Zero-quantum Coherence Research Articles

Improved 2D hydride detection for NMR-chemosensing via p‐H2 Hyperpolarization

2D NMR zero-quantum spectroscopy offers a robust and convenient way to resolve hydride resonances in non-hydrogenative ParaHydrogen Induced Polarization experiments. This approach has been recently applied to the detection and quantification of dilute components in biofluids and natural extracts. For certain classes of analytes, however, modulation of the zero-quantum coherence occurs at several kiloHertz frequency, which determines long measurement times for attaining the desired resolution in the indirect dimension. Here, we propose an alternative 2D approach to measure high-resolution NMR spectra that affords enhanced sensitivity and reduced experimental time for optimal sample throughput.

Collective long-lived zero-quantum coherences in aliphatic chains.

In nuclear magnetic resonance, long-lived coherences constitute a class of zero-quantum (ZQ) coherences that have lifetimes that can be longer than the relaxation lifetimes T2 of transverse magnetization. So far, such coherences have been observed in systems with two coupled spins with spin quantum numbers I = 1/2, where a term S0T0+T0S0 in the density operator corresponds to a coherent superposition between the singlet S0 and the central triplet T0 state. Here, we report on the excitation and detection of collective long-lived coherences in AA'MM'XX' spin systems in molecules containing a chain of at least three methylene (-CH2-) groups. Several variants of excitation by polychromatic spin-lock induced crossing (poly-SLIC) are introduced that can excite a non-uniform distribution of the amplitudes of terms such as S0S0T0S0S0T0, S0T0S0S0T0S0, and T0S0S0T0S0S0. Once the radio frequency fields are switched off, these are not eigenstates, leading to ZQ precession involving all six protons, a process that can be understood as a propagation of spin order along the chain of CH2 groups before the reconversion into observable magnetization by a second poly-SLIC pulse that can be applied to any one or several of the CH2 groups. In the resulting 2D spectra, the ω2 domain shows SQ spectra with the chemical shifts of the CH2 groups irradiated during the reconversion, while the ω1 dimension shows ZQ signals in absorption mode with linewidths on the order of 0.1Hz that are not affected by the inhomogeneity of the static magnetic field but can be broadened by chemical exchange as occurs in drug screening. The ZQ frequencies are primarily determined by differences ΔJ between vicinal J-couplings.

Origin and remedy for HSQC artifacts in proton-detected INADEQUATE spectra.

NMR pulse sequences visualizing 1JCC and nJCC bond connectivity via an intermediate state of 13C-13C double-quantum coherence and 1H detection are an indispensable tool to solve small-molecule structures at the natural abundance level of 13C. A longstanding issue with these experiments set up to display 2D spectra with single-quantum frequencies is that in addition to the 1H-13C-13C correlations of interest, appearance of HSQC-type artifacts can complicate analysis and obscure JCC connectivities. The origin of these artifacts is described and remedies for their suppression are introduced. They include refocusing of 1JCH couplings prior to creation of 13C-13C double-quantum coherence, which is known to enhance sensitivity by reducing loss into zero-quantum coherence for pairs of two protonated 13C.

Experimental indications of non-classical brain functions

Recent proposals in quantum gravity have suggested that unknown systems can mediate entanglement between two known quantum systems, if the mediator itself is non-classical. This approach may be applicable to the brain, where speculations about quantum operations in consciousness and cognition have a long history. Proton spins of bulk water, which most likely interfere with any brain function, can act as the known quantum systems. If an unknown mediator exists, then NMR methods based on multiple quantum coherence (MQC) can act as an entanglement witness. However, there are doubts that today’s NMR signals can contain quantum correlations in general, and specifically in the brain environment. Here, we used a witness protocol based on zero quantum coherence (ZQC) where we minimized the classical signals to circumvent the NMR detection limits for quantum correlation. For short repetitive periods, we found evoked signals in most parts of the brain, whereby the temporal appearance resembled heartbeat-evoked potentials (HEPs). We found that those signals had no correlates with any classical NMR contrast. Similar to HEPs, the evoked signal depended on conscious awareness. Consciousness-related or electrophysiological signals are unknown in NMR. Remarkably, these signals only appeared if the local properties of the magnetization were reduced. Our findings suggest that we may have witnessed entanglement mediated by consciousness-related brain functions. Those brain functions must then operate non-classically, which would mean that consciousness is non-classical.

