Long‐Lived States of Magnetically Equivalent Spins Populated by Dissolution‐DNP and Revealed by Enzymatic Reactions

Hyperpolarization by dissolution dynamic nuclear polarization (D ‐DNP) offers a way of enhancing NMR signals by up to five orders of magnitude in metabolites and other small molecules. Nevertheless, the lifetime of hyperpolarization is inexorably limited, as it decays toward thermal equilibrium with the nuclear spin‐lattice relaxation time. This lifetime can be extended by storing the hyperpolarization in the form of long‐lived states (LLS) that are immune to most dominant relaxation mechanisms. Levitt and co‐workers have shown how LLS can be prepared for a pair of inequivalent spins by D ‐DNP. Here, we demonstrate that this approach can also be applied to magnetically equivalent pairs of spins such as the two protons of fumarate, which can have very long LLS lifetimes. As in the case of para‐hydrogen, these hyperpolarized equivalent LLS (HELLS) are not magnetically active. However, a chemical reaction such as the enzymatic conversion of fumarate into malate can break the magnetic equivalence and reveal intense NMR signals.     

Long-lived states to monitor protein unfolding by proton NMR

The relaxation of long-lived states (LLS) corresponds to the slow return to statistical thermal equilibrium between symmetric and antisymmetric proton spin states. This process is remarkably sensitive to the presence of external spins and can be used to obtain information about partial unfolding of proteins. We detected the appearance of a destabilized conformer of ubiquitin when urea is added to the protein in its native state. This conformer shows increased mobility in the C-terminus, which significantly extends the lifetimes of proton LLS magnetisation in Ser-65. These changes could not be detected by conventional measurements of T(1) and T(2) relaxation times of protons, and would hardly be sensed by carbon-13 or nitrogen-15 relaxation measurements. Conformers with similar dynamic and structural features, as revealed by LLS relaxation times, could be observed, in the absence of urea, in two ubiquitin mutants, L67S and L69S.     

Spin selective multiple quantum NMR for spectral simplification, determination of relative signs, and magnitudes of scalar couplings by spin state selection

In the present work we demonstrate a novel method for spectral simplification and determination of the relative signs of the scalar couplings using a spin selective multiple quantum NMR experiment. A spin selective excitation of double quantum coherence of A and M spins in a weakly coupled three spin system of the type AMX, results in a doublet in the double quantum dimension whose separation corresponds to the sum of couplings of the active spins to the passive spin X. One component of the doublet has the passive spin X in mid R:alpha state while the other component has the passive spin X in mid R:beta state. The spin selective conversion of double quantum coherence to single quantum coherence does not disturb the spin states of the passive spin thereby providing the spin state selection. There will be two domains of single quantum transitions in single quantum dimension at the chemical shift positions of A and M spins. The mid R:alpha domain of A spin is a doublet because of mid R:alpha and mid R:beta states of M spin only, while that of mid R:beta domain is another doublet in a different cross section of the spectra. The scalar coupling J(AM) can be extracted from any of the mid R:alpha and mid R:beta domain transitions while the relative displacements of the two doublets between the two domains at the two chemical shifts provides the magnitude and sign of the scalar coupling J(AX) relative to the coupling J(MX). Similar result is obtained for zero quantum studies on AMX spin system. The proposed technique is discussed theoretically using product operator approach. The new spin state selective double quantum J-resolved sequence has also been developed. The methodology is confirmed experimentally on a homonuclear weakly coupled three spin system and applied to two different heteronuclear five spin systems.     

Molecular properties determined from the relaxation of long-lived spin states

The populations of long-lived spin states, in particular, populations of singlet states that are comprised of antisymmetric combinations of product states, |alpha(I)beta(S)> - |beta(I)alpha(S)>, are characterized by very long lifetimes because the dipole-dipole interaction between the two "active" spins I and S that are involved in such states is inoperative as a relaxation mechanism. The relaxation rate constants of long-lived (singlet) states are therefore determined by the chemical shift anisotropy (CSA) of the active spins and by dipole-dipole interactions with passive spins. For a pair of coupled spins, the singlet-state relaxation rate constants strongly depend on the magnitudes and orientations of the CSA tensors. The relaxation properties of long-lived states therefore reveal new information about molecular symmetry and structure and about spectral density functions that characterize the dynamic behavior.     

