Chapter 6: Bonding and Molecular Structure – Orbital Hybridization and Molecular Orbitals

Bonding and Molecular Structure: Orbital Hybridization and Molecular Orbitals

Introduction to Chemical Bonding

Chemical bonding explains how atoms combine to form molecules with specific structures and properties. Two advanced theories—Valence Bond Theory and Molecular Orbital Theory—provide deeper insight into the nature of chemical bonds beyond the basic Lewis model.

• Valence electrons are the outermost electrons involved in bonding.

• Bonding involves the overlap or mixing of atomic orbitals to form new molecular orbitals.

Advanced Theories of Chemical Bonding

Valence Bond (VB) Theory

Valence Bond Theory, developed by Linus Pauling, describes covalent bonds as the overlap of half-filled atomic orbitals from two atoms. This overlap allows two electrons of opposite spin to be accommodated in the overlapping region, forming a bond.

• Electrons are localized between atoms or exist as lone pairs.

• Each bond is formed by the overlap of one atomic orbital from each atom.

• Both electrons in the bond are simultaneously attracted to both nuclei.

Molecular Orbital (MO) Theory

Molecular Orbital Theory, developed by Robert Mulliken, treats electrons as delocalized over the entire molecule. Electrons occupy molecular orbitals (MOs) that extend across the whole molecule, not just between two atoms.

• Used for a quantitative picture of bonding and to describe molecules in excited states.

• Essential for explaining bonding in molecules that cannot be described by VB theory alone (e.g., O2, NO).

• MOs are formed by the linear combination of atomic orbitals (LCAO).

Sigma (σ) Bond Formation

A sigma (σ) bond is formed by the end-to-end (axial) overlap of atomic orbitals. This type of bond is the strongest covalent bond and is found in all single bonds.

• Examples of σ bond formation:

  • Two s orbitals overlap (e.g., H–H bond in H2).

  • One s and one p orbital overlap (e.g., H–Cl bond in HCl).

  • Two p orbitals overlap end-to-end (e.g., F–F bond in F2).

Orbital Hybridization

Orbital hybridization is the process by which atomic orbitals mix to form new, equivalent hybrid orbitals that are oriented to maximize overlap and bond strength. This concept explains molecular geometries that cannot be described by the simple overlap of atomic orbitals.

• All available valence orbitals of an atom are mixed to form hybrid orbitals.

• Hybrid orbitals have the same energy and correct geometry for bonding.

• The number of hybrid orbitals equals the number of atomic orbitals mixed.

sp3 Hybridization: Tetrahedral Geometry

In molecules like methane (CH4), one s and three p orbitals hybridize to form four equivalent sp3 hybrid orbitals, resulting in a tetrahedral electron pair geometry (bond angles ≈ 109.5°).

• Each sp3 orbital accommodates one electron pair (bonding or lone pair).

• Example: CH4 has four sp3 hybrid orbitals forming four C–H σ bonds.

sp2 Hybridization: Trigonal Planar Geometry

In molecules like BF3, one s and two p orbitals hybridize to form three equivalent sp2 hybrid orbitals, resulting in a trigonal planar geometry (bond angles ≈ 120°).

• Each sp2 orbital forms a σ bond, while the remaining unhybridized p orbital can participate in π bonding.

• Example: BF3 has three sp2 hybrid orbitals for B–F σ bonds.

sp Hybridization: Linear Geometry

When one s and one p orbital hybridize, two sp hybrid orbitals are formed, resulting in a linear geometry (bond angle = 180°).

• Example: BeCl2 (not shown in images, but standard example).

Hybridization Involving d Orbitals

For molecules with expanded octets (e.g., SF6), d orbitals can participate in hybridization, forming sp3d or sp3d2 hybrid orbitals for trigonal bipyramidal or octahedral geometries, respectively.

Summary Table: Types of Hybridization and Molecular Geometry

Type of Hybridization	Atomic Orbitals Mixed	No. of Hybrid Orbitals	Geometry	Example
sp	1 s + 1 p	2	Linear (180°)	BeCl2
sp2	1 s + 2 p	3	Trigonal planar (120°)	BF3
sp3	1 s + 3 p	4	Tetrahedral (109.5°)	CH4
sp3d	1 s + 3 p + 1 d	5	Trigonal bipyramidal (90°, 120°)	PF5
sp3d2	1 s + 3 p + 2 d	6	Octahedral (90°)	SF6

Molecular Orbital Theory: Key Concepts

Molecular Orbital Theory (MO Theory) provides a more complete description of bonding, especially for molecules with delocalized electrons or those in excited states.

• MOs are formed by the linear combination of atomic orbitals (LCAO).

• When two atomic orbitals combine, they form two MOs: one bonding (lower energy) and one antibonding (higher energy).

• Electrons fill the lowest energy MOs first, following Hund's rule and the Pauli exclusion principle.

Bond Order Calculation

Bond order indicates the strength and stability of a bond. It is calculated as:

$\text{Bond Order} = \frac{(\text{number of electrons in bonding MOs}) - (\text{number of electrons in antibonding MOs})}{2}$

• A bond order of 0 means the molecule is unstable and does not exist.

• A higher bond order indicates a stronger, more stable bond.

Comparison of Bonding Theories

• Lewis Theory: Bonds are formed by sharing electrons between atoms (localized electron pairs).

• Valence Bond Theory: Bonds are formed by the overlap of half-filled atomic orbitals (localized between two atoms).

• Molecular Orbital Theory: Electrons are delocalized in molecular orbitals spread over the entire molecule.

Summary Table: Comparison of Bonding Theories

Theory	Electron Description	Bonding Description	Strengths	Limitations
Lewis	Localized pairs	Electron sharing	Simple, intuitive	Cannot explain resonance, magnetism
Valence Bond	Localized in overlapping orbitals	Orbital overlap	Explains shapes, hybridization	Limited for delocalized systems
Molecular Orbital	Delocalized in MOs	LCAO, delocalization	Explains resonance, magnetism, excited states	More complex, less intuitive

Key Equations and Concepts

• Bond Order (MO Theory):

  • $\text{Bond Order} = \frac{(\text{number of electrons in bonding MOs}) - (\text{number of electrons in antibonding MOs})}{2}$

• Hybridization: Number of hybrid orbitals = number of atomic orbitals mixed.

• Types of Bonds: Sigma (σ) bonds are formed by end-to-end overlap; pi (π) bonds are formed by side-to-side overlap of unhybridized p orbitals (not detailed in these slides but important for double/triple bonds).

Examples and Applications

• Methane (CH4): Carbon forms four sp3 hybrid orbitals, resulting in a tetrahedral geometry.

• Boron trifluoride (BF3): Boron forms three sp2 hybrid orbitals, resulting in a trigonal planar geometry.

Additional info: For more complex molecules, hybridization can involve d orbitals (e.g., SF6 uses sp3d2 hybridization for octahedral geometry).