Dipolar Tensors Research Articles

Extending molecular dynamics with dipolar NMR tensors as constraints to chiral phosphorus compounds.

Molecular dynamics with orientational constraints (MDOC) simulations use NMR parameters as tensorial constraints in the stereochemical analysis of small molecules. 13C-31P Residual dipolar couplings-aided MDOC simulations of small phosphorus molecules determined the relative configurations of rigid molecules after including 3JH-H-couplings as additional constraints. However, flexible molecules remain a problem.

Simulation of oriented NMR spectra: Combining molecular dynamics and chemical shift tensor calculations.

Solid state NMR is widely used to study the orientation and other structural features of proteins and peptides in lipid bilayers. Using data obtained by PISEMA (Polarization Inversion Spin Exchange at Magic Angle) experiments, periodic spectral patterns arise from well-aligned α-helical molecules. Significant problems in the interpretation of PISEMA spectra may arise for systems that do not form perfectly defined secondary structures, like α-helices, or the signal pattern is disturbed by molecular motion. Here, we present a new method that combines molecular dynamics simulation with tensorial orientational constraints (MDOC) and chemical shift tensor calculations for the simulation and interpretation of PISEMA-like spectra. The calculations include the spectra arising from non α-helical molecules and molecules with non-uniform intrinsic mobility. In a first step, dipolar or quadrupolar interaction tensors drive molecular rotations and reorientations to obtain the proper mean values as observed in corresponding NMR experiments. In a second step, the coordinate snapshots of the MDOC simulations are geometry optimized with the isotropic 15 N chemical shifts as constraints using Bond Polarization Theory (BPT) to provide reliable 15 N CS tensor data. The averaged dipolar 1 H-15 N couplings and the δzz tensor components can then be combined to simulate PISEMA patterns. We apply this method to the ß-helical peptide gramicidin A (gA) and demonstrate that this method enables the assignment of most PISEMA resonances. In addition, MDOC simulations provide local order parameters for the calculated sites. These local order parameters reveal large differences in backbone mobility between L- and D-amino acids of gA.

Determination of the relative orientation between 15N-1H dipolar coupling and 1H chemical shift anisotropy tensors under fast MAS solid-state NMR

In this work, we have proposed a proton-detected three-dimensional (3D) 15N-1H dipolar coupling (DIP)/1H chemical shift anisotropy (CSA)/1H chemical shift (CS) correlation experiment to measure the relative orientation between the 15N-1H dipolar coupling and the 1H CSA tensors under fast magic angle spinning (MAS) solid-state NMR. In the 3D correlation experiment, the 15N-1H dipolar coupling and 1H CSA tensors are recoupled using our recently developed windowless C-symmetry-based C331-ROCSA (recoupling of chemical shift anisotropy) DIPSHIFT and C331-ROCSA pulse-based methods, respectively. The 2D 15N-1H DIP/1H CSA powder lineshapes extracted using the proposed 3D correlation method are shown to be sensitive to the sign and asymmetry of the 1H CSA tensor, a feature that allows the determination of the relative orientation between the two correlating tensors with improved accuracy. The experimental method developed in this study is demonstrated on a powdered U-15N L-Histidine.HCl·H2O sample.

Van der Waals Dispersion Potential between Excited Chiral Molecules via the Coupling of Induced Dipoles

The retarded van der Waals dispersion potential between two excited chiral molecules was calculated using an approach, in which electric and magnetic dipole moments are induced in each particle by fluctuations in the vacuum electromagnetic field. An expectation value of the coupling of the moments at different centres to the dipolar interaction tensors was taken over excited matter states and the ground state radiation field, the former yielding excited molecular polarisabilities and susceptibilities, and the latter field–field spatial correlation functions. The dispersion potential term proportional to the mixed dipolar polarisability is discriminatory, dependent upon molecular handedness, and contains additional terms due to transitions that de-excite each species as well as the usual u-integral term over imaginary frequency, which applies to both upward and downward transitions. Excited state dispersion potentials of a comparable order of magnitude involving paramagnetic and diamagnetic couplings were also computed. Pros and cons of the method adopted are compared to other commonly used approaches.