About long-lived nuclear spin states involved in para-hydrogenated molecules

This study deals with a spin system constituted of three nonequivalent protons, two of them originating from para-hydrogen (p-H(2)) after a hydrogenation reaction carried out in the earth magnetic field. It is shown that three singlet states are created provided indirect (J) couplings exist between the three spins, implying hyperpolarization transfer toward the third spin. Upon insertion of the sample in the NMR (Nuclear Magnetic Resonance) high field magnet, the following events occur: (i) the longitudinal two-spin orders which are parts of the singlet states survive; (ii) the other two terms (of these singlet states) tend to be destroyed by magnetic field gradients but at the same time are partly converted into differences of longitudinal polarizations. Nuclear spin relaxation is studied by appropriate NMR measurements when evolution takes place in the high field magnet or in the earth field. In the former case, relaxation is classical although complicated by numerous relaxation rates associated with both longitudinal two-spin orders and longitudinal polarizations. In the latter case, an equilibration between the singlet states first occur, their disappearance being thereafter driven by relaxation rates which remain very small because of the absence of any dipolar contribution. Thus, even in the case of a three-spin system, long-lived states exist; this unexpected property could be very useful for many applications.     

NMR implementation of adiabatic SAT algorithm using strongly modulated pulses

NMR implementation of adiabatic algorithms face severe problems in homonuclear spin systems since the qubit selective pulses are long and during this period, evolution under the Hamiltonian and decoherence cause errors. The decoherence destroys the answer as it causes the final state to evolve to mixed state and in homonuclear systems, evolution under the internal Hamiltonian causes phase errors preventing the initial state to converge to the solution state. The resolution of these issues is necessary before one can proceed to implement an adiabatic algorithm in a large system where homonuclear coupled spins will become a necessity. In the present work, we demonstrate that by using "strongly modulated pulses" (SMPs) for the creation of interpolating Hamiltonian, one can circumvent both the problems and successfully implement the adiabatic SAT algorithm in a homonuclear three qubit system. This work also demonstrates that the SMPs tremendously reduce the time taken for the implementation of the algorithm, can overcome problems associated with decoherence, and will be the modality in future implementation of quantum information processing by NMR.     

Spin state selective detection of single quantum transitions using multiple quantum coherence: simplifying the analyses of complex NMR spectra

NMR spectra of molecules oriented in liquid-crystalline matrix provide information on the structure and orientation of the molecules. Thermotropic liquid crystals used as an orienting media result in the spectra of spins that are generally strongly coupled. The number of allowed transitions increases rapidly with the increase in the number of interacting spins. Furthermore, the number of single quantum transitions required for analysis is highly redundant. In the present study, we have demonstrated that it is possible to separate the subspectra of a homonuclear dipolar coupled spin system on the basis of the spin states of the coupled heteronuclei by multiple quantum (MQ)-single quantum (SQ) correlation experiments. This significantly reduces the number of redundant transitions, thereby simplifying the analysis of the complex spectrum. The methodology has been demonstrated on the doubly 13C labeled acetonitrile aligned in the liquid-crystal matrix and has been applied to analyze the complex spectrum of an oriented six spin system.     

The Adsorption of Ag on (CdTe)<Subscript>13</Subscript> Core-Cage Nanocluster: A Computational Study

Cadmium chalcogenide semiconductor quantum dots, especially doped nanoclusters, have attracted great attention for their effects on photo generated carriers and their lifetime due to introduced trapping states by changing surface unbonded orbitals. Here, we investigate the adsorption of Ag on “magic-sized” cadmium chalcogenide (CdTe)₁₃ core-cage nanoclusters, Cd₁₃Te₁₃Ag, by first-principles density functional theory. All possible adsorption sites, top, bridge, and hollow sites, have been considered. Particular attention is paid to the energy band structures of Cd₁₃Te₁₃Ag. The study demonstrates that the hollow sites, the centers of hexagons, are the favorite Ag adsorption sites. Unlike observed shallow acceptor level of doped QDs, two unusual deep mid-gap states with different spins, spin up and spin down, are observed. These two deep states shift with Ag moving towards the core of cage. The detail properties of adsorption configurations and these two deep states are analyzed. These two deep states should have important role to their optical applications.     

