Internal Rotation Rate Research Articles

Effect of Molecular Shape and Flexibility on Gamma-Ray Directional Correlations

The perturbed angular correlation for a gamma-ray cascade from a nucleus rigidly bound to an asymmetric-top molecule in solution has been calculated, using a diffusional model for rotational reorientation. When molecular rotation is rapid [all diffusion constants Di ≫ (1/6τn), where τn is the lifetime of the intermediate nuclear state of the cascade], a treatment analogous to that in nuclear magnetic resonance leads immediately to the desired attenuation factor. On the other hand, when molecular rotation is slow [all Di≪ (ω 0/6), where ω0 is the fundamental quadrupole frequency], the derived form of the angular correlation may not contain a separable attenuation factor. These calculations are illustrated by several plots of the integral anisotropy for symmetric-top molecules of fixed shape and varying size, for several choices of the characteristic ``angle of attachment'' between the molecular symmetry axis and the principal axis of the electric field gradient at the nucleus. Finally, it is shown that the case of a tracer bound through a single flexible link to a spherical molecule is formally identical to the case of a tracer rigidly bound to a symmetric-top molecule; the resultant integral anisotropy is plotted for several fixed rates of internal rotation in spherical molecules of varying size, for several choices of the ``angle of attachment'' between the electric field gradient and the axis about which internal rotation occurs. The conclusions of practical significance are (1) the perturbed angular correlation depends only weakly on the shape of the molecule, while (2) in contrast, the correlation can be markedly affected by the presence of even relatively slow internal rotation at the site of attachment of the tracer to the molecule.

Natural-abundance carbon-13 Fourier-transform nuclear magnetic resonance spectra and spin lattice relaxation times of unfractionated yeast transfer-FNA.

High-resolution Fourier-transform nuclear magnetic resonance at 15.18 MHz was used to observe the proton-decoupled natural-abundance (13)C spectra of aqueous unfractionated tRNA from baker's yeast in the presence of Mg(+2) (8 ions per tRNA molecule), as a function of temperature in the range of 27-82 degrees C. The spectrum of thermally denatured tRNA at 82 degrees C showed numerous sharp resonances, which were assigned to specific types of carbon atoms by comparison with the (13)C spectra of mononucleotides. Only the resonance of carbon 4' of the ribose rings was appreciably shifted (by about 1.5 ppm upfield) with its average position in the mononucleotides. This effect was also seen in the spectrum of poly(A). In the spectrum of folded tRNA (52 degrees C), carbon 4' was further shifted upfield by about 1.5 ppm, and carbons 2' and 3', which yielded a single resonance at 82 degrees C, now showed two partly resolved peaks. The variation of linewidths with temperature (200 mg/ml of tRNA) was gradual in the range 27-82 degrees C, and did not reflect the expected unfolding behavior of tRNA. Moreover, dilution to 80 mg/ml at 27 degrees C had the same effect as an increase in temperature to about 45 degrees C. The line-width changes below 60 degrees were ascribed to tRNA aggregation. In contrast to the behavior of the linewidths, the (13)C spin-lattice relaxation times (T(1)) of individual ribose carbon atoms, measured by means of partially relaxed Fourier-transform spectra were practically independent of temperature up to about 60 degrees C, and increased rapidly at higher temperatures. The T(1) values indicated that the backbone of thermally denatured tRNA is undergoing rapid segmental motion, with an effective correlation time of (2.6 +/- 0.5) x 10(-10) sec. The T(1) values of folded tRNA yielded no evidence of segmental motion. The correlation time for overall rotational reorientation is about (3 +/- 1) x 10(-8) sec in the range 35-54 degrees C. Within experimental error, the T(1) values of methine carbons of the bases were equal to those of the methine carbons on the backbone at all temperatures. Only an upper limit to the rate of internal rotation of the bases could be established.