Double-quantum–zero-quantum 2D coherent spectroscopy reveals quantum coherence between collective states in an atomic vapor

We report a novel, to the best of our knowledge, double-quantum-zero-quantum two-dimensional coherent spectroscopy (2DCS) that allows direct detection of the quantum coherence between multiparticle collective states. Through correlating the double-quantum coherence and the zero-quantum coherence, signatures for coherence between collective states can be well isolated as side peaks and readily identified in the 2D spectrum. The experiment is implemented in a vapor of rubidium atoms in a collinear 2DCS setup. Good agreement with a theoretical simulation using density matrix confirms the essential role of the interatomic correlation effect in generating the side peak signals. This 2D spectrum technique paves a new avenue for studying the coherent coupling of highly excited states and many-body properties.

High-resolution diffusion-order NMR spectroscopy in inhomogeneous magnetic fields via intermolecular zero-quantum coherences

Diffusion-order NMR spectroscopy (DOSY) presents a powerful tool for studying solution mixtures by recording diffusion coefficients of individual components and separating their signals into respective 1D NMR spectra. Existing DOSY experiments, however, are generally unsuitable for measurements under adverse magnetic field conditions, because calculations for diffusion coefficients strictly rely on resolved resonances in the 1D NMR spectral domain. Herein, we propose a general DOSY method by introducing intermolecular zero-quantum coherence mechanism into molecular diffusion evolution to overcome the challenge of magnetic field inhomogeneity and to record high-resolution DOSY spectra free of magnetic field inhomogeneity. Our experimental results and theoretical interpretation suggest that the proposed method allows to diffusion analysis and component discrimination on solution mixtures under externally inhomogeneous magnetic field conditions and on intact biological tissues with field inhomogeneity internally caused by magnetic susceptibility variations. This study provides a previously unreported NMR protocol for high-resolution DOSY measurements in inhomogeneous magnetic fields, thus broadening the scope of DOSY applications and showing the promising prospect for studies on chemical and biological mixture samples.

Time-Domain Line-Shape Analysis from 2D Spectroscopy to Precisely Determine Hamiltonian Parameters for a Photosynthetic Complex.

Optical signals come from coherences between quantum states, with spectral line widths determined by the coherences' dephasing dynamics. Using a 2D electronic spectrometer, we observe weak coherence- and rephasing-time-domain signals persisting to 1 ps in the Fenna-Matthews-Olson complex at 77 K. These are coherences between the ground and excited states prepared after the complex interacts once or three times with light, rather than zero-quantum coherences that are more frequently investigated following two interactions. Here, we use these small but persistent signal components to isolate spectral contributions with narrowed peaks and reveal the system's eigenenergies.

Surprising absence of strong homonuclear coupling at low magnetic field explored by two-field nuclear magnetic resonance spectroscopy.

Strong coupling of nuclear spins, which is achieved when their scalar coupling is greater than or comparable to the difference in their Larmor precession frequencies in an external magnetic field, gives rise to efficient coherent longitudinal polarization transfer. The strong coupling regime can be achieved when the external magnetic field is sufficiently low, as is reduced proportional to the field strength. In the present work, however, we demonstrate that in heteronuclear spin systems these simple arguments may not hold, since heteronuclear spin-spin interactions alter the value. The experimental method that we use is two-field nuclear magnetic resonance (NMR), exploiting sample shuttling between the high field, at which NMR spectra are acquired, and the low field, where strong couplings are expected and at which NMR pulses can be applied to affect the spin dynamics. By using this technique, we generate zero-quantum spin coherences by means of a nonadiabatic passage through a level anticrossing and study their evolution at the low field. Such zero-quantum coherences mediate the polarization transfer under strong coupling conditions. Experiments performed with a -labeled amino acid clearly show that the coherent polarization transfer at the low field is pronounced in the spin subsystem under proton decoupling. However, in the absence of proton decoupling, polarization transfer by coherent processes is dramatically reduced, demonstrating that heteronuclear spin-spin interactions suppress the strong coupling regime, even when the external field is low. A theoretical model is presented, which can model the reported experimental results.

