Rotational Correlation Time τR Research Articles

Optimizing the Relaxivity of MRI Probes at High Magnetic Field Strengths With Binuclear GdIII Complexes.

The key criteria to optimize the relaxivity of a Gd(III) contrast agent at high fields (defined as the region ≥ 1.5 T) can be summarized as follows: (i) the occurrence of a rotational correlation time τR in the range of ca. 0.2–0.5 ns; (ii) the rate of water exchange is not critical, but a τM < 100 ns is preferred; (iii) a relevant contribution from water molecules in the second sphere of hydration. In addition, the use of macrocycle-based systems ensures the formation of thermodynamically and kinetically stable Gd(III) complexes. Binuclear Gd(III) complexes could potentially meet these requirements. Their efficiency depends primarily on the degree of flexibility of the linker connecting the two monomeric units, the absence of local motions and the presence of contribution from the second sphere water molecules. With the aim to maximize relaxivity (per Gd) over a wide range of magnetic field strengths, two binuclear Gd(III) chelates derived from the well-known macrocyclic systems DOTA-monopropionamide and HPDO3A (Gd2L1 and Gd2L2, respectively) were synthesized through a multistep synthesis. Chemical Exchange Saturation Transfer (CEST) experiments carried out on Eu2L2 at different pH showed the occurrence of a CEST effect at acidic pH that disappears at neutral pH, associated with the deprotonation of the hydroxyl groups. Then, a complete 1H and 17O NMR relaxometric study was carried out in order to evaluate the parameters that govern the relaxivity associated with these complexes. The relaxivities of Gd2L1 and Gd2L2 (20 MHz, 298 K) are 8.7 and 9.5 mM−1 s−1, respectively, +77% and +106% higher than the relaxivity values of the corresponding mononuclear GdDOTAMAP-En and GdHPDO3A complexes. A significant contribution of second sphere water molecules was accounted for the strong relaxivity enhancement of Gd2L2. MR phantom images of the dinuclear complexes compared to GdHPDO3A, recorded at 7 T, confirmed the superiority of Gd2L2. Finally, ab initio (DFT) calculations were performed to obtain information about the solution structure of the dinuclear complexes.

EPR moments for site-directed spin-labelling

The absolute-value first moment and second moment of nitroxide EPR absorption spectra, which can be used for systematic analysis in site-directed spin-labelling, are analysed in terms of the rotational mobility and angular motional amplitude of the spin probe. Spectral simulations with the stochastic Liouville equation are used to give calibrations of second and absolute-value first moments as a function of isotropic rotational correlation time τR and axial order parameter Szz, over the entire range of sensitivity to these parameters. Both moments are additive for multicomponent spectra, e.g., for multiple conformations. The absolute-value first moment has the advantage over the central line width in that it does not overemphasize fast motional components, and over the second moment in that it is less sensitive to noise in the outer wings of the spectrum and to baseline cutoff.

Characterization of the Microenvironments of Alkylamidoamine-N-oxide Surfactant Aggregates by the EPR Spin Labeling Method

Spin labeling EPR methods were applied to characterize the local microviscosity and micropolarity of micellar aggregates formed by 3-(alkanoylamino)ethyldimethylamine-N-oxides (alkyl = nonyl, undecyl and tridecyl) in an aqueous environment in the temperature range 297–337 K. Four doxylstearic derivatives: 5-doxylstearate methyl ester (5-DSE), 16-doxylstearate methyl ester (16-DSE), 5-doxylstearic acid (5-DSA) and 16-doxylstearic acid (16-DSA) were used as spin probes to monitor mainly the rotational correlation time τ R and the isotropic hyperfine splitting constant A N. In the case of anisotropic spectra, the order parameter S was also determined. The selected probes were found to be sensitive to the microenvironments whereby it was possible to characterize in detail local changes in composition and micelle formation.