Synthesis, linear and non-linear optical properties of “push-pull” chromophores based on 9,9-dimethyl-9H-fluoren-2-amine

Photophysical properties including the first hyperpolarizability of a series of chromophores (SP1-SP5) possessing “push-pull” type conjugation were investigated to evaluate the proficiency as non-linear optically active materials. The compounds are based on the 9,9-dimethyl-9H-fluoren-2-amine platform, which acts as a donor unit and different types of acceptors have been incorporated to design SP1-SP5. The first hyperpolarizability (βHRS) value was in the range of 102 × 10−30 esu to 174 × 10−30 esu, and the trends in the experimental βHRS have been rationalized in terms of the difference in the dipole moment (Δμge) of the ground and excited state, oscillator strength of the contributing absorption bands and the band gaps. The intrinsic efficiency of the non-linear response of these dipolar compounds possessing a single major dipolar hyperpolarizability tensor component βzzz was also determined from the intrinsic hyperpolarizability, a real figure of merit of the non-linear optical response. Comparison of the experimental off-resonant first hyperpolarizability, βHRS, as well as the intrinsic hyperpolarizability of this set of D-π-A chromophores, lacking linear conjugation, revealed advantage over the already reported counterparts based on benzothiazole platform.

19F NMR studies on ionic conduction pathways in tysonite-CeF3

There has been a long-standing controversy over ion conducting pathways in tysonite. To unravel the pathways in CeF3, high-resolution MAS NMR spectra of 19F in CeF3 at −40–240 °C are analyzed on the bases of the calculated dipolar coupling tensor between 19F and paramagnetic electron spins at Ce3+ to assign the three spinning-sideband manifolds for the three crystallographically inequivalent sites (F1, F2, and F3). Clearly resolved sideband manifolds for F1∼F3 at 240 °C indicate that ion exchange among the three sites is not fast enough to affect the 19F spectrum, whereas F1 motion is suggested by its broader linewidth. Further, we show that addition of only 0.1% Sr2+ in CeF3 (Ce1-xSrxF3-x (x = 0.001)) brings significant effects on F-ion mobility. While some of the F2 ions remain at the F2 site, most of the F3 ions undergo exchange motion between F1 at 240 °C. The preference of the exchange pathways in CeF3 is thus consistent with that postulated for LaF3, that is, F1–F1 exchange occurs first followed by F1–F3, and F1–F2 exchange is most restricted.

Relaxation-induced dipolar exchange with recoupling (RIDER) distortions in CODEX experiments.

Chemical shift anisotropy (CSA) and dipolar CODEX (Cenralband Only Detection of EXchange) experiments enable abundant quantitative information on the reorientation of the CSA and dipolar tensors to be obtained on millisecond-second timescales. At the same time, proper performance of the experiments and data analysis can often be a challenge since CODEX is prone to some interfering effects that may lead to incorrect interpretation of the experimental results. One of the most important such effects is RIDER (relaxation-induced dipolar exchange with recoupling). It appears due to the dipolar interaction of the observed nuclei with some other nuclei, which causes an apparent decay in the mixing time dependence of the signal intensity reflecting not molecular motion, but spin flips of the adjacent nuclei. This may hamper obtaining correct values of the parameters of molecular mobility. In this contribution we consider in detail the reasons why the RIDER distortions remain even under decoupling conditions and propose measures to eliminate them. That is, we suggest (1)using an additional filter between the cross-polarization (CP) section and the CODEX recoupling blocks that suppresses the interfering anti-phase coherence responsible for the -H RIDER and (2)recording only the cosine component of the CODEX signal since it is less prone to the RIDER distortions in comparison to the sine component. The experiments were conducted on rigid model substances as well as microcrystalline H N-enriched proteins (GB1 and SH3) with a partial back-exchange of labile protons. Standard CSA and dipolar CODEX experiments reveal a fast-decaying component in the mixing time dependence of N nuclei in proteins, which can be misinterpreted as a slow overall protein rocking motion. However, the RIDER-free experimental setup provides flat mixing time dependences, meaning that the studied proteins do not undergo global motions on the millisecond timescale.

Identification and Control of Electron-Nuclear Spin Defects in Diamond.

We experimentally demonstrate an approach to scale up quantum devices by harnessing spin defects in the environment of a quantum probe. We follow this approach to identify, locate, and control two electron-nuclear spin defects in the environment of a single nitrogen-vacancy center in diamond. By performing spectroscopy at various orientations of the magnetic field, we extract the unknown parameters of the hyperfine and dipolar interaction tensors, which we use to locate the two spin defects and design control sequences to initialize, manipulate, and readout their quantum state. Finally, we create quantum coherence among the three electron spins, paving the way for the creation of genuine tripartite entanglement. This approach will be useful in assembling multispin quantum registers for applications in quantum sensing and quantum information processing.

