Orbitals and Bonding Theories

Orbitals and Bonding Theories

• Electrons are attracted to nuclei
• Electrons behave as waves; Orbitals are wavefunctions
• Electrons are responsible for bonds in molecules

Localized Bonds

• Localized bonding involves electrons localized between two atoms, typically in pairs
• Delocalized bonding involves bonds spread over several atoms to explain chemical properties

Orbital Overlap

• Bonding orbitals form through the combination of atomic orbitals from adjacent atoms

Orbital Overlap Model

• Each electron in a molecule has a specific orbital assignment
• No two electrons in a molecule have identical descriptions due to the Pauli exclusion principle
• Electrons in molecules follow the aufbau principle by occupying the most stable orbitals
• Valence orbitals are sufficient to describe bonding, despite atoms having unlimited atomic orbitals

Diatomic Molecules: HF and F2

• HF has a strong 1s-2p overlap
• F2 has a strong 2p-2p overlap

Bonding in H2S

• H2S has a bond angle of 92.1 degrees
• H2S bonds involve 1s-3p overlap

Hybridization of Atomic Orbitals

• Atomic orbitals can be hybridized to create directional orbitals
• Mixed orbitals are in line with compound geometry
• All electrons around a central atom, whether bonding or nonbonding, must be in orbitals

Hybridization Model

• S and all p orbitals are needed for directional bonding
• S, px, py, and pz orbitals hybridize.
• New orbitals are called sp3, overlapping 1s atomic orbitals of hydrogen atoms to form CH4

General Features of Hybridization

• The number of valence orbitals from hybridization equals the number of valence atomic orbitals participating
• The steric number of an inner atom determines hybrid orbital number and type
• Hybrid orbitals create localized bonds via overlap with atomic or other hybrid orbitals
• Outer atoms don't need hybridization because they don't have limiting geometries
• Hydrogen forms localized bonds with its 1s orbital, and other outer atom bonds use valence p orbitals

sp2 Hybrid Orbitals

• These mix s orbitals with two p orbitals. A third p-orbital remains unchanged.
• It is typical for central atoms with a steric number of 3, leading to trigonal planar electron group geometry

sp Hybrid Orbitals

• Mixes a single s orbital with a p orbital, leaving the other two p-orbitals unchanged
• These are required for central atoms with a steric number of 2, linear electron group geometry

sp3d Hybrid Orbitals

• These combine an s orbital with three p orbitals and a d orbital, represented as (s+p+p+p+d)
• They're needed by central atoms with a steric number of 5, creating a trigonal bipyramidal electron group geometry

sp3d2 Hybrid Orbitals

• These combine an s orbital with three p orbitals and two d orbitals (s+p+p+p+d+d)
• Required for central atoms with a steric number of 6 (octahedral electron group geometry)

Summary of Valence Orbital Hybridization

• Steric Number 2: Linear Geometry has sp hybridization, 2 hybrid orbitals, 2 unused p orbitals
• Steric Number 3: Trigonal Planar Geometry has sp2 hybridization, 3 hybrid orbitals, 1 unused p orbital
• Steric Number 4: Tetrahedral Geometry has sp3 hybridization and 4 hybrid orbitals
• Steric Number 5: Trigonal Bipyramidal Geometry has sp3d hybridization and 5 hybrid orbitals
• Steric Number 6: Octahedral Geometry has sp3d2 hybridization and 6 hybrid orbitals

Multiple Bonds

• Double bonds have two sets of bonding electrons, requiring two sets of overlapping orbitals
• Triple bonds have three sets of bonding electrons, therefore it must require three sets of overlapping orbitals.

Sigma Bonds and Pi Bonds

• A single overlap of two orbitals is a sigma (σ) bond where electron density is along the internuclear axis
• A double overlap of two orbitals creates a pi (π) bond where electron density is above and below the bond axis

Bonding in Ethylene

• Carbons typically have sp2 hybridization
• The question of accounting for a double bond focuses on how to deal with the second electron pair

Sigma and Pi Bond Models

• A sp2 hybrid orbital on each carbon overlaps with one on the other carbon atom, forming a sigma (σ) bond
• C-H (σ) bonds are when sp2 hybrid with a 1s atomic orbital on the hydrogen atom overlaps
• Formation of an sp2 hybrid set leaves one unused valence p orbital

Bonds Involving Oxygen Atoms

• The oxygen atoms bonds
• Contains a bond bond framework
• There is a Top view
• There is a side view

Carbon vs Silicon Pi Bonds Comparison

• C-C pi bonds form due to the overlap of 2p orbitals at 133 pm
• Si-Si pi bonds form from the overlap of 3p orbitals at 210 pm

Triple Bonds

• A single bond is sigma σ
• A double bond contains sigma plus pi σ + π
• Triple Bonds contains sigma + pi + pi, σ + π + π
• This requires 2 empty p-orbitals on each atom for double orbital overlap

Acetylene C2H2 Orbitals

• Consists of C-H σ bonds (sp-1s) and C-C σ bond (sp-sp)
• Has a molecule on the x-axis with Px
• Has a molecule on the y-axis with Py

Molecular Orbital Theory

• Localized bonding theory
• Using pure s and p atomic orbitals of the atoms in a molecule produce orbitals being spread out, or delocalized, over several atoms, leading to molecular orbitals (MOs)

Principles of Molecular Orbital Theory

• 1st Principle: total number of MOs produced by interacting atomic orbitals equals the number of interacting atomic orbitals
• 2nd Principle: bonding MO is lower in energy; antibonding orbital is higher in energy
• 3rd Principle: molecule's electrons are assigned to orbitals of successively higher energy based on the aufbau principle and Hund's rule
• 4th Principle: atomic orbitals combine most effectively to form MOs when the atomic orbitals have similar energy

Bond Order in Molecular Orbital Theory

• Bond Order enables the measure of the net amount of bonding between two atoms

Homonuclear Diatomic Molecules

• Molecular orbital diagrams for O2 are generalizable to all 2nd-row diatomic molecules
• B2 is an exception to the above rule

Orbital Mixing

• In B2, overlap of 2s and 2pz orbitals stabilize σs and destabilize σρ, which is called Orbital Mixing
• The amount of Orbital Mixing depends on the amount of energy difference between 2s and 2p atoms.
• More mixing equals nearly same energy within orbitals

Three-Center π Orbitals

• Three-atom systems can delocalize electrons over all atoms

Nonbonding Molecular Orbitals

• If a lone pair is spread over outer atoms but not across the inner atom, it is a nonbonding molecular orbital
• Delocalized π systems are always present when p orbitals on more than two adjacent atoms are in the perfect position

Composite Model of Bonding

• Construct a sigma bonding framework
• Use hybrid orbitals internally and atomic orbitals toward the exterior
• For molecules that contain multiple bonds, construct a pi bonding system
• Always watch for resonance structures
• Place a pair of valence electrons that is in a atomic orbital that is not undergoing any hybridization or directly in the overall system

Extended Pi Systems

• These may form long chains or dense clusters of rings.

Band Theory of Solids

• The band theory builds on delocalized orbital concepts
• Accounts for metal properties, and explains metalloid properties like silicon's