Valence Bond Theory and Hybridization

# Page 1

1) Secant (X):

  • Definition: The secant of x, denoted as sec(x), is the limit
    ext{sec}(x) = ext{lim}_{h o 0} rac{f(x+h) - f(x)}{h}

  • Tangent Lectures 14-15

  • Relevant Functions:
    f_{ ext{m}}(x) = rac{1}{x+h} \ ext{Valence Bond Theory and Hybridization}

  • Expressed as:
    ext{lim}_{h o 0} rac{2xh + h^2}{h}

  • Simplified form:

ext{lim}_{h o 0} 2x + rac{h}{2}

# Page 2

Valence Bond Theory:

  • Focus: Orbital overlap to form covalent bonds.

  • Key Concepts:

    • Lewis Dot Structures: A visual representation describing the bonding and structure of molecules.

    • VSEPR Theory: Valence Shell Electron Pair Repulsion; used to predict molecular geometry based on electron pair repulsion.

  • Insight: Neither VSEPR nor Lewis structures explain the actual formation of covalent bonds.

  • Consideration: Electrons are modeled as delocalized waves (orbitals).

- Interference: When two waves occupy the same space, they interfere either constructively or destructively.

# Page 3

Interference of Waves:

  • Concept: Two sine waves can interfere either constructively or destructively.

  • Constructive Interference:

    • When two in-phase sine waves add together, resulting amplitude doubles:
      ext{New Amplitude} = 2 imes ext{Original Amplitude}

  • Destructive Interference:

    • When two out-of-phase sine waves cancel each other:

ext{Total Amplitude} = 0

# Page 4

Formation of Chemical Bonds:

  • Example: Covalent bonds form through constructive interference of electron waves (orbitals).

  • Requirement: For interference to happen, the orbitals must occupy the same space.

  • Valence Bond Theory:

    • Covalent bonds result from the overlap between atomic orbitals.

- Same numerical sign on orbitals is necessary for positive interference, enabling constructive overlap from different atoms to form bonds.

# Page 5

Types of Bonds in Valence Bond Theory: Sigma Bond

  • Example Molecule: H2 (simplest molecule).

  • Ground-State Hydrogen Atom:

    • Contains one electron in a 1s-orbital.

  • Behavior: As two H atoms come together, the 1s-electrons pair (↑↓) and begin to overlap.

- Result: Formation of a σ-bond (sigma bond) characterized by sausage-shaped distribution of electron density between nuclei.

# Page 6

Further Insights on Sigma Bonds:

  • Fluorine (F) Example:

    • Contains an unpaired electron in the 2p-orbital.

    • H has an unpaired electron in the 1s-orbital.

- Overlap leads to merging into a shared cloud of electron density over both atoms.

# Page 7

Bonding in N2:

  • Sigma Bond Formation:

    • Each of three 2p-orbitals holds a single electron.

- Only one of the three orbitals overlaps end-to-end to form a σ-bond due to bond angle constraints.

# Page 8

Bond Types in N2 – Pi Bond:

  • The two remaining 2p-orbitals (2px and 2py) are perpendicular to the molecular axis, creating the potential for side-by-side overlap.

- This overlap results in the formation of a π-bond.

# Page 9

Combined Bonding in N2:

  • Sigma and Pi Bonds:

- Formation of bonds results in two π-bonds merging to create a doughnut-shaped cloud surrounding the σ-bond cloud, resembling a cylindrical hot dog shape.

# Page 10

Self-Test 2F.1B:

  • Questions: How many σ-bonds and π-bonds exist in:
    (a) NH3
    (b) HCN

  • Responses:

    • Ammonia (NH3): 3 σ-bonds and 1 lone pair.

    • Hydrogen Cyanide (HCN): 2 σ-bonds and 2 π-bonds.

  • Valence-Bond Theory Summary:

    • A single bond is a σ-bond.