A Hyperpolarizable 1H Magnetic Resonance Probe for Signal Detection 15 Minutes after Spin Polarization Storage

Nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) are two extremely important techniques with applications ranging from molecular structure determination to human imaging. However, in many cases the applicability of NMR and MRI are limited by inherently poor sensitivity and insufficient nuclear spin lifetime. Here we demonstrate a cost‐efficient and fast technique that tackles both issues simultaneously. We use the signal amplification by reversible exchange (SABRE) technique to hyperpolarize the target ¹H nuclei and store this polarization in long‐lived singlet (LLS) form after suitable radiofrequency (rf) pulses. Compared to the normal scenario, we achieve three orders of signal enhancement and one order of lifetime extension, leading to ¹H NMR signal detection 15 minutes after the creation of the detected states. The creation of such hyperpolarized long‐lived polarization reflects an important step forward in the pipeline to see such agents used as clinical probes of disease.     

Magnetization Lifetimes Prediction and Measurements Using Long-Lived Spin States in Endogenous Molecules

Nuclear magnetization storage in biologically-relevant molecules opens new possibilities for the investigation of metabolic pathways, provided the lifetimes of magnetization are sufficiently long. Dissolution-dynamic nuclear polarization-based spin-order enhancement, sustained by long-lived states can measure the ratios between concentrations of endogenous molecules on a cellular pathway. These ratios can be used as meters of enzyme function. Biological states featuring intracellular amino-acid concentrations that are depleted or replenished in the course of in-cell or in-vivo tests of drugs or radiation treatments can be revealed. Progressing from already-established long-lived states, we investigated related spin order in the case of amino acids and other metabolites featuring networks of coupled spins counting up to eight nuclei. We detail a new integrated theoretical approach between quantum chemistry simulations, chemical shifts, J-couplings information from databanks, and spin dynamics calculations to deduce a priori magnetization lifetimes in biomarkers. The lifetimes of long-lived states for several amino acids were also measured experimentally in order to ascertain the approach. Experimental values were in fair agreement with the computed ones and prior data in the literature.     

Simplifying the complex 1H NMR spectra of fluorine-substituted benzamides by spin system filtering and spin-state selection: multiple-quantum-single-quantum correlation

The proton NMR spectra of fluorine-substituted benzamides are very complex (Figure 1) due to severe overlap of (1)H resonances from the two aromatic rings, in addition to several short and long-range scalar couplings experienced by each proton. With no detectable scalar couplings between the inter-ring spins, the (1)H NMR spectra can be construed as an overlap of spectra from two independent phenyl rings. In the present study we demonstrate that it is possible to separate the individual spectrum for each aromatic ring by spin system filtering employing the multiple-quantum-single-quantum correlation methodology. Furthermore, the two spin states of fluorine are utilized to simplify the spectrum corresponding to each phenyl ring by the spin-state selection. The demonstrated technique reduces spectral complexity by a factor of 4, in addition to permitting the determination of long-range couplings of less than 0.2 Hz and the relative signs of heteronuclear couplings. The technique also aids the judicious choice of the spin-selective double-quantum-single-quantum J-resolved experiment to determine the long-range homonuclear couplings of smaller magnitudes.     

Singlet state relaxation via scalar coupling of the second kind

The contribution of scalar coupling relaxation of the second kind on the relaxation behaviour of nuclear spin singlet states has been derived. The analytical equation found for the relaxation rate constant of singlet state has been compared to the equation for the relaxation of longitudinal magnetization in order to find the conditions for which the singlet state remains long-lived even in the presence of this scalar relaxation mechanism. These results are relevant when the singlet state is formed in molecules with more than two interacting spins.     

