Polarization electrostatic induction energy

Consider the particle picture of a hydrogen atom, in which a static nuclear particle of charge +e is encircled by a revolving electron particle of charge —e at a distance R. When an external electric field s acts on such a system, the perturbation can be described by a net displacement Ax of the electron under the action of theelectric force of the field, Edispi = ee (Fig. 4.1). This process can be represented as the formation of a dipole induced by the field, whose dipole moment p, is assumed as a first approximation to be proportional to the intensity of the external field. The proportionality 

This simple model reveals that the polarizability has the dimensions of a volume, since 4ks° is a dimensionless term  

The energy involved in the polarization process is always stabilizing because the induced dipole always points in the stabilizing direction (Fig. 4.2), being a sort of compliance of the polarized medium to the polarizing field. The polarization energy 

The calculation of the electric field is quite straightforward if the electron charge distribution is given in the form of a discrete array of points of charge q. The electric potential at point P due to this charge distribution plus a number of nuclei of charge Zj is given by 

The electrostatic potential energy of a charge qp at point P is then given by (P) = qp I) (P). The corresponding electrostatic field at point P, ep (the x component) is [23] 

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The total stabilization energy of a cluster rarely exceeds 25 kcal mol , i.e., a small fraction of a strong covalent bond energy (ca. 100 kcal mol ). Its partitioning into electrostatic, induction, and dispersion terms differs from cluster to cluster. In some cases, one particular energy term is dominant. More typically, many attractive terms contribute to the overall stabilization of non-covalent clusters, as it often happens to hydrogen-bonded complexes. Nevertheless, the electrostatic interaction plays a dominant role, and in the case of polar subsystems. 

In Sec. V,3 we dealt with the adsorption of ions on metallic surfaces as the problem of the polarization of an ideally polarizable structure by the ion. Dielectrics have a more restricted polarizability, the polarization resulting in the shifting of the electrons in the atoms or in groups of atoms of the dielectric to which they belong or in the mutual shifting of ions as well (34)- Instead of Eq. (16), which holds for an adsorbent of ideal polarizability, we obtain for the adsorption energy contribution due to the electrostatic induction of a dielectric ... 

Note that a distinction is made between electrostatic and polarization energies. Thus the electrostatic term, Ue e, here refers to an interaction between monomer charge distributions as if they were infinitely separated (i.e., t/°le). A perturbative method is used to obtain polarization as a separate entity. The electrostatic and polarization contributions are expressed in terms of multipole expansions of the classical coulomb and induction energies. Electrostatic interactions are computed using a distributed multipole expansion up to and including octupoles at atom centers and bond midpoints. The polarization term is calculated from analytic dipole polarizability tensors for each localized molecular orbital (LMO) in the valence shell centered at the LMO charge centroid. These terms are derived from quantum calculations on the... 

Fig. 13.5. The essence of the electrostatic and of the induction interactions (a schematic visualization), (a) the electrostatic energy ( elst — 0 — represents the classical Coulombic interaction of the frozen charge distributions of molecule A and of molecule B. the same as those of the isolated molecules, (b) The iiKhiction energy consists of two contributions. The first one, - B). means a modification of the electrostatic energy allowing a polarization of the molecule B by the frozen (i.e., unperturbed) molecule A. (c) The second contribution to the induction energy, —> A), corresponds to the exchange of the...

This (non-expanded) induction energy arises from the distortion (polarization) of the electron charge cloud of one molecule by the molecular electrostatic potential of the other. 

Therefore the basis set dependence of the electrostatic energy is not large, if these basis sets are used. However, small basis sets without polarization functions (3-2IG and 6-31G) overestimate the electrostatic energy considerably [26]. In addition, these small basis sets underestimate the induction energy, as they underestimate the molecular polarizability, as shown in Table 2. 

DPT calculations are not suitable for evaluating the inter molecular interactions of aromatic molecules, as dispersion is the major source of the attraction in the interactions of aromatic molecules, with the exception of cation/TT interactions. DPT calculations using basis sets with polarization functions provide sufficiently accurate intermolecular interaction energies for the cation/TT interactions, as DPT calculations can reproduce electrostatic and induction energies sufficiently accurately. 

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