Generalized monotonically convergent algorithms for solving quantum optimal control problems

A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to "trapping" and that relaxation processes may remove such unfavorable behavior.     

13C NMR spectroscopy in diamonds using dynamic nuclear polarization

In diamonds unpaired electrons associated with nitrogen impurities can be used to enhance the ¹³C NMR signal via the solid-state effect. ¹³C spectra of three natural and two synthetic diamonds are shown that were obtained in this manner in 10–30 min.     

In situ temperature jump high-frequency dynamic nuclear polarization experiments: enhanced sensitivity in liquid-state NMR spectroscopy

We describe an experiment, in situ temperature jump dynamic nuclear polarization (TJ-DNP), that is demonstrated to enhance sensitivity in liquid-state NMR experiments of low-gamma spins--13C, 15N, etc. The approach consists of polarizing a sample at low temperature using high-frequency (140 GHz) microwaves and a biradical polarizing agent and then melting it rapidly with a pulse of 10.6 microm infrared radiation, followed by observation of the NMR signal in the presence of decoupling. In the absence of polarization losses due to relaxation, the enhancement should be epsilon+ = epsilon(T(obs)/T(mu)(wave)), where epsilon+ is the observed enhancement, epsilon is the enhancement obtained at the temperature where the polarization process occurs, and T(mu)(wave) and T(obs) are the polarization and observation temperatures, respectively. In a single experimental cycle, we observe room-temperature enhancements, epsilon(dagger), of 13C signals in the range 120-400 when using a 140 GHz gyrotron microwave source, T(mu)(wave) = 90 K, and T(obs) = 300 K. In addition, we demonstrate that the experiment can be recycled to perform signal averaging that is customary in contemporary NMR spectroscopy. Presently, the experiment is applicable to samples that can be repeatedly frozen and thawed. TJ-DNP could also serve as the initial polarization step in experiments designed for rapid acquisition of multidimensional spectra.     

Fast characterization of functionalized silica materials by silicon-29 surface-enhanced NMR spectroscopy using dynamic nuclear polarization

We demonstrate fast characterization of the distribution of surface bonding modes and interactions in a series of functionalized materials via surface-enhanced nuclear magnetic resonance spectroscopy using dynamic nuclear polarization (DNP). Surface-enhanced silicon-29 DNP NMR spectra were obtained by using incipient wetness impregnation of the sample with a solution containing a polarizing radical (TOTAPOL). We identify and compare the bonding topology of functional groups in materials obtained via a sol-gel process and in materials prepared by post-grafting reactions. Furthermore, the remarkable gain in time provided by surface-enhanced silicon-29 DNP NMR spectroscopy (typically on the order of a factor 400) allows the facile acquisition of two-dimensional correlation spectra.     

The creation of off-diagonal elements in chemically induced dynamic nuclear polarization experiments

The nuclear density matrix created in pulsed CIDNP experiments contains off-diagonal elements whenever the resulting nuclear spin system is strongly coupled. These off-diagonal elements, which connect spin states with the same magnetic quantum number, are due to the mixing of nuclear state functions during the process of product formation. The observation of these elements by means of a two-pulse experiment is described.     

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.     

High-frequency dynamic nuclear polarization using mixtures of TEMPO and trityl radicals

In a previous communication [Hu et al., J. Am. Chem. Soc. 126, 10844 (2004)], an approach was demonstrated that improves the efficiency of the cross-effect polarization mechanism employed in high field dynamic nuclear polarization (DNP) experiments. Specifically, it was shown that tethering two TEMPO (2,2,6,6-tetramethylpiperidin-1-oxyl) radicals increases the electron-electron dipole coupling from approximately 1 MHz in solutions of monomeric TEMPO to approximately 25 MHz in a tethered biradical. The larger coupling resulted in an increase in the DNP enhancements by a factor of approximately 3-4, from 45-50 to approximately 165. Here, a second approach to improving the efficiency of the polarization process is described that involves approximately satisfying the matching condition |omega(2e)-omega(1e)|=omega(n), where omega(2e) and omega(1e) are two frequencies in the electron paramagnetic resonance (EPR) spectrum and omega(n) is the Larmor frequency of the nuclear spins being polarized. Specifically, in a mixture of TEMPO and trityl [tris (8-carboxy-2,2,6,6-tetramethyl(-d3)-benzo[1,2d:4,5-d']bis(1,3)dithiol-4-yl) methyl] radicals, the intensity maxima in the EPR spectra of these two species are approximately separated by the (1)H NMR frequency. In this case the frequency difference between the g(yy) value of TEMPO and the narrow pseudo-isotropic g-value of trityl is approximately 224 MHz and the (1)H Larmor frequency is 211 MHz. The optimal magnetic field for DNP using the mixtures was found to coincide with the trityl EPR resonance. At 90 K and 5 T, a mixture of 20 mM TEMPO and 20 mM trityl enhanced the (1)H polarization by a factor of approximately 160, an improvement over the enhancement of approximately 50 with 40 mM TEMPO. The reasons for the improvement are discussed and evidence is presented suggesting that DNP enhancement can be improved further by tethering TEMPO and trityl or two similar radicals.     

