Long-range perturbations

In the third order of long-range perturbation theory for a system of tluee atoms A, B and C, the leading nonadditive dispersion temi is the Axilrod-Teller-Mutd triple-dipole interaction [58, 59]... 

The perturbation theory described in section Al.5.2,1 fails completely at short range. One reason for the failure is that the multipole expansion breaks down, but this is not a fiindamental limitation because it is feasible to construct a non-expanded , long-range, perturbation theory which does not use the multipole expansion [6], A more profound reason for the failure is that the polarization approximation of zero overlap is no longer valid at short range. 

Note that Eq. (3.8b) corresponds to a long-range perturbative estimate, whereas Eq. (3.1 Id) pertains directly to the final MO form, so the latter gives a somewhat more accurate estimate of the actual hybridization. 

The electrostatic energy is the first-order term in long-range perturbation theory and is usually the interaction that persists over the longest range. The Coulombic interaction between the undistorted molecular charge distributions... 

A fluid where only long ranging perturbative parts of the pair interaction occur does not... 

Fig. 50. Magnetization profiles across thin Ising films [eq. (1) with H — H — 0], upper part, and near the surface of semi-infinite Heisenberg ferromagnels, lower part (where bulk behavior in the Monte Carlo simulation is enforced by an effective field boundary condition at z — 16). Note that in the Ising case (where three film thicknesses L = 5, 10, and 20 are shown) the surface layer magnetization m- — m(z — 0) is independent of L, and for L > 10 already the bulk value of the order parameter is reached in the center of the film. For the Heisenberg model, on the other hand, at a comparable temperature distance from % the free surface produces a Long-range perturbation of the local magnetization m(z). From Binder and Hohenbcrg (1974).

Long-range perturbation theory—first order... 

Long-range perturbation theory—second-order effects... 

Abstract Metal-carbonyl bonds, as found for carbon monoxide either liganded to metalloporphyrins or chemisorbed onto metal surfaces, are discussed. These two classes of systems are compared with emphasis on short range vs. long range perturbations of the vibrational bands, and Vcq. It is concluded that metalloporphyrins serve as models for terminal bondi on metal surfaces and that data obtained for carbonyl-hemes enable the isolation of non-local electronic effects, which are much discussed in connection with alkali promoters coadsorbed with CO on metal catalysts. 

In this Section, we highlight the unique physical properties of the adsorbed nanolayers and their long-range perturbations on the local structures and properties of supported polymer thin films. 

Are the Long Range Perturbations Modified in the Presence of a Solvent ... 

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