Synthesis and Characterization of a New Bioactivated Paramagnetic Gadolinium(III) Complex [Gd(DOTA-FPG)(H2O)] for Tracing Gene Expression

A smart contrast agent for magnetic resonance imaging (MRI) can be used to exploit an enzymatic activity specific to the tissue or disease state signified by converting an MRI-inactivated agent to an activated MRI agent. In this study, a beta-galactopyranose-containing gadolinium(III) complex [Gd(DOTA-FPG)(H 2O)] was designed, synthesized, and characterized as being potentially suitable for a bioactivated MRI contrast agent. The (17)O NMR experiments were conducted to estimate the water exchange rate k e x 298 and rotational correlation time tau R 298 . The k ex 298 value of [Gd(DOTA-FPG)(H 2O)] is similar to that of [Gd(DO3A-bz-NO 2)(H 2O)]. The rotational correlation time value of [Gd(DOTA-FPG)(H 2O)] is dramatically longer than that of [Gd(DOTA)(H 2O)] (-) Relaxometric studies show that the percentage change in the T 1 value of [Gd(DOTA-FPG)(H 2O)] decreases dramatically in the presence of beta-galactosidase and human serum albumin. The T(1) change percentage of [Gd(DOTA-FPG)(H 2O)] (60%) is significantly higher than those of Egad and gadolinium(III)-1-(4-(2-(1-(4,7,10-triscarboxymethyl-(1,4,7,10-tetraazacyclododecyl)))-ethylcarbamoyloxymethyl)-2-nitrophenyl)-beta- d-glucopyronuronate. The signal intensity of the MR image for [Gd(DOTA-FPG)(H 2O)] in the presence of human serum albumin and beta-galactosidase (2670 +/- 210) is significantly higher than that of [Gd(DOTA-FPG)(H 2O)] in the sodium phosphate buffer solution (1490 +/- 160). In addition, the MR images show a higher-intensity enhancement in CT26/beta-gal tumor with beta-galactosidase gene expression but not for the CT26 tumor without beta-galactosidase gene expression. We conclude that [Gd(DOTA-FPG)(H 2O)] is a suitable candidate for a bioactivated MRI contrast agent in tracing gene expression.

Thermodynamic Stability and Physicochemical Characterization of Ligand (4S)-4-Benzyl-3,6,10-tris(carboxymethyl)-3,6,10-triazadodecanedioic Acid (H5[(S)-4-Bz-ttda]) and Its Complexes Formed with Lanthanides, Calcium(II), Zinc(II), and Copper(II) Ions

A derivative of H5ttda (=3,6,10-tris(carboxymethyl)-3,6,10-triazadodecanedioic acid=N-{2-[bis(carboxymethyl)amino]ethyl}-N-{3-[bis(carboxymethyl)amino]propyl}glycine), H5[(S)-4-Bz-ttda] (=(4S)-4-benzyl-3,6,10-tris(carboxymethyl)-3,6,10-triazadodecanedioic acid=N-{(2S)-2-[bis(carboxymethyl)amino]-3-phenylpropyl}-N-{3-[bis(carboxymethyl)amino]propyl}glycine; 1) carrying a benzyl group was synthesized and characterized. The stability constants of the complexes formed with Ca2+, Zn2+, Cu2+, and Gd3+ were determined by potentiometric methods at 25.0±0.1° and 0.1M ionic strength in Me4NNO3. The observed water proton relaxivity value of [Gd{(S)-4-Bz-ttda}]2− was constant with respect to pH changes over the range pH 4.5–12.0. From the 17O-NMR chemical shift of H2O induced by [Dy{(S)-4-Bz-ttda}]2− at pH 6.80, the presence of 0.9 inner-sphere water molecules was deduced. The water proton spin-lattice relaxation rate for [Gd{(S)-4-Bz-ttda}]2− at 37.0±0.1° and 20 MHz was 4.90±0.05 mM−1 s−1. The EPR transverse electronic relaxation rate and 17O-NMR transverse-relaxation time for the exchange lifetime of the coordinated H2O molecule (τM), and 2H-NMR longitudinal-relaxation rate of the deuterated diamagnetic lanthanum complex for the rotational correlation time (τR) were thoroughly investigated, and the results were compared with those previously reported for the other lanthanide(III) complexes. The exchange lifetime (τM) for [Gd{(S)-4-Bz-ttda}]2− (2.3±1.3 ns) was significantly shorter than that of the [Gd(dtpa)(H2O)]2− complex (dtpa=diethylenetriaminepentaacetic acid). The rotational correlation time τR for [Gd{(S)-4-Bz-ttda}]2− (70±6 ps) was slightly longer than that of the [Gd(dtpa)(H2O)]2− complex. The marked increase of relaxivity of [Gd{(S)-4-Bz-ttda}]2− mainly resulted from its longer rotational time rather than from its fast water-exchange rate. The noncovalent interaction between human serum albumin (HSA) and the [Gd{(S)-4-Bz-ttda}]2− complex containing the hydrophobic substituent was investigated by measuring the solvent proton relaxation rate of the aqueous solutions. The association constant (KA) was less than 100 M−1, indicating a weaker interaction of [Gd{(S)-4-Bz-ttda}]2− with HSA.

