NMR investigations of dynamical processes in orientationally ordered and disordered NaCN,RbCN and CsCN

The nuclear spin lattice relaxation timeT ₁ of the²³Na,⁸⁵Rb,⁸⁷Rb,¹³³Cs,¹⁴N nuclei is measured in NaCN, RbCN and CsCN as a function of temperature below and above the ferroelastic phase transition temperatureT _c. BelowT _c the behaviour ofT ₁ of the alkali nuclei renders possible to determine the flip frequency of the CN molecules and its temperature dependence. AboveT _c from the¹⁴NT ₁ the correlation time τ_c of the rotational motions of the CN molecules and its temperature dependence is determined. An empirical rule is verified demonstrating that atT _c the correlation times take nearly the same values for all cyanides. For the high and low temperature phases one obtains atT _c about τ_c=5·10^?13s and τ_c=5·10^?11s, respectively. The results are discussed with respect to the mechanism of the phase transition.     

Studies of molecular motions and interactions in acetonitrile

Microwave and far-infrared absorption coefficients are reported for acetonitrile over the whole concentration range in carbon tetrachloride solution. The data have been used to compute dipole reorientational correlation functions and relaxation times as a function of concentration. These show that τ_1R ^T increases non-linearly as the acetonitrile concentration increases (in contrast to the values of τ_2R ^T obtained from light scattering measurements) and as the viscosity decreases. This behaviour is examined in terms of intermolecular correlations between rotating dipoles. Intensity data are used to provide a check on the importance of induced dipole absorption in the far-infrared spectra and to calculate ‘static’ correlation factors g ⁽¹⁾. Both g ⁽¹⁾ and the dynamic correlation factor f ⁽¹⁾ reflect the effects of strong molecular interactions in these solutions.     

The proton relaxation of methyl cyanide in the presence of Ni(II) ions,as studied by spin-echo techniques

The proton relaxation times (T ₁ and T ₂) of methyl cyanide, in the presence of Ni(II) ions, have been measured as a function of temperature and frequency by spin-echo techniques. The observed decay times (T ₂?) have also been measured as a function of the separation, t _ep, between the pulses in a Carr-Purcell train of echos. The results obtained in the limit of long pulse separation have been fitted to existing theories. The rotational correlation time of the Ni/MeCN complex, τ _R , the electron spin relaxation time, τ _S , and the distance of closest approach of the protons to the nickel have been estimated from the results. In addition the scalar coupling constant, the exchange rate τ _B and the activation energies for τ _B , τ _S and τ _R have been evaluated. The chemical exchange parameters obtained differ significantly from those obtained by previous workers. There is evidence from the pulse dependence experiments that the complex is a distorted octahedron.     

Improved Estimation of Protein Rotational Correlation Times fromN Relaxation Measurements

In the study of protein backbone dynamics by¹⁵N relaxation measurements, an initial estimation of the isotropic global correlation time, τ_m, is usually obtained from the averageT₁/T₂ratio of nuclear spins that do not exhibit slow internal motion and withT₂values not significantly shortened by chemical or conformational exchange processes. Different methods have been used for identification of the rates of internal motion. However, the number of nuclear spins included in the τ_mestimation is often larger than the number that ultimately can be fitted to a single-order parameter,S², implying that some nuclear spins involved in the initial τ_mestimation actually have an effective internal correlation time, τ_e, not as fast as assumed. As a consequence, τ_mis underestimated, since internal motion reduces theT₁/T₂ratio. This situation becomes more obvious if the molecule has a large τ_mvalue because the reduction inT₁/T₂ratio arising from internal motion is more significant than for molecules with smaller τ_mand the same degree of internal motion. This Communication describes a more reliable method for identifying nuclear spins which should be excluded from the τ_mestimation because of insufficiently rapid internal motion. This results in an improved τ_mvalue, giving a much better agreement between the number of nuclear spins fitted successfully to a single-order parameter,S², and those used in the τ_mestimation.     

