Quantum mechanical simulation of solid effect dynamic nuclear polarisation using Krylov-Bogolyubov time averaging and a restricted state-space

A strategy is described for simulations of solid effect dynamic nuclear polarisation that reduces substantially the dimension of the quantum mechanical problem. Averaging the Hamiltonian in the doubly rotating frame is used to confine the active space to the zero quantum coherence subspace. A further restriction of the Liouville space is made by truncating higher spin order states, which are weakly populated due to the presence of relaxation processes. Based on a dissipative transport equation, which is used to estimate the transport of the magnetisation starting from single spin order to higher spin order states, a minimal spin order for the states is calculated that needs to be taken into account for the spin dynamics simulation. The strategy accelerates individual spin calculations by orders of magnitude, thus making it possible to simulate the polarisation dynamics of systems with up to 25 nuclear spins.     

Solid effect dynamic nuclear polarization and polarization pathways

Using dynamic nuclear polarization (DNP)/nuclear magnetic resonance instrumentation that utilizes a microwave cavity and a balanced rf circuit, we observe a solid effect DNP enhancement of 94 at 5 T and 80 K using trityl radical as the polarizing agent. Because the buildup rate of the solid effect increases with microwave field strength, we obtain a sensitivity gain of 128. The data suggest that higher microwave field strengths would lead to further improvements in sensitivity. In addition, the observation of microwave field dependent enhancements permits us to draw conclusions about the path that polarization takes during the DNP process. By measuring the time constant for the polarization buildup and enhancement as a function of the microwave field strength, we are able to compare models of polarization transfer, and show that the major contribution to the bulk polarization arises via direct transfer from electrons, rather than transferring first to nearby nuclei and then transferring to bulk nuclei in a slow diffusion step. In addition, the model predicts that nuclei near the electron receive polarization that can relax, decrease the electron polarization, and attenuate the DNP enhancement. The magnitude of this effect depends on the number of near nuclei participating in the polarization transfer, hence the size of the diffusion barrier, their T(1), and the transfer rate. Approaches to optimizing the DNP enhancement are discussed.     

Quantum mechanical reactive scattering theory

In this article we briefly discuss a number of promising approaches to the formulation of a general, numerically exact, quantum mechanical theory of fully three-dimensional reactive atom-diatom collisions. It is noted that the ability to treat the three-dimensional H + H₂ exchange reactions is pre-requisite to any demonstration of the success of a general quantum mechanical formalism for reactivescattering. However, it is also noted that the time has come for any such theory to further demonstrate the ability to go beyond this basic, elementary atom-diatom exchange reaction. It is speculated that there now exist a number of approaches which can potentially provide such a general framework for quantum reactive scattering theory. Finally, a new generalizationof the Faddeev formalism for such systems, which is capable of inclusion ofthree body forces with a completely general form for the potential surface, is presented.     

Direct enhancement of nuclear singlet order by dynamic nuclear polarization

Hyperpolarized singlet order is available immediately after dissolution DNP, avoiding need for additional preparation steps. We demonstrate this procedure on a sample of [1,2-(13)C(2)]pyruvic acid.     

Water-soluble narrow-line radicals for dynamic nuclear polarization

The synthesis of air-stable, highly water-soluble organic radicals containing a 1,3-bis(diphenylene)-2-phenylallyl (BDPA) core is reported. A sulfonated derivative, SA-BDPA, retains the narrow electron paramagnetic resonance linewidth (<30 MHz at 5 T) of the parent BDPA in highly concentrated glycerol/water solutions (40 mM), which enables its use as polarizing agent for solid effect dynamic nuclear polarization (SE DNP). A sensitivity enhancement of 110 was obtained in high-field magic-angle-spinning (MAS) NMR experiments. The ease of synthesis and high maximum enhancements obtained with the BDPA-based radicals constitute a major advance over the trityl-type narrow-line polarization agents.     

Giant polarization in stable polymeric dielectrics

Macromolecular solids of highly aromatized structure can exhibit giant polarization. Their structures must be capable of providing long-range electron orbital delocalization. Intermolecular conformality of the orbitals of these huge molecules can result in ready carrier formation. The ready transport of these electronic holes and electronic carriers as polarons able to range over long molecular domains will then produce the giant polarization characteristic of the nomadic polarization mechanism. Recent developments in the synthesis and characterization of such materials new make available a new and interesting class of very stable organic dielectrics having dielectric constants in excess of 100. A number of such materials are described.     