Multi-site chemical exchange by nmr

The application of a recent multi-site chemical exchange formulation of the Bloch equations is made to an intramolecular and an intermolecular process. The experimental precautions to achieve a good complete line shape lit are discussed in some detail. The rates of internal rotation about the C—N bond in N,N-dimethylcarbamyl fluoride have been measured, and the relative signs of the long range couplings H—C—N—C—F 4J proton to fluorine are obtained from the exchange modified spectra as well as from the comparison of the 4J measured in the fast and slow exchange limits. A 4-site rate matrix is defined with one adjustable parameter for the spectral fit. The measurements are especially difficult because of the small chemical shift varying between 2.2 Hz and 1.4 Hz over the range of interest. The long range coupling methyl to fluorine are 0.8 ± 0.05 Hz trans and 0.3 ± 0.05 Hz cis and do not vary with temperature within 0.05 Hz for a 16.5 % solution in carbon tetrachioride. The intermolecular exchange of halogens in the dimethyltin dihalide mixtures is formulated in detail. A 15 site exchange process breaks down into 5 x 3 exclusive exchange groups and providing line positions and intensities are known with the line width in the absence of exchange, the whole spectrum can be reproduced using only 2-site rate matrix elements. Representative experimental and computed spectra are presented. The relationship of the matrix elements to chemical rate constants is derived but determinations of these constants are not yet complete. INTRODUCTION The study of chemical exchange rates through the modified transverse magnetization is well understood and the theory is highly developed (for example references 1—8). Some simple aspects of chemical exchange theory in nmr spectra for first order cases have been emphasized in a recent paper by Reeves and Shaw9. For intramolecular exchange in the first order limit, the determination of relative signs of coupling constants to non-exchanging nuclei influences the line shapes in a readily recognizable manner'°' Exchanges among many sites (Larmor frequencies) of arbitrary population, saturation effects and site-dependent relaxation times have been accommodated in this recent theory9. A single matrix diagonalization enables sub.tL.W.R. thanks the NRCC for financial support in the form of operating and capital equipment grants.

Conformational analysis in heteroaromatic carbonyl compounds. Part II. Nuclear magnetic resonance investigation of thiophen-2,5-dicarbaldehyde in liquid crystals

The 100 MHz n.m.r. spectrum of the title compound partially oriented in the nematic phase has been obtained and interpreted. The values of the direct dipolar couplings have been discussed in terms of models which take into account the possibilities of internal rotation rates either faster or slower than the molecular reorientation in the liquid crystals. It is concluded that the molecule exists in the conformations O-cis–cis(70–80%) and O-cis–trans(20–30%), whilst the proportion of the O-trans-trans rotamer is negligible.

A line width method for determining chemical exchange rates from NMR spectra

AbstractThe applicability of W½, the line‐width at one‐half height corrected for field inhomogeneity and couplings, for characterization of nuclear magnetic resonance line shapes generated by exchange averaging of chemical shifts has been investigated for the case PA = PB. The Gutowsky‐Holm equation, simplified by the assumption of a large T2º such that T = 0, was used to produce a family of curves relating W½ corrected to the rate of exchange for various ΔvAB values.The rate of internal rotation about the CN amide bond has been studied in neat N,N‐dimethyl‐formamide between 79·5 and 159° by the W½ method and the results, Ea = 24·9 and 24·1 Kcal/mole at 60 and 100 MHz do not agree with those recently reported by Rabinovitz and Pines, Ea = 20·5 Kcal/mole obtained by the total line shape method. For neat N,N‐dimethylacetamide and for solutions of DMA in dimethylsulfoxide‐d6, application of the W½ method yielded Ea, ΔH‡ and ΔS‡ values which are in excellent agreement with those obtained by Neuman and Jonas for DMA‐dε using a total line shape analysis. The thermodynamic parameters for neat N,N‐dimethylcarbamoyl chloride obtained by the total line shape and W½ methods are also in excellent agreement, 16·4 and 16·8 Kcal/mole for Ea and 15·8 and 16·2 Kcal/mole for ΔH‡, respectively.The W½ method was also used for the determination of the activation parameters for rotation about the carbon‐nitrogen bond in the following thioamides: N,N‐dimethylthiobenzamide, (Ea = 19.8 Kcal/mole), N,N‐diethylthiobenzamide, (Ea = 20·4 Kcal/mole), N,N‐dimethylphenylthio‐acetamide (Ea = 21·4 Kcal/mole). The results obtained for these thioamides are compared with the corresponding amides. Specifically N,N‐dimethylbenzamide and N,N‐diethylbenzamide were studied using the W½ method and activation energies for rotation about the carbon‐nitrogen bond of 17·5 and 15·6 Kcal/mole, respectively, were found. The relative magnitudes of these parameters are discussed on the basis of molecular geometry of the thioamides. Attention is drawn to the fact that for structurally related amides and thioamides, the barrier heights for internal rotation are not greatly different.

