Long-lived states in solution NMR: selection rules for intramolecular dipolar relaxation in low magnetic fields

Recent work has shown that singlet states of two-spin systems in low magnetic fields can have lifetimes up to an order of magnitude longer than the usual spin-lattice relaxation time. This result may enable new applications of NMR, and in particular hyperpolarized NMR via parahydrogen-induced polarization, to the study of slow processes that take place over previously inaccessible timescales. At present it is unclear whether similar results apply to multi-spin systems, or if these long lifetimes are a peculiarity of the two-spin case. Moderately long-lived states have been observed in systems containing more than two spins, although the mechanisms that prolong their lifetimes are not well understood. Here we present formalism for the study of relaxation in multi-spin systems in low magnetic fields. This approach is used to derive a family of quantum-mechanical selection rules governing intramolecular dipolar relaxation at low field that may account for the extended lifetimes observed in multi-spin systems.     

Hyperpolarized long-lived states in solution NMR: three-spin case study in low field

Recent work has shown that singlet states in two-spin systems can possess lifetimes exceeding the T(1) relaxation time, provided that the system is kept under conditions that minimize the effects of the chemical shift Hamiltonian (for instance under low magnetic field or RF irradiation). Similar observations have been made in hyperpolarized states of multi-spin systems prepared via parahydrogen-induced polarization (PHIP). However, lifetime prolongation mechanisms in multi-spin systems are still under investigation. Here we present experimental observations of a long-lived state in a three-spin system prepared by PHIP and stored at low field. The observed lifetime of the long-lived state is 144s, about twice as long as the longest T(1) measured in the system at high field. The results are analyzed using a recently proposed theory of lifetime prolongation in multi-spin systems in low field. It is shown that quantum mechanical selection rules governing intramolecular dipolar relaxation in low field account for the enhanced lifetime and spectral features of this state.     

Long-lived nuclear spin states in the solution NMR of four-spin systems

The existence of long-lived nuclear spin states in four-spin systems is explored by solution-state NMR experiments. Long-lived states are proved to exist in three different natural product molecules, each containing either a AA'BB' or a AA'XX' proton spin system. The measured state lifetimes are between four and eight times the spin-lattice relaxation time constants.     

Evolution of solid state systems containing mutually coupled dipolar and quadrupole spins: perturbation treatment

Perturbation approach to time evolution of multi-spin systems containing quadrupole and dipolar spins has been presented and discussed. The treatment comprises polarization transfer effects, field-dependent relaxation processes of dipolar as well as quadrupole spins and combined results of both of them. Complete theories dealing with various aspects of the spin dynamic processes have been proposed. Because of an educational character of this paper, relevant assumptions, limitations and even particular steps of the proposed treatments have been discussed in detail. Special emphasis is put on understanding of validity regimes of the perturbation treatment, depending on relative strengths of spin interactions and timescales of relevant motional processes affecting them. Motional regimes required for spins to be involved in essentially different evolution pathways like polarization transfers or relaxation have been illustrated by experimental examples.     

三自旋体系长寿命核自旋单重态的制备

长寿命核自旋单重态的寿命（T_S）可以长于常规的纵向弛豫时间（T₁）,基于这个独特的优势,长寿命核自旋单重态具有较好的应用价值.本文对已有脉冲序列进行了改进,给出了适用于任意三自旋弱耦合体系长寿命核自旋单重态制备的参数计算方法,发现在同一个三自旋体系内核自旋单重态具有多种不同比例系数组合的形式,并以丙烯酸为例制备出了两种长寿命核自旋单重态,实验上观察到不同的核自旋单重态的寿命存在差异,另外我们还探究了温度对丙烯酸核自旋单重态寿命的影响.     

The multiple quantum NMR dynamics in systems of equivalent spins with a dipolar ordered initial state

The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the Hamiltonian responsible for the MQ NMR dynamics (the MQ Hamiltonian) is used to develop analytic and numerical methods for the investigation of the MQ NMR dynamics in systems consisting of hundreds of spins from the “first principles.” We obtain the dependence of the intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR coherences) for systems of 200–600 spins. It is shown that these profiles may be well approximated by exponential distribution functions. We also compare the MQ NMR dynamics in the systems of equivalent spins having two different initial states, the dipolar ordered state and the thermal equilibrium state in a strong external magnetic field.     

Theoretical Study of Dipolar Relaxation of Coupled Nuclear Spins at Variable Magnetic Field

A theoretical study was made of magnetic field-dependent dipolar relaxation in two- and three-spin systems. The results for the nuclear magnetic relaxation dispersion (NMRD) curves were compared with those for the simpler model of fluctuating local fields. For both models it was found that at low fields spins tend to relax with a common T ₁-relaxation time. Sharp features in the NMRD curves coming from nuclear spin level anti-crossings are also predicted by both models. However, the simple model fails to describe the behavior of so-called long-lived spin states (LLS). We have studied the LLS as function of magnetic field and molecular geometry and simulated experimental results for the LLS in histidine amino acid obtained at the laboratory of Prof. H.-M. Vieth (Free University Berlin, Germany). In addition, we described polarization transfer in a three-spin system where two spins are protons, which are initially hyperpolarized by para-hydrogen induced polarization (PHIP), while the third spin is a spin ½ hetero-nucleus, which acquires polarization in the course of cross-relaxation.     

