Field-dependent paramagnetic relaxation enhancement in solutions of Ni(II): What happens above the NMR proton frequency of 1 GHz?

An extended set of paramagnetic relaxation enhancement (PRE) data, up to the field of 32.9 Tesla, is reported for protons in an acidified aqueous solution of a Ni(II) salt in the presence and in the absence of added glycerol. For the 55% w/w glycerol sample, a distinct maximum in the PRE vs magnetic field curve is observed for the first time. The data are analysed using the Swedish slow-motion theory, including both the intramolecular (inner-sphere) and intermolecular (outer-sphere) contributions. The results indicate that estimating the outer-sphere part in the presence of the more efficient inner-sphere term is a difficult task.

An ab initio CASSCF study of zero field splitting fluctuations in the octet ground state of aqueous [Gd(iii)(HPDO3A)(H2O)].

In this work, we present ab initio calculations of the zero-field splitting (ZFS) of a gadolinium complex [Gd(iii)(HPDO3A)(H2O)] sampled from an ab initio molecular dynamics (AIMD) simulation. We perform both post-Hartree-Fock (complete active space self-consistent field-CASSCF) and density functional theory (DFT) calculations of the ZFS and compare and contrast the methods with experimental data. Two different density functional approximations (TPSS and LC-BLYP) were investigated. The magnitude of the ZFS from the CASSCF calculations is in good agreement with experiment, whereas the DFT results in varying degrees overestimate the magnitude of the ZFS for both functionals and exhibit a strong functional dependence. It was found in the sampling over the AIMD trajectory that the fluctuations in the transient ZFS tensor derived from DFT are not correlated with those of CASSCF nor does the magnitude of the ZFS from CASSCF and DFT correlate. From the fluctuations in the ZFS tensor, we extract a correlation time of the transient ZFS which is on the sub-picosecond time scale, showing a faster decay than experimental estimates.

Spectral density mapping at multiple magnetic fields suitable for (13)C NMR relaxation studies.

Standard spectral density mapping protocols, well suited for the analysis of (15)N relaxation rates, introduce significant systematic errors when applied to (13)C relaxation data, especially if the dynamics is dominated by motions with short correlation times (small molecules, dynamic residues of macromolecules). A possibility to improve the accuracy by employing cross-correlated relaxation rates and on measurements taken at several magnetic fields has been examined. A suite of protocols for analyzing such data has been developed and their performance tested. Applicability of the proposed protocols is documented in two case studies, spectral density mapping of a uniformly labeled RNA hairpin and of a selectively labeled disaccharide exhibiting highly anisotropic tumbling. Combination of auto- and cross-correlated relaxation data acquired at three magnetic fields was applied in the former case in order to separate effects of fast motions and conformational or chemical exchange. An approach using auto-correlated relaxation rates acquired at five magnetic fields, applicable to anisotropically moving molecules, was used in the latter case. The results were compared with a more advanced analysis of data obtained by interpolation of auto-correlated relaxation rates measured at seven magnetic fields, and with the spectral density mapping of cross-correlated relaxation rates. The results showed that sufficiently accurate values of auto- and cross-correlated spectral density functions at zero and (13)C frequencies can be obtained from data acquired at three magnetic fields for uniformly (13)C-labeled molecules with a moderate anisotropy of the rotational diffusion tensor. Analysis of auto-correlated relaxation rates at five magnetic fields represents an alternative for molecules undergoing highly anisotropic motions.

Chemical Shielding Anisotropies for Chloroform Exchanging between a Free Site and a Complex with Cryptophane-D: A Cross-Correlated NMR Relaxation Study.

The case of (13)C-labeled chloroform exchanging between a free site in solution and the encaged site within the cryptophane-D cavity is investigated using the measurements of longitudinal cross-correlated relaxation rates, involving the interference of the dipole-dipole and chemical shielding anisotropy interactions. A compact theoretical expression is provided, along with an experimental protocol, based on INEPT (insensitive nuclei enhanced by polarization)-enhanced double-quantum-filtered inversion recovery measurements. The analysis of the build-up curves results in a set of cross-correlated relaxation rates for both the (13)C and (1)H spins at the two sites. It is demonstrated that the results can be given a consistent interpretation in terms of molecular-level properties, such as rotational correlation times, the Lipari-Szabo order parameter, and interaction strength constants. The analysis yields the bound-site carbon-13 chemical shielding anisotropy, ΔσC = -58 ± 8 ppm, in good agreement with most recent liquid-crystal measurements and the corresponding proton shielding anisotropy, ΔσH = 14 ± 2 ppm.

