High-resolution heteronuclear correlation spectroscopy based on spatial encoding and coherence transfer in inhomogeneous fields

Two-dimensional (2D) nuclear magnetic resonance (NMR) spectroscopy has been proven to be a powerful technique for chemical, biological, and medical studies. Heteronuclear single quantum correlation (HSQC) and heteronuclear multiple bond correlation (HMBC) are two frequently used 2D NMR methods. In combination with spatially encoded techniques, a heteronuclear 2D NMR spectrum can be acquired in several seconds and may be applied to monitoring chemical reactions. However, it is difficult to obtain high-resolution NMR spectra in inhomogeneous fields. Inspired by the idea of tracing the difference of precession frequencies between two different spins to yield high-resolution spectra, we propose a method with correlation acquisition option and J-resolved-like acquisition option to ultrafast obtain high-resolution HSQC/HMBC spectra and heteronuclear J-resolved-like spectra in inhomogeneous fields.     

Very simple combination of TROSY, CRINEPT and multiple quantum coherence for signal enhancement in an HN(CO)CA experiment for large proteins

Sensitivity enhancement in liquid state nuclear magnetic resonance (NMR) triple resonance experiments for the sequential assignment of proteins is important for the investigation of large proteins or protein complexes. We present here the 3D TROSY-MQ/CRINEPT-HN(CO)CA which makes use of a 1?N-1H-TROSY element and a 13C'-13CA CRINEPT step combined with a multiple quantum coherence during the 13CA evolution period. Because of the introduction of these relaxation-optimized elements and 10 less pulses required, when compared with the conventional TROSY-HN(CO)CA experiment an average signal enhancement of a factor of 1.8 was observed for the membrane protein-detergent complex KcsA with a rotational correlation time τ(c) of around 60 ns.     

Time-optimal coherence-order-selective transfer of in-phase coherence in heteronuclear IS spin systems

Based on principles of geometric optimal control theory, coherence transfer building blocks can be derived which achieve optimal sensitivity. Here, experimental pulse sequences are presented that achieve the best possible coherence-order-selective in-phase transfer (S(-)-->I(-)) for a heteronuclear 2-spin system for any given mixing time in the absence of relaxation. For short mixing times, the optimal experiment improves the sensitivity of isotropic mixing by up to 12.5%.     

High-resolution NMR spectra in inhomogeneous fields utilizing the CRAZED sequence without coherence selection gradients

Coherence selection gradients have been considered as indispensable for high-resolution NMR spectroscopy in inhomogeneous fields utilizing the CRAZED-type sequences. However, our experimental results demonstrate that these gradients can be omitted if an appropriate phase cycling is applied. The measured linewidth of reconstructing 1D high-resolution spectral peaks does not depend on the dipolar correlation distance determined by the coherence selection gradients, but is only affected by diffusion and T(2) relaxation. This finding suggests the need to reconsider the mechanism for the iMQC-based high-resolution spectroscopy.     

Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems

We have recently shown that the sensitivity of single- and multiple-quantum NMR experiments of half-integer (N/2) quadrupolar nuclei can be increased significantly by introducing so-called double frequency sweeps (DFS) in various pulse schemes. These sweeps consist of two sidebands generated by an amplitude modulation of the RF carrier. Using a time-dependent amplitude modulation the sidebands can be swept through a certain frequency range. Inspired by the work of Vega and Naor (J. Chem. Phys. 75, 75 (1981)), this is used to manipulate +/-(m - 1) <--> +/-m (3/2 < or = m < or = N/2) satellite transitions in half-integer spin systems simultaneously. For (23)Na (I = 3/2) and (27)Al (I = 5/2) spins in single crystals it proved possible to transfer the populations of the outer +/-m spin levels to the inner +/-1/2 spin levels. A detailed analysis shows that the efficiency of this process is a function of the adiabaticity with which the various spin transitions are passed during the sweep. In powders these sweep parameters have to be optimized to satisfy the appropriate conditions for a maximum of spins in the powder distribution. The effects of sweep rate, sweep range, and RF field strength are investigated both numerically and experimentally. Using a DFS as a preparation period leads to significantly enhanced central transition powder spectra under both static and MAS conditions, compared to single pulse excitation. DFSs prove to be very efficient tools not only for population transfer, but also for coherence transfer. This can be exploited for the multiple- to single-quantum transfer in MQMAS experiments. It is demonstrated, theoretically and experimentally, that DFSs are capable of transferring both quintuple-quantum and triple-quantum coherence into single-quantum coherence in I = 5/2 spin systems. This leads to a significant enhancement in signal-to-noise ratio and strongly reduces the RF power requirement compared to pulsed MQMAS experiments, thus extending their applicability. This is demonstrated by (27)Al 3QMAS experiments on 9Al(2)O(3). 2B(2)O(3) and the mineral andalusite. In the latter compound, Al experiences a quadrupolar-coupling constant of 15.3 MHz in one of the sites. Finally a 5QMAS spectrum on 9Al(2)O(3). 2B(2)O(3) demonstrates the sensitivity enhancement of this experiment using a double frequency sweep.     

Coherent control in the presence of intrinsic decoherence: proton transfer in large molecular systems

An efficient semiclassical approach is developed and used to calculate the coherent-control map and time dependent decoherence measure for the excited-state proton transfer dynamics associated with the keto-enolic tautomerization reaction of 2-(2'-hydroxyphenyl)-oxazole. The method extends the usual bichromatic coherent-control scenario to simulate control at finite times after photoexcitation of the system. Extensive coherent control is demonstrated in a large molecule despite the ultrafast decoherence phenomena, providing results of broad theoretical and experimental interest.     

Spin-State-Selective TPPI: A New Method for Suppression of Heteronuclear Coupling Constants in Multidimensional NMR Experiments

A novel multidimensional NMR pulse sequence tool, spin-state-selective time-proportional phase incrementation (S(3) TPPI), is introduced. It amounts to application of different TPPIs on the two components of doublets so that their frequencies can be manipulated independently. The chief application is for suppression of large heteronuclear one-bond coupling constants in indirect dimensions of multidimensional experiments without interchanging the two transverse magnetization components of doublets as conventional decoupling does, which is advantageous when they relax at different rates such as by partial compensation of dipolar and CSA relaxation contributions. For experimental confirmation we use a sample of (15)N-labeled neural cell adhesion molecule modules 1 and 2, a protein with a molecular weight of about 20 kDa. The new tool is general and can be combined with many multidimensional NMR experiments for proteins.     

Linear phase slope in pulse design: application to coherence transfer

Using optimal control methods, robust broadband excitation pulses can be designed with a defined linear phase dispersion. Applications include increased bandwidth for a given pulse length compared to equivalent pulses requiring no phase correction, selective pulses, and pulses that mitigate the effects of relaxation. This also makes it possible to create pulses that are equivalent to ideal hard pulses followed by an effective evolution period. For example, in applications, where the excitation pulse is followed by a constant delay, e.g. for the evolution of heteronuclear couplings, part of the pulse duration can be absorbed in existing delays, significantly reducing the time overhead of long, highly robust pulses. We refer to the class of such excitation pulses with a defined linear phase dispersion as ICEBERG pulses (Inherent Coherence Evolution optimized Broadband Excitation Resulting in constant phase Gradients). A systematic study of the dependence of the excitation efficiency on the phase dispersion of the excitation pulses is presented, which reveals surprising opportunities for improved pulse sequence performance.     