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

Relaxation of protons by radicals in rotationally immobilized proteins

Proton spin-lattice relaxation by paramagnetic centers may be dramatically enhanced if the paramagnetic center is rotationally immobilized in the magnetic field. The details of the relaxation mechanism are different from those appropriate to solutions of paramagnetic relaxation agents. We report here large enhancements in the proton spin-lattice relaxation rate constants associated with organic radicals when the radical system is rigidly connected with a rotationally immobilized macromolecular matrix such as a dry protein or a cross-linked protein gel. The paramagnetic contribution to the protein-proton population is direct and distributed internally among the protein protons by efficient spin diffusion. In the case of a cross-linked-protein gel, the paramagnetic effects are carried to the water spins indirectly by chemical exchange mechanisms involving water molecule exchange with rare long-lived water molecule binding sites on the immobilized protein and proton exchange. The dramatic increase in the efficiency of spin relaxation by organic radicals compared with metal systems at low magnetic field strengths results because the electron relaxation time of the radical is orders of magnitude larger than that for metal systems. This gain in relaxation efficiency provides completely new opportunities for the design of spin-lattice relaxation based contrast agents in magnetic imaging and also provides new ways to examine intramolecular protein dynamics.     

Simultaneous effects of relaxation and polarization transfer in LaF3-type crystals as sources of dynamic information

Fluorine nuclear magnetic resonance (NMR) spin-lattice relaxation dispersion has been measured for pure LaF(3) and La(1-x)Sr(x)F(3-x) for admixture concentrations x ranging from 0.01% up to 16%. The relaxation dispersion experiments have been carried out in a wide frequency range (20 kHz-40 MHz) at temperatures between 300 and 1400 K. The data have been analyzed using the recently published [J. Magn. Res. 179 (2006) 250] relaxation model for multispin systems of mutually interacting quadrupolar and dipolar nuclei. Rate constants of the fluorine ionic jumps within and among distinct fluorine sublattices have been extracted. Characteristic effects of the polarization transfer between fluorine and lanthanum spins have been observed and attributed to slow dynamics within one of the fluorine sublattices.     

High-Field Phenomena of Qubits

Electron and nuclear spins are very promising candidates to serve as quantum bits (qubits) for proposed quantum computers, as the spin degrees of freedom are relatively isolated from their surroundings and can be coherently manipulated, e.g., through pulsed electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR). For solid-state spin systems, impurities in crystals based on carbon and silicon in various forms have been suggested as qubits, and very long relaxation rates have been observed in such systems. We have investigated a variety of these systems at high magnetic fields in our multifrequency pulsed EPR/ENDOR (electron nuclear double resonance) spectrometer. A high magnetic field leads to large electron spin polarizations at helium temperatures, giving rise to various phenomena that are of interest with respect to quantum computing. For example, it allows the initialization of both the electron spin as well as hyperfine-coupled nuclear spins in a well-defined state by combining millimeter and radio-frequency radiation. It can increase the T ₂ relaxation times by eliminating decoherence due to dipolar interaction and lead to new mechanisms for the coherent electrical readout of electron spins. We will show some examples of these and other effects in Si:P, SiC:N and nitrogen-related centers in diamond.     

J-Stabilization of singlet states in the solution NMR of multiple-spin systems

Long-lived singlet states have been observed in the solution NMR of spin systems containing more than two coupled spins, despite the fact that the singlet state is expected to be quenched by small long-range J-couplings. We show that the stability of localized singlet states may be explained by taking into account the intra-pair J-coupling between the two spins which participate in the singlet state. The relatively strong intra-pair J-coupling protects the singlet state against quenching by weaker out-of-pair J-couplings.     

Change of direction of dipolar field in dilute Ising system: Paradoxical concentration independence

The local dipolar field produced by fluctuating Ising spins cannot change direction unless it is produced by two or more such spins. Nonetheless, I show that the change of orientation is independent of concentration in a dilute system. The implications fo for zero-field muon spin and NMR relaxation are discussed.     

