Electrons mutual repulsion

To see how and under what conditions stability is enhanced or diminished, we need to consider the symmetry of the orbital (9-32), Flectrons in the antisymmetric orbital r r have a 7ero probability of occurring at the node in u where U] = rj. Electron mutual avoidance of the node due to spin correlation reduces the total energy of the system because it reduces electron repulsion energy due to charge... 

Regions of high electron concentration—bonds to atoms and lone pairs attached to a central atom in a molecule— arrange themselves in such a way as to minimize mutual repulsions. 

For sodium cations and chloride anions, q = + and q2 — - 1. To complete the calculation, we need to know how closely the ions approach each other before their mutual attraction is balanced by electron cloud repulsion. In the sodium chloride crystal this distance is 313 pm. Using this value for r, we can calculate the energy released in... 

The ligands must be located at the comers of an octahedron to minimize electron-electron repulsion between the electron pairs. To give the greatest stability, the two lone pairs must be as far apart as possible, because lone pairs take up more space than bonding pairs. Placing the lone pairs at opposite ends of one axis, 180° apart, minimizes their mutual repulsion. This leaves the four fluorine atoms in a square plane around xenon ... 

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. 

In order to apply the theory, one first draws a valence bond formula with the correct constitution, including all lone electron pairs. This formula shows how many valence electron pairs are to be considered at an atom. Every electron pair is taken as one unit (orbital). The electron pairs are being attracted by the corresponding atomic nucleus, but they exercise a mutual repulsion. A function proportional to 1 /rn can be used to approximate the... 

If the central atom can still take over electrons and if a ligand has lone electron pairs, then these tend to pass over to the central atom to some degree. In other words, the electron pairs of the ligand reduce their mutual repulsion by shifting partially towards the central atom. This applies especially for small ligand atoms like O and N, particularly when high formal charges have to be allocated to them. For this reason terminal O and N atoms tend to form multiple bonds with the central atom, for example ... 

Energy expenditure due to the mutual repulsion of the bonding electron pairs and due to the repulsion between ligands that approach each other too closely. 

To derive the values of the coefficients at, Ph y, and 8i so that the bond energy is maximized and the correct molecular structure results, the mutual interactions between the electrons have to be considered. This requires a great deal of computational expenditure. However, in a qualitative manner the interactions can be estimated rather well that is exactly what the valence shell electron-pair repulsion theory accomplishes. 

Since the degree of mutual repulsion decreases in the order, free valence electron pair > double-bonded oxygen > fluorine, the observed bond angles deviate somewhat from those expected for the ideal geometries. Typical examples are FCIO2 and FCIO3 (Fig. 1). 

If all values of Cy are known, the distribution of flux between the bonds can be calculated by solving eqns (2.7) and (2.11) since they contain only the parameters g, and Cy. Unfortunately, the values of Cy cannot be determined a priori, since they depend on a knowledge of the interatomic distances which are determined by the mutual repulsion of the ions and hence by the electron density distribution. This problem is taken up in Chapter 3 where it is shown that, for a large number of equilibrium structures, the values of Cy can all be set equal. As Cy is common to all the terms in (2.11), it can be cancelled, allowing eqns (2.7) and (2.11) to be solved. 

To be consistent, the same conclusion should be drawn for the dimethyl-oxime complexes. The difficulty here is to answer the question as to why other flat, uncharged, molecules do not stack in a similar fashion. It is believed that in fact they would do so were it not for factors such as mutual repulsion of u-electrons, as in condensed hydrocarbons (214). An examination of the bond lengths shown in Fig. 10 indicates that in the dimethyl-glyoxime complexes the ir-bonding is not nearly so extensive as commonly imagined. Similarly, it is known that aromatic donor-acceptor complexes, e.g, quinhydrone, stack in a fashion very similar to the dimethylglyoximc complexes (166a), and also show abnormal dichroism (182). 

It is instructive to consider the stability of other excitations in DNA, ex-cimers and exciplexes. An excimer (exciplex) is formed when two identical (nonidentical) molecules that do not interact in their ground states do so when one of the molecules is in an excited state. As a result of charge-transfer and exchange interactions of the overlapping n electrons of the two molecules on the one hand, and their mutual repulsion on the other, the molecules are drawn together in a potential minimum at a separation smaller... 

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