Low magnetic field effects on triplet pair annihilations at canonical orientations

Using the density operator formalism, a simple analytical model is developed to study low magnetic field effects on triplet pair annihilations in organic solids. Analysis is restricted to canonical orientations where two identical triplet molecules have the same orientation and the direction of the external magnetic field is parallel to one of the principle axes of the dipolar coupling tensor for a triplet. The analytical solution reveals that the low magnetic field effect in the triplet pair arises from the anisotropic dipole-dipole coupling in a triplet. In the presence of the dipole-dipole coupling, the spin quantization axis for each triplet gradually changes with the increase of the external magnetic field from zero field to high field. The low magnetic field effect reaches a maximum when the Zeeman splitting between the spin states matches a dipole-dipole coupling component orthogonal to the external magnetic field direction. The result is also discussed with the low magnetic field effect in the radical pair with one isotropic hyperfine coupling.

SCFit: Software for single-crystal NMR analysis. Free vs constrained fitting

The design and implementation of a software package for the analysis of single-crystal NMR data is presented. The SCFit software can treat spectra arising from various interactions: (i) chemical shift tensor only; (ii) chemical shift tensor and quadrupolar coupling tensor; (iii) dipolar and indirect nuclear spin-spin coupling tensors; (iv) all four interactions. The software is demonstrated on recently reported 17O and 31P single-crystal NMR data for triphenylphosphine oxide and for two of its halogen-bonded cocrystals. The 17O single-crystal NMR data represent a case where all four above-mentioned interactions simultaneously affect the spectra. SCFit can fit the chemical shift and quadrupolar coupling in two ways: (i) through an unconstrained fitting process where all tensor parameters are freely optimized or (ii) through a constrained fitting process where the principal components of the tensors may be fixed to values known previously with high precision via the analysis of powder samples. The second strategy is explored in an effort to reduce the number of unknowns in the fitting process; an improvement in the precision of the resulting tensor orientations is noted in some cases.

Backscattering Immunity of Dipole-Exchange Magnetostatic Surface Spin Waves.

The existence of backscattering-immune spin-wave modes is demonstrated in magnetic thin films of nanoscale thickness. Our results reveal that chiral magnetostatic surface waves (CMSSWs), which propagate perpendicular to the magnetization direction in an in-plane magnetized thin film, are robust against backscattering from surface defects.CMSSWs are protected against various types of surface inhomogeneities and defects as long as their frequency lies inside the gap of the volume modes. Our explanation is independent of the topology of the modes and predicts that this robustness is a consequence of symmetry breaking of the dynamic magnetic fields of CMSSWs due to the off-diagonal part of the dipolar interaction tensor, which is present both for long- (dipole-dominated) and short-wavelength (exchange-dominated) spin waves. Micromagnetic simulations confirm the robust character of the CMSSWs. Our results open a new direction in designing highly efficient magnonic logic elements and devices employing CMSSWs in nanoscale thin films.

Peptide bond conformation in peptides and proteins probed by dipolar coupling-chemical shift tensor correlation solid-state NMR.

Multidimensional magic-angle spinning solid-state NMR experiments are described that permit cis and trans peptide bonds in uniformly 13C,15N-labeled peptides and proteins to be unambiguously distinguished in residue-specific manner by determining the relative orientations of the amide 13C' CSA and 1H-15N dipolar coupling tensors. The experiments are demonstrated for model peptides glycylglycine and 2,5-diketopiperazine containing trans and cis peptide bonds, respectively. Subsequently, the measurements are extended to two representative proteins that contain exclusively trans peptide bonds, microcrystalline B3 immunoglobulin domain of protein G and Y145Stop human prion protein amyloid fibrils, to illustrate their applicability to a wide range of protein systems.

ENDOR Characterization of (N2)FeII(μ-H)2FeI(N2)-: A Spectroscopic Model for N2 Binding by the Di-μ-hydrido Nitrogenase Janus Intermediate.

