Reduced coupling constant

We shall assume that the dominant part of the bilinear interchain coupling comes from the Coulomb interaction of CDWs on neighboring chains. Here we neglect the finite size and the tilt of molecules in the chains and associate a purely one-dimensional CDW to each chain. Then for all interchain distances dj. in (TTF)(TCNQ) q dj l, so that the Coulomb coupling constant reduces tb the asymptotic form ... 

Finally, the PCI contribution to the exchange coupling constant reduces to... 

Because J arises from the magnetic interactions of nuclei, the simplest factor affecting it is the product yjY of the two nuclear magnetogyric ratios involved. For example, in FI F is 82 FIz, i.e. x yo/yf - This totally predictable factor is sometimes discounted by quoting the reduced coupling constant =... 

Experimental confirmation of the metal-nitrogen coordination of thiazole complexes was recently given by Pannell et al. (472), who studied the Cr(0), Mo(0), and W(0) pentacarbonyl complexes of thiazole (Th)M(CO)5. The infrared spectra are quite similar to those of the pyridine analogs the H-NMR resonance associated with 2- and 4-protons are sharper and possess fine structure, in contrast to the broad, featureless resonances of free thiazole ligands. This is expected since removal of electron density from nitrogen upon coordination reduces the N quad-rupole coupling constant that is responsible for the line broadening of the a protons. 

The normal pattern of coupling constants for aromatic six-membered rings is found in the heterocyclic aza systems, except that the ortho coupling to a proton a to a heterocyclic nitrogen is reduced from 7-8 Hz to 4.5-6 Hz. The J2.3 of pyrylium salts is still lower... 

Typical coupling constants for isothiazoles are given in Table 5. The electronegative nitrogen atom reduces 3,4 and V3.5 from the values of 3.50 Hz and 0.27 Hz, respectively, in thiophene. The V values correlate quite well with rr-bond orders calculated by MO methods (74CJC833). 

The moment of inertia 1 determines the rotational constant 0 = h /IT, which is the parameter that controls the strength of quantum effects. The other parameter of the model, which is the quadrupolar coupling constant K, can be conveniently taken as the energy and temperature scale. We can thus reduce all quantities related to energies by K, and define, e.g., the dimensionless temperature = k T/K, energy = E/K, and rotational... 

Alternatively, one may attempt to estimate the integral over the derivative of the displacement field that entered in the expression for the coupling constant g= pc Jy cPr du/2. Since da is the divergence of a vector, the integral is reduced to that over a surface within the droplet s boundary ... 

The Soret, a and j3 bands in the visible spectra of platinum(IV) porphyrin complexes occur at longer wavelengths than their platinum(II) analogues,482 H NMR resonances are all shifted downfield,482 the 13C resonances of the a carbons are shifted upheld, and the H-195Pt and 13C-195Pt coupling constants are reduced.480 Whereas excitation of platinum(II) porphyrin complexes... 

Recently, much attention has been paid to the investigation of the role of this interaction in relation to the calculations for adiabatic reactions. For steady-state nonadiabatic reactions where the initial thermal equilibrium is not disturbed by the reaction, the coupling constants describing the interaction with the thermal bath do not enter explicitly into the expressions for the transition probabilities. The role of the thermal bath in this case is reduced to that the activation factor is determined by the free energy in the transitional configuration, and for the calculation of the transition probabilities, it is sufficient to know the free energy surfaces of the system as functions of the coordinates of the reactive modes. 

In a much simplified approach Hi is assumed to have the same form as (10). The only difference is that the new Hamiltonian refers to block spins only with a new effective coupling constant J and a new effective field Bx. In terms of reduced variables K = J/kT, b = B/kT, the new coupling constant and field, written as functions of the old, are... 

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