Valence shell atomic orbitals

When we discussed sp3 hybrid orbitals in Section 1.6, we said that the four valence-shell atomic orbitals of carbon combine to form four equivalent sp3 hybrids. Imagine instead that the 2s orbital combines with only two of the three available 2p orbitals. Three sp2 hybrid orbitals result, and one 2p orbital remains unchanged- The three sp2 orbitals lie in a plane at angles of 120° to one another, with the remaining p orbital perpendicular to the sp2 plane, as shown in Figure 1.13. 

In valence-bond theory, we assume that bonds form when unpaired electrons in valence-shell atomic orbitals pair the atomic orbitals overlap end to end to form cr-bonds or side by side to form ir-bonds. 

In the molecular orbital description of homonuclear diatomic molecules, we first build all possible molecular orbitals from the available valence-shell atomic orbitals. Then we accommodate the valence electrons in molecular orbitals by using the same procedure we used in the building-up principle for atoms (Section 1.13). That is,... 

Step 2 Use matching valence-shell atomic orbitals to build bonding and antibonding molecular orbitals and draw the resulting molecular orbital energy-level diagram (Figs. 3.31 and 3.32). 

In the context of an introduction to organic aspects ot photochemistry, a simple molecular orbital description of the electronic structure of organic molecules provides the most convenient qualitative framework in which to discuss the formation of electronically excited states by the absorption of light. It is normally assumed that the inner-shell electrons of the constituent atoms of a molecule remain unaltered in the molecule itself linear combinations of the remaining, valence-shell atomic orbitals then provide molecular orbitals that can be used to describe the outer electronic structure in the molecule. 

In contrast to Rydberg orbitals, unoccupied (virtual) valence orbitals (V) are relatively compact, being made up of valence-shell principal-quantum-number atomic orbitals. These arise from the splittings of valence-shell atomic orbitals that occur upon bond formation. As a consequence of their compact natures, excitations between occupied and unoccupied valence orbitals can have large transition moments. Since each molecule has only a small number of such orbitals, it is a simple matter to determine the V class of molecular orbitals for any compound from the atomic shells of the atoms comprising the molecule of Interest, and from the total number of electrons that fill the molecular shells ( ). 

By following the procedures that we detailed in Chapter 4, an MO diagram can be constructed to describe the bonding in an O], [MLs] complex. For a first row metal, the valence shell atomic orbitals are 2d, 4 and Ap. Under Oj, symmetry (see Appendix 3), the s orbital has a g symmetry, the p orbitals are degenerate with symmetry, and the d orbitals split into two sets with eg (d i and dyi yi orbitals) and t2g d y, dy and d orbitals) symmetries, respectively (Figure... 

For complexes of type MP (P = phosphorus ligand), where the acceptor atom M has an environment with microsymmetry that is Tj or Of, it is possible to simplify equation (1) considerably, because the only valence shell atomic orbital on the acceptor atom belonging to the totally symmetric representation of the molecular space group is the i orbital. This means that other atomic orbitals on the acceptor atom do not mix with the s orbital and that only totally symmetric ligand combinations need be considered. 

In VB theory, a molecule is pictured as a group of atoms bound together through localized overlap of valence-shell atomic orbitals. In MO theory, a molecule is pictured as a collection of nuclei with the electron orbitals delocalized over the entire molecule. The MO model is a quantum-mechanical treatment for molecules similar to the one for atoms in Chapter 8. Just as an atom has atomic orbitals (AOs) with a given energy and shape that are occupied by the atom s electrons, a molecule has molecular orbitals (MOs) with a given energy and... 

We have accurate observed values for only a few molecules for the ionization potentials corresponding to all the molecular orbitals built up from valence shell atomic orbitals. SFe is interesting since probably the complete set of valence orbital ionization potentials have been measured and identified. Our calculations agree well with the experiment. We consider also CO2 and SO2 where the data available to us are not complete and the agreement between our calculations and reported observations is not so completely in accord. 

Figure 6, Electron-density plots for the valence-shell atomic orbitals of sulfur, oxygen, and hydrogen as the free atoms. These plots are to the same scale as those given in Figures 2 through 5 and 7 through 10.

We hope we have demonstrated that the usual delocalized molecular orbitals obtained from self-consistent-field calculations are about as readily understood and interpretable in chemical terms as are the localized orbitals which some people have taken great pains to derive (32) from these delocalized ones. We have demonstrated also through the plots of electron density how these delocalized molecular orbitals are made up from atomic orbitals and how they may be discussed in terms of their atomic-orbital composition. This is particularly interesting for second-row atoms such as sulfur because of the diffuse nature of the parts of the valence-shell atomic orbitals which are involved in bonding. 

The valence electron configuration of the N2 molecule is 2scr 2s(7 2p7t 2pa where each of the molecular orbitals is formed by combination of one valence shell atomic orbital from... 

By following the procedures detailed in Chapter 5, an MO diagram can be constructed to describe the bonding in an Oh [MLs]" complex. For a first row metal, the valence shell atomic orbitals are 3d, 4 and Ap. Under O ... 

Assigning a particular molecular orbital to its symmetry species is like assigning a vibration to its symmetry species (Section 8.5) we need to consider the effects of the various symmetry operations on the sign and orientation of the wavefimction. One problem is that we do not necessarily know what a particular wavefunction looks like, and it is here that the symmetry adapted linear combination (SALC) approach to the construction of molecular orbitals is very useful. We begin by classifying the valence-shell atomic orbitals (AOs) of the constituent atoms, in the symmetry of the molecule, as the set of molecular orbitals (MOs) will have the same distribution of symmetry species as the set of contributing atomic orbitals. Then we can attempt to construct molecular orbitals, bearing in mind that an orbital of any particular symmetry species arises from combinations only of atomic orbitals of that same symmetry species. 

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