Proton spin-lattice relaxation by critical polarization fluctuations in KH2PO4

The observed anomalous decrease in the proton spin-lattice relaxation timeT ₁ on approaching the Curie point in a rather pure KH₂PO₄ single crystal is explained by magnetic dipolar coupling to the ferroelectric mode. The isolated “non-interacting” O?H...O proton flipping time is estimated from theT ₁ data as τ=0.66·10^?12 sec for the paraelectric phase and τ=2.24·10^?12 sec for the ferroelectric phase, in good agreement with the results obtained from other methods.     

Proton magnetic relaxation in ethylene oxide,tetrahydrofuran, and triethylene diamine as clathrate deuterates

Proton spin-lattice relaxation times (T ₁) have been measured for triethylene diamine, ethylene oxide, and tetrahydrofuran as clathrate deuterates. The results are interpreted in terms of anisotropic rotation of the guest molecules. Triethylene diamine is thought to be undergoing rotation about its C ₃ axis with a correlation time given by τ_c/s = 4·87 × 10^-14 exp (1680 K/T) at temperatures between 120 K and the decomposition point (308 K). Between 77 K and 120 K, T ₁ is dominated by conformational distortions of the guest molecule. Ethylene oxide and tetrahydrofuran rotate about at least two axes in the deuterate at rates sufficient to produce some motional narrowing. At high temperatures the relaxation is caused in both cases by rotation about an axis perpendicular to the C ₂ axis, and at lower temperatures by rotation about the C ₂ axis itself. The correlation times are for ethylene oxide τ_c/s = 6·76 × 10^-14 exp (450 K/T), T < 160 K; and for tetrahydrofuran τ_c/s = 4·79 × 10^-14 exp (470 K/T), T < 140 K.

The free induction decay shapes indicate that, in each case, low frequency motion is occurring about all axes throughout the temperature range studied (77 K to the decomposition temperature in each case). From the lack of an observable signal from the clathrate deuterates of hexamethylene tetramine and dioxan, it is deduced that there is no reorientational motion of these guests at frequencies greater than their rigid-lattice linewidths.     

The properties of liquid nitrogen

Measurements are reported of the nitrogen-nucleus spin-lattice relaxation time, T ₁, in liquid nitrogen ¹⁴N₂ and liquid nitrogen ¹⁵N₂ along the liquid-vapour coexistence line from 77·3 K up to the critical temperature and for the fluid at the critical density up to 145 K. Values of the molecular reorientational correlation time, τ _Q , and the molecular angular momentum correlation time, τ _sr , are determined. The values of τ _Q and τ _sr and the relation between them are discussed in terms of various theories of molecular reorientation in molecular liquids. The values of τ _Q and τ _sr are also compared with those predicted by computer simulation methods. It is concluded that the molecular reorientation in liquid nitrogen is not by classical reorientational diffusion except possibly at temperatures near the triple point. It is suggested that at higher temperatures the reorientation is on average by rather large angles and that the process may be quantum mechanical to some extent. (For paper I in this series see reference [8].)     

Nuclear spin–lattice relaxation and complex motion of macromolecules in solution

The NMR spectral densities of a complex motion consisting of a combination of anisotropic overall motion and internal motion have been derived. Two approximations of the equations derived for the cases of slow, J_slow (ω), and fast, J_fast (ω), internal motions are presented. These equations imply that reduction in spectral density of overall motion can be observed if the maxima of internal and overall motions spectral densities versus temperature are well separated, as for fast internal motion. Slow intramolecular motion influences the values of spectral densities of the overall motion if one of the two spins performs a motion, for example a proton in double minimum of the ¹⁵N-H?···?N hydrogen bond. The analysis presented reveals small differences between the temperature dependencies of spectral densities of the isotropic and anisotropic overall motions. The theory is illustrated by the ¹³C protonated carbon spin-lattice relaxation of α-cyclodextrin macromolecule, using the expected motional parameters: D _∥/D _⊥?≈?5 at room temperature and for a fast or slow internal motion.     