New multimeric magnetic resonance imaging agents.

The authors investigated the effect of multimerization on the relaxivity of macrocyclic gadolinium (Gd) chelates. The objective was to develop more sensitive magnetic resonance imaging (MRI) contrast agents to study biochemical processes. Covalently linked nonionic, macrocyclic, multimeric lanthanide chelates that belong to the classes of dimers, trimers, tetramers, hexamer, and octamer, in the molecular weight range approximately 1 to 5 KDa, were synthesized. The chemical linkage was based on either the amide bond or the 2-hydroxypropylidene bond. Relaxivity values, 20r1, on Gd3+ chelates and hydration numbers, Q, on Tb3+ chelates were determined. Relaxivity values increased with molecular weight and Q values were not affected, the increase in r1 in attributable to the expected increase in the overall rotational correlation time, tau r with an increase in molecular weight. The rigidity of the linkers, which is expected to affect the intrachelate rotational correlation time tau r* that makes a contribution to the overall correlation time, tau r, exerted a noticeable effect. The hydroxyl-based chelates generally had lower r1 values than the amide-based chelates. This is rationalized as arising from the longer and thereby rate-limiting effect of the tau m value for the hydroxyl chelates compared with that reported of the amide-based chelates. This rate limiting effect of tau m becomes a dominant factor controlling attainable enhanced relaxivity when multimers based on traditional chelate designs are used for MRI applications. Approaches aimed at enhancing relaxivity by modulating the water relaxation time, tau m, will be important for the future development of functional MRI contrast agents for the imaging of biochemical processes.

Combined Fluorescence and NMR Studies of Reversed HPLC Stationary Phases with Different Ligand Chain Lengths

Alkyl chain bonded “reversed” HPLC phases consisting of 6 to 30 carbon atoms are investigated by fluorescence spectroscopy, steady-state and time-resolved fluorescence anisotropy, and solid-state NMR spectroscopy. The structure and dynamics of the interphase formed by alkyl chains and liquid phase penetrating each other are studied as a function of alkyl chain length. Increasing alkyl chain lengths lead to enhanced partitioning of the fluorescent probe diphenylhexatriene (DPH) into the interphase, as monitored by fluorescence decay curves. The concomitant spectral red shift of DPH fluorescence excitation maxima is evidence of increased interphase polarizability. Time-resolved fluorescence anisotropy measurements reveal that the motion of the probe molecule in the interphase is “wobble in cone”-like. Cone angles θ and rotational correlation times τR change from θ = 63° and τR = 0.75 ns in C6 phases to θ = 42° and τR = 1.50 ns in C30 phases, thus indicating decreasing probe mobility with increasing ligand length. This interpretation is supported by 13C CP/MAS NMR spectra, which show reduced contributions of alkyl chain gauche conformations, i.e., enhanced interphase order, in phases with long alkyl chains and high surface coverage. A concomitant increase in the line-widths of 1H MAS NMR peaks indicates reduced mobility of the longer chains. The spectroscopic observations are consistent with the results of HPLC separations, where enhanced shape selectivity is found with increasing ligand length, rod-shaped molecules like DPH showing the greatest increase in retention time.

