Journal of Chemical Physics

An integrated approach to NMR spin relaxation in flexible biomolecules: Application to beta-D-glucopyranosyl-(1-->6)-alpha-D-mannopyranosyl-OMe

Mirco Zerbetto,¹ Antonino Polimeno,¹ Dmytro Kotsyubynskyy,² Leila Ghalebani,² Jozef Kowalewski,² Eva Meirovitch,³ Ulrika Olsson,⁴ and Göran Widmalm⁴

J. Chem. Phys. 131, 234501 (2009); doi:10.1063/1.3268766

The description of the reorientational dynamics of flexible molecules is a challenging task, in particular when the rates of internal and global motions are comparable. The commonly used simple mode-decoupling models are based on the assumption of statistical independence between these motions. This assumption is not valid when the time scale separation between their rates is small, a situation that was found to arise in oligosaccharides in the context of certain internal motions. To make possible the interpretation of NMR spin relaxation data from such molecules, we developed a comprehensive approach generally applicable to flexible rotators with one internal degree of freedom. This approach integrates a stochastic description of coupled global tumbling and internal torsional motion, quantum chemical calculations of the local potential and the local geometry at the site of the restricted torsion, and hydrodynamics-based calculations of the diffusive properties. The method is applied to the disaccharide -D-Glcp-(1" align="bottom" border="0">6)--D-[6-¹³C]-Manp-OMe dissolved in a DMSO-d₆/D₂O cryosolvent. The experimental NMR relaxation parameters, associated with the ¹³CH₂ probe residing at the glycosidic linkage, include ¹³C T₁ and T₂ and ¹³C-{¹H} nuclear Overhauser enhancement (NOE) as well as longitudinal and transverse dipole-dipole cross-correlated relaxation rates, acquired in the temperature range of 253–293 K. These data are predicted successfully by the new theory with only the H–C–H angle allowed to vary. Previous attempts to fit these data using mode-decoupling models failed

Derivatives of spin dynamics simulations

from Journal of Chemical Physics: All Topics

Ilya Kuprov and Christopher T. Rodgers

We report analytical equations for the derivatives of spin dynamics simulations with respect to pulse sequence and spin system parameters. The methods described are significantly faster, more accurate, and more reliable than the finite difference approximations typically employed. The resulting derivatives may be used in fitting, optimization, performance evaluation, and stability analysis of spin dynamics simulations and experiments.

A new experimental absolute nuclear magnetic shielding scale for oxygen based on the rotational hyperfine structure of HO

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Cristina Puzzarini, Gabriele Cazzoli, Michael E. Harding, Juana Vazquez, and Jurgen Gauss

The hyperfine structure in the rotational spectrum of water containing ¹⁷O has been investigated experimentally and by means of quantum-chemical calculations. The Lamb-dip technique has been used to resolve the hyperfine structure due to spin-rotation as well as spin-spin interactions and allowed the determination of the corresponding hyperfine parameters with high accuracy. The experimental investigation and, in particular, the analysis of the spectra have been supported by quantum-chemical computations at the coupled-cluster level. The experimental ¹⁷O isotropic spin-rotation constant of H2¹⁷" align="middle" border="0">O has been used in a further step for the determination of the paramagnetic part of the corresponding nuclear magnetic shielding constant, whereas the diamagnetic contribution as well as vibrational and temperature corrections have been obtained from quantum-chemical calculations. This joint procedure leads to a value of 325.3(3) ppm for the oxygen shielding in H2¹⁷" align="middle" border="0">O at 300 K, in good agreement with pure theoretical predictions, and in this way provides the basis for a new absolute oxygen shielding scale.

