Molecular polarizability prediction

Similarly, Wei et al. [18] made analogous predictions of C < 0 using hypernetted-chain theory and incorporating molecular polarizability. However, the discussion was again restricted to the plausibility of negative C under -control. 

A large number of dipole models have been developed in the past to predict the molecular polarizabilities [46,47], In these models, two atoms interact via Coulomb... 

In addition to the moments of the charge distribution, molecular polarizabilities have also seen a fair degree of study comparing DFT to conventional MO methods. While data on molecular polarizabilities are less widely available, the consensus appears to be that for this property DFT methods, pure or hybrid, fail to do as well as the MP2 level of theory, with conventional functionals typically showing errors only slightly smaller than those predicted by HF (usually about 1 a.u.), while the MP2 level has errors only 25 percent as large. In certain instances, ACM functionals have been more competitive with MP2, but still not quite as good. 

Molecular descriptors enable the correlation of 3D structures and some of their physiochemical properties. An example is the mean molecular polarizability — a property related to the distance information in a molecule, as is the stabilization of a charge due to polarizability. Molecular descriptors based on three-dimensional distances can correlate well with this property. In particular, transformed molecular descriptors enable predictions with reasonable error and are well suited for automatic interpretation systems. 

Let us have a look at the prediction of the mean molecular polarizability a , , by neural networks and RDF descriptors. can be calculated from additive contributions of the atomic static polarizability a of individual atoms i... 

FIGURE 6.16 Correlation between calculated and predicted molecular polarizability for 50 benzene derivatives encoded with one-stage filtered D2Q transformed Cartesian RDF (128 components). The standard deviation of the prediction error is 0.6 A. ... 

The topological map layer after training of a Kohonen network shows a reasonable clustering, a first hint that a reliable prediction can be achieved. Figure 6.16 displays the correlation between predicted and experimental values for molecular polarizability for the set of 50 test compounds. 

The importance of helical structures for enhancing the first hyperpolarizability has been discussed by Panda and Chandrasekhar 193 and SOS theory has been used by Moreau et a/.194 and Monshi et al 95 to investigate excited state polarizations with solvent effects. Torrens et al.196 have developed a scheme to predict molecular polarizabilities from the effect of interacting dipoles. 

The shape of the cavity has some effect on the molecular polarizabilities " - " however, the methods taking into account real molecular shapes are computationally expensive and are most appropriately utilized with accurate ab initio or density functional theory (DFT) approaches. " - " Even though spherical cavity is a crude approximation for most molecules, the predicted trends usually agree well with experiment and with the results of much more sophisticated and expensive methods. - ""... 

This formula is very important for the further discussion because it predicts the polarization catastrophe . For small molecular polarizability y, susceptibility x depends linearly on y. However, when y 3/Annv, the denominator of (13.2) tends to zero and diverges. 

The electric polarization from internal continuum (EPIC) model has been developed to accurately predict the polarizability tensor of molecules ". The EPIC approach uses an intramolecular effective dielectric constant, together with associated atomic radii, to represent the detailed molecular polarizability. For a single atom of radius R in vacuum under the influence of a uniform electric field (E), the polarizability is given by the electric fleld prefactor of the induced dipole moment (Sin is the inner dielectric) ... 

We saw in Chap. 6 that there are two main selection rules for direct excitation of a harmonic oscillator from level n to level m first, w = n 1, and second, the vibration must change the permanent dipole moment of the molecule. Arguments parallel to those we used to find the selection mles for IR absorption can be used to predict qualitatively whether or not a particular vibrational mode will contribute to off-resonance Raman scattering. The difference is that for Raman scattering we relate the scattering matrix element ai,a to the molecular polarizability (a) rather than the permanent dipole moment. If the polarizability is expanded in a Taylor s series as a function of the normal coordinate (x) for the mode, the matrix element for Raman scattering becomes... 

Monte-Carlo calculations provide us with an alternative route to the local properties in the bulk of a liquid which are closer to first principles than the above model although the molgcgle needs to be somewhat simplified. We performed several computations on model liquids in order to evaluate the electric field which a molecule undergoes from the liquid and to compare it with the values predicted by the model. The main result of this comparison is that, due to the error bars of the Monte-Carlo calculation, and to the uncertainties on the dielectric constant of the medium, the model reproduces the electric field fairly well, especially when the charge distribution reduces to a single moment. In turn, noticeable deviations appear between the model and the Monte-Carlo simulation when the charge distribution of the solute is represented by more than one dominant moment (e.g. a dipole and a quadrupole) and when the solvent is represented by point dipoles at the centre of non polarizable molecules. This is easily understandable if one bears in mind that the model replaces this medium by a continuum. Nevertheless these discrepancies are expected to be less important in the case of a real medi] m, due to the molecular polarizabilities which are nonlocal properties. ... 

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