Linear coupling constants, equations

Other Iodine Compounds. By studying the isomer shift and the quad-rupole hfs for a series of compounds, Perlow and Perlow (29) have calibrated the isomer shift scale which is independent of Equation 7. The number of p holes, hp, for the compounds of I2, KICI4 H2O, KIC12 H2O, and ICl has been inferred from the measured value of the quadrupole coupling constant, eqQ, and from the symmetry of the iodine lattice site. Since they found that the isomer shifts and hp are linearly related for these compounds, it appears that 5 electrons do not participate directly in the bonding, and the sp hybridization is negligible. Because of this linearity, they have been able to determine dh/dhp, which leads to a calibration of the isomer shift scale. 

The C—H coupling constants of the cyclopropyl methine carbons are also linearly correlated with the electron demand of the aryl substituents and, in addition, to the dihedral angle between the C—H orbital and the vacant p-orbital, as expressed by the equation AJ= (1 + 0.6 ff+)(10.9 -14.3 cos2 0), where ATis the difference in coupling constant between the cation and the neutral model compounds such as carbonyls. The dependence of the J values on the nature of the substituents is illustrated by the J values of 174, 177, 179 and 183 Hz for the Cl —H bond of 1-arylcyclopropylethyl cation for the para substituents OMe, Me, H and CF3, respectively59. 

Table 23.1 reproduces data affected by breakdown of linear diffusion for the one-electron reduction of Cp2Rh at a Pt disk electrode (r = 2 mm). At sweep rates above about 0.1 V/s, the current function is essentially constant, consistent with the simple one-electron reaction of Equation 23.8. The increase of over 10% in X that is observed at lower scan rates arises from the breakdown of linear diffusion, rather than from additional reactions coupled to Equation 23.8. The radial diffusion contribution is less than 3% [5], with convection accounting for most of the additional mass transport. 

We have followed a phenomenological approach and used the cluster model [18]. In this model the eg-type distortion interacts more strongly with the electronic state of an octahedral coordinated Cr3+ ion than the distortions of t2g symmetry. According to Ham [19], we assume that the continuum of vibrational modes with eg character can be approximated by a single mode with an effective frequency o>, mass /r and coupling constant V. The collective coordinates of the eg mode are conventionally known as Qe x2 — y2) and Qs ( 3z2 — r2). The linear Jahn-Teller Hamiltonian in equation (1) for the X state is [18] ... 

Short of the ab initio calculations, there are several semi-empirical approaches to the calculation and interpretation of electric quadrupole coupling constants. These were developed originally by Townes and Dailey [47, 48] and are well documented in the book by Gordy and Cook [49], They are based on the linear combination of atomic orbitals approximation for molecular orbitals, mentioned earlier in equation (7.266) and described in more detail in chapter 6 ... 

Fig. 5. Schematic illustration of the kinetic parameters described by the coupled rate equations of Eq. (10) for a three-level ensemble upconversion system. The solid arrows represent radiative processes and the dashed arrows represent nonradiative processes. G is the GSA rate constant, E is the ESA rate constant, Wexu is the power-independent upconversion rate parameter, and /Cn are linear decay rate constants...

As Table III indicates, the nature of the substituents in distannanes can influence both the chemical shift (S referenced relative to tetramethyltin) and the direct one-bond coupling constant, J(" Sn-" Sn). The influence of substituents on chemical shifts has been discussed in detail elsewhere (42 a) therefore, an in-depth analysis of the nature of this influence will not be repeated here. However, the influence of substituents on the J(" Sn-" Sn) values deserves some comment 43-44 a-c). In the case of peralkyidistannanes (Table III), it has been proposed that from an apparent linear correlation between J( " Sn-" Sn) and 2cr (the sum of the Taft cr constants of the six alkyl groups bound to the tin atoms), the main factor involved in determining the value of J(" Sn-" Sn) in these compounds is eff) the effective nuclear charge at the tin nucleus 43 a,b). However, an alternative proposal to explain the trend observed in Table III is based on the equation derived by Pople and Santry 45) for the coupling mechanism in a two-body spin system [Eq. (7)]. Here, s(0)... 

The marked correlation between hybridization and the C-H coupling constants has provided another mean to estimate the amount of the s character in the bridgehead C-H bond. According to this correlation, increases linearly with the s character in the bond. Figeys and coworkers formulated this in a hnear equation (equation 1)... 

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