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

Proton-driven spin diffusion in rotating solids via reversible and irreversible quantum dynamics

Proton-driven spin diffusion (PDSD) experiments in rotating solids have received a great deal of attention as a potential source of distance constraints in large biomolecules. However, the quantitative relationship between the molecular structure and observed spin diffusion has remained obscure due to the lack of an accurate theoretical description of the spin dynamics in these experiments. We start with presenting a detailed relaxation theory of PDSD in rotating solids that provides such a description. The theory applies to both conventional and radio-frequency-assisted PDSD experiments and extends to the non-Markovian regime to include such phenomena as rotational resonance (R[superscript 2]). The basic kinetic equation of the theory in the non-Markovian regime has the form of a memory function equation, with the role of the memory function played by the correlation function. The key assumption used in the derivation of this equation expresses the intuitive notion of the irreversible dissipation of coherences in macroscopic systems. Accurate expressions for the correlation functions and for the spin diffusion constants are given. The theory predicts that the spin diffusion constants governing the multi-site PDSD can be approximated by the constants observed in the two-site diffusion. Direct numerical simulations of PDSD dynamics via reversible Liouville-von Neumann equation are presented to support and compliment the theory. Remarkably, an exponential decay of the difference magnetization can be observed in such simulations in systems consisting of only 12 spins. This is a unique example of a real physical system whose typically macroscopic and apparently irreversible behavior can be traced via reversible microscopic dynamics. An accurate value for the spin diffusion constant can be usually obtained through direct simulations of PDSD in systems consisting of two [superscript 13]C nuclei and about ten [superscript 1]H nuclei from their nearest environment. Spin diffusion constants computed by this method are in excellent agreement with the spin diffusion constants obtained through equations given by the relaxation theory of PDSD. The constants resulting from these two approaches were also in excellent agreement with the results of 2D rotary resonance recoupling proton-driven spin diffusion (R[superscript 3]-PDSD) experiments performed in three model compounds, where magnetization exchange occurred over distances up to 4.9 Å. With the methodology presented, highly accurate internuclear distances can be extracted from such data. Relayed transfer of magnetization between distant nuclei appears to be the main (and apparently resolvable) source of uncertainty in such measurements. The non-Markovian kinetic equation was applied to the analysis of the R[superscript 2] spin dynamics. The conventional semi-phenomenological treatment of relxation in R[superscript 2] has been shown to be equivalent to the assumption of the Lorentzian spectral density function in the relaxatoin theory of PDSD. As this assumption is a poor approximation in real physical systems, the conventional R[superscript 2] treatment is likely to carry a significant model error that has not been recognized previously. The relaxation theory of PDSD appears to provide an accurate, parameter-free alternative. Predictions of this theory agreed well with the full quantum mechanical simulations of the R[superscript 2] dynamics in the few simple model systems we considered.National Institute of Biomedical Imaging and Bioengineering (U.S.) (Grant EB-003151)National Institute of Biomedical Imaging and Bioengineering (U.S.) (Grant EB-002026

Probing intermolecular crystal packing in γ-indomethacin by high-resolution (1)H solid-state NMR spectroscopy

An NMR crystallography approach that combines experimental solid-state magic-angle-spinning (MAS) NMR with calculation is applied to the gamma polymorph of the pharmaceutical molecule, indomethacin. First-principles calculations (GIPAW) for the full crystal structure and an isolated molecule show changes in the (1)H chemical shift for specific aliphatic and aromatic protons of over -1 ppm that are due to intermolecular CH-pi interactions. For the OH proton, (1)H double-quantum (DQ) CRAMPS (combined rotation and multiple-pulse spectroscopy) spectra reveal intermolecular H-H proximities to the OH proton of the carboxylic acid dimer as well as to specific aromatic CH protons. The enhanced resolution in (1)H DQ-(13)C spectra, recorded at 850 MHz, enables separate (1)H DQ build-up curves (as a function of the DQ recoupling time) to be extracted for the aromatic CH protons. Supported by eight-spin density-matrix simulations, it is shown how the relative maximum intensities and rates of build-up provide quantitative insight into intramolecular and intermolecular H-H proximities that characterize the crystal packing

Accurate Determination of Interstrand Distances and Alignment in Amyloid Fibrils by Magic Angle Spinning NMR

Amyloid fibrils are structurally ordered aggregates of proteins whose formation is associated with many neurodegenerative and other diseases. For that reason, their high-resolution structures are of considerable interest and have been studied using a wide range of techniques, notably electron microscopy, X-ray diffraction, and magic angle spinning (MAS) NMR. Because of the excellent resolution in the spectra, MAS NMR is uniquely capable of delivering site-specific, atomic resolution information about all levels of amyloid structure: (1) the monomer, which packs into several (2) protofilaments that in turn associate to form a (3) fibril. Building upon our high-resolution structure of the monomer of an amyloid-forming peptide from transthyretin (TTR105−115), we introduce single 1-13C labeled amino acids at seven different sites in the peptide and measure intermolecular carbonyl−carbonyl distances with an accuracy of 0.11 A. Our results conclusively establish a parallel, in register, topology for the packing of this peptide into a β-sheet and provide constraints essential for the determination of an atomic resolution structure of the fibril. Furthermore, the approach we employ, based on a combination of a double-quantum filtered variant of the DRAWS recoupling sequence and multispin numerical simulations in SPINEVOLUTION, is general and should be applicable to a wide range of systems.National Institutes of Health (U.S.) (grant no. EB-002026)National Institutes of Health (U.S.) (grant no. EB003151)Leverhulme TrustWellcome Trust (London, England)Engineering and Physical Sciences Research CouncilRoyal Society (Great Britain)Natural Sciences and Engineering Research Council of Canada (NSERC

Functional and shunt states of bacteriorhodopsin resolved by 250 GHz dynamic nuclear polarization-enhanced solid-state NMR

Observation and structural studies of reaction intermediates of proteins are challenging because of the mixtures of states usually present at low concentrations. Here, we use a 250 GHz gyrotron (cyclotron resonance maser) and cryogenic temperatures to perform high-frequency dynamic nuclear polarization (DNP) NMR experiments that enhance sensitivity in magic-angle spinning NMR spectra of cryo-trapped photocycle intermediates of bacteriorhodopsin (bR) by a factor of ≈90. Multidimensional spectroscopy of U-13C,15N-labeled samples resolved coexisting states and allowed chemical shift assignments in the retinylidene chromophore for several intermediates not observed previously. The correlation spectra reveal unexpected heterogeneity in dark-adapted bR, distortion in the K state, and, most importantly, 4 discrete L substates. Thermal relaxation of the mixture of L's showed that 3 of these substates revert to bR568 and that only the 1 substate with both the strongest counterion and a fully relaxed 13-cis bond is functional. These definitive observations of functional and shunt states in the bR photocycle provide a preview of the mechanistic insights that will be accessible in membrane proteins via sensitivity-enhanced DNP NMR. These observations would have not been possible absent the signal enhancement available from DNP.National Institute of Biomedical Imaging and Bioengineering of the National Institutes of Health (Grants EB-001960, EB-002804, EB002026, and EB-001035