19F double resonance in the presence of chemical exchange

The 19F N.M.R. spectra of CF2BrCClBr2 in CS2 from 20°c to -80°c are reported. Computer-fitting of the experimental spectra using the density matrix formalism of Alexander yields the chemical exchange correlation times and produces a computed internal rotation barrier for trans →gauche of 39·7 ± 0·5 kJ mol-1 (9·5±0·1 kcal/mole). Results of double resonance studies on the -80°c spectrum upon irradiation of the various peaks with a strong r.f. field are presented. The density matrix equations in the presence of chemical exchange and several relaxation mechanisms were solved to obtain theoretical changes in peak intensities on irradiation. The indirect spin saturation data and their relation to the rate of internal rotation and the relaxation mechanism are discussed. Random field relaxation is shown to be the important relaxation mechanism in the system. The strong irradiation of one component of a strongly coupled spin multiplet with intramolecular exchange causes indirect saturation of the transitions conne...

Molecular Motions of Deuterated Isobutylenes in the Liquid State

The temperature dependences of the deuteron spin–lattice relaxation times in 2-methyl-1, 1-propene-d2, and 2-methyl-d3-3,3,3-propene-d3 in the liquid state have been measured by the adiabatic fast passage method. Since the deuteron coupling constants were estimated from the known values for analogous systems, the experimental T1 data were analyzed in terms of the over-all reorientation of the molecules and the internal rotation of the methyl-d3 groups. The rotational diffusion constant for over-all reorientation was calculated to be D = 0.28 × 1012sec−1 at 0°C, and the upper bound for the internal rotation rate of the methyl-d3 groups was found to be 0.2 × 1012 sec−1 at 0° by assuming rotational diffusion and 0.6 × 1012 sec−1 at 0°C by considering random reorientation among three equivalent positions 120° apart.

Anisotropic Molecular Rotation in Liquid N,N-Dimethylformamide by Nuclear Magnetic Resonance

The anisotropy in the molecular rotation of N,N-dimethylformamide (DMF) in the liquid is investigated by considering the NMR relaxation times of the 14N, 17O, and formyl deuteron nuclei in DMF, DMF17O, and DMF-d1, respectively. Assuming that the molecular rotation is diffusional and that one principal diffusion axis (the z axis) is perpendicular to the molecular plane, a range of possible orientations for the diffusion axes in the plane and a corresponding range of values for each of the three diffusion constants are calculated. The range of possible orientations of the x diffusion axis, which varies little with temperature, extends over about 26°, from the direction of the x principal inertial axis toward and past the direction of the molecular dipole moment. At 280°K the diffusion constants are Dx = (2.0 ± 0.4) × 1011sec−1, Dy = (6 ± 3) × 109sec−1, and Dz = (2.9 ± 0.7) × 1010sec−1. At 390°K, Dx = (4.0 ± 0.7) × 1011sec−1, Dy = (10 ± 8) × 109sec−1 and Dz = (2.1 ± 0.7) × 1011sec−1. The ratio of the rotation rate about the ith axis in the free gas to Di is a direct measure of the extent to which rotation about the ith axis is hindered in the liquid by intermolecular interactions. Defining this ratio as χi (where larger values of χi indicate a more hindered rotation), it is found that at low temperatures χy, χz ≫ χx and at high temperatures χy ≫ χz, χx. Once the rotation of the molecular framework is known, the relaxation times of the methyl deuterons in DMF-d7 can be used to calculate the internal rotation rates of the deuterated methyl groups. These rotation rates are shown to be comparable to the rate of the molecular rotation.

