Rational Design of [13C,D14]Tert‐butylbenzene as a Scaffold Structure for Designing Long‐lived Hyperpolarized 13C Probes

Dynamic nuclear polarization (DNP) is a technique to polarize the nuclear spin population. As a result of the hyperpolarization, the NMR sensitivity of the nuclei in molecules can be dramatically enhanced. Recent application of the hyperpolarization technique has led to advances in biochemical and molecular studies. A major problem is the short lifetime of the polarized nuclear spin state. Generally, in solution, the polarized nuclear spin state decays to a thermal spin equilibrium, resulting in loss of the enhanced NMR signal. This decay is correlated directly with the spin‐lattice relaxation time T₁. Here we report [¹³C,D₁₄]tert‐butylbenzene as a new scaffold structure for designing hyperpolarized ¹³C probes. Thanks to the minimized spin‐lattice relaxation (T₁) pathways, its water‐soluble derivative showed a remarkably long ¹³C T₁ value and long retention of the hyperpolarized spin state.     

Preparation of Long-Lived States in a Multi-Spin System by Using an Optimal Control Method

The lifetime Ts of a long-lived nuclear spin state (LLS) could be much longer than the longitudinal order T₁. Many spin systems were used to produce long-lived states, including two or more homonuclear spins that couple to each other. For multiple homonuclear spins with rather small chemical shift difference, normally it is difficult to selectively control the spins and then to prepare a LLS. Herein, we present a scheme that prepares different spin orders in a multi-spin system by using optimal control and numerical calculation. By experimentally measuring the lifetime of the states, we find that for a three-spin physical system, although there are many forms of state combinations with different spin orders, each component has its own lifetime.     

Behavior of Two Almost Identical Spins during the CPMG Pulse Sequence

Multiple‐spin‐echo experiments have found wide use in nuclear magnetic resonance spectroscopy. In particular, the Carr–Purcell–Meiboom–Gill (CPMG) pulse sequence is used to determine transverse relaxation times T₂. Herein it is demonstrated, both theoretically and experimentally, that for a pair of almost identical spins‐1/2 the experimental setup can have a profound effect on the observed spin dynamics. It is shown that, in the case of dipolar relaxation, the measured T₂ values can roughly vary between the limits of identical and unlike spins, just depending on the repetition rate of π pulses with respect to chemical shift separation. Such an effect can, in the extreme narrowing regime, amount to a 50 % difference.     

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin‐free (scalar) and two‐component (spin–orbit) relativistic density functional calculations of indirect NMR nuclear spin–spin coupling (J‐coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J‐couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg₂²⁺, and Tl? X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite‐nucleus effects.     

Nuclear Magnetic Resonance Relaxivities: Investigations of Ultrahigh‐Spin Lanthanide Clusters from 10 MHz to 1.4 GHz

Paramagnetic relaxation enhancement is often explored in magnetic resonance imaging in terms of contrast agents and in biomolecular nuclear magnetic resonance (NMR) spectroscopy for structure determination. New ultrahigh‐spin clusters are investigated with respect to their NMR relaxation properties. As their molecular size and therefore motional correlation times as well as their electronic properties differ significantly from those of conventional contrast agents, questions about a comprehensive characterization arise. The relaxivity was studied by field‐dependent longitudinal and transverse NMR relaxometry of aqueous solutions containing Fe^III₁₀Dy^III₁₀ ultrahigh‐spin clusters (spin ground state 100/2). The high‐field limit was extended to 32.9 T by using a 24 MW resistive magnet and an ultrahigh‐frequency NMR setup. Interesting relaxation dispersions were observed; the relaxivities increase up to the highest available fields, which indicates a complex interplay of electronic and molecular correlation times.     

