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Clusters of coupled nuclear spins may form long-lived nuclear spin states, which interact weakly with the environment, compared to ordinary nuclear magnetization. All experimental demonstrations of long-lived states have so far involved spin systems which are close to the condition of magnetic equivalence, in which the network of spin-spin coupling...
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... The discovery of long-lived states (LLS) in nuclear magnetic resonance (NMR) has opened important perspectives [1][2][3][4][5][6][7][8][9][10]. If the lifetimes are longer than the longitudinal relaxation times 1 , one can store nuclear spin hyperpolarization [11], observe hyperpolarized metabolites in magnetic resonance imaging (MRI) [12], probe slow chemical exchange [13], determine slow diffusion rates [14,15], and detect weak interactions between potential drugs and target proteins [16][17][18]. ...
... An imbalance can also occur if the high spin temperature approximation is violated [26,27]. In systems with more than two spins, one can excite long-lived imbalances between states that belong to different symmetries of the spin permutation group [6,8,10,[28][29][30][31][32]. ...
Long-lived states (LLS) involving pairs of magnetically inequivalent but chemically equivalent proton spins in aliphatic (CH2)n chains can be excited by simultaneous application of weak selective radio frequency fields at n chemical shifts by polychromatic spin-lock induced crossing. The LLS are delocalized throughout the aliphatic chains by mixing of intrapair singlet states and by excitation of LLS comprising products of four and six spin operators. The measured lifetimes TLLS in a model compound are about 5 times longer than T1 and are strongly affected by interactions with macromolecules.
... The discovery of long-lived states (LLS) in nuclear magnetic resonance (NMR) has opened important perspectives [1][2][3][4][5][6][7][8][9][10]. If the lifetimes are longer than the longitudinal relaxation times 1 , one can store nuclear spin hyperpolarization [11], observe hyperpolarized metabolites in magnetic resonance imaging (MRI) [12], probe slow chemical exchange [13], determine slow diffusion rates [14,15], and detect weak interactions between potential drugs and target proteins [16][17][18]. ...
... To excite such an LLS, the two spins should have either different resonance frequencies (chemical inequivalence), or have different interactions with other spins (magnetic inequivalence) [24,25], or the high temperature approximation must be violated [26,27]. In systems with more than two spins, one can excite long-lived imbalances between states that belong to different symmetries of the spin permutation group [6,8,10,[28][29][30][31][32]. ...
Long-lived states (LLS) involving pairs of magnetically inequivalent but chemically equivalent proton spins in aliphatic (CH$_2$)$_n$ chains can be excited by simultaneous application of weak selective radio-frequency (RF) fields at n chemical shifts by polychromatic spin lock induced crossing (poly-SLIC). The LLS are delocalized throughout the aliphatic chain by mixing of intrapair singlet states and by excitation of LLS comprising products of four or six spins. The measured lifetimes T$_{LLS}$ in a model compound are about 5 times longer than T1, and are strongly affected by interactions with macromolecules.
... For example, in the A 3 B 2 C system of ethanol, the maximum average polarization is only 14.2% if pH 2 was added pairwise in positions A and B. If the symmetry constraints are relaxed so that six spins are nonequivalent, the maximum achievable polarization increases to 31.2% for σ initial = σ A,B ZZ and 50% for σ initial = σ A,B S , respectively ( Figure 3). Note that some similar systems were experimentally and theoretically studied in the related context of long-lived nuclear singlet spin states [36][37][38]. The process of spin order transfer discussed here is important for LLS because it gives the upper estimates for the maximum amplitude of the LLS conversion to magnetization. ...