    • A double bond comprises 1 σ-bond and 1 π-bond.

- A triple bond comprises 1 σ-bond and 2 π-bonds.

# Page 11

Carbon Bonding and Molecular Structure:

  • Question: Can Valence Bond Theory explain the bonding in carbon-containing molecules?

  • Carbon Electronic Structure:

    • Electron configuration: [He] 2s² 2px¹ 2py¹

- Carbon appears to have a valence of 2 but is actually tetravalent (valence of 4).

# Page 12

Carbon Bond Formation:

  • Carbon's ability to form 4 bonds is explained by promoting one 2s-electron to an empty 2p-orbital, resulting in configuration:

ext{Configuration} = [He] 2s¹ 2px¹ 2py¹ 2p_z¹

# Page 13

Bond Angles and Molecular Structure in Methane:

  • Methane (CH₄):

    • Methane represents 4 equivalent bonds extending in 4 directions of a tetrahedral structure.

  • Bond Angles:

    • Original 90° bond angles do not align with the observed 109.5° bond angles.

  • Conclusion:

- Recognized need for correct orbitals and shapes for proper bond angles.

# Page 14

Hybridization Concept:

  • Definition: Hybrid orbitals are formed by the linear combination of atomic orbitals, yielding an equal number of hybrid orbitals.

- Significance: Orbital hybridization allows for maximum bonding by minimizing energy states for the atoms and clarifying the molecular structure of compounds, specifically focusing on the center atom (Carbon).

# Page 15

Hybrid Orbitals SP³ of Carbon:

  • Notation for Linear Combinations:

    • Hybrid orbitals designated as:
      h1 = s + px + py + pz
      h2 = s - px - py + pz
      h3 = s - px + py - pz

h4 = s + px - py - pz

# Page 16

Hybrid Orbitals SP³ with Hydrogen:

  • Configuration: Each hybrid orbital integrates linear combinations from the original atomic orbitals.

  • Orbital Specifications:

    • s

    • pₓ

    • pᵧ

- p_z

# Page 17

Ethane (CH₂CH₂) Structure:

  • Configuration Highlights: Ethane features bonds illustrated as
    σ(2Csp³, H1s) \ H—C—C—H \ | \ H H \

- Represents the hybridization involved in bonding.

# Page 18

SP³ of Nitrogen in Ammonia:

  • Sp³ Hybridization: Ammonia forms 3 σ-bonds from overlapping.

  • Orbital Details:

- Hybridization evidenced by s, pₓ, pᵧ, and p_z orbitals forming four sp³ hybrid orbitals.

# Page 19

SP² + P in Ethene (CH₂═CH₂):

  • Configuration: Ethene features a double bond.

  • Molecular Shape: All six atoms lie in the same plane with bond angles approximating 120°, indicative of a trigonal planar arrangement.

- Implicit Hybridization: Each carbon exhibits sp² hybridization due to electron sharing.

# Page 20

Double Bond Characteristics:

  • Formation: Unhybridized p-orbitals lead to a π-bond formation through side-by-side overlap.

- Structural Implication: Unhybridized 2p-orbital persists perpendicular to the C—C plane, adding stability to π-bond arrangements.

# Page 21

Double Bond Behavior:

  • Rotation Restriction: The double bond structure inhibits independent rotation about the C—C bond due to π-bond constraints.

- Result: This feature keeps the entire ethylene molecule in a flat configuration.

# Page 22

Self-Test 2F.2B:

  • Question: Suggest a hybrid orbital structure for each carbon atom in Ethyne (C₂H₂).

- Response: Formation of 3 σ-bonds from two sp-hybridized carbon atoms; these include bonds between carbon and hydrogen atoms arranged linearly, with 2 π-bonds emerging from 2p orbitals.

# Page 23

Triple Bond Characteristics in Ethyne (Acetylene):

  • Configuration: Each carbon exhibits sp hybridization.

