A unified description for polarization-transfer mechanisms in magnetic resonance in static solids: Cross polarization and DNP

Polarization transfers are crucial building blocks in magnetic resonance experiments, i.e., they can be used to polarize insensitive nuclei and correlate nuclear spins in multidimensional nuclear magnetic resonance (NMR) spectroscopy. The polarization can be transferred either across different nuclear spin species or from electron spins to the relatively low-polarized nuclear spins. The former route occurring in solid-state NMR can be performed via cross polarization (CP), while the latter route is known as dynamic nuclear polarization (DNP). Despite having different operating conditions, we opinionate that both mechanisms are theoretically similar processes in ideal conditions, i.e., the electron is merely another spin-1/2 particle with a much higher gyromagnetic ratio. Here, we show that the CP and DNP processes can be described using a unified theory based on average Hamiltonian theory combined with fictitious operators. The intuitive and unified approach has allowed new insights into the cross-effect DNP mechanism, leading to better design of DNP polarizing agents and extending the applications beyond just hyperpolarization. We explore the possibility of exploiting theoretically predicted DNP transients for electron–nucleus distance measurements—such as routine dipolar-recoupling experiments in solid-state NMR.

Role of electron spin dynamics and coupling network in designing dynamic nuclear polarization

Dynamic nuclear polarization (DNP) has emerged as a powerful sensitivity booster of nuclear magnetic resonance (NMR) spectroscopy for the characterization of biological solids, catalysts and other functional materials, but is yet to reach its full potential. DNP transfers the high polarization of electron spins to nuclear spins using microwave irradiation as a perturbation. A major focus in DNP research is to improve its efficiency at conditions germane to solid-state NMR, at high magnetic fields and fast magic-angle spinning. In this review, we highlight three key strategies towards designing DNP experiments: time-domain "smart" microwave manipulation to optimize and/or modulate electron spin polarization, EPR detection under operational DNP conditions to decipher the underlying electron spin dynamics, and quantum mechanical simulations of coupled electron spins to gain microscopic insights into the DNP mechanism. These strategies are aimed at understanding and modeling the properties of the electron spin dynamics and coupling network. The outcome of these strategies is expected to be key to developing next-generation polarizing agents and DNP methods.

High-Field Dynamic Nuclear Polarization

Dynamic nuclear polarization (DNP) is one of the most prominent methods of sensitivity enhancement in nuclear magnetic resonance (NMR). Even though solid-state DNP under magic-angle spinning (MAS) has left the proof-of-concept phase and has become an important tool for structural investigations of biomolecules as well as materials, it is still far from mainstream applicability because of the potentially overwhelming combination of unique instrumentation, complex sample preparation, and a multitude of different mechanisms and methods available. In this review, I introduce the diverse field and history of DNP, combining aspects of NMR and electron paramagnetic resonance. I then explain the general concepts and detailed mechanisms relevant at high magnetic field, including solution-state methods based on Overhauser DNP but with a greater focus on the more established MAS DNP methods. Finally, I review practical considerations and fields of application and discuss future developments.

Low-Field Nuclear Polarization Using Nitrogen Vacancy Centers in Diamonds

It was recently demonstrated that bulk nuclear polarization can be obtained using nitrogen vacancy (NV) color centers in diamonds, even at ambient conditions. This is based on the optical polarization of the NV electron spin, and using several polarization transfer methods. One such method is the nuclear orientation via electron spin locking (NOVEL) sequence, where a spin-locked sequence is applied on the NV spin, with a microwave power equal to the nuclear precession frequency. This was performed at relatively high fields, to allow for both polarization transfer and noise decoupling. As a result, this scheme requires accurate magnetic field alignment in order preserve the NV properties. Such a requirement may be undesired or impractical in many practical scenarios. Here we present a new sequence, termed the refocused NOVEL, which can be used for polarization transfer (and detection) even at low fields. Numerical simulations are performed, taking into account both the spin Hamiltonian and spin decoherence, and we show that, under realistic parameters, it can outperform the NOVEL sequence.

