Model systems polarizable

The static electric dipole polarizability a of the model system investigated is therefore... 

Model 1 This model assumes the separability as an approximation, which has been successfully used before [18, 24—26]. In this model, the polarizability of a system X in the solution, asin(X), is obtained from the polarizability of the solute + n solvent, oc(X + nsolv), minus the polarizability of the solvent without the solute,... 

One possibility is weighting the partitioning with the original polarizabilities [108]. This may work better in the general case, but it is just as arbitrary. What will happen to local (anisotropic) polarizabilities in the condensed phases is hard to estimate without calculations. Some typical model systems can be found in Ref. [24], It is also demonstrated by the work of Augspurger and Dykstra [109] on acetylene clusters where for linear complexes an increase of the axial components of the linear and second hyperpolarizabilities are found, while van Duijnen et al. [110] for parallel clusters of butadienes and Kirtman et al. [Ill] for hexatrienes obtained a decrease in the same properties. These authors also show that well-constructed fully classical electrostatic models are able to reproduce these results. 

The behavior of the polarizability of the n-alkanes may be rationalized with reference to the simple particle-in-a-box model. In this model, the polarizability increases as the fourth power in the length of the box, which implies that the polarizability per unit length (i.e., the differential polarizability) increases as the third power in the length of the box. Obviously, in the n-alkanes, the electrons do not at all behave according to this simple model, but we may still attribute the increasing differential polarizability of the n-alkanes to a more pronounced delocalization of the electrons in the longer chains, as the electrons become more loosely attached to the system. As the chain grows, this effect becomes less important and the differential polarizability becomes constant. 

One important difference between the shell model and polarizable point dipole models is in the former s ability to treat so-called mechanical polarization effects. In this context, mechanical polarization refers to any polarization of the electrostatic charges or dipoles that result from causes other than the electric field of neighboring atoms. In particular, mechanical interactions such as steric overlap with nearby molecules can induce polarization in the shell model, as further described below. These mechanical polarization effects are physically realistic and are quite important in some condensed-phase systems. 

Qualitative trends for /3 in simple model systems two-centre model system one-dimensional NLO-phores 143 Three-centre model system (C2 and symmetry) 145 Local field factors and effective polarizabilities the reaction field model... 

These equations are used in semiempirical quantum chemical calculations of non-linear optical polarizabilities by applying perturbation theoretical expressions [the so-called sum-over-states (SOS) method]. Here we use them to derive some qualitative and very general trends in a few simple model systems. To this end we concentrate on the electronic structure, i.e. on the LCAO coefficients. We do not explicitly calculate the transition frequencies. This is justified for the qualitative discussion below since typical transition energies... 

Colloid scientists are more Interested In double layers on dispersed materials than on mercury, the classical model system of electrochemists. However, the comparison between those, l.e. between relaxed and polarizable double layers, is of great Interest, and therefore a discussion of the mercuiy-solutlon Interface will be included. Non-aqueous systems will be deferred to sec. 3.11. 

The formation of 2D Meads phases on a foreign substrate, S, in the underpotential range can be well described considering the substrate-electrolyte interface as an ideally polarizable electrode as shown in Section 8.2. In this case, only sorption processes of electrolyte constituents, but no Faradaic redox reactions or Me-S alloy formation processes are allowed to occur, The electrochemical double layer at the interface can be thermodynamically considered as a separate interphase [3.54, 3.212, 3.213]. This interphase comprises regions of the substrate and of the electrolyte with gradients of intensive system parameters such as chemical potentials of ions and electrons, electric potentials, etc., and contains all adsorbates and all surface energy. Furthermore, it is assumed that the chemical potential //Meads is a definite function of the Meads surface concentration, F, and the electrode potential, E, at constant temperature and pressure Meads (7", ). Such a model system can only be... 

The correlation, vibrational and relativistic effects to L NLO properties have been studied by selecting as model systems the Group Ilb sulfides ZnS, CdS and HgS [15]. These weakly bound systems are expected to have quite large vibrational (hyper) polarizabilities. To the best of our knowledge this was the first study which included the computation of all three contributions to the (hyper) polarizabilities. 

Table 5.21 Dipole moment p, average polarizability a and average first hyperpolarizability p for several model systems the 6-31 G basis...

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