Spin-spin coupling edition in chiral liquid crystal NMR solvent

The application of the G-SERFph pulse sequence is presented on enantiomeric mixtures dissolved in a chiral liquid crystal. It aims at editing, within one single 2D spectrum, every proton coupling which is experienced by a given proton site in the molecule, and leads to real phased T-edited spectroscopy (T=J+2D). This NMR experiment is based on the combination of homonuclear semi-selective refocusing techniques with a spatial frequency encoding of the sample. This approach, which consists in handling selectively each coupling in separate cross sections of the sample, is applied to the visualization of enantiomers dissolved in a chiral liquid crystalline phase. Advantages and limits of this methodology are widely discussed.     

Hybrid Bridgman anvil design: an optical window for in situ spectroscopy in large volume presses

The absence of in situ optical probes for large volume presses (LVPs) often limits their application to high-pressure materials research. In this article, we present a unique anvil/optical window design for use in LVPs, which consists of an inverted diamond anvil seated in a Bridgman-type anvil. A small cylindrical aperture through the Bridgman anvil ending at the back of diamond anvil allows optical access to the sample chamber and permits direct optical spectroscopy measurements, such as ruby fluorescence (in situ pressure) or Raman spectroscopy. The performance of this anvil design has been demonstrated by loading KBr to a pressure of 14.5 GPa.     

Binary choices in small and large groups: A unified model

Two different ways to model the diffusion of alternative choices within a population of individuals in the presence of social externalities are known in the literature. While Galam’s model of rumors spreading considers a majority rule for interactions in several groups, Schelling considers individuals interacting in one large group, with payoff functions that describe how collective choices influence individual preferences. We incorporate these two approaches into a unified general discrete-time dynamic model for studying individual interactions in variously sized groups. We first illustrate how the two original models can be obtained as particular cases of the more general model we propose, then we show how several other situations can be analyzed. The model we propose goes beyond a theoretical exercise as it allows modeling situations which are relevant in economic and social systems. We consider also other aspects such as the propensity to switch choices and the behavioral momentum, and show how they may affect the dynamics of the whole population.     

Sensitivity and resolution in proton solid-state NMR at intermediate deuteration levels: quantitative linewidth characterization and applications to correlation spectroscopy

We present a systematic study of proton linewidths in rigid solids as a function of sample spinning frequency and proton density, with the latter controlled by the ratio of protonated and perdeuterated model compounds. We find that the linewidth correlates more closely with the overall proton density (rho(H)) than the size of local clusters of (1)H spins. At relatively high magic-angle spinning (MAS) rates, the linewidth depends linearly upon the inverse MAS rate. In the limit of infinite spinning rate and/or zero proton concentration, the linewidth extrapolates to a non-zero value, owing to contributions from scalar couplings, chemical shift dispersion, and B(0) field inhomogeneity. The slope of this line depends on the overall concentration of unexchangeable protons in the sample and the spinning rate. At up to 30% protonation levels ( approximately 2 (1)H/100A(3)), proton detection experiments are demonstrated to have a substantial (2- to 3-fold) sensitivity gain over corresponding (13)C-detected experiments. Within this range, the absolute sensitivity increases with protonation level; the optimal compromise between sensitivity and resolution is in the range of 20-30% protonation. We illustrate the use of dilute protons for polarization transfer to and from low-gamma spins within 5A, and to be utilized as both magnetization source and detection spins. The intermediate protonation regime enhances relaxation properties, which we expect will enable new types of (1)H correlation pulse sequences to be implemented with improved resolution and sensitivity.     

Sensitivity enhancement, assignment, and distance measurement in 13C solid-state NMR spectroscopy for paramagnetic systems under fast magic angle spinning

