2.2 Valence Bond Theory and Hybridization

Valence Bond Theory and Hybridization

Valence Bond Theory (VBT) explains how atoms form covalent bonds through the overlap of atomic orbitals. Each overlapping pair of orbitals shares electron density, producing a localized bond between two nuclei. Hybridization extends this picture by mixing standard atomic orbitals into new, equivalent hybrid orbitals that account for observed molecular geometries and bond angles.

Valence Bond Theory and Bonding

Fundamentals of Valence Bond Theory

Valence Bond Theory treats a covalent bond as the result of two half-filled (or one filled and one empty) atomic orbitals overlapping in the region between two nuclei. The greater the orbital overlap, the stronger the bond.

• A sigma (σ) bond forms through end-to-end overlap along the internuclear axis. Because the electron density is concentrated directly between the nuclei, sigma bonds are the strongest type of covalent bond.
• A pi (π) bond forms through side-by-side overlap of p orbitals, with electron density above and below (or in front of and behind) the internuclear axis. Pi bonds are weaker than sigma bonds because the overlap is less direct.
• Electron domains are regions around a central atom where electrons are likely found. These include bonding pairs, lone pairs, and even single unpaired electrons. The arrangement of electron domains drives molecular shape through electron-electron repulsion.

Types of Bonds and Orbital Interactions

Sigma bonds are the first bond formed between any two atoms. They can arise from several orbital combinations:

• s–s overlap (e.g., $H_2$: each H contributes a 1s orbital)
• s–p overlap (e.g., HF: H's 1s overlaps with F's 2p)
• p–p overlap (e.g., $F_2$: head-on overlap of 2p orbitals)

Pi bonds only appear in multiple bonds, always alongside a sigma bond:

• A double bond = 1 σ + 1 π (e.g., $C_2H_4$, ethylene)
• A triple bond = 1 σ + 2 π (e.g., $C_2H_2$, acetylene)

The sigma bond allows free rotation about the bond axis, while pi bonds restrict rotation because their side-by-side overlap would break if the atoms twisted relative to each other. This distinction matters for understanding cis/trans isomerism and rigidity in multiply bonded systems.

Hybridization

Principles of Orbital Hybridization

Consider carbon: its ground-state electron configuration is $1s^2\,2s^2\,2p^2$, which suggests it should form only two bonds (two half-filled 2p orbitals). Yet carbon routinely forms four equivalent bonds, as in methane. Hybridization resolves this by mixing atomic orbitals on the same atom to produce a new set of hybrid orbitals with intermediate energy and identical shape.

Key rules:

• The number of hybrid orbitals produced equals the number of atomic orbitals mixed.
• Hybrid orbitals are degenerate (same energy), unlike the original s and p orbitals they came from.
• Any atomic orbitals not involved in hybridization (typically unhybridized p orbitals) remain available for pi bonding.

Types of Hybridization

sp hybridization — Mix one s + one p orbital → 2 sp hybrids

• Geometry: linear, 180° bond angles
• Two unhybridized p orbitals remain, available for up to two pi bonds
• Examples: $BeCl_2$, $CO_2$, $C_2H_2$ (acetylene)

sp² hybridization — Mix one s + two p orbitals → 3 sp² hybrids

• Geometry: trigonal planar, 120° bond angles
• One unhybridized p orbital remains for one pi bond
• Examples: $BF_3$, $CO_3^{2-}$, $C_2H_4$ (ethylene)

sp³ hybridization — Mix one s + three p orbitals → 4 sp³ hybrids

• Geometry: tetrahedral, 109.5° bond angles
• No unhybridized p orbitals remain; no pi bonding from the central atom
• Examples: $CH_4$, $NH_3$ (with one lone pair), $H_2O$ (with two lone pairs)

Expanded Octet Hybridization

For elements in Period 3 and beyond, d orbitals can participate in hybridization, allowing more than four bonds to a central atom.

sp³d hybridization — Mix one s + three p + one d → 5 sp³d hybrids

• Geometry: trigonal bipyramidal, with 90° and 120° bond angles
• Example: $PCl_5$

sp³d² hybridization — Mix one s + three p + two d → 6 sp³d² hybrids

• Geometry: octahedral, all bond angles 90°
• Example: $SF_6$

Note: The participation of d orbitals in hypervalent bonding is debated in modern computational chemistry. Some analyses suggest that expanded-octet molecules can be described adequately using multi-center bonding without invoking d-orbital hybridization. For this course, the sp³d/sp³d² model remains a useful predictive tool.

Determining Hybridization: A Step-by-Step Approach

1. Draw the Lewis structure for the molecule.
2. Count the steric number of the central atom: steric number = (number of bonded atoms) + (number of lone pairs on the central atom).
3. Match the steric number to hybridization:

1. Identify any leftover unhybridized p orbitals; these form pi bonds if multiple bonds are present.

Molecular Geometry

VSEPR Theory and Molecular Shapes

VSEPR (Valence Shell Electron Pair Repulsion) theory predicts the 3D arrangement of atoms around a central atom. The core idea: electron domains repel each other and arrange themselves as far apart as possible to minimize that repulsion.

There's an important distinction between electron geometry and molecular geometry:

• Electron geometry considers all electron domains (bonding + lone pairs).
• Molecular geometry describes only the positions of the atoms, ignoring lone pairs.

For example, water ($H_2O$) has four electron domains (two bonding pairs + two lone pairs), so its electron geometry is tetrahedral. But since only two of those domains are bonding, the molecular geometry is bent.

Common electron-domain geometries:

• 2 domains → linear (e.g., $CO_2$)
• 3 domains → trigonal planar (e.g., $BF_3$)
• 4 domains → tetrahedral (e.g., $CH_4$)
• 5 domains → trigonal bipyramidal (e.g., $PCl_5$)
• 6 domains → octahedral (e.g., $SF_6$)

Bond Angles and the Effect of Lone Pairs

Ideal bond angles correspond to the electron geometry (180°, 120°, 109.5°, etc.), but lone pairs compress those angles. Lone pair electrons are held closer to the nucleus than bonding pairs, so they occupy more angular space and push bonding pairs together.

• $CH_4$: four bonding pairs, no lone pairs → 109.5° (ideal tetrahedral)
• $NH_3$: three bonding pairs + one lone pair → 107° (compressed from 109.5°)
• $H_2O$: two bonding pairs + two lone pairs → 104.5° (compressed further)

The trend is clear: each additional lone pair on the central atom reduces the bond angle by roughly 2–2.5° from the ideal value. This pattern holds across many molecules and is one of the most testable predictions of VSEPR theory.