ESR Rigid-Lattice Line Shape in a System of Two Interacting Spins
TL;DR: In this paper, a theory was developed to describe the rigidlattice line shape of an electron spin resonance signal which was influenced by dipolar coupling to a second spin, and the polarization lifetime T 1 of the dipolar field was assumed short.
Abstract: A theory is developed to describe the rigid‐lattice line shape of an electron spin resonance signal which is influenced by dipolar coupling to a second spin. The polarization lifetime T1 of the dipolar field is assumed short. Computer generated plots are presented. Broadening, peak shifts, and amplitude changes are noted. Under certain conditions no observable broadening is predicted, merely an apparent decrease in spectrum amplitude. Experimental results for a nitroxide radical interacting with a paramagnetic ion are compared with theoretical curves. The results allow calculation of the distance between the two spins. Values for the directional angles of the second spin in the g tensor coordinate system of the observed spin are also calculated.
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TL;DR: The ability to time-resolve the structural features mentioned above makes SDSL a powerful approach for exploring the evolution of structure on the millisecond time scale and is anticipated to have future applications to the study of protein folding both in solution and in chaperone-mediated systems.
385 citations
Cites background from "ESR Rigid-Lattice Line Shape in a S..."
...Metal ion–nitroxide interactions in metalloproteins have also been used to estimate intramolecular distances [18]....
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TL;DR: Since ATPases and ATP synthases are almost universally involved in some form of energy transduction there is a particular need in an ATPase or ATP synthase reaction to evaluate the equilibrium constants of the steps in the mechanism and to investigate the possibility of alternate reaction pathways.
Abstract: At even the simplest level we can expect an ATPase mechanism to comprise the following four steps: the binding of ATP, the reaction of ATP with water on the enzyme, and the release of the products ADP and P1. So at the outset techniques are needed to investigate these four processes. The range of techniques needed is soon extended once questions are asked about the role of protons and metal ions, the possibility of a multistep hydrolytic process, multistep substrate and product binding processes, and protein–lipid or protein–protein interactions. Since ATPases and ATP synthases are almost universally involved in some form of energy transduction there is a particular need in an ATPase or ATP synthase reaction to evaluate the equilibrium constants of the steps in the mechanism and to investigate the possibility of alternate reaction pathways. The nature of the coupling process by the protein of the chemical reactions of ATP to the other energetic process, be it muscle contraction, active transport, respiration or photosynthesis, is likewise of profound interest. Finally we would like to know as much as possible about the ATPase or ATP synthase mechanism during the period when the various forms of energy transduction are occurring.
270 citations
TL;DR: The results establish that horseradish peroxidase (H-peroxidases) Compound I is not an enzyme peroxide complex, but a derivative in which the active site is oxidized.
254 citations
TL;DR: In this article, a double electron-electron resonance (DEER) spin-echo technique was applied to measure the electron−electron dipolar spectrum of a frozen toluene solution of the biradical, 2,6bis[(((2,2,5, 5tetramethyl]-1−oxypyrrolin‐3]-yl)carbonyl)oxy)]−anthracene.
Abstract: A DEER (double electron–electron resonance) spin–echo technique was applied to measure the electron–electron dipolar spectrum of a frozen toluene solution of the biradical, 2,6‐bis[(((2,2,5, 5‐tetramethyl‐1‐oxypyrrolin‐3‐yl)carbonyl)oxy)]‐anthracene. Modulation of the DEER spin–echo envelope was observed and identified as originating from the dipolar coupling between the two nitroxide spins of the biradical. Fourier transformation of the modulated components of the echo envelope yielded a dipolar spectrum from which a spin–pair separation of 19.73±0.14 A was calculated. Constraints on the relative orientation of the two nitroxide spin moieties were obtained by analysis of the effect of the microwave pulse orientational selectivity on the DEER modulation amplitudes. Molecular models of the studied compound exhibit structures that correspond well with the structural information deduced by DEER spectroscopy.
230 citations
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01 Jan 1963
TL;DR: In this article, the effect of changing the precession frequency of the magnetic field has been studied using NMR to study rate properties. But the effect is limited to the case of double and double resonance.
Abstract: 1. Elements of Resonance.- 2 Basic Theory.- 3. Magnetic Dipolar Broadening of Rigid Lattices.- 4. Magnetic Interactions of Nuclei with Electrons.- 5. Spin-Lattice Relaxation and Motional Narrowing of Resonance Lines.- 6. Spin Temperature in Magnetism and in Magnetic Resonance.- 7. Double Resonance.- 8. Advanced Concepts in Pulsed Magnetic Resonance.- 9. Multiple Quantum Coherence.- 10. Electric Quadrupole Effects.- 11. Electron Spin Resonance.- 12. Summary.- Problems.- Appendixes.- A. A Theorem About Exponential Operators.- B. Some Further Expressions for the Susceptibility.- D. A Theorem from Perturbation Theory.- E. The High Temperature Approximation.- F. The Effects of Changing the Precession Frequency - Using NMR to Study Rate Phenomena.- G. Diffusion in an Inhomogeneous Magnetic Field.- H. The Equivalence of Three Quantum Mechanics Problems.- I. Powder Patterns.- J. Time-Dependent Hamiltonians.- K. Correction Terms in Average Hamiltonian Theory - The Magnus Expansion.- Selected Bibliography.- References.- Author Index.
