Valence electrons repulsion

The derivation of the pseudopotentials discussed above has been developed from equation (12), in which the effect of core projection operators on the valence-valence electron repulsion has been neglected. The error introduced by this approximation can be largely removed by adding to the core repulsion operators the repulsion from the difference in valence electron density in the reference atoms between the all-electron and valence-electron calculations 33... 

After iterating to charge self-consistency, a total valence energy is calculated. This includes appropriate factors for valence electron repulsion (but excludes the core electrons) and includes nuclear repulsion (but excludes the corresponding core nuclear charges). 

The moment we contemplate more than one valence electron outside an atomic core the central assumption of our theory so far is immediately invalidated. The frozen-core and valence electrons no longer satisfy the. same equation even at the single-determinant level. The valence electron HF equation does not take the particularly simple one-electron form, which is the same as the HF equation for the isolated core, because of valence-valence electron repulsion. 

If we are able to carry through this plan then, since we have explicitly excluded the effect of the pseudopotential transformation on the valence-valence electron repulsions, then the effects of restricting the calculation to valence electrons only will be ... 

Valence electron repulsion controls the shapes of molecules... 

The first reliable energy band theories were based on a powerfiil approximation, call the pseudopotential approximation. Within this approximation, the all-electron potential corresponding to interaction of a valence electron with the iimer, core electrons and the nucleus is replaced by a pseudopotential. The pseudopotential reproduces only the properties of the outer electrons. There are rigorous theorems such as the Phillips-Kleinman cancellation theorem that can be used to justify the pseudopotential model [2, 3, 26]. The Phillips-Kleimnan cancellation theorem states that the orthogonality requirement of the valence states to the core states can be described by an effective repulsive... 

The next step came in the 1950s, with more serious attempts to include formally the effect of electron repulsion between the valence electrons. First came the jT-electron models associated with the name of Pople, and with Pariser and Parr. You might like to read the synopses of their first papers. 

The first step in reducing the computational problem is to consider only the valence electrons explicitly, the core electrons are accounted for by reducing the nuclear charge or introducing functions to model the combined repulsion due to the nuclei and core electrons. Furthermore, only a minimum basis set (the minimum number of functions necessary for accommodating the electrons in the neutral atom) is used for the valence electrons. Hydrogen thus has one basis function, and all atoms in the second and third rows of the periodic table have four basis functions (one s- and one set of p-orbitals, pj, , Pj, and Pj). The large majority of semi-empirical methods to date use only s- and p-functions, and the basis functions are taken to be Slater type orbitals (see Chapter 5), i.e. exponential functions. 

The major features of molecular geometry can be predicted on the basis of a quite simple principle—electron-pair repulsion. This principle is the essence of the valence-shell electron-pair repulsion (VSEPR) model, first suggested by N. V. Sidgwick and H. M. Powell in 1940. It was developed and expanded later by R. J. Gillespie and R. S. Nyholm. According to the VSEPR model, the valence electron pairs surrounding an atom repel one another. Consequently, the orbitals containing those electron pairs are oriented to be as far apart as possible. 

The correlation of electron motion in molecular systems is responsible for many important effects, but its theoretical treatment has proved to be very difficult. Thus many quantum valence calculations use wave functions which are adjusted to optimize kinetic energy effects and the potential energy of interaction of nuclei and electrons but which do not adequately allow for electron correlation and hence yield excessive electron repulsion energy. This problem may be subdivided into cases of overlapping and nonoverlapping electron distributions. Both are very important but we shall concern ourselves here with only the nonoverlapping case. 

Electron-electron repulsion integrals, 28 Electrons bonding, 14, 18-19 electron-electron repulsion, 8 inner-shell core, 4 ionization energy of, 10 localization of, 16 polarization of, 75 Schroedinger equation for, 2 triplet spin states, 15-16 valence, core-valence separation, 4 wave functions of, 4,15-16 Electrostatic fields, of proteins, 122 Electrostatic interactions, 13, 87 in enzymatic reactions, 209-211,225-228 in lysozyme, 158-161,167-169 in metalloenzymes, 200-207 in proteins ... 

