Premed · Premed · General Chemistry 1

Lecture 13: Hybridization and Molecular Orbital Theory

General Chemistry I

Learning Objectives

By the end of this lecture, students will be able to:

1. Explain the concept of orbital hybridization and relate it to molecular geometry
2. Determine the hybridization of a central atom from its electron-domain geometry
3. Distinguish between sigma and pi bonds in molecules
4. Describe the basic principles of molecular orbital (MO) theory
5. Construct MO diagrams for homonuclear diatomic molecules of Period 2
6. Determine bond order, magnetism, and stability from MO diagrams

Lecture Content

I. Limitations of Lewis Structures and VSEPR

Lewis structures and VSEPR theory successfully predict molecular shapes, but they do not explain why those particular geometries arise. The atomic orbitals we studied earlier (s, p, d) do not naturally point in the directions needed to account for observed bond angles. The three p orbitals, for instance, are oriented at 90 degrees to each other, yet methane has bond angles of 109.5 degrees. Two bonding theories address this gap: valence bond (VB) theory with hybridization, and molecular orbital (MO) theory.

II. Valence Bond Theory and Hybridization

Valence bond theory proposes that a covalent bond forms when atomic orbitals on two atoms overlap, sharing electron density in the region between the nuclei. Hybridization is the process by which atomic orbitals on the same atom mix to form new hybrid orbitals whose shapes and orientations match the observed molecular geometry. The number of hybrid orbitals produced always equals the number of atomic orbitals that are combined. The type of hybridization is determined by the number of electron domains surrounding the central atom.

III. Types of Hybrid Orbitals

A. sp Hybridization (2 electron domains -> Linear)

Combining one s orbital with one p orbital produces two sp hybrid orbitals oriented 180 degrees apart in a linear arrangement. Two unhybridized p orbitals remain available for pi bonding. BeCl2, CO2, and acetylene (C2H2) all feature sp-hybridized central atoms.

B. sp2 Hybridization (3 electron domains -> Trigonal Planar)

Mixing one s orbital with two p orbitals yields three sp2 hybrid orbitals arranged 120 degrees apart in a plane. One unhybridized p orbital remains perpendicular to the molecular plane and is available for pi bonding. Examples include BF3, ethylene (C2H4), formaldehyde (H2CO), and each carbon atom in graphite.

C. sp3 Hybridization (4 electron domains -> Tetrahedral)

Combining one s orbital with all three p orbitals generates four sp3 hybrid orbitals oriented at 109.5 degrees in a tetrahedral arrangement. No unhybridized p orbitals remain. CH4, NH3, H2O, and diamond carbon are all sp3 hybridized.

D. sp3d Hybridization (5 electron domains -> Trigonal Bipyramidal)

Mixing one s, three p, and one d orbital produces five sp3d hybrid orbitals arranged in a trigonal bipyramidal geometry. PCl5 and SF4 are examples.

E. sp3d2 Hybridization (6 electron domains -> Octahedral)

Combining one s, three p, and two d orbitals yields six sp3d2 hybrid orbitals arranged at 90 degrees in an octahedral geometry. SF6 and XeF4 are examples.

IV. Sigma and Pi Bonds

A sigma bond forms from head-on (end-to-end) overlap of orbitals along the internuclear axis. It is cylindrically symmetric around the bond axis, with electron density concentrated directly between the nuclei. Every single bond is a sigma bond, and sigma bonds can form from overlap of s-s, s-p, head-on p-p, or hybrid-hybrid orbitals. A pi bond forms from side-by-side (lateral) overlap of unhybridized p orbitals, placing electron density above and below (or in front of and behind) the internuclear axis. Pi bonds are weaker than sigma bonds due to less effective orbital overlap. A double bond consists of 1 sigma bond plus 1 pi bond, and a triple bond consists of 1 sigma bond plus 2 pi bonds. An important consequence is that sigma bonds allow free rotation around the bond axis, while pi bonds restrict rotation -- a fact central to cis-trans isomerism.