A Portable NMR Spectrometer With a Probe Head Combining RF and DC Capabilities to Generate Pulsed-Field Gradients

Portable nuclear magnetic resonance (NMR) spectrometers are used in various scientific fields. A vast number of applications are suitable for low-field permanent magnets. However, most of these systems lack the ability of pulsed-field gradients as these require cumbersome additional hardware. We herein report an NMR probe head that incorporates a radio frequency (RF)-coil equipped with pulsed-field gradient capabilities in a single center-tapped solenoid. We developed a circuitry allowing for the application of direct currents without disturbing the RF reception capabilities. Furthermore, we present a System-on-Chip-based NMR spectrometer. Combined with the NMR probe head, it represents a versatile low-cost system capable of field gradient generation. The probe head is characterized in terms of scatter parameters, quality factor, and transversal field homogeneity. We exhibit simulation data of the field gradient and present the required external circuitry. Experimental results show further the dephasing capabilities of the gradient and give insights into the spatial shape. Finally, the system is applied for the mapping of J-couplings in 1-butanol via zero-quantum coherences. A theoretical analysis of the pulse sequence is given for a homonuclear two-spin system. The experimental results demonstrate the potential use of this setup.

NOESY and DFT-GIAO Calculations Reveal Pervasive Errors in C20 Configurations of Taraxastane-3,20-diols: Proposals to Improve NMR Structure Determinations.

The current scientific consensus generally assigns incorrect C20 configurations to taraxastane-3β,20-diols and their oxo derivatives reported in 32 articles. Definitive configurations established here by NOESY, quantum mechanical NMR predictions, and 13C NMR γ-gauche effects warrant updating of the many erroneous structures. Suggestions to improve NMR structure determinations of such nonpolar polycyclic natural products include acquiring 2D spectra at higher resolution, suppressing zero-quantum coherence in NOESY, and judging proposed NOE correlations against H-H distances.

Excitation of singlet-triplet coherences in pairs of nearly-equivalent spins.

We present approaches for an efficient excitation of singlet-triplet coherences in pairs of nearly-equivalent spins. Standard Nuclear Magnetic Resonance (NMR) pulse sequences do not excite these coherences at all or with very low efficiency. The single quantum singlet-triplet coherences, here termed the outer singlet-triplet coherences, correspond to lines of low intensity in the NMR spectrum of a strongly-coupled spin pair (they are sometimes referred to as "forbidden transitions"), whereas the zero-quantum coherences, here termed the inner singlet-triplet coherences, do not have a direct spectral manifestation. In the present study, we investigated singlet-triplet coherences in a pair of nearly-equivalent carbon spins of the 13C-isotopomer of a specially designed naphthalene derivative with optimized relaxation properties. We propose and compare several techniques to drive the singlet-triplet coherence in strongly coupled spin pairs. First, we study different methods for efficient excitation of the outer singlet-triplet coherences. The achieved conversion efficiency of magnetization to the coherences of interest is close to the theoretically allowed maximum. Second, we propose methods to convert the outer coherences into the inner singlet-triplet coherence. The inner singlet-triplet coherence is insensitive to field inhomogeneity and can be long-lived. By probing this coherence, we perform a very precise measurement of the spin-spin J-couplings. A remarkable property of this coherence is that it can be preserved even in absence of a spin-locking radiofrequency field. Consequently, it is possible to shuttle the sample between different magnetic fields preserving the coherence. This allows one to study the field dependence of the relaxation time, TIST, of the inner singlet-triplet coherence by performing field-cycling experiments. We observed dramatic changes of the ratio TIST/T1 from about 1 (in strong fields) up to 2.4 (in weak fields), which is the evidence of a significant influence of the chemical shift anisotropy on relaxation. We have detected a remarkably long lifetime of the inner singlet-triplet coherence of about 200 s at the magnetic field of 5 mT.

Correlation distance dependence of the resonance frequency of intermolecular zero quantum coherences and its implication for MR thermometry

Correlation distance dependence of the resonance frequency of intermolecular zero quantum coherences and its implication for MR thermometry

Correlation distance dependence of the resonance frequency of intermolecular zero quantum coherences and its implication for MR thermometry.