It is well known that the association of parahydrogen (pH2) with an unsaturated molecule or a transient metalorganic complex can enhance the intensity of NMR signals; the effect is known as parahydrogen-induced polarization (PHIP). During recent decades, numerous methods were proposed for converting pH2-derived nuclear spin order to the observable magnetization of protons or other nuclei of interest, usually 13C or 15N. Here, we analyze the constraints imposed by the topological symmetry of the spin systems on the amplitude of transferred polarization. We find that in asymmetric systems, heteronuclei can be polarized to 100%. However, the amplitude drops to 75% in A2BX systems and further to 50% in A3B2X systems. The latter case is of primary importance for biological applications of PHIP using sidearm hydrogenation (PHIP-SAH). If the polarization is transferred to the same type of nuclei, i.e., 1H, symmetry constraints impose significant boundaries on the spin-order distribution. For AB, A2B, A3B, A2B2, AA’(AA’) systems, the maximum average polarization for each spin is 100%, 50%, 33.3%, 25%, and 0, respectively, (where A and B (or A’) came from pH2). Remarkably, if the polarization of all spins in a molecule is summed up, the total polarization grows asymptotically with ~1.27 and can exceed 2 in the absence of symmetry constraints (where is the number of spins). We also discuss the effect of dipole–dipole-induced pH2 spin-order distribution in heterogeneous catalysis or nematic liquid crystals. Practical examples from the literature illustrate our theoretical analysis.
... Chemically equivalent systems have the potential of supporting long-lived singlet lifetime because its symmetrical properties provide a protection against common relaxation mechanisms and thus do not allow for singlet-triplet leakage. [33,43] However, the chemically equivalent spin pair has no chemical shift difference and J-coupling difference is the only way allowing to populate singlet spin order since a transition between the two states requires a break in symmetry. [26,27] In such symmetric molecules, large (> 5 Hz) Jcoupling have mainly been investigated indicating close proximity of the additional spins to the singlet spin-pair. ...
Bimodal molecular probes combining nuclear magnetic resonance (NMR) and fluorescence have been widely studied in basic science, as well as clinical research. The investigation of spin phenomena holds promise to broaden the scope of available probes allowing deeper insights into physiological processes. Herein, a class of molecules with a bimodal character with respect to fluorescence and nuclear spin singlet states is introduced. Singlet states are NMR silent but can be probed indirectly. Symmetric, perdeuterated molecules, in which the singlet states can be populated by vanishingly small electron‐mediated couplings (below 1 Hz) are reported. The lifetimes of these states are an order of magnitude longer than the longitudinal relaxation times and up to four minutes at 7 T. Moreover, these molecules show either aggregation induced emission (AIE) or aggregation caused quenching (ACQ) with respect to their fluorescence. In the latter case, the existence of excited dimers, which are proposed to use in a switchable manner in combination with the quenching of nuclear spin singlet states, is observed
... Long-lived nuclear spin states (LLS) are configurations of nuclear spins which are protected against common relaxation or dissipation mechanisms and which display extended decay time constants [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . A seminal example is the singlet order of a spin-1/2 pair ensemble, corresponding to a population imbalance between the singlet and triplet states of the spin-1/2 pairs 10, 16 . ...
... A seminal example is the singlet order of a spin-1/2 pair ensemble, corresponding to a population imbalance between the singlet and triplet states of the spin-1/2 pairs 10, 16 . The decay time constants of such states are often many times the spinlattice relaxation time constant T 1 , with lifetimes exceeding 1 hour being observed in favourable cases 12,19 . Longlived states have been applied to the study of slow chemical and transport processes [20][21][22][23][24][25][26][27][28][29] , to the characterisation of biomolecular ligand binding [30][31][32][33][34] , and for the transport and storage of nuclear hyperpolarization 5,7,[35][36][37][38][39][40][41][42][43] . ...
