CHM.CHP.8

Chapter 8: Chemical Bonding – Advanced Theories

8.1 Valence Bond Theory

Valence Bond Theory (VBT) explains how atomic orbitals overlap to form covalent bonds in molecules. It describes the formation of bonds as the sharing of electron density between atoms, with the strength and type of bond depending on the extent and orientation of orbital overlap.

• Atomic Orbital Overlap: Covalent bonds form when atomic orbitals from two atoms overlap, allowing electrons to be shared.

• Bonding and Nonbonding Orbitals:

  • Valence orbitals participate in bonding.

  • Core orbitals are too stable and do not participate in bonding.

• Energy Diagram Example: For a fluorine atom, the 2p orbitals are valence orbitals available for bonding, while 1s orbitals are core orbitals.

Example: Describe the orbital overlap in HF. The hydrogen 1s orbital overlaps with the fluorine 2p orbital to form a sigma bond.

8.1.1 Sigma and Pi Bonds

Sigma (σ) and pi (π) bonds are the two main types of covalent bonds formed by orbital overlap.

• Sigma (σ) Bonds:

  • Formed by head-on (end-to-end) overlap of orbitals.

  • Electron density is concentrated along the axis connecting the two nuclei.

  • Present in all single bonds.

• Pi (π) Bonds:

  • Formed by side-by-side overlap of p orbitals.

  • Electron density is above and below the plane of the nuclei.

  • Present in double and triple bonds (in addition to a sigma bond).

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

Example: In ethylene (C2H4), the C=C double bond consists of one sigma and one pi bond.

8.2 Hybrid Atomic Orbitals

Hybridization is the concept of mixing atomic orbitals to form new, equivalent hybrid orbitals suitable for the pairing of electrons to form chemical bonds in specific molecular geometries.

• Hybridization: Atomic orbitals (s, p, sometimes d) combine to form hybrid orbitals (sp, sp2, sp3, etc.).

• Directional Properties: Hybrid orbitals have specific shapes and orientations that match observed molecular geometries.

• VBT Theory: Explains molecular shapes (e.g., tetrahedral) by the orientation of hybrid orbitals.

Example: In methane (CH4), the carbon atom undergoes sp3 hybridization, forming four equivalent sp3 orbitals arranged tetrahedrally.

Types of Hybridization

Steric Number	Electron Geometry	Hybridization	Number of Hybrid Orbitals	Number of Unhybridized p Orbitals	Picture
2	Linear	sp	2	2	Linear arrangement
3	Trigonal planar	sp2	3	1	Trigonal planar
4	Tetrahedral	sp3	4	0	Tetrahedral
5	Trigonal bipyramidal	sp3d	5	0	Trigonal bipyramidal
6	Octahedral	sp3d2	6	0	Octahedral

Example: In ethyne (C2H2), each carbon atom is sp hybridized, resulting in a linear geometry.

8.3 Multiple Bonds

Multiple bonds (double and triple bonds) involve both sigma and pi bonds. Resonance describes the delocalization of electrons across multiple atoms, stabilizing the molecule.

• Resonance: Some molecules cannot be represented by a single Lewis structure; instead, they are described by two or more resonance structures.

• Bonding in Multiple Bonds:

  • Double bond: 1 sigma + 1 pi

  • Triple bond: 1 sigma + 2 pi

Example: The nitrate ion (NO3-) has three equivalent resonance structures, each with a different arrangement of double and single bonds.

8.4 Molecular Orbital Theory

Molecular Orbital (MO) Theory describes the formation of molecular orbitals by the combination of atomic orbitals from different atoms. Electrons in molecules are delocalized over the entire molecule, and MO theory explains properties that localized bond theories cannot.

• Bonding and Antibonding Orbitals:

  • Bonding orbitals result from constructive interference (in-phase combination).

  • Antibonding orbitals result from destructive interference (out-of-phase combination).

• Bond Order: Indicates the strength and stability of a bond. Calculated as: $\text{Bond order} = \frac{(\text{number of bonding electrons}) - (\text{number of antibonding electrons})}{2}$

• Electron Configuration in MOs: Electrons fill molecular orbitals according to the Aufbau Principle, Pauli Exclusion Principle, and Hund's Rule.

Molecule	Electron Configuration	Bond Order
H2	($\sigma_{1s})^2$	1
He2	($\sigma_{1s})^2(\sigma_{1s}^*)^2$	0
O2	$\left(\sigma_{2s}\right)^2(\sigma_{2s}^{*})^2(\sigma_{2p_{z}})^2(\pi_{2p_{x}})^2(\pi_{2p_{y}})^2(\pi_{2p_{x}}^{*})^1(\pi_{2p_{y}}^{*})^1$	2
N2	($\sigma_{2s})^2(\sigma_{2s}^*)^2(\pi_{2p_x})^2(\pi_{2p_y})^2(\sigma_{2p_z})^2$	3

Example: O2 is paramagnetic due to two unpaired electrons in its molecular orbitals, as predicted by MO theory.

Applications and Limitations

• Applications: MO theory explains magnetic properties, color, and absorption spectra of molecules.

• Limitations: MO theory is more complex than localized bond theories and may not be necessary for simple molecules.

Example: Draw the MO diagrams for H2, He2, and He2+ and calculate their bond orders.

Additional info: These notes expand on the provided slides by including definitions, formulas, and examples for each topic, as well as reconstructed tables for hybridization and molecular orbital configurations.