Long‐Lived Spin States for Low‐Field Hyperpolarized Gas MRI

Parahydrogen induced polarization was employed to prepare a relatively long‐lived correlated nuclear spin state between methylene and methyl protons in propane gas. Conventionally, such states are converted into a strong NMR signal enhancement by transferring the reaction product to a high magnetic field in an adiabatic longitudinal transport after dissociation engenders net alignment (ALTADENA) experiment. However, the relaxation time T₁ of ～0.6 s of the resulting hyperpolarized propane is too short for potential biomedical applications. The presented alternative approach employs low‐field MRI to preserve the initial correlated state with a much longer decay time T_LLSS=(4.7±0.5) s. While the direct detection at low‐magnetic fields (e.g. 0.0475 T) is challenging, we demonstrate here that spin‐lock induced crossing (SLIC) at this low magnetic field transforms the long‐lived correlated state into an observable nuclear magnetization suitable for MRI with sub‐millimeter and sub‐second spatial and temporal resolution, respectively. Propane is a non‐toxic gas, and therefore, these results potentially enable low‐cost high‐resolution high‐speed MRI of gases for functional imaging of lungs and other applications.     

Broken symmetry density functional study of a mixed‐valence unsymmetrical dinuclear iron complex

Density functional theory (DFT) calculations with different exchange‐correlation functionals were performed for a mixed valence Fe(II)/Fe(III) binuclear complex with μ‐methoxo and two μ‐carboxylate bridging ligands, (1) with geometry optimizations being performed for all possible spin multiplicities (M_S = 2, 4, 6, 8, and 10). Within the exchange‐correlation functionals studied, only the hybrid GGA functionals B3P and B3LYP and also the pure GGA functional RPBE, predicts the geometry with high spin (S = 9/2) to be more stable than the geometry with low spin state (S = 1/2) by 20 kcal/mol, in agreement with the experimental findings. These functionals also predict the same stability order for the different spin states, being M_S = 10>8>6>2>4. The meta‐GGA functionals TPSS and TPSSh and also the pure GGA functionals BLYP and BP86 predict different stability orders. The computed average EPR g‐tensor, g_av, of 2.03, at the B3LYP level, is in good agreement with the experimental findings. Heisenberg exchange coupling constants, J, were calculated within the broken‐symmetry formalism, at the B3LYP level, showing that the two iron centers are antiferromagnetic coupling, with a very weak coupling constant of about ?7 cm^?1, in good agreement with the experimental value. Additionally, the effect of using different multiplicities of the reference geometries on the computed J value is discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Reaching Optimal Light‐Induced Intramolecular Spin Alignment within Photomagnetic Molecular Device Prototypes

Ground‐state (GS) and excited‐state (ES) properties of novel photomagnetic molecular devices (PMMDs) are investigated by means of density functional theory. These organic PMMDs undergo a ferromagnetic alignment of their intramolecular spins in the lowest ES. They are comprised of: 1) an anthracene unit (An) as both the photosensitizer (P) and a transient spin carrier (SC) in the triplet ES (³An*); 2) imino‐nitroxyl (IN) or oxoverdazyl (OV) stable radical(s) as the dangling SC(s); and 3) bridge(s) (B) connecting peripheral SC(s) to the An core at positions 9 and 10. Improving the efficiency of the PMMDs involves strengthening the ES intramolecular exchange coupling (J_ES) between transient and persistent SCs, hence the choice of 2‐pyrimidinyl (pm) as B elements to replace the original p‐phenylene (ph). Dissymmetry of the pm connectors leads to [SC‐B‐P‐B‐SC] regio‐isomers int. and ext., depending on whether the pyrimidinic nitrogen atoms point towards the An core or the peripheral SCs, respectively. For the int. regio‐isomers we show that the photoinduced spin alignment is significantly improved because the J_ES/k_B value is increased by a factor of more than two compared with the ph‐based analogue (J_ES/k_B>+400 K). Most importantly, we show that the optimal J_ES/k_B value (≈+600 K) could be reached in the event of an unexpected saddle‐shaped structural distortion of the lowest ES. Accounting for this intriguing behavior requires dissection of the combined effects of 1) borderline intramolecular steric hindrance about key An–pm linkages, which translates into the flatness of the potential energy surface; 2) spin density disruption due to the presence of radicals; and 3) possibly intervening photochemistry, with An acting as a light‐triggered electron donor while pm, IN, and OV behave as electron acceptors. Finally, potentialities attached to the [(SC)‐pm‐An‐pm]_int pattern are disclosed.     

