Valence Bond Theory and Hybrid Atomic Orbitals

Valence Bond Theory

• Valence bond theory describes a covalent bond as the overlap of half-filled atomic orbitals, resulting in a pair of electrons shared between the two bonded atoms.
• Sigma ($\sigma$) bonds are formed by end-to-end overlap and are stronger than pi ($\pi$) bonds, which are formed by side-by-side overlap.
• Single bonds are always sigma bonds, while multiple bonds consist of one sigma bond and one or two pi bonds.
• VB theory explains molecular shapes using the arrangement of hybrid orbitals that maximize overlap in covalent bonds.
• Resonance occurs when multiple valid Lewis structures can be drawn for a molecule; the actual electronic structure is an average of those shown by the individual Lewis structures.

Hybrid Atomic Orbitals

• Hybridization is introduced to explain the geometry of bonding orbitals in valence bond theory.
• Hybrid orbitals are atomic orbitals formed by mathematically combining two or more valence atomic orbitals on an atom.
• The number of hybrid orbitals formed equals the number of atomic orbitals combined.
• Use the following method to define hybridization:
  1. Draw the Lewis structure of the molecule or ion.
  2. Determine the electron-group geometry around the central atom.
  3. Specify the hybrid orbitals needed to accommodate this electron-group geometry.

sp Hybridization

• Linear electron-group geometry requires two hybrid orbitals, achieved by mixing one s and one p orbital to form two sp hybrid orbitals.
• These sp orbitals are oriented 180 degrees apart.
  • s + p \rightarrow 2 \space sp \space orbitals
• Examples include beryllium chloride ($\text{BeCl}2$) and carbon dioxide ($\text{CO}2$).

sp2 Hybridization

• Trigonal planar electron-group geometry requires three hybrid orbitals, formed by mixing one s and two p orbitals to create three sp2 hybrid orbitals.
• These sp2 orbitals point towards the corners of an equilateral triangle, 120 degrees apart.
  • s + 2p \rightarrow 3 \space sp^2 \space orbitals
• An example is boron trifluoride ($\text{BF}_3$).

sp3 Hybridization

• Tetrahedral electron-group geometry requires four hybrid orbitals, made by mixing one s and three p orbitals to generate four sp3 hybrid orbitals.
• These sp3 orbitals are directed towards the corners of a tetrahedron, approximately 109.5 degrees apart.
  • s + 3p \rightarrow 4 \space sp^3 \space orbitals
• Examples include methane ($\text{CH}4$) and water ($\text{H}2\text{O}$).

sp3d Hybridization

• Trigonal bipyramidal electron-group geometry requires five hybrid orbitals, formed by mixing one s, three p, and one d orbital, resulting in five sp3d hybrid orbitals.
  • s + 3p + d \rightarrow 5 \space sp^3d \space orbitals
• An example is phosphorus pentachloride ($\text{PCl}_5$).

sp3d2 Hybridization

• Octahedral electron-group geometry requires six hybrid orbitals, formed by mixing one s, three p, and two d orbitals, resulting in six sp3d2 hybrid orbitals.
  • s + 3p + 2d \rightarrow 6 \space sp^3d^2 \space orbitals
• An example is sulfur hexafluoride ($\text{SF}_6$).

Multiple Bonds

• Multiple bonds (double and triple bonds) consist of sigma ($\sigma$) and pi ($\pi$) bonds.
• A double bond consists of one sigma bond and one pi bond.
• A triple bond consists of one sigma bond and two pi bonds.
• Rotation around sigma bonds is allowed, but rotation around pi bonds is restricted, giving rise to geometric isomerism.
• To describe multiple bonds using hybrid orbitals:
  1. Assign hybridization using the method described earlier.
  2. Describe the $\sigma$ bonds using hybrid orbitals and the $\pi$ bonds using unhybridized p orbitals.
• For example, in ethene ($\text{H}2\text{C=CH}2$):
  • Each carbon is sp2 hybridized, forming sigma bonds with two hydrogens and the other carbon.
  • The unhybridized p orbitals on each carbon overlap side-by-side to form the pi bond.
• In ethyne ($\text{H−C≡C−H}$):
  • Each carbon is sp hybridized, forming sigma bonds with one hydrogen and the other carbon.
  • Two unhybridized p orbitals on each carbon overlap side-by-side to form the two pi bonds.

Molecular Orbital Theory

• Molecular orbital (MO) theory describes the electronic structure of molecules in terms of molecular orbitals, which are delocalized over the entire molecule.
• Molecular orbitals are formed by combining atomic orbitals.
• Bonding orbitals are lower in energy than the original atomic orbitals, while antibonding orbitals are higher in energy.
• The bond order is a measure of the stability of a molecule and is calculated as:
  • \text{Bond Order} = \frac{\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}}{2}
• A higher bond order indicates a more stable molecule.
• MO diagrams show the relative energies and occupancy of molecular orbitals.
• For diatomic molecules, MO diagrams can be constructed by combining the atomic orbitals of the constituent atoms.
• For the second-row diatomic molecules (Li2 to Ne2), the order of MOs is typically:
  • \sigma{2s} < \sigma{2s}^* < \sigma{2p} < \pi{2p} < \pi{2p}^* < \sigma{2p}^*
• However, for molecules like O2 and F2, the order is slightly different:
  • \sigma{2s} < \sigma{2s}^* < \pi{2p} < \sigma{2p} < \pi{2p}^* < \sigma{2p}^*
• MO theory can also be used to explain the magnetic properties of molecules. For example, O2 is paramagnetic because it has unpaired electrons in its $\pi_{2p}^*$ orbitals.
• Delocalized molecular orbitals are molecular orbitals that extend over more than two atoms, and are often found in molecules with resonance structures.

Examples

• Hydrogen (H2) has a bond order of 1: (2 bonding electrons - 0 antibonding electrons)/2 = 1.
• Helium (He2) has a bond order of 0: (2 bonding electrons - 2 antibonding electrons)/2 = 0, indicating that He2 does not exist.
• Diatomic molecules of the second period like N2 and O2 can be analyzed using MO theory to describe their bonding characteristics and magnetic properties.
• In summary, Molecular Orbital Theory provides a more complete description of chemical bonding that can explain properties that Valence Bond Theory cannot.