The external localization methods

Now let us consider some practical methods of localization. There are two categories of these internal and external. In the external localization methods we plan where the future MOs will be localized, and the localization procedure only slightly alters our plans. This is in contrast with the internal methods where certain general conditions are imposed that induce automatically localization of the orbitals. 

This is an amazing method, in which we first construct some arbitraiy (but linearly independent ) orbitals xi of the bonds, lone pairs, and the inner shells, the total number of these being equal to the number of the occupied MOs. Now let us project them on the space of the occupied HF molecular orbitals pj using the projection operator P  

Meunier, B. Levy, G. Berthier, Theoret. Chim. Acta 29 (1973) 49. 

Electronic Motion in the Mean Field Atoms and Molecules 

The new orbitals (pj, as linearly independent combinations of the occupied canonical orbitals (pj, span the space of the canonical occupied HF orbitals (pj). They are in general non-orthogonal, but we may apply the Lowdin orthogonalization procedure (symmetric orthogonalization, see Appendbt J, p. 977). 

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The External Localization Methods The Internal Localization Methods Examples of Eocalization... 

When a non-centrosymmetric solvent is used, there is still hyper-Rayleigh scattering at zero solute concentration. The intercept is then determined by the number density of the pure solvent and the hyperpolarizability of the solvent. This provides a means of internal calibration, without the need for local field correction factors at optical frequencies. No dc field correction factors are necessary, since in HRS, unlike in EFISHG, no dc field is applied. By comparing intercept and slope, a hyperpolarizability value can be deduced for the solute from the one for the solvent. This is referred to as the internal reference method. Alternatively, or when the solvent is centrosymmetric, slopes can be compared directly. One slope is then for a reference molecule with an accurately known hyperpolarizability the other slope is for the unknown, with the hyperpolarizability to be determined. This is referred to as the external reference method. If the same solvent is used, then no field correction factor is necessary. When another solvent needs to be used, the different refractive index calls for a local field correction factor at optical frequencies. The usual Lorentz correction factors can be used. 

An external localization method was proposed by Magnasco and Perico [20,21]. The localization criterion equals the maximization of the atomic population, obtained by using the Mulliken population analysis. The number of localized orbitals as well as their association to a given atom should be defined in advance. 

However, another study concluded that the changes of the hydrogen-bond stability may be important in biological processes. For these, the influence of local electric fields created by Li+, Na+, and Mg2+ ions on the properties and reactivity of hydrogen bonds in HF and HC1 dimer has been carried out by means of ab initio self-consistent field (SCF) method [33]. A few years later, the effect of intensity and vector direction of the external electric field on activation barriers of unimole-cular reactions were studied using the semiempirical MINDO/3 method [34]. However, both semiempirical and ab initio calculations were performed to study the multiplicity change for carbene-like systems in external electric fields of different configurations (carbene and silylene) and the factor that determines the multiplicity and hence the reactivity of carbene-like structures is the nonuniformity of the field [35]. 

In conclusion, the method of intramolecular excimer formation is rapid and convenient, but the above discussion has shown that great care is needed for a reliable interpretation of the experimental results. In some cases it has been demonstrated that the results in terms of equivalent microviscosity are consistent with those obtained by the fluorescence polarization method (described in Section 8.5), but this is not a general rule. Nevertheless, the relative changes in fluidity and local dynamics upon an external perturbation are less dependent on the probe, and useful applications to the study of temperature or pressure effects have been reported. 

Attempts have been made to identify primitive motions from measurements of mechanical and dielectric relaxation (89) and to model the short time end of the relaxation spectrum (90). Methods have been developed recently for calculating the complete dynamical behavior of chains with idealized local structure (91,92). An apparent internal chain viscosity has been observed at high frequencies in dilute polymer solutions which is proportional to solvent viscosity (93) and which presumably appears when the external driving frequency is comparable to the frequency of the primitive rotations (94,95). The beginnings of an analysis of dynamics in the rotational isomeric model have been made (96). However, no general solution applicable for all frequency ranges has been found for chains with realistic local structure. 

The principal method of introducing metal impurities into early pinch discharges was considered to be arcing. The externally applied voltages, although low, still permit the occurrence of unipolar arcing between the plasma and the wall when driven by the sheath potential. Local electron emission from a cathode spot is balanced by a uniform flow back to the surface of energetic electrons in the tail of the Maxwellian distribution. 

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