Walsh's diagram & Application to Triatomic Molecules
WALSH DIAGRAMS
We know all the systems want to be in a stable state, and the stable state is one in which it has the minimum possible energy. Same is true for the stereochemistry or the geometry of a molecule. The VSEPR theory considered that the most stable configuration of a molecule is one in which repulsive forces between the valence electron-pairs is minimum. In contrast, the molecular orbital theory (MOT) considers that the stable geometry of a molecule can be determined on the basis of the energy of molecular orbitals formed as a result of linear combination of atomic orbitals (LCAO). In 1953 A.D.Walsh proposed a simple pictoral-approach to determine the geometry of a molecule considering and calculating the energies of molecular orbitals of the molecule.
The basic approach is to calculate the energies of molecular orbitals for two limiting structures, say linear or bent to 90o for an AB2 molecule, and draw a diagram showing how the orbitals of one configuration correlate with those of the other. Then depending on which orbitals are occupied, one or the other structure can be seen to be preferred. By means of approximate MO Theory implemented by digital computers, this approach has been extended and generalized in recent years.
Walsh's approach to the discussion of the shape of an AB2 triatomic molecule (such as BeH2 and H2O) is illustrated in Fig. 1.8. The illustration shows an example of a Walsh diagram, a graph of the dependence of orbital energy on molecular geometry. A Walsh diagram for an B2A or AB2 molecule is constructed by considering how the composition and energy of each molecular orbital changes as the bond angle changes from 90o to 180o. The diagram is in fact just a more elaborate version of the correlation diagram.
Application to Triatomic Molecules
The coordinate system for the AB2 molecule is shown in Figure 1.8. The AB2 molecule has C2v symmetry when it is bent and, when linear D2h symmetry. To simplify notations, however, the linear configuration is considered to be simply an extremum of the C2v symmetry. Therefore the labels given to the orbitals through the range 90o ≤ θ < 180o are retained even when θ = 180o. The symbols used to label the orbitals are derived from the orbital symmetry properties in a systematic way, but a detailed explanation is not given here. For present purposes, these designations may be treated simply as labels.
the a atom of ab2 molecule will be assumed to have only s, px, py and pz orbitals in its valence shell, whereas each of the b atoms is allowed only a single orbital oriented to form a σ bond to a. in the linear configuration pax and paz are equivalent non-bonding orbitals labelled 2a, and b1 respectively. the orbitals sa and pay interact with σ1b and σ2b, σ orbitals on the b atoms, to form one very strongly bonding orbital, 1a, one less strongly bonding orbital, 1b2, one less strongly bonding 3a1 and 3b2. the ordering of these orbitals and in more detail, the approximate values of their energies can be estimated by an mo calculation. similarly, for the bent molecule the mo energies may be estimated. here only pza is non bonding, spacing and even the order of the other orbitals is function of the angle of bending θ. the complete pattern of orbital energies, over a range of θ, is obtained with typical input parameters. this is shown in the figure 1.8. calculations in the huckel approximation are simple to perform and give the correct general features of the diagram but for certain cases (e.g. ab2e2) very exact computations are needed for an unambiguous prediction of structure.
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