Spin coupling constants electron

A completely different type of property is for example spin-spin coupling constants, which contain interactions of electronic and nuclear spins. One of the operators is a delta function (Fermi-Contact, eq. (10.78)), which measures the quality of the wave function at a single point, the nuclear position. Since Gaussian functions have an incorrect behaviour at the nucleus (zero derivative compared with the cusp displayed by an exponential function), this requires addition of a number of very tight functions (large exponents) in order to predict coupling constants accurately. ... 

There have been numerous applications of continuum models to equilibria and reactions in solution surveys of these and extensive listings are provided by Cramer and Truhlar.16 Other studies have focused upon the effects of solvents upon solute molecular properties, such as electronic and vibrational spectra,16 dipole moments, nuclear quadrupole and spin-spin coupling constants and circular dichroism.12... 

Table 4. The isotropic indirect spin-spin coupling constant of calculated at various levels of theory. LL refers to the Levy-Leblond Hamiltonian, std refers to a full relativistic calculation using restricted (RKB) or unrestricted (UKB) kinetic balance, spf refers to calculations based on a spin-free relativistic Hamiltonian. Columns F, G and whether quaternion imaginary parts are deleted (0) or not (1) from the regular Fock matrix F prior to one-index transformation, from the two-electron Fock matrix G...

A systematic development of relativistic molecular Hamiltonians and various non-relativistic approximations are presented. Our starting point is the Dirac one-fermion Hamiltonian in the presence of an external electromagnetic field. The problems associated with generalizing Dirac s one-fermion theory smoothly to more than one fermion are discussed. The description of many-fermion systems within the framework of quantum electrodynamics (QED) will lead to Hamiltonians which do not suffer from the problems associated with the direct extension of Dirac s one-fermion theory to many-fermion system. An exhaustive discussion of the recent QED developments in the relevant area is not presented, except for cursory remarks for completeness. The non-relativistic form (NRF) of the many-electron relativistic Hamiltonian is developed as the working Hamiltonian. It is used to extract operators for the observables, which represent the response of a molecule to an external electromagnetic radiation field. In this study, our focus is mainly on the operators which eventually were used to calculate the nuclear magnetic resonance (NMR) chemical shifts and indirect nuclear spin-spin coupling constants. 

The quantitative theory of CIDNP " is developed to a state where the intensity ratios of CIDNP spectra can be computed on the basis of reaction and relaxation rates and the characteristic parameters of the radical pair (initial spin multiplicity, T) the individual radicals (electron g factors, hfcs, a) and the products (spin-spin coupling constants, J). On the other hand, the patterns of signal directions and intensities observed for different nuclei of a reaction product can be interpreted in terms of hfcs of the same nuclei in the radical cation intermediate. 

An extensive analysis of the effect of lone pairs on the nitrogen atom on spin-spin coupling constants is reviewed in the context of a description of molecular electronic structure. Several oximes are analyzed in studies of these effects and their relevance for structural determination has been pointed out. 

Isotropic electron spin nuclear spin coupling constants... 

There are many more solvent effects on spectroscopic quantities, that cannot be even briefly discussed here, and more specialized works on solvent effects should be consulted. These solvent effects include effects on the line shape and particularly line width of the nuclear magnetic resonance signals and their spin-spin coupling constants, solvent effects on electron spin resonance (ESR) spectra, on circular dichroism (CD) and optical rotatory dispersion (ORD), on vibrational line shapes in both the infrared and the UV/visible spectral ranges, among others. 

In addition to these limited procedures a number of experimental methods (vibrational spectroscopy, dipole moment measurements, electron diffraction, NMR, etc.) have been employed to determine the relative stabilities of these complexes.11,23 Intense effort has been directed towards establishing some kind of correlation between NMR parameters and stability of the borane complexes. The chemical shifts alone rarely show good correlation. However, complexation shifts (the chemical shift difference between the free and complexed borane or ligand) and various spin-spin coupling constants correlate better with calorimetric data, especially for ligands or boranes belonging to structurally similar series (Table 2).10,24... 

The reduced indirect (scalar) nuclear spin-spin coupling constant Kkl describes the interaction of the magnetic nuclei, transmitted through the surrounding electrons. Kkl is four orders of magnitude smaller than DK. 

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