Shimmed matching pulses: Simultaneous control of rf and static gradients for inhomogeneity correction

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John M. Franck, Vasiliki Demas, Rachel W. Martin, Louis-S. Bouchard, and Alexander Pines
Portable NMR systems generally suffer from poor field homogeneity and are therefore used more commonly for imaging and relaxation measurements rather than for spectroscopy. In recent years, various approaches have been proposed to increase the sample volume that is usable for spectroscopy. These include approaches based on manual shimming and those based on clever combinations of modulated radio frequency and gradient fields. However, this volume remains small and, therefore, of limited utility. We present improved pulses designed to correct for inhomogeneous dispersion across wide ranges of frequency offsets without eliminating chemical shift or spatial encoding. This method, based on the adiabatic double passage, combines the relatively larger corrections available from spatially matched rf gradients [C. Meriles et al., J. Magn. Reson. 164, 177 (2003)]. with the adjustable corrections available from time-modulated static field gradients [D. Topgaard et al., Proc. Natl. Acad. Sci. U.S.A. 101, 17576 (2004)]. We explain the origins of these corrections with a theoretical model that simplifies and expedites the design of the pulse waveforms. We also present a generalized method for evaluating and comparing pulses designed for inhomogeneity correction. Experiments validate this method and support simulations that offer new possibilities for significantly enhanced performance in portable environments.

Theory of damped quantum rotation in nuclear magnetic resonance spectra. III. Nuclear permutation symmetry of the line shape equation

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S. Szymanski
The damped quantum rotation (DQR) theory describes manifestations in nuclear magnetic resonance spectra of the coherent and stochastic dynamics of N-fold molecular rotors composed of indistinguishable particles. The standard jump model is only a limiting case of the DQR approach; outside this limit, the stochastic motions of such rotors have no kinematic description. In this paper, completing the previous two of this series, consequences of nuclear permutation symmetry for the properties of the DQR line shape equation are considered. The systems addressed are planar rotors, such as aromatic hydrocarbons' rings, occurring inside of molecular crystals oriented in the magnetic field. Under such conditions, oddfold rotors can have nontrivial permutation symmetries only for peculiar orientations while evenfold ones always retain their intrinsic symmetry element, which is rotation by 180° about the N-fold axis; in specific orientations the latter can gain two additional symmetry elements. It is shown that the symmetry selection rules applicable to the classical rate processes in fluids, once recognized as having two diverse aspects, macroscopic and microscopic, are also rigorously valid for the DQR processes in the solid state. However, formal justification of these rules is different because the DQR equation is based on the Pauli principle, which is ignored in the jump model. For objects like the benzene ring, exploitation of these rules in simulations of spectra using the DQR equation can be of critical significance for the feasibility of the calculations. Examples of such calculations for the proton system of the benzene ring in a general orientation are provided. It is also shown that, because of the intrinsic symmetries of the evenfold rotors, many of the DQR processes, which such rotors can undergo, are unobservable in NMR spectra.

Four-component relativistic theory for nuclear magnetic shielding: Magnetically balanced gauge-including atomic orbitals

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Lan Cheng, Yunlong Xiao, and Wenjian Liu

It is recognized only recently that the incorporation of the magnetic balance condition is absolutely essential for four-component relativistic theories of magnetic properties. Another important issue to be handled is the so-called gauge problem in calculations of, e.g., molecular magnetic shielding tensors with finite bases. It is shown here that the magnetic balance can be adapted to distributed gauge origins, leading to, e.g., magnetically balanced gauge-including atomic orbitals (MB-GIAOs) in which each magnetically balanced atomic orbital has its own local gauge origin placed on its center. Such a MB-GIAO scheme can be combined with any level of theory for electron correlation. The first implementation is done here at the coupled-perturbed Dirac–Kohn–Sham level. The calculated molecular magnetic shielding tensors are not only independent of the choice of gauge origin but also converge rapidly to the basis set limit. Close inspections reveal that (zeroth order) negative energy states are only important for the expansion of first order electronic core orbitals. Their contributions to the paramagnetism are therefore transferable from atoms to molecule and are essentially canceled out for chemical shifts. This allows for simplifications of the coupled-perturbed equations.