Repulsion of electrons

The physical meaning of our final equation is best seen on eqn 39. The term containing w is essentially the self-energy correction introduced by Mulliken in his analysis of electronegativities to account for the average repulsion of electrons occupying the same orbital. In order to get an idea of the orders of magnitude, let us apply eqn 39 to a model computation of FeCO, made to compare the ClPSl results of Berthier et al. [11] with those of a simple orbital scheme. Consider one of the two x systems of FeCO, treated under the assumption of full localization (and therefore strict cr — x separation)... 

A molecule is composed of positively charged nuclei surrounded by electrons. The stability of a molecule is due to a balance among the mutual repulsions of nuclear pairs, attractions of nuclear-electron pairs, and repulsions of electron pairs as modified by the interactions of their spins. Both the nuclei and the electrons are in constant motion relative to the center of mass of the molecule. However, the nuclear masses are much greater than the electronic mass and, as a result, the nuclei move much more slowly than the electrons. Thus, the basic molecular structure is a stable framework of nuclei undergoing rotational and vibrational motions surrounded by a cloud of electrons described by the electronic probability density. 

The above treatment considers the ligands in an octahedral geometry (i.e. with the ligands placed at the centre of the faces of the cube). The square planar case is simply an extension of the octahedral where two ligands are removed from the z-axis. The repulsion of electrons in d.i and dx2 2 orbitals will not be the same and the result is a square planar shape. 

The perfectly octahedral species conform to the expectations based on the simple MO derivation given above. The nonoctahedral fluoride species do not, but this difficulty is a result of the oversimplifications in the method. There is no inherent necessity for delocalized MOs to be restricted to octahedral symmetry. Furthermore, it is possible to transform delocalized molecular orbitals into localized molecular orbitals. Although the VSEPR theory is often couched in valence bond terms, it depends basically on the repulsion of electrons of like spins, and if these are in localized orbitals the results should be comparable. 

U0 is called the lattice energy of the crystal JV is Avogadro s number, used to convert energy per ion pair to energy per mole, and a is the correction factor introduced above to account for the repulsion of electron clouds. The lattice energy, t/o, then corresponds to the energy released when the requisite number of positive ions and of negative ions are condensed into an ionic crystal to form one mole of the compound. 

Electrostatic Model. A simple model that can account for the observed bond angles in a qualitative way comes from a consideration of electrostatic repulsions of electron pairs. Let us consider electron pairs around an atom as concentrations of charge placed on a more or less spherical surface, and let us assume that the electrons can move in pairs. Barring other forces, the most likely arrangement will be the one where the electron pairs exert the minimum repulsion on each other. This will be achieved when the electrons get as far away from each other as possible. Since the electrons are restricted by our assumption to a sphere, the maximum distance of separation corresponds to a maximum angle between their positions and the center of the sphere. 

The integrals describing the Coulomb repulsion of electrons in two HOs centered at the same atom appear only in the form of the reduced repulsion integrals for pairs of... 

If the rate of deposition of ions is initially greater than their rate of passage from metal into solution, the metal becomes positively charged, a double layer being formed by attraction of anions to the surface on the water side and a repulsion of electrons from the surface on the metal side. 

With R > RC the Coulomb repulsion of the electrons when they are on the same ion is the dominant electron-interaction term, so that the lowest states correspond to an exact number of electrons on each ion rather than to running waves. Although the mutual repulsion of electrons on the same ion prevents the permanent occupation of... 

The rotational barrier is now slightly higher than for ethane 14 kJ mol-1 as compared to 12 kJ mol-1. This again reflects the greater repulsion of electrons in the coplanar bonds in the eclipsed conformation rather than any steric interactions. The energy graph for bond rotation in propane would look exactly the same as that for ethane except that the barrier is now 14 kJ 1110I-1. 

All molecules exert a weak attraction upon one another. This attraction, the electronic van der Waals attraction, is the result of the mutual interaction of the electrons and nuclei of the molecules it has its origin in the electrostatic attraction of the nuclei of one molecule for the electrons of another, which is largely but not completely compensated by the repulsion of electrons by electrons and nuclei by nuclei. The van der Waals attraction is significant only when the molecules are very close together—almost in contact with one another. For monatomic molecules, such as those of a noble gas, the force of attraction is inversely proportional to the seventh power of the distance between the centers of the molecules, and hence is less than I percent as great wlien the molecules are 10 A apart as when they are 5 A apart. At small distances (about 4 A for argon, for example) the force of attraction is balanced by a force of repulsion due to interpenetration of the outer electron shells of the molecules (Fig. 15-3). 

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. 

Coulomb attraction of nuclei (depends on Rf ) J = Coulomb repulsion of electrons and Exc = XC functional. 

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