General Theoretical Background

Within a molecule, a nucleus is characterized by its magnetic properties and electronic environment and by the following consequent parameters associated with the corresponding NMR signals chemical shift, coupling constants, relaxation rates,15 and nuclear Overhauser enhancement (NOE).1617 All these values may be used to extract qualitative or quantitative information about the structure, the conformation, and the behavior of molecules in solution. 

A system containing n equivalent nuclei having spin quantum number /x and m equivalent nuclei A having /A is said to be of the type AmX if the chemical-shift difference between X and A is large. The following multiplicity rule gives the number of lines in the NMR spectrum for each of these nuclei  

The indirect spin-spin coupling is independent of molecular rotation. The coupling mechanism is known to involve the electron spins of the bonding electrons and is the result of a weak electron polarization. The interaction energy AX is proportional to the scalar product of the nuclear spins / of A and X, according to the following expression  

Theory indicates that the J x term is composed of several contributions that characterize the effect of orbital electronic motions, the polarization of electronic spins, and the Fermi contact term. The last contribution is the most significant, and affects mainly the s valence orbitals. 

Experimental Techniques for Obtaining Carbon-Proton Coupling Constants 

The studies to be reviewed below mainly refer to proton or deuteron magnetic resonance in melts or concentrated solutions of polymers of molecular masses close to or above the critical value M. Under such circumstances the predominant spin-lattice relaxation mechanism of protons (spin 1/2) is based on fluctuating dipole-dipole couplings of like spins, that is, we are dealing with the homonuclear case. Deuterons (spin 1), in contrast, possess a finite electric quadrupole moment which is subject to quadrupole coupling to local molecular electric field gradients which is much more efficient than dipolar interactions. 

The relaxation formalisms of dipolar-coupled two-spin 1/2 systems (protons) on the one hand, and of quadrupolar-coupled spin 1 nuclei (deuterons) on the other, have very much in common and lead to largely equivalent analytical expressions [2, 17]. This very much facilitates comparisons of experimental results obtained with either technique. 

The spherical harmonics Y2,m, (p) are expressed in polar coordinates, that is the polar angle d and the azimuthal angle (p. These coordinates define the orientation of the internuclear vector relative to the external magnetic flux density Bq in the case of dipolar coupHng, or the orientation of the principal electric field gradient (i.e., of a molecular axis) again relative to Bq in 

Molecular motions in the sense of reorientations of molecules or chemical groups lead to fluctuating polar coordinates, p= p(t). As a conse- 

In the frame of the Bloch/Wangsness/Redfield (BWR) relaxation theory [2, 17], the fluctuations of the spin Hamiltonians are described with the aid of (preferably normalized) autocorrelation functions of the type 

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This chapter presents new information about the physical properties of humic acid fractions from the Okefenokee Swamp, Georgia. Specialized techniques of fluorescence depolarization spectroscopy and phase-shift fluorometry allow the nondestructive determination of molar volume and shape in aqueous solutions. The techniques also provide sufficient data to make a reliable estimate of the number of different fluorophores in the molecule their respective excitation and emission spectra, and their phase-resolved emission spectra. These measurements are possible even in instances where two fluorophores have nearly identical emission specta. The general theoretical background of each method is presented first, followed by the specific results of our measurements. Parts of the theoretical treatment of depolarization and phase-shift fluorometry given here are more fully expanded upon in (5,9-ll). Recent work and reviews of these techniques are given by Warner and McGown (72). 

Table III gives an impression of what information on the excitation process can be gained from the various types of experiments. The references lead the reader to a number of papers which give the general theoretical background to the understanding of the experiments performed.

In the lipase-catalyzed resolution, temperature control of enantioselectivity has been generally accepted for its simplicity and theoretical reliability. Lowering the reaction temperature usually enhances the enantioselectivity. Here, the historical and theoretical backgrounds of the temperature control of enantioselectivity and its applicability to the method are described. Recent literatures for the lipase-catalyzed resolutions to which the low-temperature method seems to be promising to enhance the enantioselectivity are also summarized. 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Electronic structure theory, electron nuclear dynamics (END) structure and properties, 326-327 theoretical background, 324-325 time-dependent variational principle (TDVP), general nuclear dynamics, 334-337 Electronic wave function, permutational symmetry, 680-682 Electron nuclear dynamics (END) degenerate states chemistry, xii-xiii direct molecular dynamics, structure and properties, 327 molecular systems, 337-351 final-state analysis, 342-349 intramolecular electron transfer,... 

This comprehensive survey of the title topic is in three parts, the first dealing with the theoretical background and laboratory studies, with 29 references. The second part, with 21 references deals with case histories and experimental studies of industrial vapour explosions. These involved the systems molten titanium-water, molten copper-water, molten aluminium-water, smelt-water, water-various cryogenic liquids, molten salt-water and molten uranium dioxide-liquid sodium. In the third part (with a further 26 references) is discussion of the various theories which abound, and the general conclusion that superheated liquids most likely play a major role in all these phenomena [1]. A further related publication covers BLEVEs and pressure let-down explosions [2],... 

Among the many excited singlet and triplet levels, 5i and Ti have distinct properties. They are in general the only levels from which luminescence is observed (Kasha rule) also most photochemical reactions occur from Sr or Ti. Here we discuss the characterization of the lowest triplet state by electronic spectroscopy. First we treat the theoretical background that allows the absorption spectra of conjugated systems to be described, and then we discuss the routes that lead to phosphorescence emission and Ti- - Sq absorption intensity. Details of the experimental methods used to determine triplet-triplet and singlet-triplet absorption spectra, as well as phosphorescence emission spectra are given in Chapters III, IV, and V. Representative examples are discussed. 

II. General Notation, Basic Definitions, and Theoretical Background... 

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