Intermolecular structure determination of amyloid fibrils with magic-angle spinning and dynamic nuclear polarization NMR

We describe magic-angle spinning NMR experiments designed to elucidate the interstrand architecture of amyloid fibrils. Three methods are introduced for this purpose, two being based on the analysis of long-range (13)C-(13)C correlation spectra and the third based on the identification of intermolecular interactions in (13)C-(15)N spectra. We show, in studies of fibrils formed by the 86-residue SH3 domain of PI3 kinase (PI3-SH3 or PI3K-SH3), that efficient (13)C-(13)C correlation spectra display a resonance degeneracy that establishes a parallel, in-register alignment of the proteins in the amyloid fibrils. In addition, this degeneracy can be circumvented to yield direct intermolecular constraints. The (13)C-(13)C experiments are corroborated by (15)N-(13)C correlation spectra obtained from a mixed [(15)N,(12)C]/[(14)N,(13)C] sample which directly quantify interstrand distances. Furthermore, when the spectra are recorded with signal enhancement provided by dynamic nuclear polarization (DNP) at 100 K, we demonstrate a dramatic increase (from 23 to 52) in the number of intermolecular (15)N-(13)C constraints detectable in the spectra. The increase in the information content is due to the enhanced signal intensities and to the fact that dynamic processes, leading to spectral intensity losses, are quenched at low temperatures. Thus, acquisition of low temperature spectra addresses a problem that is frequently encountered in MAS spectra of proteins. In total, the experiments provide 111 intermolecular (13)C-(13)C and (15)N-(13)C constraints that establish that the PI3-SH3 protein strands are aligned in a parallel, in-register arrangement within the amyloid fibril.     

Simultaneous acquisition of multi-nuclei enhanced NMR/MRI by solution-state dynamic nuclear polarization

Dynamic nuclear polarization (DNP) has become a very important hyperpolarization method because it can dramatically increase the sensitivity of nuclear magnetic resonance (NMR) of various molecules. Liquid-state DNP based on Overhauser effect is capable of directly enhancing polarization of all kinds of nuclei in the system. The combination of simultaneous Overhauser multi-nuclei enhancements with the multi-nuclei parallel acquisitions provides a variety of important applications in both MR spectroscopy (MRS) and image (MRI). Here we present two simple illustrative examples for simultaneously enhanced multi-nuclear spectra and images to demonstrate the principle and superiority. We have observed very large simultaneous DNP enhancements for different nuclei, such as ¹H and ²³Na, ¹H and ³¹P, ¹⁹F and ³¹P, especially for the first time to report sodium ion enhancement in liquid. We have also obtained the simultaneous images of ¹⁹H and ³¹P, ¹⁹F and ³¹P at low field by solution-state DNP for the first time.     

TOTAPOL: a biradical polarizing agent for dynamic nuclear polarization experiments in aqueous media

In a previous publication, we described the use of biradicals, in that case two TEMPO molecules tethered by an ethylene glycol chain of variable length, as polarizing agents for microwave driven dynamic nuclear polarization (DNP) experiments. The use of biradicals in place of monomeric paramagnetic centers such as TEMPO yields enhancements that are a factor of approximately 4 larger (epsilon approximately 175 at 5 T and 90 K) and concurrently the concentration of the polarizing agent is a factor of 4 smaller (10 mM electron spins), reducing the residual electron nuclear dipole broadening. In this paper we describe the synthesis and characterization by EPR and DNP/NMR of an improved polarizing agent 1-(TEMPO-4-oxy)-3-(TEMPO-4-amino)propan-2-ol (TOTAPOL). Under the same experimental conditions and using 2.5 mm magic angle rotors, this new biradical yields larger enhancements (epsilon approximately 290) at lower concentrations (6 mM electron spins) and has the additional important property that it is compatible with experiments in aqueous media, including salt solutions commonly used in the study of proteins and nucleic acids.     

Dynamic nuclear polarization of quadrupolar nuclei using cross polarization from protons: surface-enhanced aluminium-27 NMR

The surface of γ-alumina nanoparticles can be characterized by dynamic nuclear polarization (DNP) surface-enhanced NMR of (27)Al. DNP is combined with cross-polarization and MQ-MAS to determine local symmetries of (27)Al sites at the surface.     