Investigation of chloromethane complexes of cryptophane-A analogue with butoxy groups using ¹³C NMR in the solid state and solution along with single crystal X-ray diffraction.

Host-guest complexes between cryptophane-A analogue with butoxy groups (cryptophane-But) and chloromethanes (chloroform, dichloromethane) were investigated in the solid state by means of magic-angle spinning (13)C NMR spectroscopy. The separated local fields method with (13)C-(1)H dipolar recoupling was used to determine the residual dipolar coupling for the guest molecules encaged in the host cavity. In the case of chloroform guest, the residual dipolar interaction was estimated to be about 19 kHz, consistent with a strongly restricted mobility of the guest in the cavity, while no residual interaction was observed for encaged dichloromethane. In order to rationalize this unexpected result, we performed single crystal X-ray diffraction studies, which confirmed that both guest molecules indeed were present inside the cryptophane cavity, with a certain level of disorder. To improve the insight in the dynamics, we performed a (13)C NMR spin-lattice relaxation study for the dichloromethane guest in solution. The system was characterized by chemical exchange, which was slow on the chemical shift time scale but fast with respect to the relaxation rates. Despite these disadvantageous conditions, we demonstrated that the data could be analyzed and that the results were consistent with an isotropic reorientation of dichloromethane within the cryptophane cavity.

Systematic theoretical investigation of the zero-field splitting in Gd(III) complexes: wave function and density functional approaches.

The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H2O)(-), Gd(III)DTPA(H2O)(2-), and Gd(III)(H2O)8(3+) in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude.

Dynamics of exocyclic groups in the Escherichia coli O91 O-antigen polysaccharide in solution studied by carbon-13 NMR relaxation.

Carbon-13 relaxation data are reported for exocyclic groups of hexopyranosyl sugar residues in the repeating unit within the Escherichia coli O91 O-antigen polysaccharide in a dilute D2O solution. The measurements of T 1, T 2 and heteronuclear nuclear Overhauser enhancements were carried out at 310 K at two magnetic fields (16.4 T, 21.1 T). The data were analyzed using the standard and extended Lipari-Szabo models, as well as a conformational jump model. The extended version of the Lipari-Szabo and the two-site jump models were most successful for the hydroxymethyl groups of Gal and GlcNAc sugar residues. Different dynamics was found for the hydroxymethyl groups associated with different configurations (D-gluco, D-galacto) of the sugar residues, the latter being faster than the former.

Stochastic modeling of flexible biomolecules applied to NMR relaxation. 2. Interpretation of complex dynamics in linear oligosaccharides.

A computational stochastic approach is applied to the description of flexible molecules. By combining (i) molecular dynamics simulations, (ii) hydrodynamics approaches, and (iii) a multidimensional diffusive description for internal and global dynamics, it is possible to build an efficient integrated approach to the interpretation of relaxation processes in flexible systems. In particular, the model is applied to the interpretation of nuclear magnetic relaxation measurements of linear oligosaccharides, namely a mannose-containing trisaccharide and the pentasaccharide LNF-1. Experimental data are reproduced with sufficient accuracy without free model parameters.

Stochastic modeling of flexible biomolecules applied to NMR relaxation. I. Internal dynamics of cyclodextrins: γ-cyclodextrin as a case study.

In this work, we address the description of the dynamics of cyclodextrins in relation with nuclear magnetic resonance (NMR) relaxation data collected for hydroxymethyl groups. We define an integrated computational approach based on the definition and parametrization of a stochastic equation able to describe the relevant degrees of freedom affecting the NMR observables. The computational protocol merges molecular dynamics simulations and hydrodynamics approaches for the evaluation of most of the molecular parameters entering the stochastic description of the system. We apply the method to the interpretation of the (13)C NMR relaxation of the -CH(2)OH group of cyclodextrins. We use γ-cyclodextrin as a case study. Results are in agreement with quantitative and qualitative analyses performed in the past with simpler models and molecular dynamics simulations. The element of novelty in our approach is in the treatment of the coupling of the relevant internal (glucopyranose ring twisting/tilting and hydroxymethyl group jumps) and global (molecular tumbling) degrees of freedom.

Inclusion of chloromethane guests affects conformation and internal dynamics of cryptophane-D host.

