Multiple-quantum N.M.R. study of molecular structure and ordering in a liquid crystal

Conformational analysis of small organic molecules using NOE and RDC data: A discussion of strychnine and α-methylene-γ-butyrolactone

To understand the properties and/or reactivity of an organic molecule, an understanding of its three-dimensional structure is necessary. Simultaneous determination of configuration and conformation often poses a daunting challenge. Thus, the more information accessible for a given molecule, the better. Additionally to (3)J-couplings, two sources of information, quantitative NOE and more recently also RDCs, are used for conformational analysis by NMR spectroscopy. In this paper, we compare these sources of conformational information in two molecules: the configurationally well-characterized strychnine 1, and the only recently configurationally and conformationally characterized α-methylene-γ-butyrolactone 2. We discuss possible sources of error in the measurement and analysis process, and how to exclude them. By this means, we are able to bolster the previously proposed flexibility for these two molecules.

Measuring dynamic and kinetic information in the previously inaccessible supra-τ(c) window of nanoseconds to microseconds by solution NMR spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool that has enabled experimentalists to characterize molecular dynamics and kinetics spanning a wide range of time-scales from picoseconds to days. This review focuses on addressing the previously inaccessible supra-tc window (defined as τ(c) < supra-τ(c) < 40 μs; in which tc is the overall tumbling time of a molecule) from the perspective of local inter-nuclear vector dynamics extracted from residual dipolar couplings (RDCs) and from the perspective of conformational exchange captured by relaxation dispersion measurements (RD). The goal of the first section is to present a detailed analysis of how to extract protein dynamics encoded in RDCs and how to relate this information to protein functionality within the previously inaccessible supra-τ(c) window. In the second section, the current state of the art for RD is analyzed, as well as the considerable progress toward pushing the sensitivity of RD further into the supra-τ(c) scale by up to a factor of two (motion up to 25 μs). From the data obtained with these techniques and methodology, the importance of the supra-τ(c) scale for protein function and molecular recognition is becoming increasingly clearer as the connection between motion on the supra-τ(c) scale and protein functionality from the experimental side is further strengthened with results from molecular dynamics simulations.

NMR dipolar constants of motion in liquid crystals: Jeener-Broekaert, double quantum coherence experiments and numerical calculation on a 10-spin cluster

Two proton quasi-equilibrium states were previously observed in nematic liquid crystals, namely the S and W quasi-invariants. Even though the experimental evidence suggested that they originate in a partition of the spin dipolar energy into a strong and a weak part, respectively, from a theoretical viewpoint, the existence of an appropriate energy scale which allows such energy separation remains to be confirmed and a representation of the quasi-invariants is still to be given. We compare the dipolar NMR signals yielded both by the Jeener-Broekaert (JB) experiment as a function of the preparation time and the free evolution of the double quantum coherence (DQC) spectra excited from the S state, with numerical calculations carried out from first principles under different models for the dipolar quasi-invariants, in a 10-spin cluster which represents the 5CB (4(')-pentyl-4-biphenyl-carbonitrile) molecule. The calculated signals qualitatively agree with the experiments and the DQC spectra as a function of the single-quantum detection time are sensible enough to the different models to allow both to probe the physical nature of the initial dipolar-ordered state and to assign a subset of dipolar interactions to each constant of motion, which are compatible with the experiments. As a criterion for selecting a suitable quasi-equilibrium model of the 5CB molecule, we impose on the time evolution operator consistency with the occurrence of two dipolar quasi-invariants, that is, the calculated spectra must be unaffected by truncation of non-secular terms of the weaker dipolar energy. We find that defining the S quasi-invariant as the subset of the dipolar interactions of each proton with its two nearest neighbours yields a realistic characterization of the dipolar constants of motion in 5CB. We conclude that the proton-spin system of the 5CB molecule admits a partition of the dipolar energy into a bilinear strong and a multiple-spin weak contributions therefore providing two orthogonal constants of motion, which can be prepared and observed by means of the JB experiment. This feature, which implies the existence of two timescales of very different nature in the proton-spin dynamics, is ultimately dictated by the topology of the spin distribution in the dipole network and can be expected in other liquid crystals. Knowledge of the nature of the dipolar quasi-invariants will be useful in studies of dipolar-order relaxation, decoherence and multiple quantum NMR experiments where the initial state is a dipolar-ordered one.

Quasiequilibrium states in thermotropic liquid crystals studied by multiple-quantum NMR

Previous work showed that by means of the Jeener-Broekaert (JB) experiment, two quasiequilibrium states can be selectively prepared in the proton spin system of thermotropic nematic liquid crystals (LCs) in a strong magnetic field. The similarity of the experimental results obtained in a variety of LC in a broad Larmor frequency range, with crystal hydrates, supports the assumption that also in LC the two spin reservoirs, into which the Zeeman order is transferred, originate in the dipolar energy and that they are associated with a separation in energy scales: A constant of motion related to the stronger dipolar interactions (S), and a second one (W) corresponding to the secular part of the weaker dipolar interactions with regard to the Zeeman and the strong dipolar part. We study the nature of these quasi-invariants in nematic 5CB (4(')-pentyl-4-biphenyl-carbonitrile) and measure their relaxation times by encoding the multiple-quantum coherences of the states following the JB pulse pair on two orthogonal bases, Z and X. The experiments were also performed in powder adamantane at 301 K which is used as a reference compound having only one dipolar quasi-invariant. We show that the evolution of the quantum states during the buildup of the quasiequilibrium state in 5CB prepared under the S condition is similar to the case of powder adamantane and that their quasiequilibrium density operators have the same tensor structure. In contrast, the second constant of motion, whose explicit operator form is not known, involves a richer composition of multiple-quantum coherences of even order on the X basis, in consistency with the truncation inherent in its definition. We exploited the exclusive presence of coherences of +/-4,+/-6,+/-8, besides 0 and +/-2 under the W condition to measure the spin-lattice relaxation time T(W) accurately, so avoiding experimental difficulties that usually impair dipolar order relaxation measurement such as Zeeman contamination at high fields and also superposition of the different quasi-invariants. This procedure opens the possibility of measuring the spin-lattice relaxation of a quasi-invariant independent of the Zeeman and S reservoirs, so incorporating a new relaxation parameter useful for studying the complex molecular dynamics in mesophases. In fact, we report the first measurement of T(W) in a LC at high magnetic fields. Comparison of the obtained value with the one corresponding to a lower field (16 MHz) points out that the relaxation of the W-order strongly depends on the intensity of the external magnetic field, similarly to the case of the S reservoir, indicating that the relaxation of the W-quasi-invariant is also governed by the cooperative molecular motions.