Distance measurements in spin-1/2 systems by 13C and 31P solid-state NMR in dense dipolar networks

In this article solid-state NMR methods for the determination of internuclear dipole-dipole couplings between homonuclear spin-1/2 nuclei are presented. They are suitable for relatively dense dipolar networks which are still dominated by 2-spin interactions. C-/R-symmetry theory is applied to create a double-quantum average Hamiltonian using phase-modulated radio-frequency irradiation and magic-angle sample-rotation. Symmetry derived pulse sequences with improved compensation against chemical shift anisotropies were found assuming a small isotropic chemical shift difference and using numerical calculations of the spin dynamics. Moreover it is shown that a constant time procedure can be used to acquire reliable double-quantum build-up curves even in systems in which damping obscures oscillations in their symmetric build-up curve. This technique is demonstrated on four crystalline model compounds with 31P and 13C spin systems typical for inorganic and biological applications. Comparison to crystal structure data indicates that the distances derived this way from 31P and 13C double-quantum NMR carry only small systematic errors caused for example by anisotropic J-coupling, dipolar contributions from adjacent spins and relaxation.     

Pairwise decoherence in coupled spin qubit networks

Experiments involving phase coherent dynamics of networks of spins, such as echo experiments, will only work if decoherence can be suppressed. We show here, by analyzing the particular example of a crystalline network of Fe8 molecules, that most decoherence typically comes from pairwise interactions (particularly dipolar interactions) between the spins, which cause "correlated errors." However, at very low T these are strongly suppressed. These results have important implications for the design of quantum information processing systems using electronic spins.     

Beyond the T1 limit: singlet nuclear spin states in low magnetic fields

Low-field nuclear spin singlet states may be used to store nuclear spin order in a room temperature liquid for a time much longer than the spin-lattice relaxation time constant T1. The low-field nuclear spin singlets are unaffected by intramolecular dipole-dipole relaxation, which is generally the predominant relaxation mechanism. We demonstrate storage of nuclear spin order for more than 10 times longer than the measured value of T1. This phenomenon may facilitate the development of nuclear spin hyperpolarization methods and may allow the study of motional processes which occur too slowly for existing NMR techniques. This is the first time that the memory of nuclear spins has been extended well beyond the T1 limit in a system lacking intrinsic magnetic equivalence.     

Fast polariton relaxation in strongly coupled organic microcavities

We consider the regime of strong light-matter coupling in an organic microcavity, where large Rabi splitting can be achieved. As has been shown, the excitation spectrum of such a structure, besides coherent polaritonic states, contains a number of strongly spatially localized incoherent excited states. These states form the majority of the excited states of the microcavity and are supposed to play the decisive role in the relaxation dynamics of the excitations in the microcavity. We consider the non-radiative transition from an incoherent excited state into one of the coherent states of the lower polaritonic branch accompanied by emission of a high-energy intramolecular phonon. It is shown that this process may determine the lifetime of incoherent excited states in the microcavity. This observation may be important in the discussion of pump–probe experiments with short pulses. This process may also play an important role for the population of the lowest energy states in organic microcavities, and hence in the problem of condensation of cavity polaritons.     

Nuclear spin-lattice relaxation mechanisms in kaolinite confirmed by magic-angle spinning

Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in ¹H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between ¹H spins is strong. ²⁹Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the ²⁹Si relaxation of relatively pure samples under static and slow-spinning conditions. ²⁷Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between ²⁷Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated.     

Decay of dipolar order in diamagnetic and paramagnetic proteins and protein gels

Magnetic relaxation in solids may be complicated by the creation and loss of dipolar order at finite rates. In tissues the molecular and spin dynamics may be significantly different because of the relatively high concentration of water. We have applied a modified Jeneer-Broekaert pulse sequence to measure dipolar relaxation rates in both dry and hydrated protein systems that may serve as magnetic models for tissue. In lyophilized and dry serum albumin, the dipolar relaxation time, T(1D) is on the order of 1 ms and is consistent with earlier reports. When hydrated by deuterium oxide, the dipolar relaxation times measured were on the order of tens of microseconds. When paramagnetic centers are included in the protein, the Jeneer-Broekaert echo decay times became the order of the decay time for transverse magnetization, i.e., the order of 10 micros or less. In the hydrated or paramagnetic systems, the dipolar relaxation times are too short to require inclusion in the quantitative analysis of magnetization transfer experiments.     

Phase modulation in dipolar-coupled A2 spin systems: effect of maximum state mixing in 1H NMR in vivo

Coupling constants of nuclear spin systems can be determined from phase modulation of multiplet resonances. Strongly coupled systems such as citrate in prostatic tissue exhibit a more complex modulation than AX connectivities, because of substantial mixing of quantum states. An extreme limit is the coupling of n isochronous spins (An system). It is observable only for directly connected spins like the methylene protons of creatine and phosphocreatine which experience residual dipolar coupling in intact muscle tissue in vivo. We will demonstrate that phase modulation of this "pseudo-strong" system is quite simple compared to those of AB systems. Theory predicts that the spin-echo experiment yields conditions as in the case of weak interactions, in particular, the phase modulation depends linearly on the line splitting and the echo time.