Nearest-neighbor coupling

Fig. 29. Phase diagram of the model Eq. (22) for coadsorption of two kinds of atoms in the temperature-coverage space. Circles indicate a second-order phase transition, while crosses indicate first-order transitions. Point A is believed to be a tricritical point and point B a bicritical point. The dashed curve shows the boundary from the Blume-Capel model on a square lattice with a nearest-neighbor coupling equal to 7 in the present model (for - 0 Eq. (22) reduces to this model), only the ordered phase I then occurs. From Lee and Landau. )...

Bixon and Jortner, Rosch and Voityuk, Olofsson and Larsson, Berlin, Burin, Siebbeles, and Ratner, Orlandi and their coworkers [4, 8, 19-31] have explored the energetics and base-base interactions associated with hole and electron transfer in DNA base-pair stacks. They find nearest-neighbor coupling inter-... 

The next typical example is a linear chain of single-state sites with only nearest-neighbor couplings (Fig. 1)... 

For nearest neighbor coupling in bigger networks of, for example, ten by ten neurons the coupling current fc(i,j) of a neuron at position (i,j) is the sum of input currents from the neighboring neurons ... 

In the model of Fig. lb, all bridge site-energies are taken equal (E ] = ocB), and similarly for the bridge nearest-neighbor couplings = /iB), and for the... 

The coefficients in Table 2-1 have been obtained entirely in the context of nearest-neighbor coupling between states. They would have been different if a... 

Figure 35. Schematic showing some nearest-neighbor coupling pathways for (a) 38(6), (b) 42(6), and (c) 43(6). All reasonable pathways have the same parity in 42(/i) (even parity) and in 43(/i) (odd...

Fig. 17.5 Electron transmission through a molecular bridge connecting two metal leads, (a) An unbiased Junction, (b) electron conduction, (c) hole conduction, (d) a local representation/nearest neighbor coupling model of a molecular bridge.

The phonons in mixed molecular crystals [107] occur practically always in the amalgamated band limit. The vibrons may occur in either limit, and these limits may be found in the same crystal, for different intramolecular modes. This is clearly illustrated by the lattice dynamics calculations and the observed Raman spectra of TCB and DCB [59, 60]. The 312 cm mode in TCB, which is a C—Cl stretch vibration, is shifted by about 2 cm" with each substitution of one Cl atom by a Cl atom. The band width of this vibration in a-TCB and p-TCB is about 0.5 cm, which implies that the nearest-neighbor coupling elements are only about 0.1 cm . So, this vibra-... 

The three separated bands are observed in the Raman spectra with the calculated splittings of 4cm and the correct intensity ratio (9 6 1). In P-DCB the situation is different, however. The width calculated for the vibron band around 328 cm (more than 10 cm ) is much larger than the corresponding band widths in a-DCB and y-DCB (which are less than 1 cm ). So in P-DCB the nearest-neighbor coupling matrix elements in the dynamical matrix for this mode are comparable with the isotope shifts in the free-molecule vibration frequency. The structure of the peak around 328 cm" in the observed Raman spectrum of P-DCB is rather complex indeed [60]. 

The lattice models have been used frequently in theoretical studies of adsorption. The wide popularity of this approach results from its flexibility and simplicity. It may be applied for systems of various dimensionahties, for many lattice geometries, for different models of adsorbate-adsorbate molecular interactions, and many spatially varying external fields. Most studies have focused on a two-dimensional or three-dimensional cubic lattice, with only isotropic nearest-neighbor couplings. The isomorphism between the Ising model and the classical lattice gas or a coarse model of binary mixture is well known and very helpfijl for theoretical analysis. The lattice models can be also appHed to describe the systems involving polymers. 

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