Insight into the drastically different triplet lifetimes of BODIPY obtained by optical/magnetic spectroscopy and theoretical computations

The triplet state lifetimes of organic chromophores are crucial for fundamental photochemistry studies as well as applications as photosensitizers in photocatalysis, photovoltaics, photodynamic therapy and photon upconversion. It is noteworthy that the triplet state lifetime of a chromophore can vary significantly for its analogues, while the exact reason was rarely studied. Herein with a few exemplars of typical BODIPY derivatives, which show triplet lifetimes varying up to 110-fold (1.4–160 μs), we found that for these derivatives with short triplet state lifetimes (ca. 1–3 μs), the electron spin polarization (ESP) pattern of the time-resolved electron paramagnetic resonance (TREPR) spectra of the triplet state is inverted at a longer delay time after laser pulse excitation, as a consequence of a strong anisotropy in the decay rates of the zero-field state sublevel of the triplet state. For the derivatives showing longer triplet state lifetimes (>50 μs), no such ESP inversion was observed. The observed fast decay of one sublevel is responsible for the short triplet state lifetime; theoretical computations indicate that it is due to a strong coupling between the T_z sublevel and the ground state mediated by the spin–orbit interaction. Another finding is that the heavy atom effect on the shortening of the triplet state lifetime is more significant for the T₁ states with lower energy. To the best of our knowledge, this is the first systematic study to rationalize the short triplet state lifetime of visible-light-harvesting organic chromophores. Our results are useful for fundamental photochemistry and the design of photosensitizers showing long-lived triplet states.

The electron spin polarization inversion and anisotropic decay of triplet substates explain the short triplet state lifetime of BODIPY derivatives.     

Hyperpolarization of cis-15N2-Azobenzene by Parahydrogen at Ultralow Magnetic Fields**

The development of nuclear spins hyperpolarization, and the search for molecules that can be efficiently hyperpolarized is an active area in nuclear magnetic resonance. In this work we present a detailed study of SABRE SHEATH (signal amplification by reversible exchange in shield enabled alignment transfer to heteronuclei) experiments on ¹⁵N₂-azobenzene. In SABRE SHEATH experiments the nuclear spins of the target are hyperpolarized through transfer of spin polarization from parahydrogen at ultralow fields during a reversible chemical process. Azobenzene exists in two isomers, trans and cis. We show that all nuclear spins in cis-azobenzene can be efficiently hyperpolarized by SABRE at suitable magnetic fields. Enhancement factors (relative to 9.4 T) reach up to 3000 for ¹⁵N spins and up to 30 for the ¹H spins. We compare two approaches to observe either hyperpolarized magnetization of ¹⁵N/¹H spins, or hyperpolarized singlet order of the ¹⁵N spin pair. The results presented here will be useful for further experiments in which hyperpolarized cis-¹⁵N₂-azobenzene is switched by light to trans-¹⁵N₂-azobenzene for storing the produced hyperpolarization in the long-lived spin state of the ¹⁵N pair of trans-¹⁵N₂-azobenzene.     

Charge and spin correlation structures of conjugated π systems: Analysis of full CI wave functions of the PPP hamiltonian

An analysis of the electronic correlation structures by means of the charge and spin correlation functions is carried out for full CI wave functions of four, five, and six membered conjugated π systems described by the Pariser–Parr–Pople Hamiltonian. The low-lying states of these systems are classified as covalent (CV ) and ionic (IN ) states depending on whether the probability of finding two electrons simultaneously at the same position is small or large. It is found that many of excited CV states, the typical ones of which are the 2¹A_g state of linear π systems, have stronger CV character than the ground CV state, and their spin coupling structures are different from each other as well as from that of the ground CV state. The spin coupling structure in the ground CV state has an “antiferromagnetic” spin arrangement in favor of antiparallel coupling between nearest neighbor spins while in excited CV states the extent of the antiparallel spin coupling between nearest neighbor sites is decreased. IN states, which are less common for low-lying states than CV ones, are also found to have characteristic modulations in the charge correlation. In particular, the charge correlations in the lowest singlet IN states, 1¹B_u of linear π systems, 1¹B_2g of cyclobutadiene and 1¹B_1U of benzene, are alternating.     

