![]() The coefficients c a and c b determine how much the specific atomic orbitals a and b contribute to the molecular orbitals. In mathematical form we can say that a molecular orbital Ψ ab = N (c aΨ a ± c bΨ b), whereby Ψ a is the atomic orbital a of atom a, and Ψ b is the atomic orbital b of atom b. Therefore, there is an amplitude associated with each vector that is associated with the wave function. A point in space is defined by a vector that points from the origin to that point in space. Any orbital is a wave function that has a specific amplitude at a particular point in space. Since orbitals are so-called vector functions they can be added and subtracted like vectors. Figure 3.1.2 The second axiom of molecular orbital theory. Linear combination means a vectorial addition or subtraction. The second axiom is that molecular orbitals can be described as a linear combination of atomic orbitals (Fig. This is a good approximation because the nuclei are much more massive than the electrons. Figure 3.1.1 The Born-Oppenheimer approximation It says that the position of the nuclei are nearly fixed relative to electron motion (Fig. The first assumption is the Born-Oppenheimer approximation. ![]() ![]() Like all theories it is based on a few basic assumptions, also called axioms. Before we apply symmetry to molecular orbital theory, however, let us briefly review the principles of molecular orbital theory. We will see that the application of symmetry to molecular orbital theory will greatly help us to understand molecular orbitals, in particular for more complex molecules. Molecular orbital theory is a bonding theory that has been developed to explain covalent bonding, but as we will see in a bit, it can also make statements about ionic bonding. Now that we have thoroughly studied symmetry, we can next apply symmetry to molecular orbital theory. \)Ĭovalent Bonding: Molecular Orbital Theory
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