McConnell’s equations

This expression may be obtained by a derivation starting with McConnell s equations, (Reuben and Fiat, 1969b). 

For positive A (XY) it is actually possible to do comparative studies of coupling constants using only localized orbitals and formal hybridization. In the simplest description using McConnell s equation (20), the Fermi contact term of the coupling is proportional to P] J AE. If we further simplify to localized bonds, the bond order proportional to the s characters of X and Y in the XY bond. If we assume equivalent hybrids, the carbon s character in CH bonds in HjC—CHj, H2C=CH2, and HC = CH will be roughly K p ), sp ) and (ip), so that comparative values of /(CH) will be... 

The McConnell equations (1958) may be contracted and terms describing the magnetization in the B site omitted. For the 2-magnetization in the A site we have, in McConnell s notation,... 

In this equation, Ao is a small constant. B is also a constant. We can determine the twisted structure of the radical by evaluating the angle 0 from the experimental value of A. McConnell s relation can be explained by hyper-conjugation, which allows some spin density to be located in the fl-hydrogen Is orbital. The -hydrogen is bonded to Cp which is bonded to (C<, ) having an unpaired electron. 

For the intermediate exchange where the resonances change upon passing from a slow into a fast regime, the lineshape can be described by McConnell s modification of the Bloch equations [17], For a first-order two-site exchange without homonuclear scalar coupling, for example, the lineshape is given by ... 

The interactions which lead to a nuclear spin-spin coupling in fluids were first formulated by Ramsey [16] in terms of a contact (Fermi) mechanism, a spin-orbital- and a spin-polarization mechanism. Both McConnell [17] and Pople and Santry [18 19] have described modifications of Ramsey s equations which are suitable for use with molecular orbitals derived from LCAO methods. The Pople and Santry treatment has an advantage in that it is capable of producing both negative and positive coupling constants. The McConnell use of the mean excitation energy approximation, which we shall mention later, neces-... 

A second steady-state method involves the analysis of the broadening of the nuclear magnetic resonance spectra of phospholipids in bilayers containing low concentrations of spin-labeled phospholipids. A theoretical analysis of the relation between this line broadening and diffusion rates has been given by Brulet and McConnell.3 [In this paper (6) is not correct the subsequent equations are nonetheless correct. For an alternative derivation, see Brulet.2] In this paper it is shown that a number of measurements of nuclear relaxation rates T71 of nuclei in phospholipids are consistent with lateral diffusion constants in the range 10 7 to 10 R cm2/s. 

We shall demonstrate this for Arnold s EPR-spectroscopic scale (ax, Table 3) [36, 39], which relates the radical substituent constant ((7rad) to the benzylic a spin densities (p) according to Eq. (17), in which px and p refer to the substituted and unsubstituted benzyl radicals. Since the a hyperfine coupling constants (a) are linearily related to the spin densities by the McConnell equation [36,38], that is, ax oc px (cf. Section III.B), the coupling constants may be used instead of the spin densities [Eq. (18)]. According to Eq. (8) (pA = pB for the symmetrically substituted cases), the D value is proportional to the square of the spin density and a trAD scale may be defined by taking the square root of the ratio of the D values instead... 

It is usual to consider T2A = 2b = 2> although the later method due to McConnell (1968) is easier to apply when these are not equal. In this case the equilibrium magnetizations in the z direction are the same for equally populated sites if the very small chemical shift effect S[Pg.197]

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