Solid effect in magic angle spinning dynamic nuclear polarization

For over five decades, the solid effect (SE) has been heavily utilized as a mechanism for performing dynamic nuclear polarization (DNP). Nevertheless, it has not found widespread application in contemporary, high magnetic field DNP experiments because SE enhancements display an ω(0) (-2) field dependence. In particular, for nominally forbidden zero and double quantum SE transitions to be partially allowed, it is necessary for mixing of adjacent nuclear spin states to occur, and this leads to the observed field dependence. However, recently we have improved our instrumentation and report here an enhancement of ? = 91 obtained with the organic radical trityl (OX063) in magic angle spinning experiments performed at 5 T and 80 K. This is a factor of 6-7 higher than previous values in the literature under similar conditions. Because the solid effect depends strongly on the microwave field strength, we attribute this large enhancement to larger microwave field strengths inside the sample volume, achieved with more efficient coupling of the gyrotron to the sample chamber. In addition, we develop a theoretical model to explain the dependence of the buildup rate of enhanced nuclear polarization and the steady-state enhancement on the microwave power. Buildup times and enhancements were measured as a function of (1)H concentration for both trityl and Gd-DOTA. Comparison of the results indicates that for trityl the initial polarization step is the slower, rate-determining step. However, for Gd-DOTA the spread of nuclear polarization via homonuclear (1)H spin diffusion is rate-limiting. Finally, we discuss the applicability of the solid effect at fields > 5 T and the requirements to address the unfavorable field dependence of the solid effect.     

Theory for cross effect dynamic nuclear polarization under magic-angle spinning in solid state nuclear magnetic resonance: The importance of level crossings

We present theoretical calculations of dynamic nuclear polarization (DNP) due to the cross effect in nuclear magnetic resonance under magic-angle spinning (MAS). Using a three-spin model (two electrons and one nucleus), cross effect DNP with MAS for electron spins with a large g-anisotropy can be seen as a series of spin transitions at avoided crossings of the energy levels, with varying degrees of adiabaticity. If the electron spin-lattice relaxation time T(1e) is large relative to the MAS rotation period, the cross effect can happen as two separate events: (i) partial saturation of one electron spin by the applied microwaves as one electron spin resonance (ESR) frequency crosses the microwave frequency and (ii) flip of all three spins, when the difference of the two ESR frequencies crosses the nuclear frequency, which transfers polarization to the nuclear spin if the two electron spins have different polarizations. In addition, adiabatic level crossings at which the two ESR frequencies become equal serve to maintain non-uniform saturation across the ESR line. We present analytical results based on the Landau-Zener theory of adiabatic transitions, as well as numerical quantum mechanical calculations for the evolution of the time-dependent three-spin system. These calculations provide insight into the dependence of cross effect DNP on various experimental parameters, including MAS frequency, microwave field strength, spin relaxation rates, hyperfine and electron-electron dipole coupling strengths, and the nature of the biradical dopants.     

Solution-state dynamic nuclear polarization at high magnetic field

The goal of dynamic nuclear polarization (DNP) is to enhance NMR signals by transferring electron spin polarization to the nuclei. Although mechanisms such as the solid effect and thermal mixing can be used for DNP in the solid state, currently, the only practical mechanism in solutions is the Overhauser effect (OE), which usually arises due to dipolar relaxation between electrons and the nuclei. At magnetic fields greater than approximately 1 T, dipolar relaxation does not result in a useful enhancement and therefore the conventional wisdom is that DNP should not work in solutions at high magnetic fields. However, scalar relaxation due to time-dependent scalar couplings has a different magnetic field dependence and can lead to substantial OE enhancements. At room temperature and at a magnetic field of 5 T (211 MHz for protons, 140 GHz for electrons), we have observed that scalar relaxation between electrons and nuclei results in NMR signal enhancements of 180, 42, -36, and 8, for 31P, 13C, 15N, and 19F, respectively.     

Scalar dynamic nuclear polarization of protons in trifluoroacetic acid solutions

Strongly scalar ¹H intermolecular dynamic nuclear polarization (DNP) of solvent ¹H nuclei in solutions of organic free radicals has now been observed at room temperature. Transient protonation of the CF₃COOH/pyridyl imidazoline-1-oxyl radical system accounts for the observed effects.     

Transient and stationary nutations in chemically induced dynamic nuclear polarization

Transient nutations are observed in nuclear magnetic resonance during continuous generation of magnetization at and near resonance in reactions leading to chemically induced dynamic nuclear polarization. Modulation of the reaction with the nutation frequency leads to stationary nutations. The phase-sensitive detection of the nutation signals is used to discriminate effects of chemically induced polarization from steady state resonance signals. For single line spectra the effects are quantitatively explained by Bloch-type equations containing magnetization production terms. Experimental results obtained during photochemical reactions of di-tert-butyl ketone demonstrate general applications of the method.     