Molecular dynamics in polystyrene from electron spin resonance (ESR) measurements: comparison between spinprobes and ‐labels attached to the chain ends

AbstractThe commercially available 15N‐TemponeN‐Tempone: 4‐oxo‐2,2,6,6‐tetramethylpiperidine‐15N‐oxyl; Tempol: 4‐hydroxy‐2,2,6,6‐tetramethylpiperidine ‐15N‐oxyl. nitroxide radical has been used for the endfunctionalization of anionically polymerized polystyrene. The temperature dependence of molecular motions of the nitroxide radicals in this chain end labeled polystyrene (PS) and a PS/Tempol mixture has been studied using cw‐ESR. Furthermore, these two samples were compared with a mixture of PS with a biradical which has a large molecular volume and is used in its unoxidized form as a polymer additive in commercial products. The temperature dependent spectra were evaluated to give T50G. This allows the volume for reorientation of the radicals and that of a polymer unit to be compared. The temperature dependent spectra were simulated in order to yield the rotational correlation time τR. In contrast to the Tempol probe radical which is highly mobile even at temperatures well below the glass transition temperature (Tg) the spin‐label strongly couples to the α‐process of polystyrene. The biradical exhibits an intermediate mobility and seems to be weakly coupled to the glass transition dynamics. Line shape analysis shows that the motional behavior of the PS/Tempol mixture can adequately be described by the model of isotropic rotational diffusion, whereas for the chain end label significant deviations from this model are observed indicating anisotropic motion due to restrictions imposed by the polymer chain.

Rotational Dynamics of Metallo-Endofullerenes in Solution

From an analysis of the temperature dependent line width of hyperfine components of solution EPR spectra of metallo-endofullerenes (M@C82, M = Sc, Y, La), the rotational correlation time τr of these nearly spherical molecules in the solvents CS2, toluene, and cis-decalin could be determined. It was found that in the low-viscosity regime near room temperature τr is close to its free rotator value, indicating nearly complete decoupling of solute dynamics from the solvent. Only at lower temperatures close to the freezing point of the solvents studied is a Stokes/Einstein relation τr ≈ η/T recovered, although with a reduction factor on the order of 100. In addition, from the spin relaxation times an estimate for the anisotropic terms in the spin Hamiltonian could be obtained.

Solvation of copper(I) perchlorate in mixed solvent systems containing acetonitrile. A63Cu,65Cu and31P nuclear magnetic resonance study

Copper(I) solvation in mixed solvent systems containing acetonitrile (AN) and co-solvents water (W), methanol (ME), dimethylformamide (DMF), trimethyl phosphate (TMPA), trimethyl phosphite (TMP) or pyridine (PY) have been studied using 63Cu, 65Cu and 31P NMR. Evidence for preferential solvation by AN is given for the first four systems whereas the latter two are characterized by strong preferential solvation of the copper(I) ion by the co-solvent. From the linewidths of the 63Cu and 65Cu signals the rotational correlation times τR of the solvates Cu(AN)+4 and Cu(PY)+4 have been determined.