Despite success of previous studies, high-resolution solid-state NMR (SSNMR) of paramagnetic systems has been still largely unexplored because of limited sensitivity/resolution and difficulty in assignment due to large paramagnetic shifts. Recently, we demonstrated that an approach using very-fast magic angle spinning (VFMAS; spinning speed 20kHz) enhances resolution/sensitivity in (13)C SSNMR for paramagnetic complexes [Y. Ishii, S. Chimon, N.P. Wickramasinghe, A new approach in 1D and 2D (13)C high resolution solid-state NMR spectroscopy of paramagnetic organometallic complexes by very fast magic-angle spinning, J. Am. Chem. Soc. 125 (2003) 3438-3439]. In this study, we present a new strategy for sensitivity enhancement, signal assignment, and distance measurement in (13)C SSNMR under VFMAS for unlabeled paramagnetic complexes using recoupling-based polarization transfer. As a robust alternative of cross-polarization (CP), rapid application of recoupling-based polarization transfer under VFMAS is proposed. In the present approach, a dipolar-based analog of INEPT (dipolar INEPT) methods is used for polarization transfer and a (13)C signal is observed under VFMAS without (1)H decoupling. The resulting low duty factor permits rapid signal accumulation without probe arcing at recycle times ( approximately 3 ms/scan) matched to short (1)H T(1) values of small paramagnetic systems ( approximately 1 ms). Experiments on Cu(dl-Ala)(2) showed that the fast repetition approach under VFMAS provided sensitivity enhancement by a factor of 8-66 for a given sample, compared with the (13)C MAS spectrum under moderate MAS at 5kHz. The applicability of this approach was also demonstrated for a more challenging system, Mn(acac)(3), for which (13)C and (1)H paramagnetic shift dispersions reach 1500 and 700 ppm, respectively. It was shown that effective-evolution-time dependence of transferred signals in dipolar INEPT permitted one to distinguish (13)CH, (13)CH(2), (13)CH(3), (13)CO2- groups in 1D experiments for Cu(DL-Ala)(2) and Cu(Gly)(2). Applications of this technique to 2D (13)C/(1)H correlation NMR under VFMAS yielded reliable assignments of (1)H resonances as well as (13)C resonances for Cu(DL-Ala)(2) and Mn(acac)(3). Quantitative analysis of cross-peak intensities in 2D (13)C/(1)H correlation NMR spectra of Cu(DL-Ala)(2) provided distance information between non-bonded (13)C-(1)H pairs in the paramagnetic system.     

Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities

A model dynamical system with a great many degrees of freedom is proposed for which the critical condition for the onset of collective oscillations, the evolution of a suitably defined order parameter, and its fluctuations around steady states can be studied analytically. This is a rotator model appropriate for a large population of limit cycle oscillators. It is assumed that the natural frequencies of the oscillators are distributed and that each oscillator interacts with all the others uniformly. An exact self-consistent equation for the stationary amplitude of the collective oscillation is derived and is extended to a dynamical form. This dynamical extension is carried out near the transition point where the characteristic time scales of the order parameter and of the individual oscillators become well separated from each other. The macroscopic evolution equation thus obtained generally involves a fluctuating term whose irregular temporal variation comes from a deterministic torus motion of a subpopulation. The analysis of this equation reveals order parameter behavior qualitatively different from that in thermodynamic phase transitions, especially in that the critical fluctuations in the present system are extremely small.Dedicated to Ilya Prigogine on the occasion of his 70th birthday.     

Energy transfer rate in double-layer graphene systems: Linear regime

We theoretically investigate the energy transfer phenomenon in a double-layer graphene (DLG) system. We use the balance equation approach in linear regime and random phase approximation screening function to obtain energy transfer rates at different electron temperatures, densities and interlayer spacings. We find that the rate of energy transfer in the DLG is qualitatively similar to that obtained in the double-layer two-dimensional electron gas but its values are an order of magnitude greater. Also, at large electron temperature differences between two graphene layers, the electron density dependence of energy transfer is significantly different, particularly in case of unequal electron densities.     

Long-lived states in solution NMR: theoretical examples in three- and four-spin systems

Long-lived spin states have been observed in a variety of systems. Although the dynamics underlying the long lifetimes of these states are well understood in the case of two-spin systems, the corresponding dynamics in systems containing more spins appear to be more complex. Recently it has been shown that a selection rule for transitions mediated by intramolecular dipolar relaxation may play a role in determining the lifetimes of long-lived states in systems containing arbitrary numbers of spins. Here we present a theory of long-lived states in systems containing three and four spins and demonstrate how it can be used to identify states that have little or no intramolecular dipolar relaxation.     

