Back-polarization

This is not an SCRF model, as the dipole moment and stabilization are not calculated in a self-consistent way. When the back-polarization of the medium is taken into account, the dipole moment changes, depending on how polarizable the molecule is. Taking only the first-order effect into account, the stabilization becomes (a is the molecular polarizability, the first-order change in the dipole moment with respect to an electric field, Section 10.1.1). 

In the quantum mechanical continuum model, the solute is embedded in a cavity while the solvent, treated as a continuous medium having the same dielectric constant as the bulk liquid, is incorporated in the solute Hamiltonian as a perturbation. In this reaction field approach, which has its origin in Onsager s work, the bulk medium is polarized by the solute molecules and subsequently back-polarizes the solute, etc. The continuum approach has been criticized for its neglect of the molecular structure of the solvent. Also, the higher-order moments of the charge distribution, which in general are not included in the calculations, may have important effects on the results. Another important limitation of the early implementations of this method was the lack of a realistic representation of the cavity form and size in relation to the shape of the solute. 

Phenylisatogen (108d) reacts with the dipolarophiles 121 regio-specifically to give isoxazolidines 122.73 The orientation of the cycloadducts is unexpected and provides an example of electron donation from oxygen, back polarization, directing the course of a... 

Qualitatively, Eq. (4-32) predicts that the more dipolar isomer will be preferentially stabilized in more polar media. Quantitatively, the expression significantly overestimates the solvent effects obtained experimentally for conformational equilibria [182], Further modifications are necessary, e.g. adjustment for back-polarization of the solute by its own reaction field, inclusion of the effect of the solute s quadrupole moment on the reaction field [197], etc. Specific solute-solvent interactions, such as those with HBD solvents, cannot be treated with this reaction field theory. For a more detailed discussion, see references [83, 182]. 

Some of the types of contributing elements combined in Eq. (1) can give rise to potential pieces that are not additive. These would involve products of property or parameter values for more than two molecules, and these are often referred to as cooperative or nonpairwise additive elements. A simple illustration is in the electrical interaction contributions. While the interaction of permanent moments is pairwise additive, involving products of moments of only two different molecules at a time, the polarization energy can have a cooperative part. For some cluster of the molecules A, B, and C, the dipole polarization energy of A will be the polarizability of A, Ka, multiplied by the square of the field experienced at A, F. That field is a sum of contributions from B and C ( F = Fb + Fc) proportional to their multipoles, and its square has a cross term, FbFc, involving a multipole of B times a multipole of C. The net interaction element includes Ka FbFc. thereby giving an overall A B C or three-body term. Mutual or back polarization can be shown to produce contributions up to A-body for a system of N species. 

When evaluated, the summation in Eq. (11) is a rank-one polytensor that represents the potential experienced at molecule A in terms of field components, field gradient components, and so on. This can be used with response properties such as shielding polarizabilities to find property changes dues to electrical influence. The evaluation is analogous to Eq. (11). The incorporation of mutual or back polarization/hyperpolarization requires a self-consistent solution for the induced moments, and this can be done iteratively [170] or if there are no hyperpolarizabilities, it can be done by matrix inversion. 

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