Electron repulsion model

The importance of Coulomb s law (Section 1-2), as evidenced, for example, by atomic attraction (Section 1-3), relative electronegativity (Table 1-2), the electron repulsion model for the shapes of molecules (Section 1-3), and the choice of dominant resonance contributors (Section 1-5). 

The polyhedral skeletal electron-counting rules do have some theoretical underpinnings as outlined in Section 22.2. This is a simple and very useful model to rationalize molecular structures that cannot be framed within the standard two-electron two-center paradigm. Similar to the valence shell electron repulsion model and the isolobal analogy there are exceptions and these exceptions are quite interesting in and of themselves. We shall restrict our coverage here to the most common patterns where Wade s rules predict a different shape or instances where the molecules are not predicted to be stable. 

VV e now wish to establish the general functional form of possible wavefunctions for the two electrons in this pseudo helium atom. We will do so by considering first the spatial part of the u a efunction. We will show how to derive functional forms for the wavefunction in which the i change of electrons is independent of the electron labels and does not affect the electron density. The simplest approach is to assume that each wavefunction for the helium atom is the product of the individual one-electron solutions. As we have just seen, this implies that the total energy is equal to the sum of the one-electron orbital energies, which is not correct as ii ignores electron-electron repulsion. Nevertheless, it is a useful illustrative model. The wavefunction of the lowest energy state then has each of the two electrons in a Is orbital ... 

The two-center two-electron repulsion integrals ( AV Arr) represents the energy of interaction between the charge distributions at atom Aand at atom B. Classically, they are equal to the sum over all interactions between the multipole moments of the two charge contributions, where the subscripts I and m specify the order and orientation of the multipole. MNDO uses the classical model in calculating these two-center two-electron interactions. 

You will see shortly that an exact solution of the electronic Schrodinger equation is impossible, because of the electron-electron repulsion term g(ri, r2). What we have to do is investigate approximate solutions based on chemical intuition, and then refine these models, typically using the variation principle, until we attain the required accuracy. This means in particular that any approximate solution will not satisfy the electronic Schrodinger equation, and we will not be able to calculate the energy from an eigenvalue equation. First of all, let s see why the problem is so difficult. 

The orbital model would be exact were the electron repulsion terms negligible or equal to a constant. Even if they were negligible, we would have to solve an electronic Schrodinger equation appropriate to CioHs " " in order to make progress with the solution of the electronic Schrodinger equation for naphthalene. Every molecular problem would be different. 

A great failing of the Hiickel models is their treatment of electron repulsion. Electron repulsion is not treated explicitly it is somehow averaged within the spirit of Hartree-Fock theory. 1 gave you a Hiickel jr-electron treatment of pyridine in Chapter 7. Orbital energies are shown in Table 8.1. 

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. 

Electrons do of course interact with each other through their mutual Coulomb electrostatic potential, so an alternative step to greater sophistication might be to allow electron repulsion into the free-electron model. We therefore start again from the free-electron model but allow for the Coulomb repulsion between the electrons. We don t worry about the fermion nature of electrons at this point. 

VSEPR model Valence Shell Electron Pair Repulsion model, used to predict molecular geometry states that electron pairs around a central atom tend to be as far apart as possible, 180-182... 

However, in the case of the electronic orbital model there is no way in which the inter-electronic repulsions can be physically reduced. This form of distinction has not been sufficiently emphasized by philosophers. I believe that the nature of the orbital model shows that not all theoretical models can be lumped together as in the work of Achinstein [1968]. 

The Lewis structures encountered in Chapter 2 are two-dimensional representations of the links between atoms—their connectivity—and except in the simplest cases do not depict the arrangement of atoms in space. The valence-shell electron-pair repulsion model (VSEPR model) extends Lewis s theory of bonding to account for molecular shapes by adding rules that account for bond angles. The model starts from the idea that because electrons repel one another, the shapes of simple molecules correspond to arrangements in which pairs of bonding electrons lie as far apart as possible. Specifically ... 

Example the n = 2 shell of Period 2 atoms, valence-shell electron-pair repulsion model (VSEPR model) A model for predicting the shapes of molecules, using the fact that electron pairs repel one another. 

If this is so, then how is it that his model works so well in other cases without that addition Well in many, though not all, cases, the additional effects of the d-electron repulsions are to modify bond lengths rather than bond angles. We discuss such an example in the next section. Before doing so, however, there is more to say about planar coordination. 

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),... 

C09-0115. The H—O—H bond angle in a water molecule is 104.5°. The H—S—H bond angle in hydrogen sulfide is only 92.2°. Explain these variations in bond angles, using orbital sizes and electron-electron repulsion arguments. Draw space-filling models to illustrate your explanation. 

C09-0133. Among the halogens, only one known molecule has the formula X 7. It has pentagonal bipyramidal geometry, with five Y atoms in a pentagon around the central atom X. The other two Y atoms are in axial positions. Draw a ball-and-stick model of this compound. Based on electron-electron repulsion and atomic size, determine the identities of atoms X and Y. Explain your reasoning. (Astatine is not involved. This element is radioactive and highly unstable.)... 

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. 

The existence of the first HK theorem is quite surprising since electron-electron repulsion is a two-electron phenomenon and the electron density depends only on one set of electronic coordinates. Unfortunately, the universal functional is unknown and a plethora of different forms have been suggested that have been inspired by model systems such as the uniform or weakly inhomogeneous electron gas, the helium atom, or simply in an ad hoc way. A recent review describes the major classes of presently used density functionals [10]. 

An important consequence of the only approximate treatment of the electron-electron repulsion is that the true wave function of a many electron system is never a single Slater determinant We may ask now if SD is not the exact wave function of N interacting electrons, is there any other (necessarily artificial model) system of which it is the correct wave function The answer is Yes it can easily be shown that a Slater determinant is indeed an eigenfunction of a Hamilton operator defined as the sum of the Fock operators of equation (1-25)... 

Once computed on a 3D grid from a given ab initio wave function, the ELF function can be partitioned into an intuitive chemical scheme [30], Indeed, core regions, denoted C(X), can be determined for any atom, as well as valence regions associated to lone pairs, denoted V(X), and to chemical bonds (V(X,Y)). These ELF regions, the so-called basins (denoted 2), match closely the domains of Gillespie s VSEPR (Valence Shell Electron Pair Repulsion) model. Details about the ELF function and its applications can be found in a recent review paper [31],... 

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