Prediction of molecular polarizability

Many physicochemical properties of a molecnle are implicitly related to its three-dimensional strnctnre. RDF descriptors seem to be a valnable tool for prediction of properties that are hard to calcnlate. This section shows an example. 

Polarizability (i.e., static dielectric polarizability), a, is a measnre of the linear response of the electronic clond of a chemical species to a weak external electric field of strength E. For isotropic molecnles, the dipole moment, fi, is 

In the general case, polarizability is anisotropic it depends on the position of the molecnle with respect to the orientation of the external electric field. To consider the orientation, a is expressed by a fnnction — atom polarizability tensor — that defines the indnced dipole moment for each possible direction of the electric field. This atom polarizability tensor a describes the distortion in the nuclear arrangement in a molecnle (i.e., the tendency of polarization in three dimensions). The polarizability determined in an experiment is an average polarizability it is the sum of polarizabilities in three principal directions that are collinear with the external field [59], 

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.  

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