Nearest-neighbor correlation parameter

An approximate nearest-neighbor interaction model, in which the states of residues i-1 and / are correlated, is also introduced a 3 x 3 matrix is required In this model. Both the 4 x4 and 3x3 matrix formulations involve four parameters (uci, and vjg). 

Every model has limitations. Even the most robust and best-validated regression model will not predict the outcome for all catalysts. Therefore, you must define the application domain of the model. Usually, interpolation within the model space will yield acceptable results. Extrapolation is more dangerous, and should be done only in cases where the new catalysts or reaction conditions are sufficiently close to the model. There are several statistical parameters for measuring this closeness, such as the distance to the nearest neighbor within the model space (see the discussion on catalyst diversity in Section 6.3.5). Another approach uses the effective prediction domain (EPD), which defines the prediction boundaries of regression models with correlated variables [105]. 

According to Eq. (23), the equilibrium number of chains in conformation c depends on the number gc of arrangements of a chain in that conformation, the conformational energy Ec, the surface parameter rjs, as well as the weight factors due to the chain-solvent interactions (/>,) and to the nearest-neighbor bond correlations In the above for-... 

In the elements p and r, the Heaviside functions vpr and vrp are included to avoid bond backfolding since a bond cannot be backward when the previous bond was forward and vice versa. In the supermatrix G, cj, characterizes a lateral bond in layer i, p, a forward bond starting from layer i, and r,- a backward bond starting from layer i. q,-, p,-, and r,-depend on three kinds of parameters. The parameters ah, a, 0, and to arise from local chain stiffness and bond arrangements, Pi from the intermolecular interactions and pLi, pzi from the nearest-neighbor bond correlations. 

The effect of the correlations between the nearest neighboring parallel bonds is important. However, it is shown that the calculations can be simplified by ignoring these correlations and by replacing the interaction parameter employed when the correlations are included with a value larger by 0.17. 

Neon, and the elements directly below it in the periodic table or the Solid State Table, form the simplest closed-shell systems. The electronic structure of the inert-gas solid, which is face-ccntercd cubic, is essentially that of the isolated atoms, and the interactions between atoms are well described by an overlap interaction that includes a correlation energy contribution (frequently described as a Van der Waals interaction). The total interaction, which can be conveniently fitted by a two-parameter Lennard-Jones potential, describes the behavior of both the gas and the solid. Electronic excitations to higher atomic states become excitons in the solid, and the atomic ionization energy becomes the band gap. Surprisingly, as noted by Pantelides, the gap varies with equilibrium nearest-neighbor distance, d, as d... 

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