Cluster dipole moment

Atomic-level response of sodium clusters to external electric field has also been studied recently [55] using a decomposition of the total cluster dipole moment and polarizability into contributions from atomic volumes. The atomic dipole moments and polarizabilities thus obtained have also been partitioned into the atomic dipole and charge-transfer components. The relative contribution of these two components as a function of the size and shape of the clusters have been studied. Also the contributions are shown to depend on the location of the atomic site in the cluster. Thus, the surface atoms have been shown to have larger contribution to the polarizability than the interior ones. The anisotropy of the total polarizabilities is also shown to correlate with the shape anisotropy of the clusters. These ab initio results on the atomic charge and dipole components that contribute to the overall cluster polarizability thus would enable one to validate the coarse-grained DFT-based results in a more detailed fashion since the coarse-grained approaches provide the atomic charges and atomic dipoles besides the overall polarizability. 

The SPC/E model approximates many-body effects m liquid water and corresponds to a molecular dipole moment of 2.35 Debye (D) compared to the actual dipole moment of 1.85 D for an isolated water molecule. The model reproduces the diflfiision coefficient and themiodynamics properties at ambient temperatures to within a few per cent, and the critical parameters (see below) are predicted to within 15%. The same model potential has been extended to include the interactions between ions and water by fitting the parameters to the hydration energies of small ion-water clusters. The parameters for the ion-water and water-water interactions in the SPC/E model are given in table A2.3.2. 

Good agreement between C(- and the dipole moment of the solvent (H20) molecules (i.e., by the hydrophilicity of metals) established by Trasatti25,31 was found and the reasons for this phenomenon were explained 428 The Valette and Hamelin data150 251 387-391 are in agreement with the data from quantum-chemical calculations of water adsorption at metal clusters 436-439 where for fee metals it was found that the electrode-H20 interaction increases as the interfacial density of atoms decreases. 

Figure 12-5 illustrates the solvation of Na and Cl" ions as NaCl dissolves in water. A cluster of water molecules surrounds each ion in solution. Notice how the water molecules are oriented so that their dipole moments align with charges of the ions. The partially negative oxygen atoms of water molecules point toward Na cations, whereas the partially positive hydrogen atoms of water molecules point toward Cl" anions. 

The exp-6 model is not well suited to molecules with large dipole moments. To account for this, Ree9 used a temperature-dependent well depth e(T) in the exp-6 potential to model polar fluids and fluid phase separations. Fried and Howard have developed an effective cluster model for HF.33 The effective cluster model is valid for temperatures lower than the variable well-depth model, but it employs two more adjustable parameters than does the latter. Jones et al.34 have applied thermodynamic perturbation theory to... 

According to the Kirkwood theory of polar dielectrics, simple relations (23) between molecular dipole moment vectors and the mean-square total dipole moment of water clusters can be used to compute the static dielectric constant of water. As the normalized mean-square total dipole moment increases towards unity, theory predicts decreases in the static dielectric constant. Since MD results indicate that the mean-square total dipole moment of interfacial water is greater than that for bulk water (48), the static dielectric... 

D l is the cluster binding energy, AD is the relative energy between the most stable and less stable structures of both and [Ei -P,s] clusters /j. is the dipole moment of the complex is the... 

The dipole moment of the adsorbed water molecules is estimated to be = 0.22 D (unit of D = 3.36 x 10 ° C m) from the slope of the observed curves shown in Fig. 5-25. Since this dipole moment is nearly one tenth of the dipole moment of gaseous water molecules (m = 1.84 D), the dipole of the adsorbed water molecules on the silver surface is suggested to be aligned almost parallel to the metal surface by forming hydrogen-bonded two-dimensional clusters of water molecules. On the other hand, bromine molecules are in the state of dissociative adsorption on the silver surface, producing adsorbed bromine atoms which receive electrons... 

Figure 2. Comparison of the 2-RDM, coupled-cluster, MRPT2, and FCI potential energy surfaces of CO in a valence double-zeta basis set, where all valence electrons are correlated (a) without an electric field and (b) with an electric field of strength 0.10 an apphed in the direction of the permanent dipole moment. The 2-RDM and MRPT2 methods accurately describe the features of the FCI potential energy surface.

Not surprisingly, formalisms with very diffuse density functions tend to yield large electrostatic moments. This appears, in particular, to be true for the Hirshfeld formalism, in which each cos 1 term in the expansion (3.48) includes diffuse spherical harmonic functions with / = n, n — 2, n — 4,... (0, 1) with the radial factor rn. For instance when the refinement includes cos4 terms, monopoles and quadrupoles with radial functions containing a factor r4 are present. For pyridin-ium dicyanomethylide (Fig. 7.3), the dipole moment obtained with the coefficients from the Hirshfeld-type refinement is 62.7-10" 30 Cm (18.8 D), whereas the dipole moments from the spherical harmonic refinement, from integration in direct space, and the solution value (in dioxane), all cluster around 31 10 30 Cm (9.4 D) (Baert et al. 1982). 

Classical relaxors [22,23] are perovskite soUd solutions like PbMgi/3Nb2/303 (PMN), which exhibit both site and charge disorder resulting in random fields in addition to random bonds. In contrast to dipolar glasses where the elementary dipole moments exist on the atomic scale, the relaxor state is characterized by the presence of polar clusters of nanometric size. The dynamical properties of relaxor ferroelectrics are determined by the presence of these polar nanoclusters [24]. PMN remains cubic to the lowest temperatures measured. One expects that the disorder -type dynamics found in the cubic phase of BaTiOs, characterized by two timescales, is somehow translated into the... 

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