5: Molecular Orbitals
Molecular Orbital Theory
Molecular Orbital (MO) Theory is a sophisticated bonding model. It is generally considered to be more powerful than Lewis and Valence Bond Theories for predicting molecular properties; however, this power comes at the price of complexity. In its full development, MO Theory requires complex mathematics, though the ideas behind it are simple. Atomic orbitals (AOs) that are localized on individual atoms combine to make molecular orbitals (MOs) that are distributed over the molecule. The simplest example is the molecule dihydrogen (H 2 ), in which two independent hydrogen 1s orbitals combine to form the \(\sigma\) bonding MO and the \(\sigma\) antibonding MO of the dihydrogen molecule (see figure). The MO’s are also called Linear Combinations of Atomic Orbitals (LCAO).
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- 5.1: Formation of Molecular Orbitals from Atomic Orbitals
- Molecular orbital theory extends from quantum theory and the atomic orbital wavefunctions ( ψ ) described by the Schrödinger equation. While the Schrödinger equation defines a Ψ for electrons in individual atoms, we can approximate a the molecular wavefunction ( Ψ would look like if we combined the ψ of individual atoms. The addition or subtraction of wavefunctions is termed linear combination of atomic orbitals (LCAO). Molecular orbital theory applied LCAO to describe bonding.
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- 5.3: Larger (Polyatomic) Molecules
- We can extend the method we used for diatomic molecules to draw the molecular orbitals of more complicated, polyatomic molecules (molecules with more than two atoms). To combine several different atoms in a molecular orbital diagram, we will group orbitals from different atoms into sets that match the symmetry of a central atom. These group orbitals are also referred to as symmetry adapted linear combinations (SALCs).
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- 5.4: BeH₂ is Linear and H₂O is Bent
- Walsh correlation diagram is a plot of molecular orbital energy as a function of some systematic change in molecular geometry. For example, the correlation between orbital energies and bond angle for an \(AH_2\) molecule. The geometry of a molecule is determined by which possible structure is lowest in energy. We can use the Walsh diagram to determine the energy trends based on which orbitals are occupied.
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- 5.5: Photoelectron Spectroscopy
- A photoelecton spectrum can show the relative energies of occupied molecular orbitals by ionization. (i.e. ejection of an electron). A photoelectron spectrum can also be used to determine energy spacing between vibrational levels of a given electronic state. Each orbital energy band has a structure showing ionization to different vibrational levels.