DNA Duplex Dynamics: NMR Relaxation Studies of a Decamer with UniformlyC-Labeled Purine Nucleotides

Dynamics in a DNA decamer duplex,d(CATTTGCATC) ·d(GATGCAAATG), were investigated via a detailed¹³C NMR relaxation study. Every 2′-deoxyadenosine and 2′-deoxyguanidine was chemically enriched with 15%¹³C and 98%¹⁵N isotopes. Six nuclear relaxation parameters [R(¹³C_z),R(¹H_z),R(2¹H_z¹³C_z),R(¹³C_x),R(2¹H_z¹³C_x) and steady-state¹³C{¹H} NOE] were measured at 600 MHz and three were measured at 500 MHz (¹H frequency) for the CH spin systems of sugar 1′, 3′, and 4′ as well as base 8 and 2 positions. A dependence of relaxation parameter values on chemical position was clearly observed; however, no sequence-specific variation was readily evident within our experimental error of ∼5–10%, except for 3′ and 5′ termini. It was demonstrated that the random 15%¹³C enrichment effectively suppressed both scalar and dipolar contributions of the neighboring carbons and protons on the relaxation parameters. To analyze dynamics via all observed relaxation parameters, full spectral density mapping (1992, J. W. Peng and G. Wagner,J. Magn. Reson.98, 308) and the “model-free” approach (1982, Lipari and Szabo,J. Am. Chem. Soc.104, 4546) were applied complementarily. A linear correlation between three spectral density values,J(ω_C),J(ω_H− ω_C), andJ(ω_H+ ω_C) was observed in plots containing all measured values, but not for the other spectral density terms includingJ(0). These linear correlations reflect the effect of overall motion and similar internal motions for each CH vector in the decamer. The correlations yielded two correlation times, 3–4 ns and 10–200 ps. One value, 3–4 ns, corresponds to the value of 3.3 ns obtained for the overall isotropic tumbling correlation time determined from analysis of¹³C T1/T2 ratios. The possibility of overall anisotropic tumbling was examined, but statistical analysis showed no advantage over the assumption of simple isotropic tumbling. Lack of correlations entailingJ(0) implies that a relatively slow chemical exchange contributes to yielding of effectiveJ_eff(0) values. Based on spectral density mapping and the T1/T2 ratio analysis, three basic assumptions were initially employed (and subsequently justified) for the model-free calculation: isotropic overall tumbling, one internal motion, and the presence of chemical exchange terms. Except for terminal residues, the order parameterS²and the corresponding fast internal motion correlation time were determined to be about 0.8 ± 0.1 and 20 ± 20 ps, respectively, for the various CH vectors. Only a few differences were observed between or within sugars and bases. The internal motion is very fast (ps–ns time scale) and its amplitude restricted; e.g., assuming a simple wobble-in-a-cone model, the internal motion is restricted to an angular amplitude of ±22.5° for each of the 1′, 3′, 4′, 2, and 8 positions in the purine nucleotides in the entire duplex.     

Effective action in higher derivative (Super)gravities

'The one-loop effective action (EA) with an accuracy up to linear curvature terms ind=4R ²-gravity, conformal gravity, andN=1,d=4 conformal supergravity on the backgroundR ₄×T_4–k,k=1, 2, 3 is calculated. (Here,R _k is thek-dimensional curved space, T_n is then-dimensional torus). The one-loop EA in multidimensionalR ²-gravity and ind=10 conformal supergravity on the backgroundR ₄ ×T _d–4 is also obtained. The mechanism of inducing the Einstein gravity from the EA of considered theories of higher derivative (super)gravity is presented.We are grateful to I. L. Bukhbinder for the numerous discussions of considered questions.     

Molecular motion in liquid benzene by nuclear magnetic resonance

The proton spin-lattice relaxation time, T ₁, has been measured for a series of mixtures of benzene in perdeuterobenzene for the liquid in equilibrium with its vapour over the temperature range from below the normal freezing point up to the critical temperature. The two contributions to T ₁ due to interactions within the molecule (T _{1 intra}) and between molecules (T _{1 inter}) have been separated and are found to be very different in magnitude and in variation with temperature. The variation and magnitude of T _{1 inter} correlates well with other translational motion dependent properties such as self diffusion and viscosity. The correlation of T _{1 intra} with other re-orientation dependent properties such as deuteron T ₁ and Rayleigh scattering is poor.