Electron and nuclear spin dynamics in the thermal mixing model of dynamic nuclear polarization

A novel mathematical treatment is proposed for computing the time evolution of dynamic nuclear polarization processes in the low temperature thermal mixing regime. Without assuming any a priori analytical form for the electron polarization, our approach provides a quantitative picture of the steady state that agrees with the well known Borghini prediction based on thermodynamic arguments, as long as the electrons-nuclei transition rates are fast compared to the other relevant time scales. Substantially different final polarization levels are achieved instead when the latter assumption is relaxed in the presence of a nuclear leakage term, even though very weak, suggesting a possible explanation for the deviation between the measured steady state polarizations and the Borghini prediction. The proposed methodology also allows us to calculate nuclear polarization and relaxation times, once the electrons/nuclei concentration ratio and the typical rates of the microscopic processes involving the two spin species are specified. Numerical results are shown to account for the manifold dynamic behaviours of typical DNP samples.     

A 140 GHz prepolarizer for dissolution dynamic nuclear polarization

Apart from their very classical use to build polarized targets for particle physics, the methods of dynamic nuclear polarization (DNP) have more recently found application for sensitivity enhancement in high-resolution NMR, both in the solid and in the liquid state. It is often thought that the possible signal enhancement in such applications deteriorates when the DNP is performed at higher fields. We show that for a dissolution-DNP method that uses conventional (2,2,6,6-tetramethylpiperidine 1-oxyl) radicals as the paramagnetic agent, this is not the case for fields up to 5 T.     

High-field dynamic nuclear polarization with high-spin transition metal ions

We report the dynamic nuclear polarization of (1)H spins in magic-angle-spinning spectra recorded at 5 T and 84 K via the solid effect using Mn(2+) and Gd(3+) complexes as polarizing agents. We show that the magnitude of the enhancements can be directly related to the effective line width of the central (m(S) = -1/2 → +1/2) EPR transition. Using a Gd(3+) complex with a narrow central transition EPR line width of 29 MHz, we observed a maximum enhancement of ～13, which is comparable to previous results on the narrow-line-width trityl radical.     

High-field Overhauser dynamic nuclear polarization in silicon below the metal-insulator transition

Single crystal silicon is an excellent system to explore dynamic nuclear polarization (DNP), as it exhibits a continuum of properties from metallic to insulating as a function of doping concentration and temperature. At low doping concentrations DNP has been observed to occur via the solid effect, while at very high-doping concentrations an Overhauser mechanism is responsible. Here we report the hyperpolarization of (29)Si in n-doped silicon crystals, with doping concentrations in the range of (1-3)?× 10(17) cm(-3). In this regime exchange interactions between donors become extremely important. The sign of the enhancement in our experiments and its frequency dependence suggest that the (29)Si spins are directly polarized by donor electrons via an Overhauser mechanism within exchange-coupled donor clusters. The exchange interaction between donors only needs to be larger than the silicon hyperfine interaction (typically much smaller than the donor hyperfine coupling) to enable this Overhauser mechanism. Nuclear polarization enhancement is observed for a range of donor clusters in which the exchange energy is comparable to the donor hyperfine interaction. The DNP dynamics are characterized by a single exponential time constant that depends on the microwave power, indicating that the Overhauser mechanism is a rate-limiting step. Since only about 2% of the silicon nuclei are located within 1 Bohr radius of the donor electron, nuclear spin diffusion is important in transferring the polarization to all the spins. However, the spin-diffusion time is much shorter than the Overhauser time due to the relatively weak silicon hyperfine coupling strength. In a 2.35 T magnetic field at 1.1 K, we observed a DNP enhancement of 244 ± 84 resulting in a silicon polarization of 10.4 ± 3.4% following 2 h of microwave irradiation.     

Kinematic approximation in the theory of stimulated nuclear polarization in radical recombination

Within the kinematic approximation, we have developed the theory of stimulated nuclear polarization (SNP) in reactions of geminal recombination of radicals in a strong d.c. magnetic field. We have obtained analytical formulas which are applicable for analysis of SNP effects occurring when the reactions are carried out in nonviscous solutions. The result is represented in the form of integrals with respect to the Green's function determining the kinematics of reagent approach. As an illustration of the proposed theory, we have calculated the polarization of nuclei formed in the reaction products of p-benzoquinone in CD₃OD and in C₆D₆ with addition of phenol, and we compare with experiment.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 5, pp. 519–527, September–October, 1988.The authors thank K. M. Salikhov and Yu. A. Grishin for discussion of the results of the work.