Because the resonance frequency of water-fat intermolecular zero-quantum coherences (iZQCs) reflects the water-fat frequency separation at the microscopic scale, these frequencies have been proposed and used as a mean to obtain more accurate temperature information. The purpose of this work was to investigate the dependence of the water-fat iZQC resonance frequency on sample microstructure and on the specific choice of the correlation distance. The effect of water-fat susceptibility gradients on the water-methylene iZQC resonance frequency was first computed and then measured for different water-fat emulsions and for a mixture of porcine muscle and fat. Similar measurements were also performed for mixed heteronuclear spin systems. A strong dependence of the iZQC resonance frequency on the sample microstructure and on the specific choice of the correlation distance was found for spin systems like water and fat that do not mix, but not for spin systems that mix at the molecular level. Because water and fat spins do not mix at the molecular level, the water-fat iZQC resonance frequency and its temperature coefficient are not only affected by sample microstructure but also by the specific choice of the correlation distance. Magn Reson Med 79:1429-1438, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Zero Quantum Coherence in a Series of Covalent Spin-Correlated Radical Pairs

Photoinitiated subnanosecond electron transfer within covalently linked electron donor-acceptor molecules can result in the formation of a spin-correlated radical pair (SCRP) with a well-defined initial singlet spin configuration. Subsequent coherent mixing between the SCRP singlet and triplet ms = 0 spin states, the so-called zero quantum coherence (ZQC), is of potential interest in quantum information processing applications because the ZQC can be probed using pulse electron paramagnetic resonance (pulse-EPR) techniques. Here, pulse-EPR spectroscopy is utilized to examine the ZQC oscillation frequencies and ZQC dephasing in three structurally well-defined D-A systems. While transitions between the singlet and triplet ms = 0 spin states are formally forbidden (Δms = 0), they can be addressed using specific microwave pulse turning angles to map information from the ZQC onto observable single quantum coherences. In addition, by using structural variations to tune the singlet-triplet energy gap, the ZQC frequencies determined for this series of molecules indicate a stronger dependence on the electronic g-factor than on electron-nuclear hyperfine interactions.

Coherent evolution of singlet spin states in PHOTO-PHIP and M2S experiments.

A consistent theoretical description of the spin dynamics underlying photo-PHIP (para-hydrogen induced polarization) experiments is given and validated experimentally: spectra from zero-quantum coherence (ZQC) "in-phase" and "out-of-phase" were obtained and evolution of ZQCs and the population of singlet spin state was tracked and modeled. Data from recent literature [O. Torres et al., J. Am. Chem. Soc., 2014] are reinterpreted. Advantages of using M2S sequences such as APSOC for detecting photo-PHIP are demonstrated. A sequence for 2D ZQ spectroscopy based on APSOC is proposed and the fundamental principles of ZQ spectroscopy are formulated. This investigation opens a new way to obtain information on the sign of J-couplings using ZQ spectroscopy. The proposed method is also useful to track the redistribution of the singlet spin population in various PHIP related experiments, which is essential for efficient polarization transfer to target nuclei.

Theoretical Description of Pulsed RYDMR: Refocusing Zero-Quantum and Single Quantum Coherences

Abstract A theoretical description of pulsed reaction yield detected magnetic resonance (RYDMR) is proposed. In RYDMR, magnetic resonance spectra of radical pairs (RPs) are indirectly detected by monitoring their recombination yield. Such a detection method is significantly more sensitive than conventional electron paramagnetic resonance (EPR), but design of appropriate pulse sequences for RYDMR requires additional effort because of a different observable. In this work various schemes for generating spin-echo like signals and detecting them by RYDMR are treated. Specifically, we consider refocusing of zero-quantum coherences (ZQCs) and single-quantum coherences (SQCs) by selective as well as by non-selective pulses and formulate a general analytical approach to pulsed RYDMR, which makes an efficient use of the product operator formalism. We anticipate that these results are of importance for RYDMR studies of elusive paramagnetic particles, notably, in organic semiconductors.

Isolated Ground-State Vibrational Coherence Measured by Fifth-Order Single-Shot Two-Dimensional Electronic Spectroscopy.

