Lecture Notes #2

Molecule Orbitals + Hybridization

Learning Goals

• Understand the essentials of Molecular Orbital (MO) Theory for organic chemistry.

• Define and describe hybrid orbitals.

• Explain how hybrid orbitals influence chemical properties.

Electron Orbitals

Nature of Electron Orbitals

• Electrons are not tiny particles orbiting a nucleus; they possess mass (like particles) but also exhibit wave-like behavior.

• Electrons exist in atomic orbitals (AO), which are regions of space around the nucleus where there is a probability of finding an electron.

• The shape of atomic orbitals is derived from the Schrödinger Equation (Quantum Theory).

Atomic Orbitals: Energy and Shape

Lowest Energy Orbitals

• The lowest energy atomic orbital is held closest to the nucleus due to the attraction between the negative electron and the positive nucleus.

• 1s orbital: Spherical shape, lowest energy.

• The wavefunction of an orbital can be phased positive or negative; shading in diagrams represents the phase (sign) of the function, not the charge.

Increasing Energy Orbitals

• As electrons are added, orbitals move farther from the nucleus, resulting in increased energy.

• This leads to the formation of nodes (regions of zero electron density) and changes in the phase of the wavefunction.

• 2s orbital: Spherical, with a node.

• 2p orbitals: Dumbbell-shaped, with the nucleus at the center of the node. Each side of the dumbbell is called a lobe.

Molecular Orbital Theory (MO)

Formation and Rules

• Bonds form when atomic orbitals overlap, creating molecular orbitals (MOs).

• In MO theory, electrons belong to the entire molecule, not just individual atoms.

• Rules for MO Formation:

  • Atomic orbitals must be similar in energy and correctly oriented in space to overlap and form an MO.

  • Regions of overlap with cylindrical symmetry form σ (sigma) orbitals.

  • Side-by-side overlap forms π (pi) orbitals.

  • No real overlap due to improper orientation results in nonbonding orbitals.

• The number of MOs is a linear combination of AOs: $n ext{ AOs} ightarrow n ext{ MOs}$ Example: 4 atomic orbitals produce 4 molecular orbitals.

• Same phase and orientation: bonding MO (where electrons are shared).

• Opposite phase and orientation: antibonding MO (region of space where electrons destabilize the bond).

Types of Bonds

AOs	MO	Type of Bond
in-phase	σ	σ bond
in-phase (side)	π	π bond
none	nonbonding	nonbonding (n) orbital
out-of-phase	σ*	σ* (antibonding)
out-of-phase (side)	π*	π* (antibonding)

Bond Rotation

Rotation Around Bonds

• σ bonds can rotate freely around the bond axis; phase and orientation remain unchanged.

• π bonds cannot rotate freely; improper orientation or phase leads to bond breaking.

Hybridization and Molecular Geometry

The Problem with Geometry

• Methane (CH4) has four single bonds formed from carbon's valence orbitals.

• According to VSEPR theory, CH4 should be tetrahedral (bond angles of 109.5°) to minimize repulsion.

• However, carbon's valence AOs (2s, 2px, 2py, 2pz) are all 90° apart.

• Solution: Mix AOs within the atom to create new MOs with ideal geometry, stabilizing the molecule.

Tetrahedral Geometry (sp3 Hybridization)

• Mix all valence AOs: s + p + p + p = 4 sp3 MOs (25% s, 75% p).

• Each sp3 orbital forms a σ bond with hydrogen in CH4.

• Example: Ammonia (NH3) also uses sp3 hybridization for its geometry.

Trigonal Planar Geometry (sp2 Hybridization)

• Mix (s + p + p) + p = 3 sp2 + p (33% s, 67% p).

• sp2 orbitals form σ bonds; the remaining p orbital forms a π bond.

• Example: Ethylene (C2H4) has sp2 hybridization at each carbon.

Linear Geometry (sp Hybridization)

• Mix (s + p) + p + p = 2 sp (50% s, 50% p) + p + p.

• sp orbitals form σ bonds; two p orbitals form π bonds.

• Example: Acetylene (C2H2) has sp hybridization at each carbon.

General Rules for Hybridization

• If C, N, O, F, etc. can participate in:

  • 2 π bonds → linear (sp)

  • 1 π bond → trigonal planar (sp2)

  • 0 π bonds → tetrahedral (sp3)

Examples

• In acetylene (C2H2), each carbon is sp hybridized (linear geometry).

• In ethylene (C2H4), each carbon is sp2 hybridized (trigonal planar geometry).

• In methane (CH4), carbon is sp3 hybridized (tetrahedral geometry).

Practice Questions

Question 1

If four atomic orbitals are used to make molecular orbitals, how many molecular orbitals are produced?

• Answer: Four

Question 2

What kind of molecular orbital, if any, will be generated when the following atomic orbitals are combined: 1s + 2px?

• Answer: Antibonding

Summary Table: Types of Bonds from AO Overlap

AO Overlap	MO Formed	Bond Type
in-phase (end-to-end)	σ	σ bond
in-phase (side-to-side)	π	π bond
none	n	nonbonding
out-of-phase (end-to-end)	σ*	σ* (antibonding)
out-of-phase (side-to-side)	π*	π* (antibonding)

Additional info: These notes cover foundational concepts in molecular orbital theory and hybridization, which are essential for understanding structure and bonding in organic chemistry (Ch. 1), as well as the basis for functional group reactivity and molecular geometry.