Comparison of kinetic results obtained by NMR line shape and equilibration methods

Rates of internal rotation around carbonyl-to-nitrogen bonds are determined for the rotamers IA and IB of N-benzyl-N,2,4,6-tetramethylbenzamide by equilibration of IA and for N,N,2,4,6-pentamethylbenzamide (II) by 1H-NMR line shapes. The activation parameters (Table V) obtained by the two methods agree well within error limits. This represents the first experimental confirmation of the soundness of kinetic measurements by line shapes. The range of rate constants accessible by the two techniques amounts to almost 10 7 sec −1. Further molecular systems are suggested as suitable for such a comparison; the nitrosamines VIIA and VIIB, for example, will allow both methods to be applied to the isomers of the same compound. Steric contributions to the free enthalpies of activation are evaluated for the internal rotation in some 2,4,6-trisubstituted benzamides.

THE DESCRIPTION AND USE OF A SPIN-ECHO SPECTROMETER TO STUDY CHEMICAL EXCHANGE

A spin-echo spectrometer, suitable for studies of chemical exchange, is described. The performance of the apparatus is described and illustrated. From a Carr–Purcell sequence of pulses T2 measurements have been made using two alternative schemes for the correction of cumulative error in the width of π pulses. Agreement is satisfactory and the standard errors in each method are ± 5% of the average T2. The Meiboom and Gill method of phase-shifting the r.f. in the first pulse has the advantage of more flexibility in the choice of pulse intervals.A theory developed by Bloom, Reeves, and Wells for the dependence of T2 measured in a Carr–Purcell experiment on pulse intervals in the presence of a suitable exchange process has been tested experimentally for two molecules. The rate constants for the hindered internal rotation about the N=N bond in N,N -dimethylnitrosamine agree for the following sets of data: (a) a previous high-resolution study by Phillips, (b) a repeated high-resolution study made in this work, (c) spin-echo studies using the complete closed expression for a two site exchange process, and (d) the approximate expression derived for the limit of fast pulse repetition rates.A similar study by the spin-echo method of the rates of internal rotation about the C=N bond in N,N-dimethyltrifluoroacetamide does not agree with a previous high-resolution study. Since the chemical shift between the inequivalent methyl groups is so small, it is suggested that the rates of rotation in this molecule are much better evaluated by the spin-echo method.The spin-echo method can more easily take account of variations with temperature of the natural relaxation time and the chemical shift. The non-selective nature of an experiment with such a large H1 field remains a disadvantage at this time. The selective deuteration of sites unaffected by exchange is in general difficult enough to limit the scope of the spin-echo method when protons are observed.

Direct measurement of the rate of internal rotation in a formamide

0 0II / RI I N + / RI (1) R-C-N .-. (2) R-C= R2 R2 Because of the contribution of (2), the amide is a better electron donor and extractant than it might be otherwise. This formulation also implies that there is double bond character in the carbonyl to nitrogen bond. This double bond character was recognized a number of years ago when it was shown by proton magnetic resonance (PMR) spectroscopy that rotation is sufficiently slow around the carbonyl to nitrogen bond in certain disubstltuted amides to permit the observation of cls-trans isomers (~) . The kinetic quantities for this rotation were calculated from analysis of PMR signal shapes (a) . Since that time there have been a number of additional studies of this phenomenon (s) .

Nuclear magnetic resonance and rotational isomerism in substituted ethanes

This paper deals with the classification of high-resolution nuclear magnetic resonance spectra of substituted ethanes and similar molecules. In particular, the forms of the spectra for individual rotational isomers of long lifetime are compared with those appropriate to rapid internal conversion. The use of nuclear resonance data to deduce information about the rate of internal rotation is discussed in detail.