Mean molecular polarizability

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. 

Table 7-1 lists some comparisons between experimental mean molecular polarizabilities and those estimated by Eq. (6). In this scheme, the estimation of mean molecular polarizability for acetic add needs five values, values for sp -C, for sp -C, for sp -O, for sp -O, and for a hydrogen atom. 

Table 7,1. Experimental mean molecular polarizabilities and values calculated by Eq. (6).

Until now, we have discussed the use of additivity schemes to estimate global properties of a molecule such as its mean molecular polarizability, its heat of formation, or its average binding energy to a protein receptor. 

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))... 

In many chemical applications, however, it would be more interesting to know how polarizability can stabilize a charge introduced into a molecule. Thus, rather than the global molecular property, mean molecular polarizability, a local, site-specific value for polarizability is needed. 

Mean molecular polarizability can be calculated through the Lorenz-Lorentz- Equation from refractive index, n, molecular weight, MW, and density, d, of a compound, demonstrating that the parameters can be derived from these elementary molecular properties (Figure 3). 

The diamagnetic susceptibility of carbonyl dibromide has never been measured. It has been estimated, however, from the computed value of the mean molecular polarizability (89.24 X 10"25 cm3) the mass diamagnetic susceptibility, Xm> estimated as... 

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... 

The next example illustrates the different representation of normal and wavelet-transformed RDF descriptors. The first 50 training compounds were selected from a set of 100 benzene derivatives. The remaining 50 compounds were used for the test set. Compounds were encoded as low-pass filtered D20 Cartesian RDF descriptors, each of a length of 64 components, and were divided linearly into eight classes of mean molecular polarizability between 10 and 26 AT... 

Since the mean molecular polarizability is a property that is related to the distance information in a molecule — as is the stabilization of a charge due to polarizability — it is reasonable that RDF descriptors correlate with this property. 

Mean Molecular Polarizability quantifies the ease with which an entire molecule undergoes distortion in a weak external field. 

Mean molecular polarizabilities and anisotropies may be obtained from measurements of dielectric polarization, refractive indexes, Kerr con-... 

Here Pe is the electric dipole induced by the electric field in a molecule having mean molecular polarizability y. Then we used the Lorentz approximation for the local field acting on a molecule and found corresponding field induced polarization. From that we have obtained the electric susceptibility of the dielectric (Eq. 7.18) ... 

An electrostatic interaction model has been presented for the calculation of the static electronic polarizability of hydrocarbons, which, contrary to previous models, can describe aliphatic, olefinic, and aromatic systems. It is based on the representation of the C and H atoms by induced electric charges and dipoles, where the actual values of the charges and dipoles are those that minimize the electrochemical energy of the molecule. The electrostatic interactions are described in terms of normalized propagators, which improves both the consistency and the numerical stability of the technique. The calibration of the model is sought by reproducing the molecular polarizabilities obtained by current density functional theory for a set of 48 reference structures. An excellent agreement with the reference data has been obtained as evidenced by the relative errors on the mean molecular polarizabilities of 0.5, 1.4, and 1.9% for alkanes, alkenes, and aromatic molecules, respectively. 

Molecular and bond polarizabilities are estimated from Raman intensities and force constants. The Wolkenstein bond polarizability is tested using relative Raman intensities of M(CH3)4 (M = 0, Si, Ge, Sn, Pb) [17] see also [26]. The mean molecular polarizability was calculated to be 15.9 x 10 [38], 17.626 x 10 " cm [28]. For calculation of mean molecular polarizability derivatives using a delta-function potential model, see [26]. 

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