multiple-pulses and magic-angle spinning (MAS) for both the excitation and conversion of DQ coherences and their evolution under homonuclear dipolar decoupling. This is made possible in this two-dimensional experiment by an effective combination of homonuclear dipolar decoupling method of phase modulated Lee–Goldburg and symmetry adapted sequence for homonuclear dipolar recoupling under MAS. DQ spectra of monoethyl fumaric acid, glycine, and histidine are presented to highlight the utility of the pulse scheme together with some of the existing drawbacks.

Advanced 1H Solid‐State NMR Spectroscopy on Hydrogels, 2

AbstractSummary: Advanced 1H solid‐state NMR methods are applied for studying the hydrogen bond formation occurring in polymer hydrogels based on N‐isopropylacrylamide (NIPAAm) and methacrylic acid (MAA). For P(NIPAAm‐co‐MAA) copolymers collapsed at low pH, two populations of water can be distinguished in 1H magic‐angle spinning (MAS) NMR spectra, one of which is probably situated near stable hydrogen‐bonded regions, while the other behaves similarly to free water. The pH‐induced polymer collapse can be followed in detail using 2D 1H‐1H double quantum (DQ) MAS NMR experiments on dried samples. For collapsed copolymers as well as interpenetrating polymer networks, the appearance of characteristic signals shows that hydrogen bonding takes place between NIPAAm and MMA monomers. The temperature dependence of the DQ spectra indicates that acid‐amide hydrogen bonds formed between both comonomers are more stable than the acid‐acid hydrogen bonds formed among MAA moieties alone. Correspondingly, by analyzing 1H‐1H DQ sideband patterns, a relatively short distance of 270 pm is found for the NIPAAm‐MMA hydrogen bond. Finally, the pH dependence of the DQ spectra demonstrates that hydrogen bonding phenomena are directly related to the polymer collapse. magnified image

Dynamics and Orientation Ordering of Water in Lyotropic Liquid Crystals Using 2H Double Quantum Filtered NMR Spectral Analysis

AbstractThe alignment of lyotropic liquid crystals in a magnetic field has been studied by line shape analysis of the T1 process and 2D 2H double quantum filtered (DQF) NMR to investigate water dynamics and orientational feature in Cetyltrimethylammonium bromide (CTAB)/Sodium Salicylate (NaSal)/D2O liquid crystals. The same system but in powder form was also examined. In the ordered liquid‐crystalline phase, the single quantum line shapes showed splitting of doublets due to the residual quadrupolar interaction, while the double quantum spectra observed splitting patterns with damped oscillation. The modified cone model is invoked to describe the restricted motions of bound D2O molecules. Ten to thirteen bound water molecules are found to associate with each CTAB molecule and the correlation time of wobbling motion of the bound water is in the time scale of 10−8 s. At 10°C, the motional correlation times of water in the powder sample have the same magnitude as those in the oriented sample. This study shows that the analysis of DQF relaxation spectra provides a more detailed source of motional information than the normally used measurements.

Dipolar and J encoded DQ MAS spectra under rotational resonance.

A two-dimensional (2D) double-quantum (DQ) experiment under rotational resonance (R(2)) conditions is introduced for evaluating dipolar couplings in rotating solids. The contributions from the R(2)-recoupled dipolar interaction and the J coupling can be conveniently separated in the resulting 2D R(2)-DQ spectrum, so that the unknown dipolar coupling can readily be extracted, provided that the values of the involved J coupling constants are known. Since the measured parameters are integral intensity ratios between suitably chosen absorption peaks in the 2D spectrum, the proposed method is characterized by a reduced sensitivity to relaxation parameters. The effect of rotor-modulated terms, including chemical shift anisotropy, is efficiently averaged out by synchronizing the excitation/reconversion time with the rotor period. All of these features are demonstrated theoretically by the example of two model systems, namely, isolated spin-pairs and a three-spin system. The results of the theoretical models are applied to both (13)C and (1)H nuclei to extract dipolar couplings in uniformly (13)C labeled L-alanine and a crosslinked natural rubber.

High-Resolution Double-Quantum 31P MAS NMR Study of the Intermediate-Range Order in Crystalline and Glass Lead Phosphates

The authors have investigated the structure of binary lead phosphate glasses using 1D {sup 31}P MAS and 2D {sup 31}P double-quantum NMR. The distribution of the Q{sub n} phosphate species, determined from the simulation of 1D MAS spectra, indicates a significant disproportionation reaction (2Q{sub n} {leftrightarrow} Q{sub n+1} + Q{sub n{minus}1}) near the pyrophosphate composition. As demonstrated on crystalline reference samples, 2D double-quantum experiments can be used to determine the connectivities between Q{sub n} groups. This allows the authors to probe the phosphorus connectivity scheme in the glass network and to show that the Q{sub n} chemical shift is influenced by the type of the bonded PO{sub 4} tetrahedron. By analyzing quantitative 1D MAS spectra and 2D double-quantum spectra, the phosphorus connectivity scheme in the glass structure and its evolution with composition have been determined.

New EPR spectra in diamonds with a high concentration of nitrogen atoms

Abstract The EPR spectrum of a synthetic diamond, containing a high concentration of isolated substitutional nitrogen, N S (the P1 EPR centre), shows in addition to the spectrum of P1 three other features not previously observed in nitrogen containing diamond: 1. an ‘allowed’ pair spectrum close to that of P1 corresponding to interacting pairs of N S at three sites separated by 0.357–0.564 nm; 2. a ‘forbidden’ pair spectrum at about half of the magnetic field required for P1, with hyperfine structure characteristic of a pair of interacting nuclei with I =1, each with the same hyperfine parameters as P1: corresponding to a superposition of many pairs of separation greater than 0.7 nm; 3. a double quantum spectrum of P1, being an exact replica of the normal spectrum at twice the magnetic field.

Determination of local structure in solid nucleic acids using double quantum nuclear magnetic resonance spectroscopy

A theoretical analysis of dipolar recoupling with a windowless multipulse irradiation (DRAWS) is presented. Analytical expressions that describe the degree to which the DRAWS pulse sequence recouples the dipolar interaction as a function of offset and spinning rate are derived using Floquet theory. Numerical methods are used to assess the performance of DRAWS in the preparation and detection of multiple quantum coherence. Simulations indicate that the mutual orientation of two or more CSA tensors can be obtained with high accuracy from double quantum spectra prepared and detected by DRAWS irradiation (DQDRAWS). These expectations are born out by experiment and in particular, the mutual orientation of three 13C CSA tensors in selectively labeled 2-deoxythymidine are determined from DQDRAWS data. The results of the DQDRAWS analysis of CSA tensor orientation in 2-deoxythymidine are shown to be in excellent agreement with results obtained by conventional methods. Using these CSA tensor orientations and an independent measurement of internuclear distance, a practical strategy is proposed and executed for deriving the mutual orientation of purine and pyrimidine bases in a DNA dodecamer from DQDRAWS data. The DQDRAWS method for determining the mutual orientation of rigid bodies in macromolecules is compared and contrasted to distance-based methods.