Chemical Bonding II: Molecular Geometry and Hybridization of Atomic Orbitals

Chemical Bonding II: Molecular Geometry and Hybridization of Atomic Orbitals

Valence Shell Electron Pair Repulsion (VSEPR) Model

The VSEPR model is used to predict the geometry of molecules based on the repulsion between electron pairs (bonding and nonbonding) in the valence shell of the central atom.

• Valence shell: The outermost electron-occupied shell of an atom, containing electrons involved in bonding.

• Basic Principle: Electron pairs around a central atom arrange themselves to minimize repulsion, determining the molecular geometry.

VSEPR Geometries for Molecules with No Lone Pairs on the Central Atom

Class	# of atoms bonded to central atom	# lone pairs on central atom	Arrangement of electron pairs	Molecular Geometry	Bond Angle	Example
AB2	2	0	Linear	Linear	180°	CO2
AB3	3	0	Trigonal planar	Trigonal planar	120°	NO3-
AB4	4	0	Tetrahedral	Tetrahedral	109.5°	CH4
AB5	5	0	Trigonal bipyramidal	Trigonal bipyramidal	90°, 120°	PCl5
AB6	6	0	Octahedral	Octahedral	90°	SF6

VSEPR Geometries for Molecules with Lone Pairs on the Central Atom

Class	# of atoms bonded to central atom	# lone pairs on central atom	Arrangement of electron pairs	Molecular Geometry	Bond Angle	Example
AB2E	2	1	Trigonal planar	Bent	<120°	NO2-
AB3E	3	1	Tetrahedral	Trigonal pyramidal	<109.5°	NH3
AB2E2	2	2	Tetrahedral	Bent	<109.5°	H2O

Effect of Lone Pairs on Bond Angles

• Lone pairs occupy more space than bonding pairs, causing bond angles to decrease from the ideal geometry.

• Order of repulsion strength: lone pair–lone pair > lone pair–bonding pair > bonding pair–bonding pair.

• Example: In NH3, the H–N–H bond angle is 107.3° (less than 109.5° in CH4), and in H2O, the H–O–H bond angle is 104.5°.

Rules for Applying the VSEPR Model

1. Write the Lewis structure, considering only electron pairs around the central atom.

2. Count the number of electron pairs (bonding and lone pairs). Treat double and triple bonds as single electron domains.

3. Predict the geometry based on the number of electron domains.

4. When predicting bond angles, remember that lone pairs repel more strongly than bonding pairs.

Multiple Central Atoms: For molecules with more than one central atom, assign geometry to each central atom separately using the VSEPR model.

Polarity of Molecules

The polarity of a molecule depends on both the polarity of its bonds and its molecular geometry.

• Dipole moment (μ): A quantitative measure of molecular polarity, given by:

$\mu = Q \times r$

• Where Q is the charge and r is the distance between charges.

• Polar covalent bond: A bond with greater electron density around one atom.

• Polar molecules: Molecules with a net dipole moment (e.g., HCl, HF).

• Nonpolar molecules: Molecules with no net dipole moment (e.g., F2, O2, CO2).

• The overall molecular polarity is the vector sum of individual bond dipoles.

Important:

• Molecules with lone pairs on the central atom are generally polar.

• Molecules with no lone pairs and all identical atoms bonded to the central atom are generally nonpolar.

Valence Bond Theory

Valence bond theory describes covalent bond formation as the overlap of atomic orbitals from each atom involved in the bond.

• Each shared pair of electrons uses one valence orbital from each bonded atom.

• Example: In HF, the bond is formed by overlap of a 1s orbital on H and a 2p orbital on F.

• Three features of this bonding description:

  • Orientation of the bond is along the axis of the overlapping orbitals.

  • Each atomic orbital used for bonding is singly occupied in the separate atoms.

  • Filled valence orbitals not used in bonding become lone pairs.

Hybridization of Atomic Orbitals

Hybrid orbitals are formed by mixing two or more atomic orbitals on the same atom, resulting in new orbitals with different shapes and directional properties.

• The type and number of atomic orbitals mixed determine the energy and directionality of the hybrid orbitals.

• Hybridization explains observed molecular geometries that cannot be described by simple atomic orbitals.

Types of Hybridization

• sp hybridization: Mixing one s and one p orbital forms two sp hybrid orbitals (linear geometry, 180° bond angle). Example: BeCl2.

• sp2 hybridization: Mixing one s and two p orbitals forms three sp2 hybrid orbitals (trigonal planar geometry, 120° bond angle). Example: BF3.

• sp3 hybridization: Mixing one s and three p orbitals forms four sp3 hybrid orbitals (tetrahedral geometry, 109.5° bond angle). Example: CH4, NH3, H2O.

• sp3d and sp3d2 hybridization: Involves d orbitals for expanded octets (trigonal bipyramidal and octahedral geometries). Examples: PCl5, SF6.

Determining Hybridization State

1. Draw the Lewis structure of the molecule.

2. Predict the arrangement of electron pairs (bonding and lone pairs) using the VSEPR model.

3. Count the number of electron domains (bonding + lone pairs) around the atom; this equals the number of hybrid orbitals needed.

# of Bonded Atoms + Lone Pairs	Hybridization	Examples
2	sp	BeCl2
3	sp2	BF3
4	sp3	CH4, NH3, H2O
5	sp3d	PCl5
6	sp3d2	SF6

Single and Multiple Bonds

• Sigma (σ) bond: Formed by head-to-head overlap of orbitals along the internuclear axis. All single bonds are sigma bonds.

• Pi (π) bond: Formed by sideways overlap of p orbitals above and below the plane of the nuclei. Double bonds consist of one sigma and one pi bond; triple bonds consist of one sigma and two pi bonds.

Example: In ethylene (C2H4), each carbon is sp2 hybridized, and the double bond consists of one sigma and one pi bond.

Summary Table: Sigma and Pi Bonds

Bond Type	Number of Sigma Bonds	Number of Pi Bonds
Single	1	0
Double	1	1
Triple	1	2

Isomerism and Molecular Structure

• Isomers: Compounds with the same molecular formula but different structures (e.g., cis/trans isomers in alkenes).

• Arrangement of atoms and hybridization affect the physical and chemical properties of molecules.

Examples and Applications

• Use the VSEPR model to predict the geometry of SiBr4 (tetrahedral), CS2 (linear), NO3- (trigonal planar), and ClNO (bent or linear depending on structure).

• Determine the hybrid orbitals of carbon in various organic molecules (e.g., sp3 in CH3–CH3, sp2 in CH2=CH2, sp in HC≡CH).

• Identify the orbitals forming bonds in H2CCN and count sigma and pi bonds.

• For nitrous acid (HONO), determine the hybridization of nitrogen and the central oxygen atom.

Additional info: These notes provide a comprehensive overview of molecular geometry and hybridization, essential for understanding chemical bonding and molecular structure in General Chemistry.