Orbitals

Orbitals Learning Objectives

  • Review the following themes:

    • VSEPR Theory

    • Atomic Orbitals

    • Valence Bond Theory (VBT)

    • Molecular Orbital Theory (MOT)

    • Hybridized Atomic Orbitals

Overview

  • Understanding chemical reactions necessitates knowledge of orbitals and molecular shapes.

  • This unit ties into the upcoming topic of resonance, which students often find challenging.

  • Although this material revisits first-year chemistry, it is crucial and should not be underestimated.

  • Note: Sections 3.2 and 3.3 elaborate on theories relevant to many course concepts but will not be included in direct assessments.

VSEPR Theory (Section 3.1)

  • Definition: Valence Shell Electron Pair Repulsion Theory (VSEPR) predicts spatial arrangement of atoms in molecules or ions (polyatomic).

  • Principle: Electron pairs (lone pairs and sigma bonds) position themselves to maximize separation.

Summary Table of Shapes

  • Tetrahedral (Electronic)

    • Atomic Geometry: Tetrahedral

    • Bond Angles: Approximately 109.5°

  • Trigonal Planar (Electronic)

    • Atomic Geometry: Trigonal planar

    • Bond Angles: Approximately 120°

  • Linear (Electronic)

    • Atomic Geometry: Linear

    • Bond Angles: 180°

  • Additional Geometries:

    • Trigonal Pyramidal: Atomic Geometry: Trigonal pyramidal; Bond Angles: 107° (e.g., Nitrogen)

    • Bent: Atomic Geometry: Bent; Bond Angles: 105°

Key Concepts

  • Types of Shapes:

    • Arrangement of Electron Pairs: Includes bonds (sigma) and lone electron pairs.

    • Atomic Geometry: Considers only bonds.

  • Example: A trigonal pyramidal molecule exhibits a tetrahedral electronic arrangement (but not vice versa).

  • Focus in Course: Arrangements of electron pairs.

Quantum Mechanics and Atomic Orbitals (Section 3.2)

  • Quantum Mechanics Overview:

    • Description of bonding considering the wave nature of electrons.

  • Use of wave equations results in wave functions ($$) that describe electron energy states.

  • Probability Density: When $$ is squared ($^2$), it represents the probability of electron location.

  • Shapes of orbitals (s, p, d, f) emerge from three-dimensional plots of $^2$.

Key Definitions

  • Orbital: Region of space with high probability of finding an electron.

  • Node: Regions where $ = 0$ indicating zero probability for locating an electron.

  • Energy Levels of Orbitals: Seeded by nodes; more nodes = higher energy orbitals.

Principles of Electron Configuration

  1. Aufbau Principle: Fill lowest energy orbitals first.

  2. Pauli Exclusion Principle: Each orbital holds a maximum of two electrons with opposite spins.

  3. Hund’s Rule: For orbitals of equivalent energy, fill each with a single electron before pairing.

  • Example: Oxygen Configuration ($1s^2 2s^2 2p^4$)

Valence Bond Theory and Molecular Orbital Theory (Section 3.3)

  • Covalent Bonding Explanation:

    • VBT: Bonds form through overlapping atomic orbitals due to constructive interference (results in bonding orbitals).

    • MOT: Evaluates consequences of atomic overlap; employs Linear Combination of Atomic Orbitals (LCAO).

    • Bonding vs. Antibonding Orbitals:

    • Bonding (constructive interference): creates stable bonds.

    • Antibonding (destructive interference): results in higher energy, unstable orbitals (e.g., $1s^*$).

Example: Hydrogen Molecule (H2)

  • Two 1s orbitals combine:

    • Producing $ ext{1s}$ bonding ($ ext{σ}$) orbital.

    • Producing $ ext{1s}$ antibonding ($ ext{σ}^*$) orbital.

Combination of p Orbitals

  • P orbitals interact:

    • Head-on Combination: Forms $ ext{σ}$ bond.

    • Sideways Combination: Forms $ ext{π}$ bond.

Note on Examination

  • Information from Sections 3.2 and 3.3 is supportive but not exam-tested material.

Hybridization of Orbitals (Section 3.4)

  • Example - BeCl2:

    1. Electronic Configuration: $ ext{Be}: 1s^2 2s^2$; $ ext{Cl}: 1s^2 2s^2 2p^6 3s^2 3p^5$.

    2. VSEPR Prediction: BeCl2 is linear (Cl-Be-Cl).

    3. Issue: Paired valence electrons in Be inhibit bonding.

    4. Solution: Promote an electron from 2s to 2p orbital to allow bonding.

    5. Hybridization: Combination of one 2s and one 2p orbital into two “sp hybridized orbitals.”

Characteristics of Hybridization

  • Hybridization Process:

    • The hybridization results in two orbitals having identical energy.

  • Hybridization Implications: Linear Structures (sp hybridized):

    • Atoms with similar linear electronic arrangements will exhibit sp configuration.

Example - Acetylene (C2H2)

  • Hybridization: Carbon atom has two sp hybridized orbitals (forming $ ext{σ}$ bonds) and occupies two unhybridized p orbitals (forming two $ ext{π}$ bonds for a triple bond).

Example - Ethylene (C2H4)

  • Hybridization of Carbons:

    • Trigonal planar arrangement (sp2 hybridized) leading to three $ ext{σ}$ and one $ ext{π}$ bond.

Example - Methane (CH4)

  • Hybridization: sp3 hybridized, thus no p orbitals remain for π bonding.

Influence of Lone Pairs on Hybridization

  • Example: NH3 has a steric number of 4 (3 σ bonds + 1 lone pair).

    • Geometry: Trigonal pyramidal compared to tetrahedral geometry of CH4.

Steric Number and Geometry

  • Steric Number: Sum of sigma bonds and lone pairs.

  • Examples:

    • Methane (CH4): Steric number = 4, geometry = tetrahedral.

    • Ammonia (NH3): Steric number = 4, geometry = trigonal pyramidal.

    • Water (H2O): Steric number = 4, geometry = bent.

  • Steric numbers dictate electronic arrangements and bond angles as well:

    • SN3 = trigonal planar.

    • SN2 = linear.

Summary of Hybridization and Geometry

  • Hybridization illustrates the geometry around a central atom and the roles of lone pairs in reactivity, particularly involving bond formations.

Questions for Practice (Sections 3.9-3.10)

  • Fill in diagrams for electronic configurations.

  • Analyze bonding configurations in chemical compounds like pyridine.

  • Determine hybridizations and steric numbers in various molecular structures.