The population imbalance between nuclear singlet states and triplet states of strongly coupled spin-1/2 pairs, also known as nuclear singlet order, is well protected against several common relaxation mechanisms. We study the nuclear singlet relaxation of ¹³C pairs in aqueous solutions of 1,2-¹³C2 squarate over a range of pH values. The ¹³C singlet order is accessed by introducing ¹⁸O nuclei in order to break the chemical equivalence. The squarate dianion is in chemical equilibrium with hydrogen-squarate (SqH⁻) and squaric acid (SqH2) characterized by the dissociation constants pK1 = 1.5 and pK2 = 3.4. Surprisingly, we observe a striking increase in the singlet decay time constants TS when the pH of the solution exceeds ∼10, which is far above the acid–base equilibrium points. We derive general rate expressions for chemical-exchange-induced nuclear singlet relaxation and provide a qualitative explanation of the TS behavior of the squarate dianion. We identify a kinetic contribution to the singlet relaxation rate constant, which explicitly depends on kinetic rate constants. Qualitative agreement is achieved between the theory and the experimental data. This study shows that infrequent chemical events may have a strong effect on the relaxation of nuclear singlet order.
... 11 Understandably, other molecular symmetries could treat groups of 31 P nuclei as distinct, thus, resulting in a larger number of pertinent scalar couplings. 13 As the ability of the system to sustain long-lived spin coherences is starkly related to the asymmetry in the coupling network, [14][15][16][17][18] the spin physics of PMs is inherently linked to the molecule's point group symmetries. Further, the presence of an inversion center in the PM, as found for S 6 , would render the intramolecular dipolar coupling block-diagonal in a basis of well-defined parity under exchange of two 31 P nuclei related by inversion. ...
The Posner molecule, $\text{Ca}_9(\text{PO}_4)_6$, has long been recognized to have biochemical relevance in various physiological processes. It has found recent attention for its possible role as a biological quantum information processor, whereby the molecule purportedly maintains long-lived nuclear spin coherences among its ${^{31}\text{P}}$ nuclei (presumed to be symmetrically arranged), allowing it to function as a room temperature qubit. The structure of the molecule has been of much dispute in the literature, although the $\text{S}_6$ point group symmetry has often been assumed and exploited in calculations. Using a variety of simulation techniques (including \textit{ab initio} molecular dynamics and structural relaxation), rigorous data analysis tools and by exploring thousands of individual configurations, we establish that the molecule predominantly assumes low symmetry structures ($\text{C}_\text{s}$ and $\text{C}_\text{i}$) at room temperature, as opposed to the higher symmetry configurations explored previously. Our findings have important implications on the viability of this molecule as a qubit.
... This was thoroughly analysed by Stevanato et al. for a cis-and transderivative of 2,3-13 C 2 -butenedioic acid. [30] The enhancement factor for the observation of singlet order via the 15 N channel reaches ɛ~400 and~30 via the 1 H channel. A factor of 10 between these values is expected, because 1 H spins in thermal equilibrium have an approximately 10 times higher polarization than 15 N spins. ...
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.
... The majority of long-lived spin operators may be found in systems with internal symmetry [43][44][45][46][47][48][49][50][51][52][53][54] . Typical examples include symmetric arrangements of the spin interaction network with respect spin permutations. ...
... The characterisation of long-lived spin operators may then be based on group theoretical techniques [55][56][57] . Symmetry projection operators have been particularly useful in the characterisation of long-lived spin operators [43][44][45][46][47][48][50][51][52][53][54] . Nonetheless, some small caveats remain. ...
... Analytic results for the centralizer of generic relaxation algebra are challenging. But it is well known that longlived spin operators predominantly arise whenever the coherent and fluctuating contributions display some type of internal symmetry [43][44][45][46][47][48][49][50][51][52][53][54] . The relaxation algebra then consists of a set spin operators invariant under some symmetry group G. ...