Vibrations play a critical role in many photochemical and photophysical processes in which excitations reside on the electronically excited state. However, difficulty in assigning signals from spectroscopic measurements uniquely to a specific electronic state, ground or otherwise, has exposed limitations to their physical interpretation. Here, we demonstrate the selective excitation of vibrational coherences on the ground electronic state through impulsive Raman scattering, whose weak fifth-order signal is resonantly enhanced by coupling to strong electronic transitions. The six-wave mixing signals measured using this technique are free of lower-order cascades and represent correlations between zero-quantum vibrational coherences in the ground state and single-quantum coherences between the ground and electronic states. We believe that this technique has the potential to shed much-needed insight onto some of the mysteries regarding the origin of long-lived coherences observed in photosynthetic and other coupled chromophore systems.

High-resolution nuclear magnetic resonance measurements in inhomogeneous magnetic fields: A fast two-dimensional J-resolved experiment.

High spectral resolution in nuclear magnetic resonance (NMR) is a prerequisite for achieving accurate information relevant to molecular structures and composition assignments. The continuous development of superconducting magnets guarantees strong and homogeneous static magnetic fields for satisfactory spectral resolution. However, there exist circumstances, such as measurements on biological tissues and heterogeneous chemical samples, where the field homogeneity is degraded and spectral line broadening seems inevitable. Here we propose an NMR method, named intermolecular zero-quantum coherence J-resolved spectroscopy (iZQC-JRES), to face the challenge of field inhomogeneity and obtain desired high-resolution two-dimensional J-resolved spectra with fast acquisition. Theoretical analyses for this method are given according to the intermolecular multiple-quantum coherence treatment. Experiments on (a) a simple chemical solution and (b) an aqueous solution of mixed metabolites under externally deshimmed fields, and on (c) a table grape sample with intrinsic field inhomogeneity from magnetic susceptibility variations demonstrate the feasibility and applicability of the iZQC-JRES method. The application of this method to inhomogeneous chemical and biological samples, maybe in vivo samples, appears promising.

Establishing resolution-improved NMR spectroscopy in high magnetic fields with unknown spatiotemporal variations.

A half-century quest for higher magnetic fields has been an integral part of the progress undergone in the Nuclear Magnetic Resonance (NMR) study of materials' structure and dynamics. Because 2D NMR relies on systematic changes in coherences' phases as a function of an encoding time varied over a series of independent experiments, it generally cannot be applied in temporally unstable fields. This precludes most NMR methods from being used to characterize samples situated in hybrid or resistive magnets that are capable of achieving extremely high magnetic field strength. Recently, "ultrafast" NMR has been developed into an effective and widely applicable methodology enabling the acquisition of a multidimensional NMR spectrum in a single scan; it can therefore be used to partially mitigate the effects of temporally varying magnetic fields. Nevertheless, the strong interference of fluctuating fields with the spatial encoding of ultrafast NMR still severely restricts measurement sensitivity and resolution. Here, we introduce a strategy for obtaining high resolution NMR spectra that exploits the immunity of intermolecular zero-quantum coherences (iZQCs) to field instabilities and inhomogeneities. The spatial encoding of iZQCs is combined with a J-modulated detection scheme that removes the influence of arbitrary field inhomogeneities during acquisition. This new method can acquire high-resolution one-dimensional NMR spectra in large inhomogeneous and fluctuating fields, and it is tested with fields experimentally modeled to mimic those of resistive and resistive-superconducting hybrid magnets.

Multi-spin echo spatial encoding provides three-fold improvement of temperature precision during intermolecular zero quantum thermometry.

Intermolecular multiple quantum coherences (iMQCs) are a source of MR contrast with applications including temperature imaging, anisotropy mapping, and brown fat imaging. Because all applications are limited by signal-to-noise ratio (SNR), we developed a pulse sequence that detects intermolecular zero quantum coherences with improved SNR. A previously developed pulse sequence that detects iMQCs, HOMOGENIZED with off resonance transfer (HOT), was modified with a multi-spin echo spatial encoding scheme (MSE-HOT). MSE-HOT uses a series of refocusing pulses to generate a stack of images that are averaged in postprocessing for higher SNR. MSE-HOT performance was quantified by measuring its temperature accuracy and precision during hyperthermia of ex vivo red bone marrow samples. MSE-HOT yielded a three-fold improvement in temperature precision relative to previous pulse sequences. Sources of improved precision were 1) echo averaging and 2) suppression of J-coupling in the methylene protons of fat. MSE-HOT measured temperature change with an accuracy of 0.6°C. MSE-HOT improved the temperature accuracy and precision of HOT to a level that is sufficient for hyperthermia of bone marrow.