Sigma and Pi Bonds & Hybrid Orbitals – Vocabulary

Required Documents

• Summary handout: “Geometry and Polarity for Molecules and Polyatomic Ions 2” (posted on the module’s Learning Activities page)

Covalent-Bond Formation Basics

• A covalent bond forms when each bonding atom supplies one unpaired valence electron.
  • These singly occupied orbitals must overlap to share the two electrons.
• For every covalent-bond type you should be able to state:
  • Which specific orbitals overlap.
  • The spatial (geometric) nature of the overlap.
  • The relative bond strength.
  • Whether the bond is found in single, double or triple bonds.

Theories of Covalent Bonding

• Valence Bond (VB) Theory
  • Basis for VSEPR shapes.
  • Explains actual molecular geometries reasonably well.
• Molecular Orbital (MO) Theory
  • More mathematically involved; explains magnetic & other electronic properties.
  • Not examined in this course.

Sigma (\sigma) vs Pi (\pi) Bonds

• Two fundamental covalent-bond classes:
  • \sigma bond
  • Formed by direct (head-on) overlap of orbitals.
  • Overlap region lies along the internuclear axis.
  • \pi bond
  • Formed by lateral (side-to-side) overlap of two unhybridized p orbitals.
  • Overlap region is above & below (or in front of & behind) the internuclear axis.

Relative Strength

• Bond strength ≈ attraction of both nuclei for the shared e⁻ pair.
• \sigma bonds are stronger than \pi bonds because head-on overlap allows greater electron density between nuclei.

Relationship to Bond Order

• Single bond = 1 \sigma
• Double bond = 1 \sigma + 1 \pi
• Triple bond = 1 \sigma + 2 \pi
  • Thus a double bond is stronger than a single bond but < 2 × as strong, because the extra \pi contribution is weaker.
  • Triple bond likewise < 3 × single-bond strength.

Which Orbitals Overlap?

• \pi bond: strictly p–p sideways overlap.
• \sigma bond:
  • 1s vs hybrid orbital when H is involved.
  • Hybrid orbital vs hybrid orbital (or vs unhybridized p) for other atoms.
• Non-bonding (lone-pair) electrons also occupy hybrid orbitals.

Hybridization – Core Ideas

• Shapes/orientations of isolated-atom orbitals do not predict observed molecular angles → orbitals must reorganize when bonding.
• Hybrid orbitals form only in atoms that are covalently bonded; they do not exist in isolated atoms.
• Generating n hybrid orbitals consumes n atomic orbitals; \Sigma n is conserved.
• All hybrids in a set are equivalent in shape & energy.
• The hybridization adopted is dictated by electron-pair geometry from VSEPR.

Mapping Domains → Hybrids → Angles

• 4 electron domains → ideal 109.5^{\circ} → sp^{3}
• 3 electron domains → 120^{\circ} → sp^{2}
• 2 electron domains → 180^{\circ} → sp

Example 1 – CFH₃ (Tetrahedral, sp^{3})

• Lewis structure: central C bonded to F + 3 H.
• C: four \sigma bonds → needs 4 hybrid orbitals.
  • One 2s electron is promoted to the vacant 2p to yield four unpaired e⁻.
  • 1s + 3p \rightarrow 4\,sp^{3} hybrids oriented tetrahedrally (109.5°).
• F: one \sigma bond + three lone pairs = 4 domains → also sp^{3}.
  • Even though the original three 2p orbitals are at 90°, hybridization re-orients them to 109.5°.
• Resulting overlaps
  • C–F \sigma: sp^{3}{\text{C}} ∩ sp^{3}{\text{F}}
  • C–H \sigma (×3): sp^{3}{\text{C}} ∩ 1s{\text{H}}
  • F lone pairs: occupy remaining sp^{3}_{\text{F}} hybrids.

Example 2 – COH₂ (Formaldehyde, Trigonal Planar sp^{2})

• Lewis: O=CH₂ (double bond C=O).
• C: 3 \sigma + 1 \pi → needs 3 hybrids + leave 1 p unhybridized.
  • 1s + 2p \rightarrow 3\,sp^{2} hybrids (planar, 120°).
• O: 1 \sigma + 2 lone pairs + 1 \pi → also 3 hybrids + 1 p.
• Overlaps
  • C–O \sigma: sp^{2}{\text{C}} ∩ sp^{2}{\text{O}}
  • C–H \sigma (×2): sp^{2}{\text{C}} ∩ 1s{\text{H}}
  • C=O \pi: lateral overlap p{\text{C}} ∩ p{\text{O}} (above & below plane).
  • O lone pairs: fill remaining two sp^{2}_{\text{O}} hybrids.

Example 3 – C₂H₂ (Acetylene, Linear sp)

• Lewis & actual geometry: H–C≡C–H (180°).
• Each C: 2 \sigma + 2 \pi → needs 2 hybrids; leave 2 p orbitals unhybridized.
  • 1s + 1p \rightarrow 2\,sp hybrids (linear).
• Overlaps
  • C≡C \sigma: sp{\text{C1}} ∩ sp{\text{C2}}
  • C–H \sigma (×2): sp{\text{C}} ∩ 1s{\text{H}}
  • Two \pi bonds: orthogonal p_{\text{C}} pairs overlap sideways in two perpendicular planes.

Comprehensive Domain/Hybrid/Angle Table

Skills & Expectations

• From any Lewis structure you must be able to:
  • Label each bond as \sigma or \pi.
  • Specify the orbital on each atom that participates in that bond (e.g.
    sp^{3}, sp^{2}, sp, p, 1s).
• Drawing 3-D “balloon” hybrid-orbital pictures is not required.

Practice Problem Outline (Slide 25 Recap)

• Given a complex organic fragment containing F, C, N, O & H atoms, you filled a table:
  • For every bond you identified: type (σ/π), domain count → hybrid on first atom, domain count → hybrid on second atom.
  • Examples:
  • F₁–C₂ \sigma: F (4 domains → sp^{3}) vs C (3 domains → sp^{2}).
  • C₄≡N₅ triple bond contains 1 \sigma (sp–sp) + 2 \pi (p–p) overlaps.

Energetic Footnote – s→p Promotion

• Occasionally an s electron is promoted to p (e.g. C in CFH₃) to create enough unpaired electrons.
  • Energy cost < energy released by forming additional bonds, so overall thermodynamically favorable.

Real-World Implications & Connections

• Magnetic properties (paramagnetism/diamagnetism) are better rationalized by MO theory; VB theory remains preferred for routine shape and hybridization predictions.
• Bond strength hierarchy (triple > double > single) underpins reactivity trends in organic & inorganic chemistry.
• Hybridization provides a quantitative basis for explaining macroscopic molecular shape → critical for drug binding, material properties, enzymatic specificity.
• Understanding \pi bonds clarifies conjugation & resonance (delocalized \pi systems), foundational for UV–Vis absorption and color in organic dyes.

What Comes Next in the Course

• Unit 6 will focus on quantitative composition:
  • Percent mass of elements in compounds.
  • Empirical & molecular formula determination from experimental data.
  • Solution concentration calculations (molarity, mass %, etc.).