Molecular Orbitals for the Water Molecule

The water molecule possesses two mirror planes of symmetry, as shown in Fig. 6-3. One mirror plane lies in the plane of the diagram through which the whole molecule reflects into itself across the plane. The other, through the oxygen nucleus in the yz plane of the figure, and shown by the dotted line, reflects Ha into Hb and vice versa. 

Step (B) Classify O atomic orbitals yz mirror plane 

The hydrogen orbitals do not form a combination of symmetry type (iii) and so leave the oxygen orbital as nonbonding. 

We are now ready to apply the ideas in the preceding three sections to the construction of molecular orbitals in octahedral complexes. 

Symmetry Metal orbital Ligand group orbital 

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The molecular orbitals are summarised in the Table, together with LCAO forms. Table. Molecular orbitals for the water molecule. ... 

Figure 2 Localized molecular orbitals for the water molecule...

To see how this useful procedure works, let us consider the bonds and the molecular orbitals of the water molecule. Fig. 2 shows a Lewis diagram of H2O, with two lines for OH bonds and two pairs of dots for lone pairs of electrons. The point group is C2 and the lone pairs are placed above and below the plane of the molecule. For a discussion of the stereochemistry of lone pairs, the reader should consult the papers by Gillespie >. 

The concept of hybridization of atomic orbitals was subsequently introduced, in an attempt to interpret the difference between the actual bond angle for the water molecule and the value of 90° considered in the previous model. This concept had already been introduced to interpret, for example, the tetrahedral geometry of the methane molecule. We shall come back to this subject later in the chapter, to conclude that, although it is possible to establish a correlation between molecular geometry and hybrid orbitals, it is not correct to take the latter as the basis of an explanation of the former. This distinction is very important in teaching. 

Let us carry out the Hartree-Fock calculations for the water molecule. We focus on a subsequent calculation of the localized molecular orbitals and get five doubly occupied molecular orbitals, as shown in Fig. 8.30. 

From the quantitative point of view the calculation of the energy (and other properties) associated to VB wavefunctions was hampered by the non-orthogonality of the atomic orbitals centered on the different atoms of the molecule. In addition, and quite disappointing, was the fact that, in most cases, to achieve the same accuracy as calculations based on the Molecular Orbital (MO) model, several ionic structures had to be considered in the VB wavefunction. For example, even considering 20 covalent and 39 ionic structures in the VB wave-function for the water molecule, the energy of the VB wavefunction is still not comparable to the results based on the HF model using the same basis set. Thus, besides the poor performance when compared to the MO calculations, the consideration of the ionic structures caused the VB theory to loose its most important characteristics chemical interpretability and compactness of the wavefunction. 

These two references are useful for molecular orbital theory of the water molecule. 

The possible wave functions for the molecular orbitals for molecules are those constructed from the irreducible representations of the groups giving the symmetry of the molecule. These are readily found in the character table for the appropriate point group. For water, which has the point group C2 , the character table (see Table 5.4) shows that only A1 A2, B1 and B2 representations occur for a molecule having C2 symmetry. 

To deal with the molecular orbitals for water it is useful to examine the effect of certain symmetry operations on the molecule. We choose a set of rectangular Cartesian axes (Fig. 4) so that the x axis bisects the angle between the bonds and the z axis is perpendicular to the nuclear plane. 

On the other hand we can also see that the degeneracy of the orbitals, yz>, zx>, and xy>, depends on the relative orientation of the water molecules. If, for example, the water molecule no. 1 is rotated around its central ion to ligator bond 45° so as to have its molecular plane lying in X — Y, and at the same time water molecule no. 2 is rotated 90° around its bond to the central ion, the above three orbitals obtain the Ti-pertur-bation energies e , en and 2en, respectively. We have a pseudotetra-gonal perturbation. 

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