Nuclear long-lived spin states represent spin density operator configurations that are exceptionally well protected against spin relaxation phenomena. Their long-lived character is exploited in a variety of Nuclear Magnetic Resonance (NMR) techniques. Despite growing importance of long-lived spin states in modern NMR strategies for their identification have changed little over the last decade. The standard approach heavily relies on a chain of group theoretical arguments. In this paper we present a more streamlined method for the calculation of such configurations. Instead of focusing on the symmetry properties of the relaxation superoperator, we focus on its corresponding relaxation algebra. This enables us to analyse long-lived spin states with Lie algebraic methods rather than group theoretical arguments. We show that the centralizer of the relaxation algebra forms a basis for the set of long-lived spin states. The characterisation of the centralizer on the other hand does not rely on any special symmetry arguments and its calculation is straightforward. We outline a basic algorithm and illustrate advantages by considering long-lived spin states for some spin-1/2 pairs and rapidly rotating methyl groups.
... The second reason is that even in the free form the molecular geometry of cis-ABZ is not symmetric, making possible for the dipolar interactions of the protons in the phenyl rings with 15 N to drive the relaxation of the 15 N singlet order. This was thoroughly analysed by Stevanato et al. for a cis-and trans-derivative of 13 C2-fumarate 28 . ...
Development of the methods to exploit nuclear hyperpolarization and search for molecules whose nuclear spins can be efficiently hyperpolarized is an active area in nuclear magnetic resonance. Of particular interest are those molecules that have long nuclear relaxation times, making them to be suitable candidates as contrast agents in magnetic resonance imaging. In this work, we present a detailed study of SABRE SHEATH (Signal Amplification By Reversible Exchange in Shield Enabled Alignment Transfer to Heteronuclei) experiments of 15N,15N' azobenzene. In SABRE SHEATH experiments nuclear spins of the target are hyperpolarized by transfer of spin polarization from parahydrogen at ultralow fields during a reversible chemical process. The studied system is complicated, and we are concerned only about a subset of the data, presenting details for the molecules that experience fast chemical exchange at the catalytic complex and thus are involved in polarizing the free azobenzene. 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 several thousands of times for 15N spins and a few tens of times for the 1H spins. There are two approaches to observe either hyperpolarized magnetization of 15N/1H spins or hyperpolarized singlet order of the 15N spin pair. We compare these approaches and present the field dependencies of SABRE experiments for them. No hyperpolarization of trans 15N,15N' azobenzene was observed. The results presented here will be useful for further experiments where hyperpolarized cis-15N,15N' azobenzene is switched by light to trans 15N,15N' azobenzene for storing the produced hyperpolarization in the long-lived spin state of the 15N pair of trans-15N,15N' azobenzene.
... 24 The spectrum of [2,3-13 C 2 ]-fumarate is more complicated and consists of three main lines around 13 C-1 H J-coupling as expected from a numerical simulation [ Figure 4b]. [2,3-13 C 2 ]fumarate provides an intriguing possibility for creation of the long-lived 4-spin state as demonstrated in ref 26. In addition, hyperpolarized fumarate is often used in preclinical MRI studies as an in vivo probe for cell necrosis and can be produced by an inexpensive parahydrogen-induced polar-ization technique. ...
Nuclear magnetic resonance (NMR) spectroscopy is a well-established analytical technique used to study chemicals and their transformations. However, high-field NMR spectroscopy necessitates advanced infrastructure, and even cryogen-free benchtop NMR spectrometers cannot be readily assembled from commercially available components. We demonstrate construction of a portable zero-field NMR spectrometer employing a commercially available magnetometer and investigate its applications in analytical chemistry. In particular, J-spectra of small representative biomolecules [¹³C]-formic acid, [1-¹³C]-glycine, [2,3-¹³C]-fumarate, and [1-¹³C]-d-glucose were acquired, and an approach relying on the presence of a transverse magnetic field during the detection was investigated for relaxometry purposes. We found that the water relaxation time strongly depends on the concentration of dissolved d-glucose in the range of 1–10 mM suggesting opportunities for indirect assessment of glucose concentration in aqueous solutions. Extending analytical capabilities of zero-field NMR to aqueous solutions of simple biomolecules (amino acids, sugars, and metabolites) and relaxation studies of aqueous solutions of glucose highlights the analytical potential of noninvasive and portable ZULF NMR sensors for applications outside of research laboratories.