Off-resonance NOVEL

Dynamic nuclear polarization (DNP) is theoretically able to enhance the signal in nuclear magnetic resonance (NMR) experiments by a factor γe/γn, where γ's are the gyromagnetic ratios of an electron and a nuclear spin. However, DNP enhancements currently achieved in high-field, high-resolution biomolecular magic-angle spinning NMR are well below this limit because the continuous-wave DNP mechanisms employed in these experiments scale as ω0-n where n ∼ 1-2. In pulsed DNP methods, such as nuclear orientation via electron spin-locking (NOVEL), the DNP efficiency is independent of the strength of the main magnetic field. Hence, these methods represent a viable alternative approach for enhancing nuclear signals. At 0.35 T, the NOVEL scheme was demonstrated to be efficient in samples doped with stable radicals, generating 1H NMR enhancements of ∼430. However, an impediment in the implementation of NOVEL at high fields is the requirement of sufficient microwave power to fulfill the on-resonance matching condition, ω0I = ω1S, where ω0I and ω1S are the nuclear Larmor and electron Rabi frequencies, respectively. Here, we exploit a generalized matching condition, which states that the effective Rabi frequency, ω1Seff, matches ω0I. By using this generalized off-resonance matching condition, we generate 1H NMR signal enhancement factors of 266 (∼70% of the on-resonance NOVEL enhancement) with ω1S/2π = 5 MHz. We investigate experimentally the conditions for optimal transfer of polarization from electrons to 1H both for the NOVEL mechanism and the solid-effect mechanism and provide a unified theoretical description for these two historically distinct forms of DNP.

Pulsed Dynamic Nuclear Polarization with Trityl Radicals

Continuous-wave (CW) dynamic nuclear polarization (DNP) is now established as a method of choice to enhance the sensitivity in a variety of NMR experiments. Nevertheless, there remains a need for the development of more efficient methods to transfer polarization from electrons to nuclei. Of particular interest are pulsed DNP methods because they enable a rapid and efficient polarization transfer that, in contrast with CW DNP methods, is not attenuated at high magnetic fields. Here we report nuclear spin orientation via electron spin-locking (NOVEL) experiments using the polarizing agent trityl OX063 in glycerol/water at a temperature of 80 K and a magnetic field of 0.34 T. (1)H NMR signal enhancements up to 430 are observed, and the buildup of the local polarization occurs in a few hundred nanoseconds. Thus, NOVEL can efficiently dynamically polarize (1)H atoms in a system that is of general interest to the solid-state DNP NMR community. This is a first, important step toward the general application of pulsed DNP at higher fields.

An apparatus for pulsed ESR and DNP experiments using optically excited triplet states down to liquid helium temperatures

In standard Dynamic Nuclear Polarization (DNP) electron spins are polarized at low temperatures in a strong magnetic field and this polarization is transferred to the nuclear spins by means of a microwave field. To obtain high nuclear polarizations cryogenic equipment reaching temperatures of 1 K or below and superconducting magnets delivering several Tesla are required. This equipment strongly limits applications in nuclear and particle physics where beams of particles interact with the polarized nuclei, as well as in neutron scattering science. The problem can be solved using short-lived optically excited triplet states delivering the electron spin. The spin is polarized in the optical excitation process and both the cryogenic equipment and magnet can be simplified significantly. A versatile apparatus is described that allows to perform pulsed dynamic nuclear polarization experiments at X-band using short-lived optically excited triplet sates. The efficient (4)He flow cryostat that cools the sample to temperatures between 4 K and 300 K has an optical access with a coupling stage for a fiber transporting the light from a dedicated laser system. It is further designed to be operated on a neutron beam. A combined pulse ESR/DNP spectrometer has been developed to observe and characterize the triplet states and to perform pulse DNP experiments. The ESR probe is based on a dielectric ring resonator of 7 mm inner diameter that can accommodate cubic samples of 5mm length needed for neutron experiments. NMR measurements can be performed during DNP with a coil integrated in the cavity. With the presented apparatus a proton polarization of 0.5 has been achieved at 0.3 T.