Cryptophane-D is composed of two nonequivalent cyclotribenzylene caps bound together by three OCH2CH2O bridges in a syn arrangement. Host-guest complexes with chloroform and dichloromethane were investigated in solution by NMR spectroscopy. Variable temperature NMR (1)H and (13)C spectra showed effects of chemical exchange between the free and bound guest and of conformational exchange for the host, strongly and specifically affected by guest binding. We found in particular that the carbon-13 chemical shifts for the linkers connecting the two cyclotribenzylene units are very informative. The NMR results were supported by DFT calculations. The guest exchange was also studied quantitatively, either by EXSY measurements (for chloroform as guest) or by line-shape analysis (for dichloromethane as guest). In the case of chloroform guest, we also investigated cross-relaxation between the guest and host protons, as well as carbon-13 longitudinal relaxation and heteronuclear NOE at three different fields. The results were interpreted in terms of orientation and dynamics of the guest inside the host cavity. Putting together various types of evidence resulted in remarkably detailed insight into the process of molecular recognition of the two guests by cryptophane-D host.

Carbon-13 NOESY and equivalent protons: methyl iodide dynamics.

We have shown that proton-coupled carbon-13 2D NOESY experiments, performed on degenerate spin systems, can provide unique quantitative information about anisotropic reorientational motions and molecular geometry. Relevant theory for AX(2) and AX(3) spin systems is presented, assuming the dipole-dipole and random field relaxation mechanisms of (13)C nucleus, and demonstrated on methyl iodide solution in chloroform. Agreement with experimental intensities of all the six independent peaks is very good in the whole range of mixing times (up to 45 s).

Behavior of two almost identical spins during the CPMG pulse sequence.

Multiple-spin-echo experiments have found wide use in nuclear magnetic resonance spectroscopy. In particular, the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence is used to determine transverse relaxation times T(2). Herein it is demonstrated, both theoretically and experimentally, that for a pair of almost identical spins-1/2 the experimental setup can have a profound effect on the observed spin dynamics. It is shown that, in the case of dipolar relaxation, the measured T(2) values can roughly vary between the limits of identical and unlike spins, just depending on the repetition rate of pi pulses with respect to chemical shift separation. Such an effect can, in the extreme narrowing regime, amount to a 50% difference.

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

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 beta-D-Glcp-(1-->6)-alpha-D-[6-(13)C]-Manp-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.

NMR relaxation interference effects and internal dynamics in gamma-cyclodextrin.

Multiple-magnetic field (9.4, 14.1 and 21.1 T) measurements of (13)C spin-lattice and spin-spin relaxation rates, the heteronuclear Overhauser enhancement and cross-correlated relaxation rates (CCRRs) in the methylene groups are reported for gamma-cyclodextrin in water/dimethylsulfoxide solution at 323 and 343K. The CCRRs are obtained from differences in the initial relaxation rates of the components of the CH(2) triplet in the (13)C spectra. The relaxation data are analyzed using the Lipari-Szabo approach and a novel modification of the two-site jump model. According to the latter model, inclusion of the dipolar (CH,CH(')) cross-correlated longitudinal and transverse relaxation is important for estimating the rate of the conformational jumps in the hydroxymethyl group. Using the dynamic information from the jump model, we have also used the differences in the initial relaxation rates for the triplet components to estimate the anisotropy of the chemical shielding tensor.

Inclusion complexes of cryptophane-E with dichloromethane and chloroform: A thermodynamic and kinetic study using the 1D-EXSY NMR method.

Complexation equilibria and kinetics of exchange of chloroform and dichloromethane molecules between the cavity of cryptophane-E and bulk solution were investigated using NMR methods. Using one-dimensional magnetization transfer (1D-EXSY type sequence), chemical exchange rates were measured in different temperature ranges, limited by the equilibrium constant values of the complexes and the boiling points of the guest substances. From the kinetic data, activation energies were calculated using the Arrhenius equation. From the temperature-dependence of the association constant data, the enthalpy and entropy of complexation were estimated and compared with values for similar complexes of other cryptophanes.

Carbon-13 NMR relaxation study of 1,8-bis(dimethylamino)naphthalene in isotropic solution.

Carbon-13 nuclear spin relaxation in 1,8-bis(dimethylamino)naphthalene (DMAN) was investigated in a dimethylformamide- d 7 solution. In addition, the chemical shielding tensors were measured in the crystalline powder. Detailed analysis of (13)C longitudinal relaxation in this molecule yielded its rotational diffusion tensor. Comparison to the protonated form of DMAN, DMANH(+), leads to conclusions concerning interaction of the latter with its counterion.

