Electron Spin Relaxation in Liquids

I. Superoperators, Time-Ordering, and Density Operators.- Superoperators.- Time-ordering.- Density operators.- II. Stochastic Processes.- Stochastic (random) variables and probability.- General remarks on stochastic (random) processes.- The relaxation function.- Gaussian and Markov processes.- The relaxation function.- Gaussian and Markov processes.- Master equation.- Fokker-Planck equation.- Functional integration technique of Kac.- III. An Introduction to the Stochastic Theory of E.S.R. Line Shapes.- The jump model.- The isotropic rotational diffusion model.- IV. Projection Operators.- "Non-Markoffian" master equation.- Application to the interaction between a spin system and a bath.- The Redfield approximation.- The two jump models.- V. Cumulant Expansion.- One-dimensional moment and cumulant expansions.- Multivariable moment and cumulant expansions.- Expansions.- Generalization.- Conclusion.- VI. Linear Response Theory and Spin Rotation.- Spin relaxation.- Derivation of the Bloch equations.- Concluding remarks.- VII. Two Approaches to the Theory of Spin Relaxation: I. The Redfield-Langevin Equation II. The Multiple Time Scale Method.- The Redfield-Langevin equation.- Motivation.- Derivation of the equation of motion for G??, (t).- The Redfield-Langevin equation - the lowest order result.- Stochastic properties of the Redfield-Langevin eq..- The Bloch-Langevin equation.- Further remarks.- Generalizations of the lowest order result.- Semiclassical treatment.- Further stochastic interpretation of the spin problem.- The multiple time scale method.- Derivation of the equations of motion.- VIII. ESR Relaxation and Line Shapes from the Generalized Cumulant and Relaxation Matrix Viewpoint.- General approach.- Relaxation matrix and spectral lineshapes.- Properties of the relaxation matrix.- Non-asymptotic solutions.- Stochastic averaging.- Gaussian processes.- Markov processes.- Diffusion models.- Internal rotations.- Anisotropic rotational diffusion.- Summation of the generalized moments for a Markoff process: stochastic Liouville equation.- IX. Spin Relaxation via Quantum Molecular Systems.- Strong collisional relaxation.- General formulation.- Applications.- Gas-phase relaxation.- Quantum effects of methyl group tunneling.- Spin relaxation via vibronic relaxation.- Non-resonant effects.- X. Electron Spin Relaxation in Liquids. Selcted Topics.- Hamiltonian: terms which determine frequencies.- Hamiltonian: terms which determine relaxation.- Complete hamiltonian and density matrix.- Time-dependent perturbation expansions.- $${/rm{/mathord{/buildrel{/lower3pt/hbox{$/scriptscriptstyle/rightharpoonup$}}/over M} }}$$(t) related to '$${/rm{/mathord{/buildrel{/lower3pt/hbox{$/scriptscriptstyle/rightharpoonup$}}/over S} }}$$(t)$${/rm{/mathord{/buildrel{/lower3pt/hbox{$/scriptscriptstyle/rightharpoonup$}}/over S} }}$$'; pulse experiments.- Line widths: cw experiments.- Spin autocorrelation function.- Line shapes in absence of relaxation 251 Line widths and reorientation: detailed derivation.- Discussion of results.- Analysis of experiments.- Second order corrections.- Several interacting nuclei.- Breakdown of spin-hamiltonian; Orbach processes.- Appendices.- XI. Spin-Rotation Interaction.- Basic theory of the interaction.- The full relaxation problem.- The dynamical problem.- Appendices.- 3j-symbols.- Spherical tensors.- Rotation matrices.- XII. Electron Spin Relaxation in 6S State Ions.- Adaption of Redfield's theory.- Relaxation via rotational modulation of the zero-field splitting.- Relaxation via the quartic terms.- Collisional fluctuations of the zero-field splitting.- Modifications demanded by a hyperfine interaction.- Symmetric linewidth variations in the spectra of manganese(II) ions.- XIII. Magnetic Resonance Line Shapes in Slowly Tumbling Molecules.- Expressions for the line shapes.- Reduction to algebraic equations.- Computational algorithms.- Reduction to an eigenvalue problem.- Reduction of band-width to tridiagonal 356 Diagonalization of a complex symmetric tridiagonal matrix.- Estimating rates of convergence.- Applications and comparison with experiments.- Diagonalization programs.- XIIIA. Appendix: Symmetry and the Slowly Tumbling Spin System.- Application of group theory.- XIV. ESR Line Shapes and Saturation in the Slow Motional Region - The Stochastic Liouville Approach.- General approach.- Free radicals of S=$${1 /over 2}$$; no saturation.- Axially symmetric secular g-tensor.- Asymmetric secular g-tensor.- g-tensor plus END-tensor including pseudosecular terms.- One nuclear spin of I = 1.- Saturation.- Rotationally invariant T1.- g-tensor (axially symmetric).- Triplets.- General solutions.- Perturbation theory.- Summary of spectra.- XV. Electron Spin Relaxation in Liquid Crystals.- Nematic liquid crystals.- The static spin hamiltonian.- The linewidth calculation.- The line shape.- XVI. Two Problems Involving ESR in Liquid Crystals.- Thin film ESR (rapid tumbling).- Slow tumbling ESR of a free radical in a bulk liquid crystal.- XVII. The ESR Line Shape of Triplet Excitons in Disordered Systems: The Anderson Theory Approach.- The static line shape.- The magneto-selection theory.- Line shape and symmetry of the triplet state.- The magneto-photo-selection.- The incoherent exciton line shape.- The experimental problem.- The single-channel transfer model.- The exciton line shape of a trimer.- The secular approximation.- The adiabatic approximation.- A line shape formula for the general case.- Simulation of the experimental data.- Excitons in thermal equilibrium.- The multi-channel transfer model.- The vibronic coupling approach of the exciton.- The coherent exciton states.- The incoherent exciton states.- The factors controlling the exciton diffusion.- XVIII. ESR Saturation and Double Resonance in Liquids.- to saturation: a simple line.- ELDOR.- ENDOR.- General approach.- Transition probabilities.- ELDOR - Generalized no saturation of observing mode.- ENDOR - Limiting enhancements.- Expressions for transition probabilities.- Heisenberg spin exchange and chemical exchange.