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.     

Local density functional theory applied to spin coupling in Fe6S supercluster

Using density functional theory (DFT), the multiplicity of the ground state was determined for Fe₆S₆Cl ions as well as the order of the excited spin states. A method to determine the exchange integrals J of the Fe₆S cluster is presented based on these results and a spin‐coupling algebra. The following order of the spin states was established with respect to the total spin 5/2, 1/2, 7/2, 3/2, 9/2, 11/2, 15/2, 13/2, and 17/2. We also calculated the Heisenberg coupling parameters J₁, J₂, J₃, and J₄ as 22, 146, −130, and 81 cm⁻¹, respectively. The possibility of the ground state of high multiplicity as well as the necessary conditions for such state are discussed. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 39–51, 1999     

Ultrafast Two‐Dimensional NMR Relaxometry for Investigating Molecular Processes in Real Time

Nuclear spin–lattice (T₁) and spin–spin (T₂) relaxation times provide versatile information about the dynamics and structure of substances, such as proteins, polymers, porous media, and so forth. Multidimensional experiments increase the information content and resolution of NMR relaxometry, but they also multiply the measurement time. To overcome this issue, we present an efficient strategy for a single‐scan measurement of a 2D T₁–T₂ correlation map. The method shortens the experimental time by one to three orders of magnitude as compared to the conventional method, offering an unprecedented opportunity to study molecular processes in real‐time. We demonstrate that, despite the tremendous speed‐up, the T₁–T₂ correlation maps determined by the single‐scan method are in good agreement with the maps measured by the conventional method. The concept of the single‐scan T₁–T₂ correlation experiment is applicable to a broad range of other multidimensional relaxation and diffusion experiments.     

Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polarization‐consistent basis sets in the Kohn–Sham basis set limit

Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) in the Kohn–Sham (KS) complete basis set (CBS) limit. Correlation‐consistent cc‐pVxZ and cc‐pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ‐pVxZ, unc‐ccJ‐pVxZ, and aug‐cc‐pVTZ‐J) and polarization‐consistent pc‐n and pcJ‐n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT‐predicted isotropic shieldings, spin–spin values, and the experimental values was good and similar for the modified correlation‐consistent and polarization‐consistent basis sets. The BHandH method predicted the most accurate ¹H, ¹⁷O isotropic shieldings and ¹J(OH) coupling constant (deviations from experiment of about ? 0.2 and ? 1 ppm and 0.6 Hz, respectively). The performance of BHandH for predicting water isotropic shieldings and ¹J(OH) is similar to the more advanced methods, second‐order polarization propagator approximation (SOPPA) and SOPPA(CCSD), in the basis set limit. Copyright © 2008 John Wiley & Sons, Ltd.     

Electronic Communication between S=1/2 Spins in Negatively‐charged Double‐caged Fullerene C60 Derivative Bonded by Two Single Bonds and Pyrrolizidine Bridge

Radical anion salt {cryptand[2.2.2] (K⁺)}₂(bispheroid)^2??3.5C₆H₄Cl₂ ( 1 ) of the double‐caged fullerene C₆₀ derivative, in which fullerene cages are linked by a cyclobutane bridging cycle and additionally by a pyrrolizidine moiety, was obtained. Each fullerene cage in this derivative accepts one electron on reduction, thus forming the (bispheroid)^2? dianions with two interacting S=1/2 spins on the neighboring cages. Low‐temperature magnetic measurements reveal a singlet ground state of the bispheroid dianions whereas triplet contributions prevail at increased temperature. An estimated exchange interaction between two spins J/k_B=?78 K in 1 indicates strong magnetic coupling between them, nearly two times higher than that (J/k_B=?44.7 K) in previously studied (C₆₀^?)₂ dimers linked via a cyclobutane bridge only. The enhancement of magnetic coupling in 1 can be explained by a shorter distance between the fullerene cages and, possibly, an additional channel for the magnetic exchange provided by a pyrrolizidine bridge. Quantum‐chemical calculations of the lowest electronic state of the dianions by means of multi‐configuration quasi‐degenerate perturbation theory support the experimental findings.     