Sensitivity enhancement of the central-transition signal of half-integer spin quadrupolar nuclei in solid-state NMR: features of multiple fast amplitude-modulated pulse transfer

Sensitivity enhancement of solid-state NMR spectrum of half-integer spin quadrupolar nuclei under both magic-angle spinning (MAS) and static cases has been demonstrated by transferring polarisation associated with satellite transitions to the central m=-1/2-->1/2 transition with suitably modulated radio-frequency pulse schemes. It has been shown that after the application of such enhancement schemes, there still remains polarisation in the satellite transitions that can be transferred to the central transition. This polarisation is available without having to wait for the spin system to return to thermal equilibrium. We demonstrate here the additional sensitivity enhancement obtained by making use of this remaining polarisation with fast amplitude-modulated (FAM) pulse schemes under both MAS and static conditions on a spin-3/2 and a spin-5/2 system. Considerable signal enhancement is obtained with the application of the multiple FAM sequence, denoted as m-FAM. We also report here some of the salient features of these multiple FAM sequences with respect to the nutation frequency of the pulses and the spinning frequency.     

Towards beyond-1 GHz solution NMR: internal 2H lock operation in an external current mode

We have commenced a project to develop a beyond-1 GHz solution NMR spectrometer using a HTS coil. Due to a small residual resistance present in the HTS conductor and joint resistance between conductors, a stable persistent current sufficient for NMR measurements is unlikely. Therefore, a current has to be supplied to the HTS coil from an external power supply. The ripple of an external power supply causes a field fluctuation which must be stabilized. In this study we show results of NMR measurements using a 500-600 MHz NMR in such an external current mode: the field fluctuations are stabilized by an internal 2H lock. The field fluctuation from the external power supply comprises a major field fluctuation component at low frequencies, 0.003-0.005 Hz, and superimposed minor field ripples at 2 Hz and 50 Hz. The former limits the time interval of the internal 2H lock, while the latter generates sidebands in the NMR spectrum. Sideband and baseline noise are controlled by appropriate selection of the feedback loop parameters of the lock. The quality of the 1D-solution NMR spectra observed in external current mode is equivalent to that obtained in persistent current mode. However, if the feedback loop time is as short as the gradient pulse width, refocusing of the NMR signal is lost and NMR peaks disappear. The 2D-NOESY and the 2D-HSQC spectra of ubiquitin in an external current mode have been acquired. The quality of the 2D spectra is equivalent to those obtained in persistent current mode; i.e. the internal 2H lock operates stably over an experimental time interval of 40-50 min. To realize a beyond-1 GHz NMR spectrometer, further investigations must be made of (i) the long term stability of a DC power supply, (ii) the enhancement of the compensation field limit for the internal 2H lock, (iii) the extension of the helium refill time interval, and (iv) a method to correct the field homogeneity in the external current mode.     

On laplace integrals and transfer operators in large dimension: Examples in the nonconvex case

This Letter gives detailed proofs concerning the analysis of the pair correlations for a nonconvex model. Using the transfer matrix approach, the problem is reduced to the analysis of the spectral properties of this transfer operator. Although the problem is similar to the semiclassical study of the Kac operator presented in a paper with M. Brunaud, which was devoted to the study of exp-(v/2) exp h ² exp-(v/2) for h small, new features appear for the model exp-(v/2h) exp h exp-(v/2h). Our principal results concern the splitting of this operator between the two largest eigenvalues. We give an upper and a lower bound for this splitting in the semi-classical regime. As a corollary, we get good control of the decay of the pair correlation. Some of the results were announced in a previous paper. Related WKB constructions will be developed in a later paper.Inspired by papers by M. Kac [15, 16].