Molecular orbitals repulsive interaction

Improvement of the MO method involves better orbitals, better account of interelectronic repulsion, and introduction of mixing of different electron configurations in the molecular orbitals ( configuration interaction ). Improved MO calculations give much more accurate energies at the minimum of a plot such as Figure 21-11, but the bonds still do not dissociate properly, for the same reason as with the simple MO method. 

The chief drawbacks to the crystal field approach are in its concept of the repulsion of orbitals by the ligands and its lack of any explanation for bonding in coordination complexes. As we have seen in all our discussions of molecular orbitals, any interaction between orbitals leads to both higher and lower energy molecular orbitals. The purely electrostatic approach does not allow for the lower (bonding) molecular orbitals, and thus fails to provide a complete picture of the electronic structure. 

We find, as a general result, that the attractive interaction between CO and metal d-electrons is due to the bonding interaction with the 27t orbitals. Repulsive interactions are due to the interactions between doubly occupied metal orbitals and those in the molecule. The molecular orbitals involved are the Aa, 5cr and Itt orbitals. 

The first term includes the electrostatic attractions and repulsions between the net charges on pairs of atoms, one from each molecule. The second involves interactions between occupied and vacant molecular orbitals on the two molecules. The hypothesis is that the reaction proceeds in a way to produce the most favorable... 

Imagine a model hydrogen molecule with non-interacting electrons, such that their Coulomb repulsion is zero. Each electron in our model still has kinetic energy and is still attracted to both nuclei, but the electron motions are completely independent of each other because the electron-electron interaction term is zero. We would, therefore, expect that the electronic wavefunction for the pair of electrons would be a product of the wavefunctions for two independent electrons in H2+ (Figure 4.1), which I will write X(rO and F(r2). Thus X(ri) and T(r2) are molecular orbitals which describe independently the two electrons in our non-interacting electron model. 

The first interaction, between CO 5c and Rh d,2, gives two new molecular orbitals. The bonding orbital has mostly 5<7 character, and it is customary to call it 5c. However, the level is lower than in free CO. UPS spectra reveal this shift immediately (see the spectrum of CO/Fe in Fig. 3.20) and indicate that its energy is close to that of the CO 1ft level. The antibonding chemisorption orbital has mainly d,2 character and is shifted upwards in energy. If the latter falls below the Fermi level, the 5c - d,2 interaction is entirely repulsive. For CO/Rh(100) the calculations indicate that the dz2 level falls across the Fermi level, such that the repulsion is partially relieved. 

Under the Born-Oppenheimer approximation, two major methods exist to determine the electronic structure of molecules The valence bond (VB) and the molecular orbital (MO) methods (Atkins, 1986). In the valence bond method, the chemical bond is assumed to be an electron pair at the onset. Thus, bonds are viewed to be distinct atom-atom interactions, and upon dissociation molecules always lead to neutral species. In contrast, in the MO method the individual electrons are assumed to occupy an orbital that spreads the entire nuclear framework, and upon dissociation, neutral and ionic species form with equal probabilities. Consequently, the charge correlation, or the avoidance of one electron by others based on electrostatic repulsion, is overestimated by the VB method and is underestimated by the MO method (Atkins, 1986). The MO method turned out to be easier to apply to complex systems, and with the advent of computers it became a powerful computational tool in chemistry. Consequently, we shall concentrate on the MO method for the remainder of this section. 

Like atomic orbitals (AOs), molecular orbitals (MOs) are conveniently described by quantum mechanics theory. Nevertheless, the approach is more complex, because the interaction involves not simply one proton and one electron, as in the case of AOs, but several protons and electrons. For instance, in the simple case of two hydrogen atoms combined in a diatomic molecule, the bulk coulombic energy generated by the various interactions is given by four attractive effects (proton-electron) and two repulsive effects (proton-proton and electron-electron cf figure 1.20) ... 

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