Mobility of anionic spin probes in water‐containing nylon 6 film

AbstractThe rotational mobility of anionic spin probes in water‐containing nylon 6 film was investigated by means of electron spin resonance (ESR) measurements for comparison with the results for nonionic spin probes reported previously. The extrema separation of the ESR spectra, 2Az′ increased with time owing to the evaporation of water. In the higher temperature region, 2Az′ increased steeply with time at first, and then more slowly, whereas for the nonionic spin probes, 2Az′ increased gradually and monotonically with time. This fact suggests that the anionic probe molecules are more strongly affected by water than the nonionic ones, i.e., the former probes are located in hydrophilic regions and the latter in hydrophobic regions. T50G, which can be empirically correlated with the glass transition temperature of the polymer Tg decreased with increasing water content. The decreasing tendency for the anionic spin probes was stronger than that for the nonionic ones. This fact also indicates that the local environment around the probe molecules varies from probe to probe. The rotational correlation time τR decreased markedly with an increase in water content. The Arrhenius plots of τR showed two crossover points. The crossover points in the higher temperature region Tn decreased greatly with increasing water content. The difference in Tn between dried and water‐containing films was larger than that for T50G. The activation energy for rotation, E, also decreased with increasing water content. It is suggested that water concentrates around the anionic spin probes and makes their rotation much easier.

ESR studies of 0−2 adsorbed on Ti supported surfaces: Analysis of motional dynamics

Temperature-dependent ESR spectra of O−2 adsorbed on Ti ions supported on porous Vycor glass were observed over the range 4.2 to 400 °K. These spectra were obtained under normal high vacuum conditions as well as under UHV conditions (P⩽10−9 Torr) and are very well resolved. It was observed that the line position of the g̃ tensor component that is perpendicular to the internuclear axis of O−2 remained constant with temperature, whereas the other two components of the g̃ tensor shift in position with temperature, and are accompanied by drastic line shape changes. This observation indicates that the molecular motion of O−2 on the surface is highly anisotropic, consisting essentially of planar rotation about the axis perpendicular to the internuclear axis of O−2 and parallel to the normal to the surface. Furthermore, the observation of nonequivalent 17O hfs of O−2 suggests that the internuclear axis of O−2 might be tilted slightly from the surface and/or one oxygen is closer to the Ti4+. The ESR line shapes were simulated for the different possible models: Brownian diffusion, jump diffusion (from weak jump to strong jump), approximate free diffusion, and discrete jump. It was found that the theoretical spectra calculated using the model of weak jump rotational diffusion best fit the observed spectra in the temperature range below 57.4 °K. However, in the temperature range above 57.4 °K, although the Brownian diffusion model seems the best among the models used, none of the present models used could successfully reproduce the observed line shapes. The rotational correlation time τR∥ was found to range between 10−5 sec (below 14.5 °K) and 10−9 sec (263 °K). The values of τR∥ depend strongly on the model used in the lower temperature range, but were essentially independent of model above 100 °K. The activation energy for rotational diffusion was estimated to be 0.5 kcal/mole above 100 °K. The line shape below 15 °K is independent of temperature, although the O−2 spectrum appears to exhibit residual motional effects. This observation suggests that coherent quantum mechanical motion is predominant below 15 °K. This matter is discussed in some detail, and the appropriate theory to investigate quantum effects on the motional dynamics is outlined including possible isotope effects on the motion. Spectral observation of possible interaction between C2H4 and O−2 on the surface is presented. Also discussed are the techniques for preparing samples with strong well-resolved signals and for removing the other types of O−2 signals, which do not show significant temperature-dependent spectral changes. The show.

