The MOs of a Homonuclear Diatomic Molecule

The following sketches show the atomic orbital wave functions (with phases) used to construct some of the MOs of a homonuclear diatomic molecule. For each sketch, determine the type of MO that will result from mixing the atomic orbital wave functions as drawn. Use the same labels for the MOs as in the Closer Look box on phases. 

In a simple LCAO MO treatment of a homonuclear diatomic molecule the two solutions for the energy are E = —When the two atoms are infinitely apart, the total energy of the system will be 2Hn, the energy of the two separated atoms. Using this as the reference state, the potential energy of a two-electron homonudear diatomic molecule is... 

Problem 10-5. In a homonuclear diatomic molecule, taking the molecular axis as z, the pair of LCAO-MO s tpi = 2p A + PxB and tp2 = 2 PyA + 2 PyB forms a basis for a degenerate irreducible representation of D h, as does the pair 3 = 2pxA PxB and 4 = PxA — PxB Identify the symmetry species of these wave functions. Write down the four-by-four matrices for the direct product representation by examining the effect of the group elements on the products 0i 03, 0i 04, V 2 03) and 02 04- Verify that the characters of the direct product representation are the products of the characters of the individual representations. 

Consider a homonuclear diatomic molecule A2, whose two atoms A are identical. For the sake of simplicity, we will assume that each atom uses one (and only one) valence AO to form the bond. These interacting AOs, which we will call q and following procedure is used to calculate the resulting MOs ... 

Our comparison shows that the LCAO method includes an ionic contribution to the bond, but the VB method does not. In fact, the simple MO approach suggests that the bond in H2 is 50% covalent and 50% ionic, which is contrary both to experience and intuition. Because the electronegativities of the two atoms in a homonuclear diatomic molecule are the same, there is no reason to expect any ionic contribution to the bond, much less such a large one. The complete absence of ionic contributions in the VB wave function suggests this method is not well suited for polar molecules such as HR Thus, the truth in describing the chemical bond and molecular structure appears to lie somewhere between the LCAO and... 

We consider symmetry in Chapter 3, but it is useful at this point to consider the labels that are commonly used to describe the parity of a molecular orbital. A homonuclear diatomic molecule (e.g. H2, CI2) possesses a centre of inversion (centre of symmetry), and the parity of an MO describes the way in which the orbital behaves with respect to this centre of inversion. 

Fig. 3-11. Energy level diagram showing the formation of bonding and antibonding MO s from two equivalent atomic orbitals in a homonuclear diatomic molecule.

Let us consider an element in the first short Period having 2s and 2p orbitals in its valence shell. When two such atoms are combined into a homonuclear diatomic molecule, the two sets of atomic orbitals may combine into various MO s. Before we can specify the electronic structures of the diatomic molecules of these elements, we must know the relative energies of these MO s. 

The atomic orbitals of the atoms that form homonuclear diatomic molecules have identical energies, and both atoms contribute equally to a given MO. Therefore, in the molecular orbital equations, the coefficients associated with the same atomic orbitals of... 

Sigma and pi molecular orbitals made by taking linear combinations of the 2p AOs in a homonuclear diatomic molecule. The AOs will also generate a set of and k MOs having the same shapes and energies as those derived from the 2py AOs, but lying perpendicular to the plane of the paper. 

Transitions between electronic states of the same MO configuration are always forbidden in a homonuclear diatomic molecule. Explain why this must be true. 

A homonuclear diatomic molecule MO of ttu symmetry is to be expressed as a linear combination of AOs centered on the nuclei, which lie on the z axis. Which of the AOs in the following list can contribute to the MO ... 

Figure 3.28 A schematic energy diagram for valence MOs of homonuclear diatomic molecules (following Mulliken). The order of 02P and 7t2p MOs should be reversed for 14 or fewer electrons.

Fig. 7.5. MO energy diagram for homonuclear diatomic molecule X2 (where X is an atom in the Period Li—>Ne), (a) with neglect of 2s-2p overlap and (b) with 2s-2p overlap included.

In Chapter 1 we saw that in moving from homonuclear to heteronuclear diatomics a new factor enters - the atom characters are distributed differently over the filled and unfilled MOs. As only the filled orbitals contribute to the atomic charges, the Mulliken charge distribution reflects the polarity of the molecule. Similar information for the HOMO and FUMO permitted us to discuss properties such as Lewis acidity and basicity in terms of frontier-orbital characteristics. As we were able to unravel the DOS of the metal chain in terms of AO type, we can also interrogate the DOS of a heteroatomic system for information on the distribution of atomic character over the total DOS. That is, we can reveal the contributions or character of a chosen atom to the DOS. We can begin to appreciate the power of this tool by... 

In this section we consider homonuclear diatomic molecules (those composed of two identical atoms) formed by elements in Period 2 of the periodic table. The lithium atom has a 1 s22s electron configuration, and from our discussion in the previous section, it would seem logical to use the Li Is and 2s orbitals to form the MOs of the Li2 molecule. However, the Is orbitals on the lithium atoms are much smaller than the 2s orbitals and therefore do not overlap in space to any appreciable extent (see Fig. 14.33). Thus the two electrons... 

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