Pseudorandom Selective Excitation in NMR

In this work, average Hamiltonian theory is used to study selective excitation in a spin-1/2 system evolving under a series of small flip-angle $\theta-$pulses $(\theta\ll 1)$ that are applied either periodically [which corresponds to the DANTE pulse sequence] or aperiodically. First, an average Hamiltonian description of the DANTE pulse sequence is developed; such a description is determined to be valid either at or very far from the DANTE resonance frequencies, which are simply integer multiples of the inverse of the interpulse delay. For aperiodic excitation schemes where the interpulse delays are chosen pseudorandomly, a single resonance can be selectively excited if the $\theta$-pulses' phases are modulated in concert with the time delays. Such a selective pulse is termed a pseudorandom-DANTE or p-DANTE sequence, and the conditions in which an average Hamiltonian description of p-DANTE is found to be similar to that found for the DANTE sequence. It is also shown that averaging over different p-DANTE sequences that are selective for the same resonance can help reduce excitations at frequencies away from the resonance frequency, thereby improving the apparent selectivity of the p-DANTE sequences. Finally, experimental demonstrations of p-DANTE sequences and comparisons with theory are presented.Comment: 23 pages, 8 figure

Welcoming natural isotopic abundance in solid-state NMR: probing π-stacking and supramolecular structure of organic nanoassemblies using DNP

The self-assembly of small organic molecules is an intriguing phenomenon, which provides nanoscale structures for applications in numerous fields from medicine to molecular electronics. Detailed knowledge of their structure, in particular on the supramolecular level, is a prerequisite for the rational design of improved self-assembled systems. In this work, we prove the feasibility of a novel concept of NMR-based 3D structure determination of such assemblies in the solid state. The key point of this concept is the deliberate use of samples that contain 13C at its natural isotopic abundance (NA, 1.1%), while exploiting magic-angle spinning dynamic nuclear polarization (MAS-DNP) to compensate for the reduced sensitivity. Since dipolar truncation effects are suppressed to a large extent in NA samples, unique and highly informative spectra can be recorded which are impossible to obtain on an isotopically labeled system. On the self-assembled cyclic diphenylalanine peptide, we demonstrate the detection of long-range internuclear distances up to ∼7 Å, allowing us to observe π-stacking through 13C–13C correlation spectra, providing a powerful tool for the analysis of one of the most important non-covalent interactions. Furthermore, experimental polarization transfer curves are in remarkable agreement with numerical simulations based on the crystallographic structure, and can be fully rationalized as the superposition of intra- and intermolecular contributions. This new approach to NMR crystallography provides access to rich and precise structural information, opening up a new avenue to de novo crystal structure determination by NMR

The Magnus expansion and some of its applications

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to built up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving at any order certain symmetries of the exact solution. The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.Comment: Report on the Magnus expansion for differential equations and its applications to several physical problem

DNP Enhanced Frequency-Selective TEDOR Experiments in Bacteriorhodopsin

We describe a new approach to multiple [superscript 13]C–[superscript 15]N distance measurements in uniformly labeled solids, frequency-selective (FS) TEDOR. The method shares features with FS-REDOR and ZF- and BASE-TEDOR, which also provide quantitative [superscript 15]N–[superscript 13]C spectral assignments and distance measurements in U-[[superscript 13]C,[superscript 15]N] samples. To demonstrate the validity of the FS-TEDOR sequence, we measured distances in [U-[superscript 13]C,15N]-asparagine which are in good agreement with other methods. In addition, we integrate high frequency dynamic nuclear polarization (DNP) into the experimental protocol and use FS-TEDOR to record a resolved correlation spectrum of the Arg-[superscript 13]Cγ–[superscript 15]Nε region in [U-[superscript 13]C,15N]-bacteriorhodopsin. We resolve six of the seven cross-peaks expected based on the primary sequence of this membrane protein.National Institute of Biomedical Imaging and Bioengineering (U.S.) (Grant Number EB-001960)National Institute of Biomedical Imaging and Bioengineering (U.S.) (Grant Number EB-002804)National Institute of Biomedical Imaging and Bioengineering (U.S.) (Grant Number EB-001035)National Institute of Biomedical Imaging and Bioengineering (U.S.) (Grant Number EB-002026

NMR-Based Structural Modeling of Graphite Oxide Using Multidimensional 13C Solid-State NMR and ab Initio Chemical Shift Calculations

Chemically modified graphenes and other graphite-based materials have attracted growing interest for their unique potential as lightweight electronic and structural nanomaterials. It is an important challenge to construct structural models of noncrystalline graphite-based materials on the basis of NMR or other spectroscopic data. To address this challenge, a solid-state NMR (SSNMR)-based structural modeling approach is presented on graphite oxide (GO), which is a prominent precursor and interesting benchmark system of modified graphene. An experimental 2D C-13 double-quantum/single-quantum correlation SSNMR spectrum of C-13-labeled GO was compared with spectra simulated for different structural models using ab initio geometry optimization and chemical shift calculations. The results show that the spectral features of the GO sample are best reproduced by a geometry-optimized structural model that is based on the Lerf-Klinowski model (Lerf, A. et al. Phys. Chem. B 1998, 102, 4477); this model is composed of interconnected sp(2), 1,2-epoxide, and COH carbons. This study also convincingly excludes the possibility of other previously proposed models, including the highly oxidized structures involving 1,3-epoxide carbons (Szabo, I. et al. Chem. Mater. 2006, 18, 2740). C-13 chemical shift anisotropy (CSA) patterns measured by a 2D C-13 CSA/isotropic shift correlation SSNMR were well reproduced by the chemical shift tensor obtained by the ab initio calculation for the former model. The approach presented here is likely to be applicable to other chemically modified graphenes and graphite-based systems

Numerical simulations in nuclear magnetic resonance : theory and applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2003.Vita.Includes bibliographical references.Exact numerical simulations of NMR experiments are commonly required for the engineering of new techniques and for the extraction of structural and dynamic parameters from the spectra. The calculations can be very demanding, especially in the case of solid-state problems. We propose a number of new algorithms that drastically improve the efficiency of these calculations. Among the most important ones are the integration of the equation of motion of the propagator via Chebyshev expansion of the matrix exponential, explicit utilization of the sparsity of the Hamiltonian, and a novel methodology for the simulation of solid-state NMR experiments. We also describe SPINEVOLUTION, a highly optimized computer program developed based on these advanced techniques to be a powerful and easy to use tool for the simulation and data fitting of general NMR experiments. Benchmarked on a series of examples, SPINEVOLUTION was consistently found orders of magnitude faster than another recently developed and widely popular NMR simulation package SIMPSON. The program should be of great utility to people working in NMR for the design and optimization of new experiments, theoretical research, data fitting, etc. A novel strategy for the efficient design of shaped pulses for NMR experiments was developed and implemented in SPINEVOLUTION. The most important component of this approach is our technique for the global optimization on the space of smooth functions, the Grid Search in the Reduce-Dimension Fourier Space (GREDFOS). A series of low-power amplitude-modulated selective excitation pulses have been developed using this strategy. The pulses of this E-Family provide selective excitation with the precision that was not available previously. The pulses were shown to perform well in both liquid and solid state NMR experiments.(cont.) The Magnus expansion is fundamental to the NMR theory. It also explains the paradoxical success of the integration-by-exponentiation method that has been widely used for the integration of the equation of motion with a time-dependent Hamiltonian. We discuss several aspects of the convergence of the expansion that had been left open so far. An unexpected geometrical picture of the long-term behavior of the effective Hamiltonian of a two-level system is also presented.by Mikhail M. Veshtort.Ph.D