The biomimetic diiron complex 4-(N2)2, featuring two terminally bound Fe-N2 centers bridged by two hydrides, serves as a model for two possible states along the pathway by which the enzyme nitrogenase reduces N2. One is the Janus intermediate E4(4H), which has accumulated 4[e-/H+], stored as two [Fe-H-Fe] bridging hydrides, and is activated to bind and reduce N2 through reductive elimination (RE) of the hydride ligands as H2. The second is a possible RE intermediate. 1H and 14N 35 GHz ENDOR measurements confirm that the formally Fe(II)/Fe(I) 4-(N2)2 complex exhibits a fully delocalized, Robin-Day type-III mixed valency. The two bridging hydrides exhibit a fully rhombic dipolar tensor form, T ≈ [- t, + t, 0]. The rhombic form is reproduced by a simple point-dipole model for dipolar interactions between a bridging hydride and its "anchor" Fe ions, confirming validity of this model and demonstrating that observation of a rhombic form is a convenient diagnostic signature for the identification of such core structures in biological centers such as nitrogenase. Furthermore, interpretation of the 1H measurements with the anchor model maps the g tensor onto the molecular frame, an important function of these equations for application to nitrogenase. Analysis of the hyperfine and quadrupole coupling to the bound 14N of N2 provides a reference for nitrogen-bound nitrogenase intermediates and is of chemical significance, as it gives a quantitative estimate of the amount of charge transferred between Fe and coordinated N, a key element in N2 activation for reduction.

Tuning nuclear depolarization under MAS by electron T1e.

The Cross-Effect (CE) Dynamic Nuclear Polarization (DNP) mechanism under Magic Angle Spinning (MAS) induces depletion or "depolarization" of the NMR signal, in the absence of microwave irradiation. In this study, the role of T1e on nuclear depolarization under MAS was tested experimentally by systematically varying the local and global electron spin concentration using mono-, bi- and tri-radicals. These spin systems show different depolarization effects that systematically tracked with their different T1e rates, consistent with theoretical predictions. In order to test whether the effect of T1e is directly or indirectly convoluted with other spin parameters, the tri-radical system was doped with different concentrations of GdCl3, only tuning the T1e rates, while keeping other parameters unchanged. Gratifyingly, the changes in the depolarization factor tracked the changes in the T1e rates. The experimental results are corroborated by quantum mechanics based numerical simulations which recapitulated the critical role of T1e. Simulations showed that the relative orientation of the two g-tensors and e-e dipolar interaction tensors of the CE fulfilling spin pair also plays a major role in determining the extent of depolarization, besides the enhancement. This is expected as orientations influence the efficiency of the various level anti-crossings or the "rotor events" under MAS. However, experimental evaluation of the empirical spectral diffusion parameter at static condition showed that the local vs. global e-e dipolar interaction network is not a significant variable in the commonly used nitroxide radical system studied here, leaving T1e rates as the major modulator of depolarization.

Analytical models for coupling reliability in identical two-magnet systems during slow reversals

This paper follows previous works which investigated the strength of dipolar coupling in two-magnet systems. While those works focused on qualitative analyses, this manuscript elucidates reversal through dipolar coupling culminating in analytical expressions for reversal reliability in identical two-magnet systems. The dipolar field generated by a mono-domain magnetic body can be represented by a tensor containing both longitudinal and perpendicular field components; this field changes orientation and magnitude based on the magnetization of neighboring nanomagnets. While the dipolar field does reduce to its longitudinal component at short time-scales, for slow magnetization reversals, the simple longitudinal field representation greatly underestimates the scope of parameters that ensure reliable coupling. For the first time, analytical models that map the geometric and material parameters required for reliable coupling in two-magnet systems are developed. It is shown that in biaxial nanomagnets, the x̂ and ŷ components of the dipolar field contribute to the coupling, while all three dimensions contribute to the coupling between a pair of uniaxial magnets. Additionally, the ratio of the longitudinal and perpendicular components of the dipolar field is also very important. If the perpendicular components in the dipolar tensor are too large, the nanomagnet pair may come to rest in an undesirable meta-stable state away from the free axis. The analytical models formulated in this manuscript map the minimum and maximum parameters for reliable coupling. Using these models, it is shown that there is a very small range of material parameters which can facilitate reliable coupling between perpendicular-magnetic-anisotropy nanomagnets; hence, in-plane nanomagnets are more suitable for coupled systems.