Molecular structure extracted from residual dipolar couplings: Diphenylmethane dissolved in a nematic liquid crystal

This paper describes an analysis of 1H-1H residual dipolar couplings (RDCs) in diphenylmethane (DPM) dissolved in a nematic liquid crystal, reported by Celebre et al. [J. Chem. Phys. 118, 6417 (2003)]. In that article, the conformational distribution function for DPM was extracted from the RDCs, using the additive potential (AP) model which is based on the molecular-field theory. The AP approach is a powerful, and frequently used, tool for analysis of the nuclear-magnetic-resonance (NMR) parameters in liquid crystals. It requires, however, a priori knowledge of the functional form of the torsional potential, which may even for a simple molecule, such as DPM, be complicated to determine. Here, we analyze the same set of the RDCs using our APME procedure, which is a hybrid model based on the AP approach and maximum entropy (ME) theory. The APME procedure does not require any assumptions about the functional form of the torsional potential and, in contrast with the ME method, is applicable to weakly ordered systems. In the investigation reported in the present study, the results from the APME analysis are in good agreement with the AP interpretation, whereas the ME approach essentially fails in the extraction of the conformational distribution function for DPM.

Multiple-quantum NMR spectra of partially oriented indene: a new approach to estimating order in a nematic phase

Multiple-quantum proton NMR spectra of the 8-spin system of indene partially oriented in a nematic mesophase were acquired using a magnetic field gradient (MFG) method. Six-, seven- and eight-quantum spectra were solved to yield all intramolecular dipolar couplings (D(ij)) which were used to determine the molecular shape. The spectral widths of multiple-quantum spectra are dependent on molecular orientation and geometry and a novel method was developed to estimate the Saupe order parameters from the observed spectral widths of the high-order multiple-quantum spectra.

The NMR spectra of samples dissolved in liquid-crystalline phases: automatic analysis with the aid of multiple quantum spectra--the case of flexible molecules

Homonuclear N(S) = 0 and heteronuclear N(S) not equal 0 multiple quantum spectra, involving changes in the magnetic number m(I) by (N(I)-1), (N(I) - 2), and (N(I)-3), with N(I) and N(S) the number of interacting nuclei of magnetogyric ratio gamma(I) and gamma(S), are used for the automatic analysis of (1)H NMR spectra of flexible molecules dissolved in liquid-crystalline phases. The automatic procedure has been applied to study molecules of general formula Ph-CH(2)-X starting from a parameter set having all the spectral parameters set to zero. The results of such an analysis are then used as starting parameters for analysis of the single quantum spectrum. The method was first tested when X = Br and X = H in order to compare strategies differing for the types of parameters used and was then applied to the analysis of 3-phenylprop-1-yne.

Measurement of interproton, nuclear spin dipolar couplings in liquid crystalline samples by combining variable angle sample spinning, isotope dilution, and deuterium decoupling

The proton NMR spectra of liquid crystalline samples can be simplified by selective, partial deuteration followed by deuterium decoupling. This leaves strong peaks from the protons at the undeuterated sites, but also weak resonances from the coupling of these protons to those at low abundance (2% in the present case) at the deuterated sites. The weak resonances can be separated from the strong by recording spectra while spinning the sample at a series of angles to the magnetic field. Copyright 1997 Academic Press. Copyright 1997Academic Press

Multiple-Quantum Nuclear Magnetic Resonance Spectroscopy

A nuclear magnetic resonance (NMR) event is popularly viewed as the flip of a single spin in a magnetc field, stimulated by the absorption or emission of only one quantum of radio-frequency energy. Nevertheless, resonances between nuclear spin states that differ by more than one unit in the Zeeman quantum number also can be induced in systems of coupled spins by suitably designed sequences of radio-frequency pulses. Pairs of states excited in this way oscillate coherently at the frequencies of the corresponding multiple-quantum transitions and produce a response that may be monitored indirectly in a two-dimensional time-domain experiment. The pattern of multiple-quantum excitation and response, influenced largely by the concerted interactions of groups of coupled nuclei, simplifies the NMR spectrum in some instances and provides significant new information in others. Applications of multiple-quantum NMR extend to problems in many different areas, ranging from studies of the structure and function of proteins and nucleic acids in solution to investigations of the arrangements of atoms in amorphous semiconductors. The specific spectroscopic techniques are varied as well and include methods designed, for example, to simplify spectral analysis for liquids and liquid crystals, eliminate inhomogeneous broadening, study interatomic connectivity in liquid-state molecules, identify clusters of atoms in solids, enhance the spatial resolution in solid-state imaging experiments, and probe correlated molecular motions.