Exploring Weak Ligand–Protein Interactions by Long‐Lived NMR States: Improved Contrast in Fragment‐Based Drug Screening

Ligands that have an affinity for protein targets can be screened very effectively by exploiting favorable properties of long‐lived states (LLS) in NMR spectroscopy. In this work, we describe the use of LLS for competitive binding experiments to measure accurate dissociation constants of fragments that bind weakly to the ATP binding site of the N‐terminal ATPase domain of heat shock protein 90 (Hsp90), a therapeutic target for cancer treatment. The LLS approach allows one to characterize ligands with an exceptionally wide range of affinities, since it can be used for ligand concentrations [L] that are several orders of magnitude smaller than the dissociation constants K_D. This property makes the LLS method particularly attractive for the initial steps of fragment‐based drug screening, where small molecular fragments that bind weakly to a target protein must be identified, which is a difficult task for many other biophysical methods.     

Theory of long-lived nuclear spin states in solution nuclear magnetic resonance. I. Singlet states in low magnetic field

We have recently demonstrated the existence of exceptionally long-lived nuclear spin states in solution-state nuclear magnetic resonance. The lifetime of nuclear spin singlet states in systems containing coupled pairs of spins-12 may exceed the conventional relaxation time constant T1 by more than an order of magnitude. These long lifetimes may be observed if the long-lived singlet states are prevented from mixing with rapidly relaxing triplet states. In this paper we provide the detailed theory of an experiment which uses magnetic field cycling to observe slow singlet relaxation. An approximate expression is given for the magnetic field dependence of the singlet relaxation rate constant, using a model of intramolecular dipole-dipole couplings and fluctuating external random fields.     

Role of the spin magnitude of the magnetic ion in determining the frustration and low-temperature properties of kagome lattices

In view of the variety of low-temperature magnetic properties reported recently for kagome lattices with transition-metal ions in different oxidation states, we have investigated the low-energy spectrum and low-temperature thermodynamic properties of antiferromagnetic kagome lattices with varying magnitudes of site spins, employing quantum many-body Heisenberg models. The ground state and the low-lying excitation spectrum are found to depend strongly on the nature of the spin magnitude of the magnetic ions. The system remains highly frustrated if spins are half-odd-integer in magnitude, while the frustration is very weak or almost absent for integer spins or mixed-spin systems. In fact, for a mixed-spin kagome system with a certain magnitude, the whole system behaves as a classical magnet with a ferrimagnetic ground state without any frustration. These theoretical findings are consistent with a few experimental observations recently reported in the literature and would be of value in designing new kagome systems with unusual and interesting low-temperature magnetic properties.     

Slow relaxation of longitudinal multispin orders in weakly and strongly coupled two‐spin systems

Longitudinal multispin order (LOMO) corresponds to a nonequilibrium population distribution in spin systems that exhibit scalar (J), dipolar, or quadrupolar coupling. We investigated the relaxation of longitudinal two‐spin order (2‐LOMO) in systems that had either weakly or strongly J‐coupled spins. Our results indicated longer relaxation times for the 2‐LOMO state compared with the corresponding longitudinal single‐spin state (1‐LOMO). Accessing nuclear spin states that have relaxation times longer than T₁, without the use of external contrast agents, is potentially useful for in vivo imaging and also for studying systems using dynamically hyperpolarized nuclear spins where longer life times are sought to increase the time available to study (bio)chemical events. Copyright © 2012 John Wiley & Sons, Ltd.     

A Nuclear Singlet Lifetime of More than One Hour in Room‐Temperature Solution

Nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) are supremely important techniques with numerous applications in almost all branches of science. However, until recently, NMR methodology was limited by the time constant T₁ for the decay of nuclear spin magnetization through contact with the thermal molecular environment. Long‐lived states, which are correlated quantum states of multiple nuclei, have decay time constants that may exceed T₁ by large factors. Here we demonstrate a nuclear long‐lived state comprising two ¹³C nuclei with a lifetime exceeding one hour in room‐temperature solution, which is around 50 times longer than T₁. This behavior is well‐predicted by a combination of quantum theory, molecular dynamics, and quantum chemistry. Such ultra‐long‐lived states are expected to be useful for the transport and application of nuclear hyperpolarization, which leads to NMR and MRI signals enhanced by up to five orders of magnitude.