Induction energies

The induction energy is the energy resulting from the distortion of one molecule by the mean electric field due to the other molecules. Like the electrostatic energy, it is absent in the case of a pair of inert-gas atoms. The main contribution to the induction energy is due to the electric dipole induced in the I th molecule by the field resulting from the charge distribution of the other 

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. 

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If the long-range mteraction between a pair of molecules is treated by quantum mechanical perturbation theory, then the electrostatic interactions considered in section Al.5.2.3 arise in first order, whereas induction and dispersion effects appear in second order. The multipole expansion of the induction energy in its fill generality [7, 28] is quite complex. Here we consider only explicit expressions for individual temis in the... 

The induction energy is inlierently non-additive. In fact, the non-additivity is displayed elegantly in a distributed polarizability approach [28]. Non-additive induction energies have been found to stabilize what appear to be highly improbable crystal structures of the alkalme earth halides [57]. 

A charge transfer contribution is often identified in perturbative descriptions of intennolecular forces. This, however, is not a new effect but a part of the short-range induction energy. It is possible to separate the charge transfer part from the rest of the induction energy [80]. It turns out to be relatively small and often negligible. Stone [28] has explained clearly how charge transfer has often been a source of confusion and error. 

Knowles P J and Meath W J 1986 Non-expanded dispersion and induction energies, and damping functions, for molecular interactions with application to HP.. . He Mol. Phys. 59 965... 

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... 

For the case of a polar molecule interacting with a nonpolar molecule, an induction energy term should be considered see Section 13.5 of [178]. This additional interaction modifies the interaction parameters as... 

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

Note that the induction energy, unlike the electrostatic energy, is not temperature dependent although both vary as r 6. 

For two interacting polar molecules, the induction energy averaged over all orientations is... 

Equation (32) represents the first-order electrostatic energy, whereas equations (33), (34) represent the second-order contributions for the induction and dispersion energies, respectively Ers = closed-shell neutral atoms, then the electrostatic and induction energies vanish for large values of r, and the dispersion energy is the first nonzero term of the interaction energy. 

Similarly, for spherically symmetric interactions, the asymptotic forms of the induction energy and the dispersion energy are... 

The antisymmetrizing operator also affects the form of the electrostatic, induction, and dispersion energies. For example, in the case of neutral, spherically symmetric systems, the electrostatic and induction energies (which vanish in the limit of negligible orbital overlap) display a dependence on r similar to the first-order exchange energy,67... 

For ion-atom interactions, and possibly for other interactions in which the induction energy plays an important role, it is also justified to study the latter separately from the remaining extended-Hartree-Fock energy. In relation to this, we note that by combining equations (40), (43) one obtains... 

The induction energy, E, is obtained when the reduced resolvent R0, Eq. (1-24), is restricted to terms where one of the monomers is in the ground state and the other in the excited state. The corresponding expression is given by... 

It follows directly from the Eq. (1-85) that the expression for the induction energy can be rewritten as,... 

The exchange-induction energy is an energetic effect resulting from the antisym-metrization of the induction wave function,... 

The second-order dispersion energy is defined as the difference between the second-order polarization and induction energies, E = E j — E J. One can also use the following direct definition... 

Similarly as in the case of the induction energy, Eq. (1-92), can be rewritten in terms of the dynamic susceptibilities of the isolated monomers ... 

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