The observed variation in T _{1 intra} and in particular the broad maximum at higher temperatures is then interpreted as due to a combination of dipolar and spin-rotation effects. This interpretation results in good agreement between the activation energies for re-orientational molecular motion deduced from proton T ₁ and deuteron T ₁. It supports the Hubbard theory for the relation between the dipolar and spin-rotation correlation times τ_d and τ_sr. It gives a rough value, 3·8 kc/s, for the spin-rotation interaction constant for protons in benzene. Reasonable values for τ_d and τ_sr are predicted and for all temperatures τ_sr < τ_d as expected.

There is clearly a considerable difference between the re-orientational and translational motion of the molecules in liquid benzene but the exact nature of the difference cannot be elucidated.     

μ+SR in amorphous spin glasses Pd75Fe5Si20 and Pd75Fe5P20

The zero-field muon spin relaxation functionG _zz (t) has been measured as a function of reduced temperaturet=T/T _g in the amorphous metallic spin glasses Pd₇₅Fe₅Si₂₀ and Pd₇₅Fe₅P₂₀. The results are in qualitative agreement with earlier measurements on dilute alloy spin glasses, including an onset of static order belowT _g and a [t/(t-1)]² dependence of the correlation time τ_c aboveT _g. Both samples have the same τ_c (t) aboveT _g and almost identical static width Δ_S→Δ_o?43 μS^?1) asT»0, but thet-dependence of Δ_s nearT _g differs markedly.     

Quasiparticle lifetime of electron–electron interactions for two-dimensional electron gases with magnetic field

We theoretically study the electron–electron scattering rate τ_ee⁻¹for electrons in a two-dimensional electron gas with a perpendicular magnetic field, within theGWand plasmon-pole approximations, as functions of temperatureT, impurity scattering rate Γ and magnetic fieldB. The τ_ee⁻¹increases with increasingTand increasing Γ, and shows the structure of the Landau levels asBis changed.     

Mobility and structure of human serum albumin powders in water-acetonitrile mixtures by1H NMR relaxation and FTIR spectroscopy

The effect of acetonitrile on protein dynamics was investigated for solid human serum albumin samples at various hydration levels. Temperature dependences of¹H nonselective nuclear magnetic resonanceT ₁ andT ₂ relaxation times at 27 MHz have been measured and data were interpreted in terms of three kinds of internal motions in the protein. Microdynamic parameters of the motions were obtained within a “model-free” approach. It was found that acetonitrile hardly affects the fast motions but noticeably influences the slow motion of side chain groups, shortening the correlation time and increasing the amplitude of the motion. The acetonitrile effect on dynamics is likely based on the appearance of additional free volume as a result of the formation of rigid helical parts in the protein structure. Water, plasticizing the protein structure, promotes the action of organic solvent. A definite part of side chain groups, slowly moving in the same frequency window as the rest of protein side chain groups, performs less constrained “liquidlike” motion. The relative population of these highly movable protons is closely correlated with the increment of the helical structure induced by water and acetonitrile.     

Molecular dynamics of poly(ethylene 2,6-naphthalate)-polycarbonate composite by nuclear magnetic resonance

The aim of the work was to examine molecular dynamics of a series of poly(ethylene 2,6-naphthalate)-polycarbonate blends with changing weight ratio of copolymers by off-resonance nuclear magnetic resonance technique. It was shown that this technique provides information about the correlation times of the internal motions. The spectral density function amplitudes were estimated on the basis of the dispersion of the spin-lattice relaxation time off-resonanceT _lp^off. The measurements were performed for two series of blends which had been injection moulded with and without compatibilizer. The new polymer materials were also characterized using differential scanning calorimetry. Samples obtained after injection moulding and annealing became amorphous, which indicates that a reaction of transesterification process between the two polymers occurred.     

