## 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 GĂ¶ran Widmalm^{4}

### 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*-Glc

*p*-(1" align="bottom" border="0">6)--

*D*-[6-

^{13}C]-Man

*p*-OMe dissolved in

^{ }a DMSO-d

_{6}/D

_{2}O cryosolvent. The experimental NMR relaxation parameters, associated with

^{ }the

^{13}CH

_{2}probe residing at the glycosidic linkage, include

^{13}C

^{ }

*T*

_{1}and

*T*

_{2}and

^{13}C-{

^{1}H} 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

Ilya Kuprov and Christopher T. RodgersWe

^{ }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

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

^{ }hyperfine structure in the rotational spectrum of water containing

^{17}O

^{ }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

^{17}O isotropic spin-rotation constant of H2

^{17}" 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 H2

^{17}" 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

John M. Franck, Vasiliki Demas, Rachel W. Martin, Louis-S. Bouchard, and Alexander PinesPortable

^{ }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

S. SzymanskiThe

^{ }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

Lan Cheng, Yunlong Xiao, and Wenjian LiuIt

^{ }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.

## No comments:

Post a Comment