  • Detail: Carbon retains two unhybridized p-orbitals contributing to the formation of two π-bonds.

- Bond Dynamics: Two π-bonds form cylindrical symmetries around the triple bond, affecting bond strength.

# Page 24

SP² + P Bonding in Benzene (C₆H₆):

  • Molecular Layout: All C and H atoms occupy the same plane, forming a cyclic arrangement.

- Structure Overview: Six hybridized sp² carbon atoms lead to the structure of benzene.

# Page 25

Benzene Resonance Structures:

  • Significance: Multiple resonance structures express the delocalization of π-electrons throughout the benzene ring.

- Structure Examined: Each carbon neighbor contributes to the overall resonance hybrid structure characterized by distributed electrons.

# Page 26

Types of Geometries and Hybrid Bonds:

  • Hybridization Effects:

    • Linear Geometry: Formed from sp hybrid orbitals (2 total).

    • Trigonal Planar Geometry: Established from sp² hybrid orbitals (3 total).

- Tetrahedral Geometry: Originated from sp³ hybrid orbitals (4 total).

# Page 27

Other Hybrid Orbitals:

  • Key Properties:

    • Sp² hybrid orbitals form only three σ-bonds (one p-bond unaccounted).

- Sp hybrid orbitals involve formation of two σ-bonds (remaining two p-bonds unhybridized).

# Page 28

Trigonal Bipyramidal and Octahedral Hybrid Bonds:

- Significance of Hybridization: Vital to account for structures with five σ-bonds (trigonal bipyramidal) or six σ-bonds (octahedral).

# Page 29

Coefficient of Hybrid Bonds:

- Trigonal Bipyramidal Structure: Characterized by five electron pairs and necessitating the use of a d-orbital alongside s- and p-orbitals.

# Page 30

Octahedral Structures:

  • Comprised of six electron pairs.

- Involves hybridization from two d-orbitals alongside one s-orbital and three p-orbitals.

# Page 31

Overview of Hybridization Types:

  • Hybridization Names: These denote the types and counts of orbitals combined.

    • For example, sp² hybrids arise from the combination of an s orbital with two p orbitals.

  • Common Molecular Shapes:

- Detailed on the left-hand column corresponding to orbital geometries.

# Page 32

Assigning Hybridization for Phosphorus in PCl₅:

  • Steps to determine molecular structure:

    1. Draw the Lewis structure.

    2. Determine electron arrangement around the central atom.

    3. Identify molecular shape.

    4. Determine hybridization from atomic orbitals involved.

5. Establish sp³d hybridization for bonds in Trigonal bipyramidal arrangements.

# Page 33

Example Structure for Formic Acid (HCOOH):

  • Construct Lewis Structure:

    • Use VSEPR model for electron arrangements around the central C and O atoms.

    • Oxygen: 2 single bonds and 2 lone pairs, leading to a tetrahedral arrangement.

- Carbon: Bonds to three atoms with no lone pairs, resulting in trigonal planar arrangements.

# Page 34

Continued Structure for Formic Acid:

  • Identify Hybridization and Bond Angles:

    • Carbon (sp² hybridized) has a bond angle of 120°.

    • Oxygen (sp³ hybridized) has angles near 109.5°.

- Bond Connectivity: Neighbors formed through σ-bonds, with a π-bond created from the overlap of p-orbitals on C and O.

# Page 35

Bonding Characteristics Across Periods:

  • Observations: Period 2 elements (C, N, O) readily form double bonds.

    • Particularly noted for oxygen.

  • Observation: Period 3 elements rarely form double bonds due to their increased size; bond lengths increase, leading to ineffective p-orbital overlap, hindering optimal bonding interactions.

The equations for page 15, describing the SP

3 hybrid orbitals of carbon, are:

h1 = s + px + py + pz
h2 = s - px - py + pz
h3 = s - px + py - pz
h4 = s + px - py - pz