Long‐lived states in an intrinsically disordered protein domain

Long‐lived states (LLS) are relaxation‐favored spin population distributions of J‐coupled magnetic nuclei. LLS were measured, along with classical ¹H and ¹⁵N relaxation rate constants, in amino acids of the N‐terminal Unique domain of the c‐Src kinase, which is disordered in vitro under physiological conditions. The relaxation rates of LLS can probe motions and interactions in biomolecules. LLS of the aliphatic protons of glycines, with lifetimes approximately four times longer than their spin–lattice relaxation times, are reported for the first time in an intrinsically disordered protein domain. LLS relaxation experiments were integrated with 2D spectroscopy methods, further adapting them for studies on proteins. Copyright © 2013 John Wiley & Sons, Ltd.     

On the Controversial Fitting of Susceptibility Curves of Ferromagnetic CuII Cubanes: Insights from Theoretical Calculations

This paper reports a theoretical analysis of the electronic structure and magnetic properties of a tetranuclear Cu^II complex, [Cu₄(HL)₄], which has a 4+2 cubane‐like structure (H₃L=N,N′‐(2‐hydroxypropane‐1,3‐diyl)bis(acetylacetoneimine)). These theoretical calculations indicate a quintet (S=2) ground state; the energy‐level distribution of the magnetic states confirm Heisenberg behaviour and correspond to an S₄ spin–spin interaction model. The dominant interaction is the ferromagnetic coupling between the pseudo‐dimeric units (J₁=22.2 cm^?1), whilst a weak and ferromagnetic interaction is found within the pseudo‐dimeric units (J₂=1.4 cm^?1). The amplitude and sign of these interactions are consistent with the structure and arrangement of the magnetic Cu 3d orbitals; they accurately simulate the thermal dependence of magnetic susceptibility, but do not agree with the reported J values (J₁=38.4 cm^?1, J₂=?18.0 cm^?1) that result from the experimental fitting. This result is not an isolated case; many other polynuclear systems, in particular 4+2 Cu^II cubanes, have been reported in which the fitted magnetic terms are not consistent with the geometrical features of the system. In this context, theoretical evaluation can be considered as a valuable tool in the interpretation of the macroscopic behaviour, thus providing clues for a rational and directed design of new materials with specific properties.     

Spin‐Labeled Heparins as Polarizing Agents for Dynamic Nuclear Polarization

A potentially biocompatible class of spin‐labeled macromolecules, spin‐labeled (SL) heparins, and their use as nuclear magnetic resonance (NMR) signal enhancers are introduced. The signal enhancement is achieved through Overhauser‐type dynamic nuclear polarization (DNP). All presented SL‐heparins show high ¹H DNP enhancement factors up to E=?110, which validates that effectively more than one hyperfine line can be saturated even for spin‐labeled polarizing agents. The parameters for the Overhauser‐type DNP are determined and discussed. A striking result is that for spin‐labeled heparins, the off‐resonant electron paramagnetic resonance (EPR) hyperfine lines contribute a non‐negligible part to the total saturation, even in the absence of Heisenberg spin exchange (HSE) and electron spin‐nuclear spin relaxation (T_1ne). As a result, we conclude that one can optimize the use of, for example, biomacromolecules for DNP, for which only small sample amounts are available, by using heterogeneously distributed radicals attached to the molecule.     

