The Continuum Energy

For a 1 1 electrolyte at a randomly-chosen closest approach distance of 7.16 A, Eq. (78) divided by V2 predicts an electroneutrality length of 10.4 A at 0.1 M, where k is 9.6 A, and (k + a, ) would be 17.0 A. If salt-like effective lattice spacings134,166,167 

This should be a summation, but numerical integration is sufficiently accurate. 

As noted in Section IV-5, 4+ cations will have a layer of single somewhat oriented water dipoles of moderate eA around the 

Energy calculations for ionic lattices show 6a = 1l6. Molten salts can form transient dipoles and multipoles as ion pairs and clusters, but it is unlikely that these contribute to a dielectric constant. For charge transfer in molten salts, the equivalent of an FC process is the change in electroneutrality length as valence changes. 

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J. Troe Prof. Schinke, in your HCO results, when you compare the fluctuating quantum results with RRKM results, you observe that the RRKM curve is above the average quantum data. Can the reason be that you use an inadequate p( ) for the continuum energy range ... 

Because we have already included the vdW energies in the continuum energy up to second order, only higher-order contributions would arise from the replacement of the continuum by a real... 

In Figure 10.2a we show the hE n(t) continuum coefficients [Eq. (10.44)] function of time, at different intensities. The onset of off-resonance processes- typified by a nonmonotonic behavior At off-pul se-center energies, the continuii coefficients rise and fall with the pulse, with the effect becoming more pronouns the further away from the line center the continuum energy levels are. In the wings of the pulse the continuum coefficients are zero at the end of the pulse, giv rise to a pure transient, otherwise known as a virtual state. These results should compared to the weak-field transients discussed in Section 2.1 and shown inFi ... 

It follows that an equation of Bom type, but based on different physical principles (Eq. 56) is a good approximation for the continuum energy in dipolar liquids up to the onset of dielectric saturation at x = 3, provided it is integrated from an appropriate distance somewhat less than that of the superdipole center of the innermost solvation shell from the central ion. This corrected radius will differ from the distance from the ion to the dipole centers of the solvation shell under consideration by about 50% more than the radius of a water molecule. 

The laser frequencies are tuned to induce one-photon resonant transitions from 0) to the intermediate states and to be in one-photon resonance with the transitions from the intermediate states to the continuum energy E of the degenerate multichannel states (I = Similar schemes have... 

For a solid surface, where the surface jumps in discrete steps, the continuum energy of Eq. (3.1) may not be accurate enough to account for all the thermodynamic properties. If one considers a fluctuating solid surface described by the height (in the z direction) of a column located in the xy plane, a more accurate accounting of the extra area is given by the expression... 

It is important to mention that the displacement of the interfacial nodes, U/, are not degrees of freedom in the continuum calculation Because the interfacial nodes coincide with interface atoms, r/, they are moved as atoms and appear as fixed nodes with prescribed displacements to the other elements of the continuum region. Lastly, it must be remarked that this formulation of the continuum/atomistic coupling does not allow for the use of a unique energy functional because E includes the elastic energy of the pad atoms, whose energy is already implicitly contained in the continuum energy, E. ... 

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