London electrostatic interaction energy

Except at absolute zero, every molecule must have one or more sources of electrostatic potential. Even if a molecule bears no net electrostatic charge, atomic dipoles which result from the motion of electrons in their orbits around a nucleus will give rise to dispersive van der Waals or London interactions. These atomic dipoles insure that a solute molecule has a small but finite electrostatic interaction energy with the surrounding solution molecules. For example, in aqueous ethanol solutions, the dipole—dipole interaction between ethanol and water molecules becomes the primary interaction energy. Ethanol molecules are not ionic, so use of the Debye—Huckel equation (57), based on Coulombic interaction, carmotbe used to determine the activity coefficient of an aqueous ethanol solution. At sensible... 

The third component to the electrostatic interaction is caused by the motion of the electron cloud, which creates an oscillating field. It couples to the oscillating field of the neighboring molecules, which gives an attractive contribution to the total energy. This should be obvious, from the following example. Consider the frozen electron distribution of a nonpolar molecule (e.g., a noble gas). The instantaneous distribution possesses a dipole moment, which for the same reason as described above, induces a dipole in neighboring molecules, which in turn act on the first molecule, etc. This contribution is denoted the dispersion term or the London term [9]. Note that this contribution is only approximately pairwise additive. 

According to SAPT formulation of the first-order interaction energy, the Heitler-London term consists of electrostatic and exchange contributions (the former obtained from the perturbation theory formula) ... 

The contribution of the London energy to the lattice energy of the alkali halides is indeed small in comparison with the electrostatic interaction but the transition from NaCl- to CsCl type of lattice nevertheless depends on it. The geometrical condition, r+/r > 0.71, is not sufficient in fact KF with r+/r = 1.00 has the NaCl lattice (p. 32). 

In the theory developed by Derjaguin and Landau (24) and Verwey and Overbeek (25.) the stability of colloidal dispersions is treated in terms of the energy changes which take place when particles approach one another. The theory involves estimations of the energy of attraction (London-van der Walls forces) and the energy of repulsion (overlapping of electric double layers) in terms of inter-oarticle distance. But in addition to electrostatic interaction, steric repulsion has also to be considered. 

Dispersional Interaction between Molecules. We still wish to consider briefly energies due to interaction between fluctuating induced electric charge distributions of atoms and molecules. In constrast to electrostatic and induced interactions, these are present even when the molecules do not possess permanent electric moments. These dispersional interactions cannot be dealt with on a classical electrostatics level owing to their relation to London s quantum dispersion theory, they have been termed London dispersional interactions. 

Kirkwood31 has also considered, and treated by statistical mechanics, the orientation polarization but not the deformation effects in a polar liquid. He considers a sphere in vacuocontaining a set of nondeformable molecules characterized by an internal moment p (and not fi). The total potential energy U is divided in two parts Ulf due to London-Van der Waals and dipole forces, is practically independent of the field U2 is due to electrostatic interactions of the dipoles with the external field. In Kirkwood s model, one finds ... 

In addition to electrostatic, exchange, and induction (a.k.a. deformation) energy, the fourth principal contributor to the interaction energy is the so-called dispersion energy [39]. This quantity is closely related to the London forces that are well known from freshman chemistry texts that originate from instantaneous fluctuations of the electron density of one molecule, which cause a sympathetic series of instantaneous density fluctuations in its partner. Dispersion, by its very nature, is attractive. In terms of ab initio molecular orbital theory, the dispersion energy is not present at the SCF level, but is a byproduct of the inclusion of electron correlation into the calculation. The reader is hence alerted to the fact that calculations that do not include electron correlation (and there are many such, particularly in the early literature) cannot be expected to include this fourth, and sometimes very important, component of the noncovalent force. 

The zeroth-order wavefunction yields the first-order perturbation to the energy when combined with the operator V, which describes the interactions between electrons and nuclei on the two different molecules. This first-order correction, known as the Heitler-London interaction energy,may be thought of as consisting of two terms. The first is the classical Coulombic interaction between the charge clouds of the (undistorted) subunits, commonly known as the electrostatic energy, and computed as... 

---