Molecular Orbitals

Abstract

Molecular orbital theory uses group theory to describe the bonding in molecules ; it comple-ments and extends the introductory bonding models in Chapter 3 . In molecular orbital theory the symmetry properties and relative energies of atomic orbitals determine how these orbitals interact to form molecular orbitals. The molecular orbitals are then occupied by the available electrons according to the same rules used for atomic orbitals as described in Sections 2.2.3 and 2.2.4 . The total energy of the electrons in the molecular orbitals is compared with the initial total energy of electrons in the atomic orbitals. If the total energy of the electrons in the molecular orbitals is less than in the atomic orbitals, the molecule is stable relative to the separate atoms; if not, the molecule is unstable and predicted not to form. We will first describe the bonding, or lack of it, in the first 10 homonuclear diatomic molecules (H 2 through Ne 2) and then expand the discussion to heteronuclear diatomic molecules and molecules having more than two atoms. A less rigorous pictorial approach is adequate to describe bonding in many small mole-cules and can provide clues to more complete descriptions of bonding in larger ones. A more elaborate approach, based on symmetry and employing group theory, is essential to under-stand orbital interactions in more complex molecular structures. In this chapter, we describe the pictorial approach and develop the symmetry methodology required for complex cases. 5.1 Formation of Molecular Orbitals from Atomic Orbitals As with atomic orbitals, Schrödinger equations can be written for electrons in molecules. Approximate solutions to these molecular Schrödinger equations can be constructed from linear combinations of atomic orbitals (LCAO) , the sums and differences of the atomic wave functions. For diatomic molecules such as H 2 , such wave functions have the form ⌿ = c a c a + c b c b