Mean polarizability method

We will start the discussion of the problem of surface excitons in disordered media considering macroscopic states. It is necessary to know the dielectric constant tensor to determine these states.We will use here the mean polarizability method, which we discussed in Chapter5 and which we apply for a cubic molecular crystal whose molecules differ only in the isotopic composition of the nuclei. 

As an example of an application of the mean field method we shall consider the theory of the dielectric anisotropy of the nematic phase. The low frequency dielectric anisotropy of a molecule is determined by two factors (i) the polarizability anisotropy which for the elongated molecules of nematogenic compounds always makes a positive contribution (i.e., a... 

Wu et al. calculated the interaction-induced electric properties of the FH-NH3 hydrogen-bonded complex. The authors relied on second-order Moller-Plesset perturbation theory with large standard basis sets. Their best values were obtained with a aug-cc-pVTZ basis augmented with bond-centered functions. The results were suitable corrected for basis set superposition errors (BSSE) with the counterpoise (CP) method. The reported values are p = 0.4762 for the dipole moment, amt= 0.8057 e ao Eh for the mean polarizability and = 3.31 e ao Eh for the mean first hyperpolarizability. It is worth noticing that without the BSSE corrections the values for the above properties are p = 0.4757 for the dipole moment, aj ,= 0.7235 e ao Eh for the mean polarizability and ) ( = 3.66... 

Method performance on the computation of the mean poiarizabilities of Ga Asm clusters with m + n = 6 in comparison with the performance on the computation of the mean polarizabilities of Gae and Ase clusters... 

In Fig. 17 we show the histogram of interaction-induced mean polarizability for all methods. With the notable exception of the BHandHLYP method the interaction property aint(H20)2 is negative for all ab initio methods and positive for the DFT... 

We have investigated and closely analyzed the predictive capability of DPT methods in the calculation of electric polarizabilities and hyperpolarizabilities for three difficult cases the sodium tetramer, the new compound HXel, and the interaction (hyper)polarizability of the two moieties in the weakly bonded water dimer. In the first two cases we have shown that the ab initio and DPT methods offer a quite different picture of the electric polarizability and hyperpolarizability. In the case of (H20)2 we are led to two drastically divergent pictures as the two classes of methods clearly differ even in the sign of the interaction-induced mean polarizability and h3q)erpolarizability. 

The next step towards increasing the accuracy in estimating molecular properties is to use different contributions for atoms in different hybridi2ation states. This simple extension is sufficient to reproduce mean molecular polarizabilities to within 1-3 % of the experimental value. The estimation of mean molecular polarizabilities from atomic refractions has a long history, dating back to around 1911 [7], Miller and Sav-chik were the first to propose a method that considered atom hybridization in which each atom is characterized by its state of atomic hybridization [8]. They derived a formula for calculating these contributions on the basis of a theoretical interpretation of variational perturbation results and on the basis of molecular orbital theory. 

In Section 7.1.2 a method for the calculation of mean molecular polarizability was presented. Mean molecular polarizability can be calculated from additive contributions of the atoms in their various hybridization states in a molecule (see Eq. (6)). Mean molecular polarizability, a, expresses the magnitude of the dipole moment, fi, induced into a molecule imder the influence of an external field, E (Eq. (15))... 

While Onsager s formula has been widely used, there have also been numerous efforts to improve and generalize it. An obvious matter for concern is the cavity. The results are very sensitive to its size, since Eqs. (33) and (35) contain the radius raised to the third power. Within the spherical approximation, the radius can be obtained from the molar volume, as determined by some empirical means, for example from the density, the molar refraction, polarizability, gas viscosity, etc.90 However the volumes obtained by such methods can differ considerably. The shape of the cavity is also an important issue. Ideally, it should be that of the molecule, and the latter should completely fill the cavity. Even if the second condition is not satisfied, as by a point dipole, at least the shape of the cavity should be more realistic most molecules are not well represented by spheres. There was accordingly, already some time ago, considerable interest in progressing to more suitable cavities, such as spheroids91 92 and ellipsoids,93 using appropriate coordinate systems. Such shapes... 

The infinite sum may be avoided by means of the closure method 2 I >< Pm = 1. An average energy is chosen for all the excited states, which enables the polarizability to be written in terms of a constant denominator and matrix elements for the ground-state wavefunction only. This is only a rough approximation which, though widely applied in approximate calculations, is of little use for more than an order of magnitude estimate of a. 

---