Neurotoxin II bound to acetylcholine receptors in native membranes studied by dynamic nuclear polarization NMR

Methods enabling structural studies of membrane-integrated receptor systems without the necessity of purification provide an attractive perspective in membrane protein structural and molecular biology. This has become feasible in principle since the advent of dynamic nuclear polarization (DNP) magic-angle-spinning NMR spectroscopy, which delivers the required sensitivity. In this pilot study, we observed well-resolved solid-state NMR spectra of extensively (13)C-labeled neurotoxin II bound to the nicotinic acetylcholine receptor (nAChR) in native membranes. We show that TOTAPOL, a biradical required for DNP, is localized at membrane and protein surfaces. The concentration of active, membrane-attached biradical decreases with time, probably because of reactive components of the membrane preparation. An optimal distribution of active biradical has strong effects on the NMR data. The presence of inactive TOTAPOL in membrane-proximal situations but active biradical in the surrounding water/glycerol "glass" leads to well-resolved spectra, yet a considerable enhancement (ε = 12) is observed. The resulting spectra of a protein ligand bound to its receptor are paving the way for further DNP investigations of proteins embedded in native membrane patches.     

−22-Fold of 1H signal enhancement in-situ low-field liquid NMR using nanodiamond as polarizer of overhauser dynamic nuclear polarization

Nanodiamond (ND) polarizer can be used for dynamic nuclear polarization (DNP), owing to unpaired electrons provided by surface defects. However, ¹H enhancement via Overhauser DNP (ODNP) using ND in-situ liquid has been found much smaller than traditional radicals. Herein, we study the surface properties of ND using electron spin resonance (ESR) and Raman methods firstly. Then the enhancement of ¹H ODNP is explored using ND as polarizer with different nanoparticle sizes and concentrations at home-built 0.06 T DNP spectrometer. The surface of ND with the size of 30 nm is further modification via high temperature air oxidized and the enhancement was measured. The results show that nanoparticle sizes and Raman peak intensity ratio of sp²/sp³ hybridization are approximate negative correlation and positive correlation to enhancement, respectively. Furthermore, there is no significant enhancement in the oxidation group, and a −22.5-fold ¹H ODNP enhancement is achieved in-situ liquid at room temperature, which demonstrate the ND can be used as an efficient enhancer. We expect ND to play a greater role in biomedical research, especially for multimodal imaging with improving the performance of ND surface.     

High-frequency dynamic nuclear polarization using biradicals: a multifrequency EPR lineshape analysis

To date, the cross effect (CE) and thermal mixing (TM) mechanisms have consistently provided the largest enhancements in dynamic nuclear polarization (DNP) experiments performed at high magnetic fields. Both involve a three-spin electron-electron-nucleus process whose efficiency depends primarily on two electron-electron interactions--the interelectron distance R and the correct electron paramagnetic resonance (EPR) frequency separation that matches the nuclear Larmor frequency, /omega(e2)-omega(e1)/ = omega(n). Biradicals, for example, two 2,2,6,6-tetramethyl-piperidine-1-oxyls (TEMPOs) tethered with a molecular linker, can in principle constrain both the distance and relative g-tensor orientation between two unpaired electrons, allowing these two spectral parameters to be optimized for the CE and TM. To verify this hypothesis, we synthesized a series of biradicals--bis-TEMPO tethered by n ethylene glycol units (a.k.a. BTnE)--that show an increasing DNP enhancement with a decreasing tether length. Specifically at 90 K and 5 T, the enhancement grew from approximately 40 observed with 10 mM monomeric TEMPO, where the average R approximately 56 A corresponding to electron-electron dipolar coupling constant omega(d)2 pi = 0.3 MHz, to approximately 175 with 5 mM BT2E (10 mM electrons) which has R approximately 13 A with omega(d)2 pi = 24 MHz. In addition, we compared these DNP enhancements with those from three biradicals having shorter and more rigid tethers-bis-TEMPO tethered by oxalyl amide, bis-TEMPO tethered by the urea structure, and 1-(TEMPO-4-oxyl)-3-(TEMPO-4-amino)-propan-2-ol (TOTAPOL) TOTAPOL is of particular interest since it is soluble in aqueous media and compatible with DNP experiments on biological systems such as membrane and amyloid proteins. The interelectron distances and relative g-tensor orientations of all of these biradicals were characterized with an analysis of their 9 and 140 GHz continuous-wave EPR lineshapes. The results show that the largest DNP enhancements are observed with BT2E and TOTAPOL that have shorter tethers and the two TEMPO moieties are oriented so as to satisfy the matching condition for the CE.     

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.