31P nmr spin‐lattice relaxation studies of deoxyoligonucleotides

AbstractTemperature‐dependent conformational transitions of deoxyoligonucleotides have been monitored by measuring 31P chemical shifts, spin‐lattice relaxation times (T1), and 31P‐{H} nuclear Overhauser enhancements (NOEs). The measured NOE ranged from 30 to 80%, compared to the theoretical maximum of 124% for a dipolar relaxation mediated by rapid isotropic rotation. The observed 3′‐5′ phosphate diester 31P T1 showed a similar temperature dependence over the range 2–75°C for both double‐ and single‐stranded oligonucleotides, and for dinucleotides. The results show that dipole–dipole interactions dominate the internucleotide phosphate relaxation rate in oligonucleotides. The same is true of terminal phosphate groups at low temperature; but at higher temperature another process, possibly due to contamination by paramagnetic ions, becomes dominant. The rotational correlation time τR calculated from the dipole–dipole relaxation rate of the internucleotide phosphate in d(pA)2 at 16°C is τR = 5.0 × 10−10 sec, implying a Stokes radius for isotropic rotation of 7.6 Å. The T1 and NOE values for the double‐helical octanucleotide d(pA)3pGpC(pT)3 are consistent with dominance of dipole–dipole relaxation and isotropic rotation of a sphere of radius 14 Å, a reasonable dimension for the double helix. Activation energies for the rotation of dinucleotides range from 4 to 6 kcal/mol, close to the value of 4 kcal/mol expected for isotropic rotation. In order to test the possible effect of internal motion of correlation time τG on the results, we considered a model in which the nucleotide chain rotates about the P‐O bonds. Comparison of the calculation with our experimental results shows that internal motion with τG ≅ 10−9 sec, as found from other studies to be present for large nucleic acids, would not influence out T1 and NOE values enough to be distinguished from isotropic rotation. However, we can conclude that τG cannot be as fast as 10−10 sec, even for dinucleotides.

An ESR and ENDOR study of spin relaxation of semiquinones in liquid solution

A quantitative test of the ENDOR theory for free radicals in solution has been developed experimentally using the semiquinone (SQ) radical anions of parabenzo- (PBSQ), duro- (DSQ), and 2,5-dimethyl-para-benzo- (2,5-DPMBSQ) dissolved in ethyl alcohol (EtOH) and dimethoxyethane (DME) solvents. It is shown that, in general, an ENDOR signal arising from a molecule containing four or less equivalent nuclei, such as PBSQ, can be analyzed rigorously whereas a molecule containing more than four equivalent nuclei, such as DSQ, which, in principle, could be analyzed rigorously, practically is best analyzed using approximate forms of the ENDOR theory. It is shown that 2,5-DMPBSQ may be analyzed using a combination of both the rigorous and approximate forms of the ENDOR theory. The analysis involves calculation of the ENDOR relaxation parameters, T2n, Ωn, and Ωe,n, from the experimental ENDOR percent enhancement and linewidth studies. A comparison was made by performing the ESR linewidth and saturation studies to obtain values of We, the electron spin–lattice relaxation probability, and Wn, the nuclear spin-relaxation probability and then using this information to predict the observed ENDOR relaxation parameters in terms of the theory. The over-all behavior of the experimental results was found to be fully consistent with the general trends predicted by the theory and expected from the quantitative measurements obtained from the ESR studies. This work describes in detail the instrumentation and experimental methods necessary to measure relaxation parameters of organic free radicals in solution. A comprehensive section describing the effects of modulation amplitude, microwave power, coherence broadening or splitting, and pulse rate is given along with methods for analyzing ENDOR line shapes in their presence. The results and analyses of all ESR and ENDOR experiments are described in detail. Analysis of the rotational correlation time τR, obtained from the ESR studies, shows the radical anions in DME solution are most likely solvated and affected by the counterion and/or supporting electrolyte while PBSQ in EtOH is most likely dissociated. A comparison of the experimental and theoretical magnitudes of We leads to the possibility that for small molecules in liquids a Brownian model of reorientation by infinitesimal jumps need not be satisfactory and that jumps of large angle would be needed to better fit the experimental data. The effect of Heisenberg exchange on ENDOR signals is analyzed and discussed in detail, leading to the conclusion that the intermolecular electron–electron dipolar interaction as well as Heisenberg exchange make contributions to the concentration dependent portion of the linewidth. However, the latter contributes much more to the ESR linewidths as compared to the ENDOR widths for PBSQ in EtOH. The above analysis is modified to include charge effects. Finally it is shown that for methyl group ENDOR cross relaxation from modulation of the isotropic hyperfine splitting via methyl group rotation is not the dominant nuclear relaxation mechanism and all methyl group ENDOR analyses are consistent with a Wn derived from the pseudosecular terms of the anisotropic electron–nuclear dipolar interaction.

