Welcome
Content
Introduction
Linear Combination of Atomic Orbitals
H2 and He2 - The Simplest Examples
The Effect of Electronegativity
p-Orbitals and p-Overlap
Combining AOs to Build MOs
The AH2 Walsh Diagram
Larger Molecules
Reactions
Elementary Symmetry
Glossary
Molecules in VRML
General Information - Installation - Use
| 2.1. H2 and He2 - the Simplest Examples The simplest example of the LCAO approximation is the combination of two s-AOs to form s- (bonding) and s*- (antibonding) MOs. This is shown in Figure 2.2 for the dihydrogen molecule. Figure 2.2a shows the simple orbital interaction diagram, whereas Figure 2.2b shows 3D-electron density contour plots for the AOs and MOs. Figure 2.2a Schematic orbital interaction diagram for a system consisting of two s-orbitals. Figure 2.2b Orbital electron density plots for the AOs and MOs shown in Figure 2.2a. From left to right: s-AO, s-MO, s*-MO. It is useful to define the conventions used in Figure 2.2a and all other orbital interaction diagrams in this book. The thick horizontal lines represent orbital energy levels and, although it is not explicitly shown, the diagram implies a vertical energy scale. The dashed connecting lines signify orbital interactions. Thus, the two s-orbitals, which have the same energy, interact with each other to form the s- and s*-MOs. The s-MO is stabilised by DE1 relative to the energy level of the two AOs and the s*-MO is destabilised by DE2. It is important to note that DE1 is always slightly smaller than DE2. If we now add the electrons to the orbital interaction diagram, we find that H2, with two electrons (see Figure 2.3a), can form a closed-shell singlet state in which the electrons are paired in the stabilized s-orbital to give a strong bond (the total energy of the two electrons is lower than in the two separated atoms). If, however, we consider He2, with four electrons (see Figure 2.3b), we must doubly occupy both the s- and the s*-orbitals. Because E1 is smaller than E2, this situation gives a higher energy than for the four electrons in the two separated atoms. He2 thus does not form a bond. Figure 2.3 Electron occupations for (a) H2 and (b) He2. The stabilisation and destabilisation energies, E1 and E2, depend on the overlap between the AOs. The closer the two atoms approach each other, the larger the overlap and the larger the energy splitting. This effect can be tested using demonstration 1. H2 and He2 -The Simplest Examples Next: The Effect of Electronegativity p-Orbitals and p-Overlap Combining AOs to Build MOs The AH2 Walsh Diagram