Reduced coupling constant , with

Figure 2. The nearest-neighbor concurrence C(l,2) for different values of the anisotropy parameter y = 1, 0.7, 0.3, 0 with an impurity located at = 3 as a function of the reduced coupling constant A = 7/2/i, where J is the exchange interaction constant and h is the strength of the external magnetic field. The curves correspond to different values of the impurity strength a = 0,0.5,1,1.5 with system size iV = 201.

All terms contributing to either JM N or Jm,n are proportional to the magnetogyric ratio of both coupled nuclei, M and N. Since this is a nuclear property not associated with the molecular electronic structure, the reduced coupling constants, Km,n or Km,n are often quoted instead of Jm,n or Jm,n, respectively. They are related by... 

Before presenting the results for the electronic transmission, it is useful to first consider the dependence of the real and imaginary parts of P(E) on temperature and on the reduced coupling constant Jo/ c- Both functions are shown in Fig. 39. We see that around the Fermi level at E = 0 the real part is approximately linear, ReP(E) E while the imaginary part shows a Lorentzian-like behavior. The imaginary part loses intensity and becomes broadened with increasing temperature or Jo, while the slope in the real part decreases when k T or Jo are increased. 

The dependence of/on y means that the coupling constant itself (but not the reduced coupling constant) changes with isotopic substitution even though the electron distribution in the molecule is unchanged. For example, on deuterium substitution,... 

Isotropic effective /-coupling tensors (/) with a scaling factor s 1 are characteristic for ideal homonuclear Hartmann-Hahn experiments and, in particular, for homonuclear isotropic mixing experiments (see Section X). Isotropic effective /-coupling tensors can also be created between heteronuclear spins i and m (see Section XI) however, this results in a reduced effective coupling constant with a scaling factor i 1/3 [see Eq. (115)]. 

Figure 11 Contour plot (adapted with permission from Ref. [38]) of the 2D 30.4 MHz N/ H HETCOR of tris(trimethylstannyl)amine, e3Sn>3N (25 °C 50% in C D basic 2D INEPT-based heteronuclear shift correlation). The drawn line in the formula shows the path of polarization transfer and the broken line connects those spins for which the sign of reduced coupling constants are compared. Four crosspeaks are visible corresponding to satellites. The positive tilt of those satellites corresponding to...

A selection of coupling constants V( Sn,X) for X nuclei throughout the periodic table is listed in Table 1, together with the reduced coupling constants... 

Figure 2.1.9 Contour plots of the 50.4 MHz /V/ H (left) and 186.5 MHz 2D" Sn/ H shift correlations of N enriched (ca. 10%) PhN(SnMes)2. The experiments serve for comparison of signs of reduced coupling constants K,and positive and negative tilts of the cross peaks indicate alike or different signs of K, respectively. In the formulae A to D, the arrows indicate the path of H polarization transfer, and the dashed lines from the respective passive to the active nuclei show which reduced coupling constants are compared with respect to their signs. Thus, in the /V/ /-/ correlation, Sn or Sn is the passive nucleus, and in the " Sn/ /-/ correlation N (labeled C ) and Sn (labeled D ) are the passive nuclei. Since it is known that K (Sn, Hms) < 0, all other signs (see results ) follow unambiguously. (Adapted from Reference 119.)...

Table 1. Computed Fermi contact terms, total coupling constants 2hJX-y (Hz), reduced coupling constants [2hKX-Y (x 1019) N A"2 m 3], and X-Y distances (A) for X-H-Y hydrogen bonds with X, Y = 13C, 15N, 170, and F2.

Table 3. Computed X-Y and Y-H distances (A), Fermi-contact terms and coupling constants lhJH Y (Hz), and reduced coupling constants [lhKH-Y (x 1019) N A-2 nf3J for complexes with traditional X-H-Y hydrogen bonds with Y = l5N, l70, and l9F.

The factor tC (not to be confused with the reduced coupling constant K) yields the relativistic effect. The nonrelativistic limit, which is given by taking c oo, yields /C = 1 and eq. (4.8) leads to the nonrelativistic Hamiltonian in the electromagnetic fields. We may insert w = p + A into the right-hand side of eq. (4.8) to obtain... 

We compare in Table 6 calculated [107] reduced coupling constants KM() based on BP86 with experiment. The agreement is in general good with the possible exception of Mn04. The largest contribution comes from the Fermi-contact term... 

Group IV hydrides may be associated with the corresponding increase in effective nuclear charge 232a). From Table la it may be seen that the reduced coupling constants of the 5d elements Pt and W are larger than those of the 4d element Rh. 

Figure 3. Increase of K(C,I) and of a corrections to C(1) shieldings with formal hybridization of C(l). Reduced coupling constants and corrections to shieldings taken...

Alkaloids of the yellow oxocularine group are easily recognized by UV absorption maxima at about 400 nm (in neutral solution), by bathochromic shifts in acid media, and by conjugated carbonyl absorption at 1670 cm in the IR spectra. Characteristic features of the mass spectra are the appearance of a strong molecular ion (usually the base peak). In the H-NMR spectra the absence of aliphatic protons and the presence of a pair of aromatic proton doublets with a reduced coupling constant (5.5-5.7 Hz) for H-3 and H-4, both clearly differentiated from benzenoid protons, are noted. These are the essential spectroscopic data needed for structural determination of oxocularines. 

---