Upconversion-pumped population kinetics for4I13/2 and4I11/2 laser states of Er3+ ion in several host crystals

Population kinetics of the upper⁴I_11/2 and lower⁴I_13/2 laser states of the Er³⁺ ion were studied experimentally and theoretically in (Er)BaY₂F₈, (Er)YLF, (Er)YSGG, (Er)CaF₂ and (Er)YALO. Fluorescence from these states to the⁴I_15/2 ground state was excited through upconversion simultaneously with the⁴I_11/2 →⁴I_13/2 lasing using 1.53 µm radiation from an erbium : glass laser for optical pumping. Lifetimes of both states are altered during lasing by co-operative energy transfer processes: the lifetime of the lower state τ₁ is shortened and that of the upper state τ₂ increased with the resultant ratio τ₂/τ₁>1. After lasing the lifetime ratio returns to the ‘normal’ value τ₂/τ₁ <1; that is, one obtained under weak ultraviolet excitation. Kinetic rate equations for the population density functions for both laser states were set up and solved by approximation in three time domains. It was assumed that only one co-operative energy transfer process operates in the laser crystals and determines the population inversion kinetics. Consistency relationships for comparison of the theoretical results with the experiment were developed. Only (Er)BaY₂F₈ spectral features showed close agreement with theory, resulting in a high score of 94% for the overall correlation in the consistency test, whereas all other crystals scored <50%. As a result of this high correlation, a close match between theoretical and experimental population decay curves was shown for (Er)BaY₂F₈. Most probably, more than one energy transfer process shapes the decay curves and determines the population inversion kinetics for the other laser crystals. (Er)YALO showed little lifetime change for the laser states, apparently due to inefficient co-operative energy transfer processes. As a result it probably lased in a self-terminating short-pulse mode.     

Quantitative Measurement of Transverse and Longitudinal Cross-Correlation betweenC–H Dipolar Interaction andC Chemical Shift Anisotropy: Application to aC-Labeled DNA Duplex

Measurement of both longitudinal and transverse relaxation interference (cross-correlation) between¹³C chemical shift anisotropy and¹³C–¹H dipolar interactions is described. The ratio of the transverse to longitudinal cross-correlation rates readily yields the ratio of spectral densitiesJ(0)/J(ω_C), independent of any structural attributes such as internuclear distance or chemical shift tensor. The spectral density at zero frequencyJ(0) is also independent of chemical exchange effects. With limited internal motions, the ratio also enables an accurate evaluation of the correlation time for overall molecular tumbling. Applicability of this approach to investigating dynamics has been demonstrated by measurements made at three temperatures using a DNA decamer duplex with purines randomly enriched to 15% in¹³C.     

Nuclear spin lattice relaxation and electric field gradient in liquid indium

We have measured the nuclear spin lattice relaxation time in liquid indium from 130°C to 300°C to be: 1/T ₁=(1.98 × 0.0082T) × 10³ sec^-1. The relaxation rate consists of two significant parts: (1/T ₁) _K from the nuclear magnetic hyperfine interaction, and (1/T ₁) _Q from the nuclear quadrupole interaction. We calculate (1/T ₁) _K from the the modified Korringa relation using a correction factor of order unity for electron-electron interactions. The hyperfine term is linear in T and accounts for the second term in 1/T ₁. Within experimental error the remaining rate, (1/T ₁) _Q , is temperature independent, and theoretically varies as the product of the square of the electric field gradient, q, and τ_c, a typical time between field gradient fluctuations. Making use of the x-ray RDF, we construct a simple model for liquid indium and calculate the ionic and electronic contributions, q _I and q _E, to the electric field gradient, to be q _I=1.4 × 10²⁴/cm³ and q _E=8.5 × 10²⁴/cm³. The calculation of q _E assumes covalent bonding between nearest neighbours. Taking q _I and q _E to be of opposite sign, we find that the correlation time τ_c is 1.6 × 10^-13 sec. When we further identify τ _c with the correlation time for diffusion in a three-dimensional random walk, we are able to calculate the r.m.s. jump distance, Δr _D, involved in self-diffusion, Δr _D=0.38 Å. This value is consistent with the x-ray peak width of 0.38 Å which we used earlier to calculate the electric field gradient.