ESR studies of anisotropic rotational reorientation and slow tumbling in liquid and frozen media. II. Saturation and nonsecular effects

Careful studies are described of the ESR line shapes and saturation behavior for the peroxylamine disulfonate (PADS) radical dissolved in a range of glycerol-water mixtures. This permitted studies where the rotational correlation time τR ranged from 3 × 10−12 sec to &amp;lt; 10−6 sec. The unsaturated line shapes for 10−10 &amp;lt; τR &amp;lt; 10−9 sec are, as in Paper I, readily interpreted in terms of anisotropic rotational diffusion, but for τR &amp;lt; 10−10 sec anomalous behavior of the linewidths, which could be attributed to nonsecular spectral densities, occurs. Supporting experiments at 35 GHz, and also on 17O-labeled PADS, are in excellent agreement with values of τR and N = 4.7 (the ratio of the two components of the axially symmetric diffusion tensor), and they supply further information on the anomalous behavior of the nonsecular spectral densities. A phenomenological treatment based on the memory function approach was found to qualitatively reproduce some observed features. The saturation studies were performed over both the motional narrowing and slow-tumbling regions. The motional narrowing results could be analyzed in a straightforward manner to yield values of We, the electron-spin flip rate, which are found to exhibit a weak dependence on τR, roughly as τR−(1/4) for the glycerol solvents. The stochastic Liouville method is applied to an analysis of slow-tumbling saturated spectra and generally reasonable agreement with experiment is achieved for the simplifying assumptions utilized. The rotationally invariant We obtained from the slow-tumbling analyses are found to agree with the values of We extrapolated from the motional-narrowing region. Other aspects of the slow-tumbling saturation experiments and analysis are discussed.

An ESR Study of Anisotropic Rotational Reorientation and Slow Tumbling in Liquid and Frozen Media

A careful study is described of the ESR lineshapes for the peroxylamine disulfonate (PADS) radical dissolved in 85% glycerol solution and in frozen water and D2O. In the frozen media, spectra characteristic of rotational correlation times τR ranging from 1.0 × 10−11sec to &amp;gt; 10−6sec are obtained, while the range in glycerol is from 1 × 10−10sec to &amp;gt;10−6sec. The very rapid rotational motion in frozen water is taken to imply that PADS is rotating in a clathrate cage. The activation energies in ice and 85% glycerol are 14.7 ± 0.1 and 11.3 ± 0.1 kcal/mole, respectively, (from motional-narrowing data). The value for ice is very similar to that obtained for other rate processes in ice. The lineshapes for τR ≲ 10−9sec are analyzed in terms of the familiar spin-relaxation theories valid in the motionally narrowed region. These results are well fitted by the model of axially symmetric rotational diffusion with the symmetry axis in the plane of the N, O, and S atoms and parallel to a line passing through the two S atoms. Diffusion about this axis is found to be 2.9 ± 1 and 4.7 ± 1 times faster for frozen water and glycerol solvent, respectively than about the other axes over a wide range of values of average τR̄. It was possible to obtain these results, because accurate measurements of the g and A tensors for PADS in these media could be made from the well-resolved rigid spectra at X band and 35 GHz; the intrinsic widths in D2O are only about 1.5 G. The spectra in the slow-motional region τ R¯ &amp;gt;10−9sec were simulated utilizing the slow tumbling formulation of Freed, Bruno, and Polnaszek appropriately generalized to include completely asymmetric g and A tensors. The simulated spectra are found, in general, to be in quite good agreement with experimental observations. The agreement is clearly improved by introducing axially symmetric rotational diffusion, as found for the motional-narrowing region, into the simulations. Spectra are simulated for Brownian rotational diffusion as well as for simplified models of free diffusion, which includes inertial effects, and for diffusion by jumps of substantial angle. Improved agreement with experiment is found with some of these latter models. What appears to be a surprisingly small nonsecular linewidth contribution in the motional-narrowing region is briefly discussed in terms of these models.