Cyano-bridged Ln^3＋-Cr^3＋ Binuclear Complexes [Ln（L）x（H2O）y^- Cr（CN）6]·mL·nH2O （Ln=La-Nd,x=5, y=2, m=1 or 2, n=2 or 2.5; Ln-Sm-Dy,Er, x=4, y=3, m=0, n=1.5 or 2.0; L= 2-pyrrolidinone）： Structure,Magnetism and Spin Density Map

In order to shed light upon the nature and mechanism of 4f-3d magnetic exchange interactions, a series of binuclear complexes of lanthanide（3＋） and chromium（3＋） with the general formula [Ln（L）5（H2O）2Cr（CN）6]·mL· nH2O （Ln=La （1）, Ce （2）, Pr （3）, Nd （4）; x=5, y=2, m=1 or 2, n=2 or 2.5; L=2-pyrrolidinone） and [Ln（L）4（H2O）3Cr（CN）6] ·nH2O （Ln=Sm （5）, Eu （6）, Gd （7）, Tb （8）, Dy （9）, Er （10）; x=4, y=3, m=0, n= 1.5 or 2.0; L=2-pyrrolidinone） were prepared and the X-ray crystal structures of complexes 2, 6 and 7 were determined. All the compounds consist of a Ln-CN-Cr unit, in which Ln^3＋ in a square antiprism environment is bridged to an octahedral coordinated Cr^3＋ ion through a cyano group. The magnetic properties of the complexes 3 and 6-10 show an overall antiferromagnetic behavior. The fitting to the experimental magnetic susceptibilities of 7 give g= 1.98, J=0.40 cm^-1, zJ＇= -0.21 cm^-1 on the basis of a binuclear spin system （Scd=7/2, Scr=3/2）, revealing an intra-molecular Gd^3＋-Cr^3＋ ferromagnetic interaction and an inter-molecular antiferromagnetic interaction. For 7 the calculation of quantum chemical density functional theory （DFT）, combined with the broken symmetry approach, showed that the calculated spin coupling constant was 20.3 cm^-1, supporting the observation of weak ferromagnetic intra-molecular interaction in 7. The spin density distributions of 7 in both the high spin ground state and the broken symmetry state were obtained, and the spin coupling mechanism between Gd^3＋ and Cr^3＋ was discussed.     

Lifetime of Parahydrogen in Aqueous Solutions and Human Blood

Molecular hydrogen has unique nuclear spin properties. Its nuclear spin isomer, parahydrogen (pH₂), was instrumental in the early days of quantum mechanics and allows to boost the NMR signal by several orders of magnitude. pH_2-induced polarization (PHIP) is based on the survival of pH₂ spin order in solution, yet its lifetime has not been investigated in aqueous or biological media required for in vivo applications. Herein, we report longitudinal relaxation times (T₁) and lifetimes of pH₂ ( ) in methanol and water, with or without O₂, NaCl, rhodium-catalyst or human blood. Furthermore, we present a relaxation model that uses T₁ and for more precise theoretical predictions of the H₂ spin state in PHIP experiments. All measured T₁ values were in the range of 1.4–2 s and values were of the order of 10–300 minutes. These relatively long lifetimes hold great promise for emerging in vivo implementations and applications of PHIP.     

Electron Decoupling with Chirped Microwave Pulses for Rapid Signal Acquisition and Electron Saturation Recovery

Dynamic nuclear polarization (DNP) increases NMR sensitivity by transferring polarization from electron to nuclear spins. Herein, we demonstrate that electron decoupling with chirped microwave pulses enables improved observation of DNP‐enhanced ¹³C spins in direct dipolar contact with electron spins, thereby leading to an optimal delay between transients largely governed by relatively fast electron relaxation. We report the first measurement of electron longitudinal relaxation time (T_1e) during magic angle spinning (MAS) NMR by observation of DNP‐enhanced NMR signals (T_1e=40±6 ms, 40 mM trityl, 4.0 kHz MAS, 4.3 K). With a 5 ms DNP period, electron decoupling results in a 195 % increase in signal intensity. MAS at 4.3 K, DNP, electron decoupling, and short recycle delays improve the sensitivity of ¹³C in the vicinity of the polarizing agent. This is the first demonstration of recovery times between MAS‐NMR transients being governed by short electron T₁ and fast DNP transfer.