Expanding the horizons for structural analysis of fully protonated protein assemblies by NMR spectroscopy at MAS frequencies above 100 kHz

The recent breakthroughs in NMR probe technologies resulted in the development of MAS NMR probes with rotation frequencies exceeding 100 kHz. Herein, we explore dramatic increases in sensitivity and resolution observed at MAS frequencies of 110–111 kHz in a novel 0.7 mm HCND probe that enable structural analysis of fully protonated biological systems. Proton- detected 2D and 3D correlation spectroscopy under such conditions requires only 0.1–0.5 mg of sample and a fraction of time compared to conventional 13C-detected experiments. We discuss the performance of several proton- and heteronuclear- (13C-,15N-) based correlation experiments in terms of sensitivity and resolution, using a model microcrystalline fMLF tripeptide. We demonstrate the applications of ultrafast MAS to a large, fully protonated protein assembly of the 231-residue HIV-1 CA capsid protein. Resonance assignments of protons and heteronuclei, as well as 1H-15N dipolar and 1HN CSA tensors are readily obtained from the high sensitivity and resolution proton-detected 3D experiments. The approach demonstrated here is expected to enable the determination of atomic-resolution structures of large protein assemblies, inaccessible by current methodologies.

Model based object localization and shape estimation using electric sense on underwater robots

Recently, biologists have shown that the weakly electric fish are able to estimate the electric nature, the localization and the 3D geometric properties of an object using active electric sense. Incredibly, the Gnathonemus petersii performs this task in the dark only by moving towards and around the object, its vision is not required. In this paper, we proposed to address the challenging issue of object localization and shape estimation using a real underwater robot equipped with artificial electric sense. To that end, we used a corrected version of the dipolar tensor dedicated to small objects [Ammari et al., 2014] able to capture the electric response of big objects (typically objects whose size is about the one half of the robot length < 10cm). The principal contribution consists in the development of a multi-scale exhaustive search algorithm based on this tensor that allows to estimate in a same step the localization, orientation and shape of an object from electric currents measured along a given trajectory close to the object. Over 108 experiments, our method shows good results as on average we obtained 18% of shape error, 25° of orientation error and 1cm of localization error within a range of [5, 11]cm distance with the robot. These results are promising since the problem solved is known to be complex localization and shape being intricately linked in the electrical measurements [Rasnow, 1996].

Hybrid NMR: A Union of Solution- and Solid-State NMR.

Hybrid NMR (hdNMR) is a powerful new tool that combines the strengths of solution- and solid-state NMR to measure dipolar, chemical shift, and quadrupolar tensors in aqueous solution. We introduce the theory of hdNMR and partially randomly oriented (PRO) crystalline hydrogel samples. PRO samples produce randomly oriented spectra with characteristic Pake patterns from the solid state, yet they maintain the high-resolution dispersion of solution NMR experiments. With new pulse sequences, we show how hdNMR can be used to measure with high precision the 1Hα-13Cα dipolar tensor and carboxylate chemical shift anisotropy tensor of aspartate. These measurements contain detailed information on the distribution of electron density, interatomic distances, and the orientation dependence of molecular motion.

Determining the relative orientation between the chemical shift anisotropy and heteronuclear dipolar tensors in static solids by SEDOR NMR

The measurement of the dipolar interaction between two spins provides the distance between nuclei. A better structural picture emerges when the distance is combined with the orientation of the internuclear vector in the principal axis system of the chemical shift anisotropy tensor. The SEDOR experiment is used on a static sample of alanine to show that the orientation of the vector connecting the nitrogen and carboxylate carbon nuclei can be accurately determined in the CSA PAS of the 13C carboxylate spin.

On the properties of residual dipolar coupling alignment tensors: Simulations illuminate how residual dipolar couplings depend on the relative orientations of the magnetic field, the director of the alignment phase and the bond vectors

AbstractThe measurement of residual dipolar couplings (RDCs) exhibited by samples prepared in suitable alignment media can help in the elucidation of macromolecular structures. For any dipolar interactions that are not averaged to zero by molecular reorientations RDCs provide information about the possible orientations of the averaged interactions to the magnetic field. As such they contain information about the permitted relative positions of different motionally averaged bond vectors. This situation is often induced using nematic liquid crystalline phases with which the macromolecule under study interacts. While a single set of RDC measurements does not produce unique solutions for the orientation of each bond, multiple independent RDC datasets can be combined to restrict each bond to two diametrically opposed orientations. Attempts to obtain such datasets have primarily focused on performing experiments with multiple alignment media that interact with the macromolecule of interest in a different way. Other work has attempted to control the orientation of the media itself relative to that of the magnetic field. The latter has been explored using pre‐formed gels and might also be potentially realized using the application of different external fields during signal acquisition. This article seeks to clarify which approaches might generate independent RDC datasets and their utility in further restricting possible bond orientations using pictorial representations of simulated data.