Classical induction energy

We reobtain the classical induction energy (1.5). The permanent dipole p at particle 1 polarizes particle 2, the induced field lowers the energy of dipole pi, and vice versa. 

Attempts to calculate of the classical induction energy of an assembly of molecules described by permanent dipoles and possessing a point dipole polarizability have encountered some problems. If we describe the permanent... 

At first glance the induction energy is a very classical term, and conceptually a simple one. A multipole moment on A induces another multipole moment on B, and eventually they interact electrostatically. Different mechanisms behind induction interaction in a variety of molecular settings were elucidated and composed into an elegant theory [7]. 

It is easy to see that the first term corre nds with the classical polarization (or induction) energy of molecule B in the electric field of the electronic charge distribution plus the nuclei of A, the second term with the induction energy of molecule A in the field of q plus the nuclei of B, while the third term, the dispersion energy, has no classical equii ent. 

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...

The mass of this object can be any, null or positive, as no inductive energy is attributed to this pole, which is called a reference or a frame of reference. Classically, it is viewed as a mathematical system of coordinates with an origin chosen generally at the position of the moving body at time f=0. 

Electrization For naming D, the term electric induction is more respectful of the physical reality, but induced is classically related to the electromagnetic induction and refers to the inductive energy that can be confusing. We... 

In the presence of an external magnetic induction B this dipole Pm has a potential energy given by the laws of classical electromagnetism as... 

From this point of view it is of interest to examine the consequences of full ther-malization of the classical Drude oscillators on the properties of the system. This is particularly important given the fact that any classical fluctuations of the Drude oscillators are a priori unphysical according to the Bom-Oppenheimer approximation upon which electronic induction models are based. It has been shown [12] that under the influence of thermalized (hot) fluctuating Drude oscillators the corrected effective energy of the system, truncated to two-body interactions is... 

In addition to the static induction effects included in I/scf, the hot Drude oscillators give rise to a 1/r6, temperature-dependent, attractive term. This jkg Ta2/r6 term is the classical thermodynamic equivalent of the London quantum dispersive attraction IEa2/r6. It corresponds to a small perturbation to the London forces, because k T is at least two orders of magnitude smaller than the typical ionization energy IE. The smaller the temperature of the Drude motion, the closer the effective potential is to the SCF potential, making Eq. (9-57) independent of mo, the mass of the oscillators. 

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