Ramsey theory

Ramsey theory, 22 201-204 Random-fragmentation model, Szilard-Chalmers reaction and, 1 270 Random-walk process, correlated pair recombination, post-recoil annealing effects and, 1 288-290 Rare-earth carbides, neutron diffraction studies on, 8 234-236 Rare-earth ions energy transfer, 35 383 hydration shell, 34 212-213 Rare gases... 

For hydrogen, the Ramsey theory is relatively easy to apply, but, as we see in Section 4.5, external perturbations from neighboring functional groups and solvent molecules are of comparable magnitude to the basic electronic terms, so that the theory is quantitatively of little practical value. For other nuclei, this theory could predict chemical shielding rather accurately if we had true wave functions and knowledge of the energies of all excited states. In practice, approximations must be made, but acceptable results can be obtained provided some fundamental aspects are kept in mind. 

Helgaker et alP presented a fully analytical implementation of spin-spin coupling constants at the DFT level. They used the standard procedure for linear response theory to evaluate second-order properties of PSO, FC and SD mechanisms. Their calculation involves all four contributions of the nonrelativistic Ramsey theory. They tested three different XC functionals -LDA (local density approximation), BLYP (Becke-Lee-Yang-Parr), " and B3LYP (hybrid BLYP). All three levels of theory represent a... 

Signal Averaging Empirical Hamiltonian Nuclear Spin Energy Levels The Ramsey Theory of the NMR Chemical Shift (4(g))... 

The Ramsey Theory of the NMR Spin-Spin Coupling Constants... 

The Ramsey theory of the NMR spin-spin coupling constants (4(D)... 

THE RAMSEY THEORY OF NMR SPIN-SPIN COUPLING CONSTANTS... 

Ramsey theory (p. 666) diamagnetic effect (p. 668) paramagnetic effect (p. 668) coupling constant (p. 668) direct spin-spin interaction (p. 669) diamagnetic spin-orbit contribution (p. 669) paramagnetic spin-orbit (p. 670) spin-dipole contribution (p. 670)... 

The spin-dipolar and the Fermi contact terms of the Ramsey theory [12, 13] are obtained from the general expression for the current density... 

The Ramsey theory of indirect nuclear spin-spin coupling [12, 13] can be reformulated in terms of linear superposition of two current density fields, 7"" and 7"", induced in the electrons of a molecule by nuclear magnetic dipoles m/ and my [3, 51, 52, 61]. Graphical representations of the interference pattern within the total current density vector field, together with corresponding density maps, Eq. (7.57), are very useful to elucidate coupling pathways and to rationalize the exchange of spin information between coupled nuclei. 

Ramsey theory [cf. (209), Ch. 7] developed by Kern and Lipscomb 188a) to eliminate the need for a knowledge of excited states. More recently, Buckingham and Stephens 42a) have shown that this treatment is inadequate in complexes where the panmu etic shielding contributes substantially to the total shielding. 

---