<image>A detailed diagram showing sigma and pi bond formation in ethylene (C2H4). Top panel: two sp2-hybridized carbon atoms approaching each other. The head-on overlap of one sp2 orbital from each C forms the C-C sigma bond (shown as electron density along the bond axis). Each C also forms two sigma bonds with H atoms using remaining sp2 orbitals. Bottom panel: the unhybridized p orbital on each C (perpendicular to the molecular plane) overlaps side-by-side to form the pi bond, shown as two lobes of electron density above and below the molecular plane. Labels clearly identify: "sigma bond (head-on overlap)" and "pi bond (lateral overlap of p orbitals)." The bond angles of 120 degrees are marked.</image>

V. Counting Sigma and Pi Bonds

Quick rules make counting straightforward: a single bond contributes 1 sigma and 0 pi bonds; a double bond contributes 1 sigma and 1 pi; a triple bond contributes 1 sigma and 2 pi. In HCN (H-C≡N), the H-C single bond provides 1 sigma, and the C≡N triple bond provides 1 sigma plus 2 pi, for a total of 2 sigma and 2 pi bonds. In CH2=CH-CH=CH2, the total is 9 sigma bonds and 2 pi bonds.

VI. Introduction to Molecular Orbital (MO) Theory

Molecular orbital theory takes a fundamentally different approach from valence bond theory. Rather than localizing electrons between two specific atoms, MO theory distributes electrons over the entire molecule in molecular orbitals formed by the linear combination of atomic orbitals (LCAO). When two atomic orbitals combine, they produce two molecular orbitals: a bonding MO (formed by constructive interference, lower in energy than the parent atomic orbitals, with electron density concentrated between nuclei) and an antibonding MO (formed by destructive interference, higher in energy, with a node between nuclei, designated with an asterisk). The total number of molecular orbitals formed always equals the number of atomic orbitals combined.

VII. MO Diagrams for Homonuclear Diatomic Molecules

A. H2 and He2

In H2, two 1s atomic orbitals combine to form a bonding sigma_1s and an antibonding sigma*_1s. The two electrons fill the bonding orbital, giving a bond order of (2 - 0)/2 = 1, confirming that H2 is a stable molecule. In hypothetical He2, four electrons would fill both the bonding and antibonding orbitals, resulting in a bond order of (2 - 2)/2 = 0. He2 therefore does not exist as a stable molecule.

B. Period 2 Diatomics (Li2 through Ne2)

For molecules from O2 through Ne2, the standard energy ordering of molecular orbitals is: sigma_2s, sigma_2s, sigma_2p, pi_2p (degenerate pair), pi_2p (degenerate pair), sigma*_2p. For Li2 through N2, however, a modified ordering applies in which the pi_2p orbitals fall below sigma_2p, a consequence of s-p mixing (interaction between the 2s and 2p orbitals). This distinction is important for correctly predicting electronic properties.

C. Bond Order from MO Diagrams

Bond order is calculated as (number of bonding electrons - number of antibonding electrons) / 2. A positive bond order indicates a stable molecule, and higher bond order corresponds to a stronger, shorter bond. A bond order of zero means the molecule does not exist.

VIII. Magnetism from MO Theory

A molecule is diamagnetic if all of its electrons are paired, in which case it is weakly repelled by a magnetic field. A molecule is paramagnetic if it has one or more unpaired electrons, causing it to be attracted to a magnetic field. MO theory correctly predicts that O2 is paramagnetic, with two unpaired electrons occupying the degenerate pi*_2p orbitals. This is a notable triumph of MO theory, because Lewis structures predict O2 to be diamagnetic (all electrons paired) -- a clear failure of the Lewis approach. Nitrogen (N2) has all electrons paired and is correctly predicted to be diamagnetic, with a bond order of 3 (a triple bond).

<image>A side-by-side MO energy diagram for N2 and O2. For N2 (left): atomic orbitals of two N atoms on either side, with molecular orbitals in the center. Filling order (bottom to top): sigma_2s (2e), sigma_2s (2e), pi_2p (4e, two degenerate orbitals), sigma_2p (2e). Total: 10 electrons. Bond order = (8-2)/2 = 3. Labeled "diamagnetic." For O2 (right): sigma_2s (2e), sigma_2s (2e), sigma_2p (2e), pi_2p (4e), pi*_2p (2e with one electron in each degenerate orbital, following Hund's rule). Total: 12 electrons. Bond order = (8-4)/2 = 2. Two unpaired electrons highlighted in red, labeled "paramagnetic." The different ordering of sigma_2p and pi_2p between N2 and O2 is clearly indicated with an annotation about s-p mixing.</image>

IX. Summary: Valence Bond Theory vs. MO Theory

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