Dynamic nuclear polarization at high magnetic fields

Dynamic nuclear polarization (DNP) is a method that permits NMR signal intensities of solids and liquids to be enhanced significantly, and is therefore potentially an important tool in structural and mechanistic studies of biologically relevant molecules. During a DNP experiment, the large polarization of an exogeneous or endogeneous unpaired electron is transferred to the nuclei of interest (I) by microwave (microw) irradiation of the sample. The maximum theoretical enhancement achievable is given by the gyromagnetic ratios (gamma(e)gamma(l)), being approximately 660 for protons. In the early 1950s, the DNP phenomenon was demonstrated experimentally, and intensively investigated in the following four decades, primarily at low magnetic fields. This review focuses on recent developments in the field of DNP with a special emphasis on work done at high magnetic fields (> or =5 T), the regime where contemporary NMR experiments are performed. After a brief historical survey, we present a review of the classical continuous wave (cw) DNP mechanisms-the Overhauser effect, the solid effect, the cross effect, and thermal mixing. A special section is devoted to the theory of coherent polarization transfer mechanisms, since they are potentially more efficient at high fields than classical polarization schemes. The implementation of DNP at high magnetic fields has required the development and improvement of new and existing instrumentation. Therefore, we also review some recent developments in microw and probe technology, followed by an overview of DNP applications in biological solids and liquids. Finally, we outline some possible areas for future developments.

Electron-nuclear cross polarization

We describe the coherent polarization transfer from an unpaired electron to neighboring nuclei via electron-nuclear cross polarization (eNCP) in a doubly, tilted rotating frame. Although the experiment superficially resembles the well-known Hartmann-Hahn cross polarization (CP) process introduced by Pines et al., that is widely used in solid-state nuclear magnetic resonance (SSNMR), it differs in significant respects. In particular, eNCP requires an alternative treatment due to the very different sizes of the specific terms in the spin Hamiltonian. We derive analytical expressions for the matching condition for optimal polarization transfer and verify their correctness with experimental results obtained with electron detected CP experiments performed on powder samples of BDPA radical dispersed in a protonated polystyrene matrix and with numerical simulations. We use fully protonated BDPA as an example of polarization transfer to strongly coupled nuclei. In contrast, perdeuterated BDPA serves as an example of the transfer of polarization from electrons to weakly coupled nuclei. In addition, we performed CP on a paramagnetic crystal to determine the influence of resolved hyperfine structure on the CP process. It is shown that almost no structure is observed in the corresponding electron-(1)H CP matching curve. It appears that only a restricted number of hyperfine coupled (1)H's contribute to the observed signal intensities in the CP experiment.

Sensitivity Enhancement by Matched Microwave Pulses in One- and Two-Dimensional Electron Spin Echo Envelope Modulation Spectroscopy

The concept of microwave pulse matching is applied to three-pulse electron spin echo envelope modulation and sublevel correlation (HYSCORE) spectroscopy. Matched pulses enhance the efficiency of forbidden transfers and may drastically increase the signal intensity of basic frequency and combination frequency transitions in these conventional pulse EPR experiments. The theory of matched pulses is extended to the case of strong and largely isotropic hyperfine interactions, and numerical simulations are presented to gain a deeper insight into the inner working of the matched-pulse approach. It is shown that the enhancement of combination frequencies in matched HYSCORE can be used to determine the relative sign of hyperfine coupling constants as well as the number of equivalent nuclei. The enormous capacity of the approach is demonstrated on ordered and disordered systems. In particular, it is shown that in HYSCORE experiments the signal-to-noise ratio improvement for strongly coupled nitrogens and for proton combination peaks may be considerably larger than one order of magnitude, corresponding to a reduction in measuring time of more than a factor of 100. Copyright 1998 Academic Press.

Polarization-enhanced NMR spectroscopy of biomolecules in frozen solution

Large dynamic nuclear polarization signal enhancements (up to a factor of 100) were obtained in the solid-state magic-angle spinning nuclear magnetic resonance (NMR) spectra of arginine and the protein T4 lysozyme in frozen glycerol-water solutions with the use of dynamic nuclear polarization. Polarization was transferred from the unpaired electrons of nitroxide free radicals to nuclear spins through microwave irradiation near the electron paramagnetic resonance frequency. This approach may be a generally applicable signal enhancement scheme for the high-resolution solid-state NMR spectroscopy of biomolecules.