J value

As for CIDNP, the polarization pattern is multiplet (E/A or A/E) for each radical if Ag is smaller than the hyperfme coupling constants. In the case where Ag is large compared with the hyperfmes, net polarization (one radical A and the other E or vice versa) is observed. A set of mles similar to those for CIDNP have been developed for both multiplet and net RPM in CIDEP (equation (B1.16.8) and equation (B1.16.9)) [36]. In both expressions, p is postitive for triplet precursors and negative for singlet precursors. J is always negative for neutral RPs, but there is evidence for positive J values in radical ion reactions [37]. In equation (B 1.16.8),... 

As was shown in the preceding discussion (see also Sections Vin and IX), the rovibronic wave functions for a homonuclear diatomic molecule under the permutation of identical nuclei are symmetric for even J rotational quantum numbers in and E electronic states antisymmeUic for odd J values in and E elecbonic states symmetric for odd J values in E and E electronic states and antisymmeteic for even J values in Ej and E+ electeonic states. Note that the vibrational ground state is symmetric under pemrutation of the two nuclei. The most restrictive result arises therefore when the nuclear spin quantum number of the individual nuclei is 0. In this case, the nuclear spin function is always symmetric with respect to interchange of the identical nuclei, and hence only totally symmeUic rovibronic states are allowed since the total wave function must be symmetric for bosonic systems. For example, the nucleus has zero nuclear spin, and hence the rotational levels with odd values of J do not exist for the ground electronic state f EJ") of Cr. 

Next, we address some simple eases, begining with honronuclear diatomic molecules in E electronic states. The rotational wave functions are in this case the well-known spherical haimonics for even J values, Xr( ) symmetric under permutation of the identical nuclei for odd J values, Xr(R) is antisymmetric under the same pemrutation. A similar statement applies for any type molecule. 

Finally, let us consider molecules with identical nuclei that are subject to C (n > 2) rotations. For C2v molecules in which the C2 rotation exchanges two nuclei of half-integer spin, the nuclear statistical weights of the symmetric and antisymmetric rotational levels will be one and three, respectively. For molecules where C2 exchanges two spinless nuclei, one-half of the rotational levels (odd or even J values, depending on the vibrational and electronic states)... 

Because the total angular momentum P still commutes with Hj-ot, each such eigenstate will contain only one J-value, and hence Tn can also be labeled by a J quantum number ... 

If one has available Cy j values for the system from an SCF ealeulation performed earlier at a nearby moleeular geometry, one ean use these Cy i values to begin the SCF proeess. 

The strategy we take is to generate the J,J> state (i.e., the state with maximum M-value) and to then use J. to generate J,J-1>, after whieh the state J-1,J-1> (i.e., the state with one lower J-value) is eonstrueted by finding a eombination of the produet states in terms of whieh J,J-1> is expressed (beeause both J,J-1> and J-1,J-1> have the same M-value M=J-1) whieh is orthogonal to J,J-1> (beeause... 

Notiee that these states have M-values given as (j+j )i sinee this is the maximum M-value, it must be that the J-value eorresponding to this state is J= j+j. ... 

States With One Lower M-Value But the Same J-Value... 

J + 1 different M values that arise for eaeh J value. 

J Value assumed in calculating n.(indcpendent) from y4(N2> or Point B. 

The activation energies for the decomposition (subscript d) reaction of several different initiators in various solvents are shown in Table 6.2. Also listed are values of k for these systems at the temperature shown. The Arrhenius equation can be used in the form ln(k j/k j) (E /R)(l/Ti - I/T2) to evaluate k j values for these systems at temperatures different from those given in Table 6.2. 

A feature of the N2 spectrum is an intensity alternation of 1 3 for the J value of the initial level of the transition even odd. This is an effect due to the nuclear spin of the nuclei, which will now be discussed in some detail. 

The saturation magnetization, J), is the (maximum) magnetic moment per unit of volume. It is easily derived from the spia configuration of the sublattices eight ionic moments and, hence, 40 ]1 per unit cell, which corresponds to = 668 mT at 0 K. This was the first experimental evidence for the Gorter model (66). The temperature dependence of J) (Fig. 7) is remarkable the — T curve is much less rounded than the usual BdUouia function (4). This results ia a relatively low J) value at RT (Table 2) and a relatively high (—0.2%/° C) temperature coefficient of J). By means of Mitssbauer spectroscopy, the temperature dependence of the separate sublattice contributions has been determined (68). It appears that the 12k sublattice is responsible for the unusual temperature dependence of the overall J). 

Substitution for Fe has a drastic effect on intrinsic magnetic properties. Partial substitution by or decreases J) without affecting seriously, resulting in larger and values. Substitution by Ti and Co causes a considerable decrease in K , the uniaxial anisotropy (if j > 0) may even change into planar anisotropy (if < 0). Intermediate magnetic stmctures are also possible. For example, preferred directions on a conical surface around the i -axis are observed for substitution (72). For a few substitutions the value is increased whereas the J) value is hardly affected, eg, substitution of Fe byRu (73) or by Fe compensated by at Ba-sites (65). 

Proton-proton coupling constants of benzo rings of benzazoles can illuminate the bonding in such compounds. Thus, comparison of the J values for naphthalene with those for benzotriazoles of different types (Table 13) shows evidence of bond fixation, particularly in the 2-methyl derivative (98) (71PMH(4)l2l). 

The J value is defined as the elastic potential difference between the linear and nonlinear elastic bodies with the same geometric variables [52,53]. The elastic potential energy for a nonlinear elastic body is expressed by ... 

The more stable diastereomer in each case is the one having both methyl groups equatorial. The free-energy difference favoring the diequatorial isomer is about the same for each case (about 1.9 kcal/mol) and is close to the — A(j value of the methyl group (1.8 kcal/mol). This implies that there are no important interactions present that are not also present in methylcyclohexane. This is reasonable since in each case the axial methyl group interacts only with the 3,5-diaxial hydrogens, just as in methylcyclohexane. 

Noting J m = 95g enables the x, values to be calculated from equation 1.32 and the (j) value from equation 1.33. 

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