Introduction to Molecular Orbital Theory in Organic Chemistry

Molecular orbital (MO) theory is a fundamental concept in organic chemistry that explains the electronic structure of molecules and their reactivity. Understanding how atomic orbitals combine to form molecular orbitals, and how these orbitals influence chemical behavior, is essential for predicting reaction mechanisms and outcomes.

Class 1 Review: Orthogonality of Orbitals

Orthogonal Orbitals

Orthogonality in orbitals refers to the mathematical property where the overlap integral between two orbitals is zero, meaning they do not interact or mix. This concept is crucial for understanding bonding and molecular orbital formation.

• Orthogonal Orbitals: Two orbitals are orthogonal if their spatial overlap is zero. For example, a px and a py orbital on the same atom are orthogonal.

• Application: Orthogonality determines which atomic orbitals can combine to form molecular orbitals.

Example: In the provided images, pairs of orbitals such as px and py are orthogonal.

Orthogonality to π Molecular Orbitals

• πCC Molecular Orbital: Formed by the sideways overlap of p orbitals on adjacent carbon atoms.

• σCC and σCH Molecular Orbitals: These are orthogonal to the πCC orbital because they involve end-to-end overlap along different axes.

Example: The σCC bond (along the internuclear axis) is orthogonal to the πCC bond (above and below the plane).

Class 1 Review: Molecular Orbital Energy Diagrams

MO Energy Diagrams

Molecular orbital energy diagrams illustrate the relative energies of bonding, non-bonding, and antibonding orbitals formed from atomic orbitals.

• Bonding Orbitals (σ, π): Lower in energy, electrons in these orbitals stabilize the molecule.

• Antibonding Orbitals (σ*, π*): Higher in energy, occupation destabilizes the molecule.

• Non-bonding Orbitals: Orbitals that do not participate in bonding, energy similar to atomic orbitals.

Example: The diagram shows how 2p and 2sp hybrid orbitals combine to form σCC, πCC, and their antibonding counterparts.

Lecture 2: Principles of Molecular Orbital Theory and Reactivity

Indicators of Molecular Reactivity

MO theory provides four main indicators to assess a molecule's reactivity:

• Charge: Molecules with formal charges are often more reactive.

• "Surviving" Atomic Orbitals: Non-bonding or lone pair orbitals can participate in reactions.

• Poorly Overlapping Atomic Orbitals: Weak overlap leads to higher energy, more reactive orbitals.

• MOs from AOs with Poor Energy Match: Large energy differences between combining atomic orbitals result in less stable MOs, increasing reactivity.

Frontier Molecular Orbital (FMO) Theory

FMO theory focuses on the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) as the key orbitals involved in chemical reactions.

• HOMO: The most energetic electron-containing orbital; often donates electrons in reactions.

• LUMO: The lowest energy orbital that can accept electrons; often accepts electrons in reactions.

• HOMO-LUMO Gap: The energy difference between HOMO and LUMO; a smaller gap generally means higher reactivity.

Example: Nucleophiles have high-energy HOMOs, while electrophiles have low-energy LUMOs.

Reactive Compounds: Features and Examples

General Features of Reactive Compounds

• Presence of Charge: Ions are typically more reactive than neutral molecules.

• Non-bonding Orbitals: Lone pairs or "surviving" atomic orbitals can participate in reactions.

• Poor Overlap: Weakly overlapping orbitals result in higher energy, more reactive electrons.

• Poor Energy Match: MOs formed from atomic orbitals with large energy differences are less stable and more reactive.

Table: Reactivity and Molecular Orbitals of Selected Compounds

Additional info: The table above summarizes the relative energies of the frontier molecular orbitals (FMOs) and their impact on reactivity. Compounds with higher HOMO energies are better electron donors, while those with lower LUMO energies are better electron acceptors.

Frontier Molecular Orbitals in Nucleophilic Substitution (SN2) Reactions

Reactivity Trends in Alkyl Halides

• Order of Reactivity: Iodoethane > Bromoethane > Chloroethane > Fluoroethane (for SN2 reactions with NaSEt in Et2O)

• Leaving Group Strength: Iodide is the best leaving group, followed by bromide, chloride, and fluoride.

• Mechanism: SN2 reactions proceed via a concerted, single-step mechanism where the nucleophile attacks the electrophilic carbon as the leaving group departs.

Arrow Formalism: Curved arrows show electron flow from the nucleophile's HOMO to the electrophile's LUMO (usually the σ* C–X antibonding orbital).

Interacting MOs: The nucleophile's HOMO interacts with the alkyl halide's LUMO (σ* orbital).

Stereochemistry: Stereospecificity and Stereoselectivity

Definitions

• Stereospecific Reaction: The stereochemistry of the reactant determines the stereochemistry of the product. Every stereoisomer of the reactant leads to a different stereoisomer of the product.

• Stereoselective Reaction: A reaction where one stereoisomer is formed preferentially over others, but not necessarily exclusively.

Example: SN2 reactions are stereospecific, leading to inversion of configuration at the reaction center.

Mechanism: Arrow Formalism and Electron Pushing

Arrow Formalism

• Curved Arrows: Indicate the movement of electron pairs during a reaction.

• Resonance Arrows: Show delocalization of electrons within a molecule.

• Bond Formation and Cleavage: Arrows start at electron-rich sites (lone pairs or bonds) and point to electron-deficient sites (atoms or bonds).

Example: In an SN2 reaction, the arrow goes from the nucleophile's lone pair to the electrophilic carbon, and another arrow from the C–X bond to the leaving group.

Acid-Base Chemistry and pKa Values

Acid-Base Definitions

• Acid: Proton donor.

• Base: Proton acceptor.

• Conjugate Acid-Base Pairs: When an acid donates a proton, it forms its conjugate base; when a base accepts a proton, it forms its conjugate acid.

pKa and Strength: The lower the pKa, the stronger the acid. The stability of the conjugate base is a key factor in acid strength.

• Element Effect: The more electronegative the atom bearing the negative charge, the more stable the conjugate base.

Example: Acetic acid (pKa ≈ 4.8) is a stronger acid than ethanol (pKa ≈ 16) because the acetate ion is stabilized by resonance.

Carbocation Stability

Factors Affecting Carbocation Stability

• Hyperconjugation: Delocalization of electrons from adjacent σ bonds stabilizes the carbocation.

• Resonance: Delocalization of positive charge over multiple atoms increases stability.

• Inductive Effects: Electron-donating groups stabilize carbocations by dispersing positive charge.

Order of Stability: Tertiary > Secondary > Primary > Methyl carbocation.

Example: The tert-butyl carbocation is more stable than the ethyl carbocation due to greater hyperconjugation.

Application: Molecular Orbital Theory in Organic Reactions

Connecting MO Energies to Reactivity

• Relative MO Energies: Molecules with higher-energy HOMOs are better nucleophiles; those with lower-energy LUMOs are better electrophiles.

• pKa Rationalization: MO theory explains why resonance and electronegativity stabilize conjugate bases, lowering pKa values.

• Effect of Pi Bonds and Heteroatoms: Pi bonds and electronegative substituents can stabilize carbocations via resonance and inductive effects.

Example: The presence of a pi bond adjacent to a carbocation center allows for resonance stabilization, as in allylic carbocations.

Summary Table: Key Concepts in MO Theory and Reactivity

Additional info: The structure of tetrodotoxin (shown in the first image) is an example of a complex organic molecule whose reactivity and biological activity can be analyzed using molecular orbital theory.