Electron cloud superposition

Paracyclophane also has a compact structure in solution, as is readily seen on comparing its partition coefficient with that of p-xylene for the system octanol/water 32>. Rigid superposition of the benzene rings leads to an intramolecular delocalization of the hydrophobic -electron clouds and hence to an increased affinity for the aqueous phase. Accordingly, the logarithm of the partition coefficient is found to be smaller than the value observed for p-xylene, and not twice as large, as would be expected for completely hydrophobic surfaces. 

The resonance between the covalent and ionic bond structures of a molecule produces, by the superposition of the electron clouds of the ionic bond and of the covalent bond, a transitional electron cloud. This is discussed below in terms of wave mechanics. The electron cloud of the bond, however, will of course be continuous and the splitting into component parts, which this method of treatment has incurred, is the direct result of the attempt to describe a complex chemical bond in terms of two simpler types of bonds which may be represented by classical structural symbols. 

The theory of Born and Mayer has been extended by the work of Landshoff using the methods of quantum mechanics. Taking sodium chloride as an example, Landshoff accepts the assumption that the lattice consists of Na+ and Cl ions and calculates the ionic interaction energy on the basis of the Heitler-London theory using the known distributions of electrons in the Na+ and Cl " ions. In addition to the correction terms of Bom and Mayer, additional interactions related to the superposition of the electron clouds, the attraction between electrons and nuclei and the mutual repulsion of electrons are incorporated. The values obtained by this more exact method, however, differ from the values given in Table CXLVII by only a few kcals, the value for sodium chloride being 183 kcals. 

On the weak end of noncovalent interactions, we find van der Waals forces (<5 kJ mol ) which arise from the interaction of an electron cloud polarized by adjacent nuclei. Van der Waals forces are a superposition of attractive dispersion interactions, which decrease with the distance r in a dependence, and exchange repulsion decreasing with... 

The wave function for an atom simultaneously depends on (describes) all the electrons in the atom. The Schrodinger equation is much more complicated for atoms with more than one electron than for a one-electron species such as a hydrogen atom, and an explicit solution to this equation is not possible even for helium, let alone for more complicated atoms. We must therefore rely on approximations to solutions of the many-electron Schrodinger equation. One of the most common and useful of these is the orbital approximation. In this approximation, the electron cloud of an atom is assumed to be the superposition of charge clouds, or orbitals, arising from the individual electrons these orbitals resemble the atomic orbitals of hydrogen (for which exact solutions are known), which we described in some detail in the previous section. Each electron is described by the same allowed combinations of quantum numbers (w, m(, and /,)... 

The repulsive part of the lattice energy is due to repulsion between the electron clouds of ions when they come too close to each other. The superposition of both types of energy leads to an equilibrium distance between the ions and to a network potential energy with respect to the energy of the system when all the ions are at an infinite distance from each other. For kinetic studies, it is convenient to take the potential energy of the lattice of an ideal solid as the origin of energies. 

In quantitative modeling of PESs the description of the molecular shape as a superposition of atomic components remains an attractive approach, but it is clear from the earlier discussion that it must be extended to accommodate two important factors. The atomic shape is not a rigid, but rather a soft, exponentially decaying electronic charge cloud. In addition, it should be anisotropic with the anisotropy depending not only on the atom itself, but also on its partner in the chemical bond. 

The Heitler-London method, although approximate, has the advantage that a physical picture of the nature of the chemical bond may easily be obtained. The bond is formed by two electrons, one from each atom with opposite spin and owing to the transfer of the electrons, two states arise, which on superposition yield a transitional cloud, which serves to bond the atoms together. Such a bond is termed the homopolar or covalent bond. This physical picture of the bond is clearly the basis of the electron pair bond of Lewis. 

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