Comparison of different methods for calculating the paramagnetic relaxation enhancement of nuclear spins as a function of the magnetic field.

The enhancement of the spin-lattice relaxation rate for nuclear spins in a ligand bound to a paramagnetic metal ion [known as the paramagnetic relaxation enhancement (PRE)] arises primarily through the dipole-dipole (DD) interaction between the nuclear spins and the electron spins. In solution, the DD interaction is modulated mostly by reorientation of the nuclear spin-electron spin axis and by electron spin relaxation. Calculations of the PRE are in general complicated, mainly because the electron spin interacts so strongly with the other degrees of freedom that its relaxation cannot be described by second-order perturbation theory or the Redfield theory. Three approaches to resolve this problem exist in the literature: The so-called slow-motion theory, originating from Swedish groups [Benetis et al., Mol. Phys. 48, 329 (1983); Kowalewski et al., Adv. Inorg. Chem. 57, (2005); Larsson et al., J. Chem. Phys. 101, 1116 (1994); T. Nilsson et al., J. Magn. Reson. 154, 269 (2002)] and two different methods based on simulations of the dynamics of electron spin in time domain, developed in Grenoble [Fries and Belorizky, J. Chem. Phys. 126, 204503 (2007); Rast et al., ibid. 115, 7554 (2001)] and Ann Arbor [Abernathy and Sharp, J. Chem. Phys. 106, 9032 (1997); Schaefle and Sharp, ibid. 121, 5387 (2004); Schaefle and Sharp, J. Magn. Reson. 176, 160 (2005)], respectively. In this paper, we report a numerical comparison of the three methods for a large variety of parameter sets, meant to correspond to large and small complexes of gadolinium(III) and of nickel(II). It is found that the agreement between the Swedish and the Grenoble approaches is very good for practically all parameter sets, while the predictions of the Ann Arbor model are similar in a number of the calculations but deviate significantly in others, reflecting in part differences in the treatment of electron spin relaxation. The origins of the discrepancies are discussed briefly.

Quinuclidine complex with alpha-cyclodextrin: a diffusion and 13C NMR relaxation study.

The stability of an inclusion complex of quinuclidine with alpha-cyclodextrin in solution was investigated by NMR measurements of the translational diffusion coefficient. A 1:1 stoichiometry model yielded an association constant of 35 +/- 3 M(-1). The guest molecules exchange rapidly between the host cavity and the bulk solution. The reorientational dynamics of the guest and host molecules was studied using carbon-13 NMR relaxation at two magnetic fields. The relaxation of the host nuclei showed very little dependence on the guest-host concentration ratio, while the 13C spins in quinuclidine were sensitive to the solution composition. Using mole-fraction data, it was possible to extract the relaxation parameters for the bound and free form of quinuclidine. Relaxation rates of the guest molecule, free in solution, were best described by an axially symmetric model, while the data of the complex species were analyzed using the Lipari-Szabo method. Applying the axially symmetric model to the complexed quinuclidine indicated that the anisotropy of its reorientation in the bound form was increased.

Nuclear-spin relaxation in nonrigid molecules: discrete multisite local dynamics combined with anisotropic molecular reorientation.

Nuclear-spin relaxation is considered in a molecular system undergoing two types of dynamic processes: asymmetric-top small-step rotational diffusion and discrete multisite local jumps. The two processes are assumed to be uncorrelated. Time correlation functions for relevant rank-two interactions and corresponding spectral density functions are derived for a general relation between the characteristic rate constants. In addition, limiting cases of fast and slow local motions and of some specific jump conditions are also investigated.

Dynamics of chloromethanes in cryptophane-E inclusion complexes: a 2H solid-state NMR and X-ray diffraction study.

In this paper, we present a variable temperature (2)H solid-state NMR investigation of cryptophane-E:chloroform and cryptophane-E:dichloromethane inclusion complexes. The (2)H line shapes and nuclear spin relaxation rates were analyzed in terms of the distribution of C-D bond orientations and the time scale of the guest dynamics. It was found that encaged chloroform produces broad (2)H spectra, and that its reorientation is relatively slow with a correlation time of approximately 0.17 mus at 292 K. In contrast, the (2)H line shapes of encaged dichloromethane are narrow and the motion of this guest molecule is fast with a correlation time of approximately 1.4 ps at 283 K. The (2)H NMR data were complemented by an X-ray diffraction study of the cryptophane-E:dichloromethane structure, which was utilized in the analysis of the NMR parameters.