4,921 citations
TL;DR: In this paper, the modified Bloch equations for nuclear magnetic resonance are modified to describe the magnetic resonance of a single nuclear species X which is transferred back and forth between two (or more) magnetic environments (A,B) by kinetic molecular processes.
Abstract: The Bloch equations for nuclear magnetic resonance are modified to describe the magnetic resonance of a single nuclear species X which is transferred back and forth between two (or more) magnetic environments (A,B) by kinetic molecular processes. The modified Bloch equations involve the usual assumptions of the Bloch theory and, in addition, require (a) that the X nuclear relaxation times be independent of the molecular exchange rates, and (b) that the X nuclear magnetization in A relax independently of the X magnetization in B, and vice versa. The modified Bloch equations are easily solved in the slow passage case, with arbitrary rf saturation. Earlier relations between reaction rates, and resonance line shapes, which were developed by Gutowsky, McCall, and Slichter, and extended by a number of other investigators, are easily derived using the modified Bloch equations. In the present work the modified equations are used to show how rapid exchange rates can sometimes be measured in solutions where the X r...
1,453 citations
TL;DR: The theory is applied to spin-lattice relaxation of a coupled nuclear spin system in a metal, for arbitrary externally applied fixed magnetic field.
Abstract: A general procedure is given for finding the equation of motion of the density matrix of a system in contact with a thermal bath, as for example a nuclear spin system weakly coupled to a crystal lattice. The thermal bath is treated both classically and quantum mechanically, and the theory is similar to, and a generalization of, conventional theories of time proportional transition probabilities. Relaxation of the system by the thermal bath is expressed by a linear matrix operator, and it is stressed that elements of this operator can be regarded as secular or nonsecular perturbations on the equation of motion and can be treated accordingly. When the motion of the system is slow compared to that of the thermal bath, the equation of motion can be expressed in an operator form which is independent of representation. If the system has a time-dependent Hamiltonian which varies slowly compared to the motion of the thermal bath, the same equation of motion is obeyed and the system is relaxed by the bath toward a Boltzmann distribution with respect to its instantaneous Hamiltonian. If the time variation of the Hamiltonian is more rapid, higher order corrections to the equation of motion must be applied. The theory is applied to spin-lattice relaxation of a coupled nuclear spin system in a metal, for arbitrary externally applied fixed magnetic field.
1,416 citations
TL;DR: In this article, it was shown that the distortion of the hydrated complex by collisions with other water molecules is responsible for the decrease in T2 in Mn++ (and other) solutions in very high magnetic fields.
Abstract: The proton relaxation time in solutions of paramagnetic ions depends, among other factors, on the relaxation time of the electron spins, τs. It is shown that the latter, for ions of the iron group, is determined mostly by the distortion of the hydrated complex by collisions with other water molecules. The theory provides a quantitative explanation for the decrease in T2 in Mn++ (and other) solutions in very high magnetic fields. The experimentally observed field and temperature dependence of the proton relaxation times, T1 and T2, for ions of the iron group is compared with theory and the features which depend on τs are stressed.
1,192 citations
TL;DR: In this paper, the magnetic dipole-dipole interaction was used as a perturbation of the proton two-spin system within the water molecule; the effect of more distant protons, neglected in this calculation, gave a finite width to the component lines.
Abstract: Fine structure has been observed in the nuclear paramagnetic resonance absorption line for protons in crystalline hydrates. The magnetic field of 6820 gauss was provided by a permanent magnet, the inherent stability of which facilitated detailed study of line shape. Measurements on a single crystal of CaSO4·2H2O show a splitting into four component lines with maximum separation varying from zero to 22 gauss, depending upon the direction of the externally applied magnetic field in the crystal. Both the number of component lines and the dependence of their spacing on field direction are calculated by treating the magnetic dipole‐dipole interaction as a perturbation of the proton two‐spin system within the water molecule; the effect of the more distant protons, neglected in this calculation, gives a finite width to the component lines. Variation of the splitting with field direction determines the orientation of the line joining protons in the water molecule, which is found to be consistent with positions ascribed to hydrogen nuclei in the lattice through simple considerations of chemical bonding. The distance between protons in the water molecule is measured by the splitting to be 1.58A for CaSO4·2H2O; if one assumes an H–O–H bond angle of 108°, the O–H distance is 0.98A. Powdered hydrates show a characteristic fine structure arising from isotropic distribution in solid angle of single crystal granules. This type of fine structure determines the proton‐proton distance somewhat less accurately than does the single crystal experiment.
1,084 citations