As well as a bonding pair of electrons, a fluorine molecule also possesses lone pairs of electrons that is, pairs of valence electrons that do not take part in bonding. The lone pairs on one F atom repel the lone pairs on the other F atom, and this repulsion is almost enough to overcome the favorable attractions of the bonding pair that holds the atoms together. This repulsion is one of the reasons why fluorine gas is so reactive the atoms are bound together as F2 molecules only very weakly. Among the common diatomic molecules, only H2 has no lone pairs. 

In a molecule that has lone pairs or a single nonbonding electron on the central atom, the valence electrons contribute to the electron arrangement about the central atom but only bonded atoms are considered in the identification of the shape. Lone pairs distort the shape of a molecule so as to reduce lone pair-bonding pair repulsions. 

For planar unsaturated and aromatic molecules, many MO calculations have been made by treating the a and n electrons separately. It is assumed that the o orbitals can be treated as localized bonds and the calculations involve only the tt electrons. The first such calculations were made by Hiickel such calculations are often called Hiickel molecular orbital (HMO) calculations Because electron-electron repulsions are either neglected or averaged out in the HMO method, another approach, the self-consistent field (SCF), or Hartree-Fock (HF), method, was devised. Although these methods give many useful results for planar unsaturated and aromatic molecules, they are often unsuccessful for other molecules it would obviously be better if all electrons, both a and it, could be included in the calculations. The development of modem computers has now made this possible. Many such calculations have been made" using a number of methods, among them an extension of the Hiickel method (EHMO) and the application of the SCF method to all valence electrons. ... 

The Mg + dicadon [42] with AN+2 (N= 1) valence electrons has a stable structure in agreanent with the rule, but this is a local energy minimum. The linear structure is more stable because it minimizes the Coulomb repulsion. This is in contrast to the tetrahedral stmcture of the Li dication with two electrons (N= 0). The six electron systems caimot form closed-shell structures in the tetrahedron, but the two electron systems can do. 

To minimize electron-electron repulsion, put three of the 3 p electrons in different orbitals, all with the same spin, and then place the fourth electron, with opposite spin, in the first orbital. In accord with Hund s rule, this gives the same value of JHj to all electrons that are not paired. Here is the energy level diagram for the valence electrons ... 

Sulfur, in Group 16, has six valence electrons. The configurations show six electrons with = 3, so the configuration is consistent with the valence electron count. The electrons are spread among the three 3 p orbitals, which minimizes electron-electron repulsion. 

The most stable shape for any molecule maximizes electron-nuclear attractive interactions while minimizing nuclear-nuclear and electron-electron repulsions. The distribution of electron density in each chemical bond is the result of attractions between the electrons and the nuclei. The distribution of chemical bonds relative to one another, on the other hand, is dictated by electrical repulsion between electrons in different bonds. The spatial arrangement of bonds must minimize electron-electron repulsion. This is accomplished by keeping chemical bonds as far apart as possible. The principle of minimizing electron-electron repulsion is called valence shell electron pair repulsion, usually abbreviated VSEPR. 

Methane has four pairs of valence electrons, each shared in a chemical bond between the carbon atom and one of the hydrogen atoms. The electron density in each C—H bond is concentrated between the two nuclei. At the same time, methane s four pairs of bonding electrons repel one another. Electron-electron repulsion in methane is minimized by keeping the four C—bonds as far apart as possible. 

Having introduced methane and the tetrahedron, we now begin a systematic coverage of the VSEPR model and molecular shapes. The valence shell electron pair repulsion model assumes that electron-electron repulsion determines the arrangement of valence electrons around each inner atom. This is accomplished by positioning electron pairs as far apart as possible. Figure 9-12 shows the optimal arrangements for two electron pairs (linear),... 

With a steric number of 6, xenon has octahedral electron group geometry. This means the inner atom requires six directional orbitals, which are provided by an. s p d hybrid set. Fluorine uses its valence 2 p orbitals to form bonds by overlapping with the hybrid orbitals on the xenon atom. The two lone pairs are on opposite sides of a square plane, to minimize electron-electron repulsion. See the orbital overlap view on the next page. 

The molecular geometry of a complex depends on the coordination number, which is the number of ligand atoms bonded to the metal. The most common coordination number is 6, and almost all metal complexes with coordination number 6 adopt octahedral geometry. This preferred geometry can be traced to the valence shell electron pair repulsion (VSEPR) model Introduced In Chapter 9. The ligands space themselves around the metal as far apart as possible, to minimize electron-electron repulsion. 

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