Dipole induction energy

There are other forces, principally electrical in nature, present in molecular arrays whose constituents possess a permanent dipole (H2O, NH3). The energy resulting from such dipole-dipole interaction is also called the orientation energy. A charged species can also induce a dipole (induction energy). 

The second term on the right-hand side of equation (1.3) is responsible for the non-addivity. Thus the dipole induction energy of an atom midway between two ions of charge q is zero (since the field vanishes at that point), although the induction energy of the atom with each of the ions separately is —j(xq R 4neQ), where a is the polarizability of the atom and 2R the separation of the ions. 

Interesting properties of the induced dipole polarizable model can be derived by simple mathematical manipulation. A particularly important one relates the minimum of the energy with converged values of the induced dipole. By combining Eqs. (9-9) and (9-10), the induction energy can be rewritten as... 

Inductive effects on dipole moments and the effects of intervening atoms on electrostatic interaction energies are represented by polarizability centers In conjunction with bond centered dipoles. Solvation energies are estimated by means of a continuum dlpole-quadrupole electrostatic model. Calculated energies of a number of conformations of meso and racemic 2,4-dichloropentane and the iso, syndio, and hetero forms of 2,4,6-triehloroheptane give satisfactory representations of isomer and conformer populations. Electrostatic effects are found to be quite important. 

Dipole-dipole interactions have been used to assess the conformational populations of 2-haloketones (Eliel et al., 1965). With respect to SS, however, there are few applications in which these and related effects are considered. It is interesting that dipole induction and London dispersion effects were used some thirty years ago to account for the high endo over exo preference in the Diels-Alder reaction (Wassermann, 1965). Although effects are small for any pair of atoms, there are many closely packed atoms in a Diels-Alder transition state. At a carbon-carbon distance of 2-0 a between the atoms to be bonded, the energy favoring endo addition is 2-7 for dipole induction and 3-4 kcal/mole for dispersion in the reaction of cyclopentadiene with p-benzoquinone (Wassermann, 1965). These nonbonding attractive energies cooperate with the secondary HMO effects discussed earlier to lead to an endo product. 

The average induction energy (called Debye energy) between a polar molecule with dipole moment // and a non-polar molecule with polarizability a is... 

Van der Waals interactions are noncovalent and nonelectrostatic forces that result from three separate phenomena permanent dipole-dipole (orientation) interactions, dipole-induced dipole (induction) interactions, and induced dipole-induced dipole (dispersion) interactions [46]. The dispersive interactions are universal, occurring between individual atoms and predominant in clay-water systems [23]. The dispersive van der Waals interactions between individual molecules were extended to macroscopic bodies by Hamaker [46]. Hamaker s work showed that the dispersive (or London) van der Waals forces were significant over larger separation distances for macroscopic bodies than they were for singled molecules. Through a pairwise summation of interacting molecules it can be shown that the potential energy of interaction between flat plates is [7, 23]... 

The physisorption of alkanes in zeolites is essentially due to van der Waals forces. The main contributions to the stabilization are the induction energy, roughly speaking the electrostatic interaction of the dipole moment induced by the electric field of zeolite with the framework charge distribution and the... 

The sum of ion-induced dipole and dipole-induced dipole energies are often referred to as induction energy. 

In several cases, the polarizability distribution can be found by chemical intuition. For instance, in the case of naphthalene, which is made up of two identical fragments, the polarizability can be decomposed into two equivalent parts. Also, group or atom contributions can be deduced from a variety of schemes such as Stone s approach [74], the theory of atoms in molecules [75], the localization of molecular orbitals into chemical functions [76], atom/ bond additivity [77], the use of the acceleration gauge for the electric dipole operator [78], quantum mechanically determined induction energies [79], or calculated molecular quadrupole polarizabilities and their derivatives with respect to molecular deformations [80]. Several of these models consider charge... 

Quadrupole induction pair potential energy is less than dipole induction pair potential energy. 

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... 

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