Jack H. Freed

Theory of Linewidths in Electron Spin Resonance Spectra

A general theory of the linewidths in the electron spin resonance spectra of dilute solutions of free radicals has been developed in terms of the relaxation‐matrix theory of Bloch, Redfield, and Ayant. In contrast to previous theories, it is shown that a composite line arising from a set of degenerate nuclear‐spin states should, in general, consist of a sum of superimposed lines of Lorentzian shape with different widths rather than a single line with an over‐all Lorentzian shape. A single Lorentzian line is still obtained, however, as a limiting case when the variation of the widths of the different components of a composite line is small compared to the average width. Although the non‐Lorentzian shape of a composite line is often difficult to observe experimentally, a number of other observable properties are predicted by the present development that are outside the scope of the previous theories. For example, linewidth effects resulting from differences in the widths of the separate components of a comp...

Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids

It is shown how the equilibrium pair correlation function between spin‐bearing molecules in liquids may be incorporated as an effective force in the relative diffusion expressions, and how one may solve for the resulting time correlation functions and spectral densities needed for studies of spin relaxation by translational diffusion. The use of finite difference methods permits the solution no matter how complex the form of the pair correlation function (pcf) utilized. In particular, a Percus–Yevick pcf as well as one corrected from computer dynamics, both for hard spheres, are utilized. Good agreement with the experiments of Harmon and Muller on dipolar relaxation in liquid ethane is obtained from this analysis. Effects of ionic interactions in electrolyte solutions upon dipolar relaxation are also obtained in terms of Debye–Huckel theory for the pcf. Analytic solutions are given which are appropriate for the proper boundary‐value problem for the relative diffusion of molecules (i.e., a distance of mini...

Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids. II. Finite jumps and independent T1 processes

Hwang and Freed have previously given solutions for the relative diffusion of molecules that include the proper boundary condition (i.e., an excluded volume due to a distance of minimum approach) which has usually been neglected in spin relaxation theories. In this work their results are extended to include effects of (1) one type of spin that is rapidly relaxing, (2) diffusion by jumps of finite size, and (3) frequency‐dependent diffusion coefficients in the theory of spin relaxation by intermolecular dipolar interactions. These results are mathematically simpler and sounder than those commonly employed. In particular, it is shown that for case (2) measurements of J (O), the zero‐frequency spectral density cannot solely be used to determine the jump size, in constrast to the Torrey theory, which did not consider the boundary‐value problem.

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 > 10−6sec are obtained, while the range in glycerol is from 1 × 10−10sec to >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 a...

Stochastic‐molecular theory of spin–relaxation for liquid crystals

The theory of spin relaxation for liquid crystals is examined with the objective of properly analyzing the statistical interdependence of the faster rotational reorientation of the individual spin‐bearing molecules and the (slower) director or order‐parameter fluctuations. The analysis is presented in terms of a composite Markov process including both types of motions. It is shown that one recovers a sum of spectral‐density terms which, in lowest order in fluctuations, correspond to (1) reorientation of the molecule relative to the equilibrium potential of mean torque, (2) effects of director fluctuations, and (3) a negative cross‐term between these two processes which bears a simple relation to (2). Detailed results are given for the particular models of director fluctuations in the nematic phase, quasicritical order fluctuations on either side of the isotropic–nematic phase transition, and slow fluctuations in the local structure. Effects of localized cooperative modes of molecular reorientation are als...

Calculation of ESR spectra and related Fokker–Planck forms by the use of the Lanczos algorithm

The applicability of the Lanczos algorithm in the general ESR (and NMR) line shape problem is investigated in detail. This algorithm is generalized to permit tridiagonalization of complex symmetric matrices characteristic of this problem. It is found to yield very accurate numerical solutions with at least order of magnitude reductions in computation time compared to previous methods. It is shown that this great efficiency is a function of the sparsity of the matrix structure in these problems as well as the efficiency of selecting an approximation to the optimal basis set for representing the line shape problem as distinct from actually solving for the eigenvalues. Furthermore, it is found to aid in the analysis of truncation to minimize the basis set (MTS), which becomes nontrivial in complex problems, although the efficiency of the method is not very strongly dependent upon the MTS. It is also found that typical Fokker–Planck equations arising from stochastic modeling of molecular dynamics have the pro...

Reconstruction of the chemotaxis receptor-kinase assembly.

In bacterial chemotaxis, an assembly of transmembrane receptors, the CheA histidine kinase and the adaptor protein CheW processes environmental stimuli to regulate motility. The structure of a Thermotoga maritima receptor cytoplasmic domain defines CheA interaction regions and metal ion–coordinating charge centers that undergo chemical modification to tune receptor response. Dimeric CheA–CheW, defined by crystallography and pulsed ESR, positions two CheWs to form a cleft that is lined with residues important for receptor interactions and sized to clamp one receptor dimer. CheW residues involved in kinase activation map to interfaces that orient the CheW clamps. CheA regulatory domains associate in crystals through conserved hydrophobic surfaces. Such CheA self-contacts align the CheW receptor clamps for binding receptor tips. Linking layers of ternary complexes with close-packed receptors generates a lattice with reasonable component ratios, cooperative interactions among receptors and accessible sites for modification enzymes.

Multiple-quantum ESR and distance measurements

Abstract It is shown that allowed double-quantum coherences (DQC) can now be routinely generated in disordered and oriented solids containing nitroxide biradicals and random distributions of stable radicals. The Pake doublets obtained from DQC pathways can be effectively used to determine long (∼30 A) distances in the former case, and concentrations in the latter. The DQC signals are strong and often comparable to standard single-quantum signals. In the limit of non-selective pulses their interpretation becomes independent of complicating features which affect other ESR distance methods.

ESR line shapes in the slow‐motional region: Anisotropic liquids

It is shown how the analysis of Freed et al. for ESR lineshapes in the slow tumbling region may be generalized to include anisotropic liquids. Particular emphasis is given to the case of nitroxide radicals in liquid crystal environments with cylindrically symmetric restoring potentials U (β). It is found that when |U(β)|≲ kT, spectral appearances are qualitatively (but not quantitatively) similar to those for isotropic liquids. In particular, the spectra are sensitive to the model of reorientation. They are also predicted to be a very sensitive indicator of effects of anisotropic viscosity. The analysis given for the motional narrowing region yields analytic expressions for the needed spectral densities, where previously only numerical results had been obtained. The analytic expressions are valid when |U(β)|≲ kT. Analytic solutions to the rotational diffusion equation appropriate for |U(β)|≫kT are given and it is outlined how they may be applied to magnetic resonance.

Quantum Effects of Methyl‐Group Rotations in Magnetic Resonance: ESR Splittings and Linewidths

The effects of internal rotations of methyl groups on ESR hyperfine lines are analyzed in terms of a quantum‐mechanical description of the motion. The classical description of rotational averaging is replaced by (1) spin—rotational coupling from a hyperfine operator, and (2) rotational relaxation by thermal collisions. In the absence of collisions, the effects of (1) lead to a static set of splittings whose values depend upon the relative magnitudes of the hyperfine‐versus‐tunneling frequencies. In the presence of frequent collisions, represented by a strong‐collision model, the effects of (1) lead to line broadening, the detailed nature of which also depends on the hyperfine‐versus‐tunneling frequencies. In general, results predicted from a classical treatment of the motion are obtained when the hyperfine frequency is significantly greater, while quantum effects become important for relatively larger tunneling frequencies. The results are illustrated by application to relevant experimental observations. ...