ESR Studies of Coordination to the Sixth Position of Vanadyl Acetylacetonate

The electron spin resonance spectra of vanadyl acetylacetonate (VOacac2) and a number of its adducts have been examined in benzene solution at ambient temperatures. It is found that the magnitude of the vanadium nuclear hyperfine splitting constant decreases from 108.19 to 105.3 G as amine adducts are formed, while the g value increases from 1.9695 to 1.9699. The anisotropies of the axially symmetric g and hyperfine tensors, Δg and b, and the rotational correlation time τR have been calculated from the linewidths of VOacac2, VOacac2·pyridine, and VOacac2·piperidine in benzene solution. The correlation time increases from 2.4×10−11 to 3.0×10−11 sec, |b| increases from 2.1×109 to 2.3×109 rad/sec, and |Δg| decreases from 0.034 to 0.029 on coordination of pyridine. Although the g values calculated from the electronic spectra using the theories of Ballhausen and Gray or Kivelson and Lee decrease slightly on adduct formation rather than increase as observed experimentally, the calculated anisotropies Δg follow the experimental trend. Analysis of the line broadening observed for mixtures of VOacac2 and an adduct allows the estimation of the rate of exchange of amine between the adduct and bulk solvent. Line shapes for the −72 line have been calculated for the intermediate exchange-rate region and compared with experimental spectra. For the reaction VOacac2+pyridine⇌ lim krkfVOacac2·pyridine,kr=1.3×107 sec−1, kf=1.0×109M−1·sec−1. For the similar reaction with piperdine, kr≤2×106 sec−1, kf≤2.8×109M−1·sec−1; and for 2-picoline, kr=7×107 sec−1, kf=5×107M−1 sec−1.

Method for Separating the Inter- and Intramolecular Contributions to T1 in Liquids When the Pressure Varies. Rotational Correlation Time vs Pressure

It is shown that to separate the intramolecular and intermolecular contributions to the spin—lattice relaxation time T1 in liquids measured as a function of pressure and/or temperature, it is only necessary to perform this separation at a single pressure and temperature if the self-diffusion coefficient D and density are also known as a function of pressure and/or temperature. T1 may be separated by solution measurements in which the liquid under study is dissolved in a solvent identical to it but magnetically inert. The intramolecular part of T1 and, hence, the intermolecular part also are obtained by extrapolation to infinite dilution. Such solution measurements would be cumbersome to perform as a function of pressure and/or temperature. It is argued that the results of such a separation may be extended to other pressures and temperatures if appropriate self-diffusion and density data are available. To examine the usefulness of this idea, the pressure dependence of the rotational correlation time τR for benzene is derived from data already in the literature. Cyclohexane (assumed to be a rigid molecule) is similarly treated except that the separation data were not available and had to be determined. The behavior of τR and D as a function of pressure is compared to the behavior of the viscosity and also to the predictions based on the theories of Debye and Hill. The discrepancies which are observed are discussed in terms of molecular shape and internal reorientation.

ESR Linewidths in Solution. I. Experiments on Anisotropic and Spin—Rotational Effects

The linewidths of the hyperfine components of the ESR spectra of vanadyl acetylacetonate in liquid toluene have been measured as a function of concentration, temperature, and applied field. The g-tensor and hyperfine-tensor components have been determined and used, along with the spectral data, to determine the Debye rotational correlation time τR. This analysis agrees very well with the experimental observations. A residual linewidth, not dependent upon the above mechanism, and independent of nuclear quantum number and applied field, has been studied and found to vary as T/η, where η is the viscosity. This residual linewidth is ascribed to a spin—rotational interaction.