Conjugation

Conjugation

• Pi bonds consist of the interaction of electrons in adjacent and parallel p orbitals like a transverse wave.
• When p orbitals are adjacent and parallel we say they are conjugated but we usually don't emphasis it until we have more than two orbitals interacting, an extended Pi system.
• Our models do not adequately represent these interactions.
• Can you give all adjacencies of an extended Pi system in an adjacency matrix?  How many ones?
•  Three conjugated p orbitals in a linear system are part of an allylic system.
• Linear transverse waves have a fundamental motion and a series of harmonics.
• The full range of motion is called the envelope.
• The + and - signs or color coding indicate the phases of the waves and not charge!
• The mathematics used to model the behavior of waves is called wave mechanics or quantum mechanics because wave motion is digital (breaks down into smaller states) not analog (doesn't just get bigger)!

Maximum Wavelength of Absorption

• For linear systems, the energy of Pi systems is spread out like the rungs of the latter with a lower and upper bound of ± 2.
• For even systems half of the molecular orbitals are bonding and half are anti-bonding.
• For odd systems, one orbital is non-bonding.
• Absorption of electro magnetic radiation moves electrons from one molecular orbital to another.
• The smallest jump which leads to the longest wave length of absorption is due to moving an electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO).
• Because of the upper and lower bounds, and number of rungs in the latter requires that the HOMO-LUMO gap get smaller the longer the Pi system, the longest or maximum wave length of absorption also increases.
• For isolated double bonds the absorption is below 200 nm (far ultraviolet).
• Conjugated Pi systems absorb above 200 nm (near ultraviolet).
• Ten alternating unsatuarations (20 carbons) and longer absorb above 400 nm, the visible.
• Color in organic molecules is due to conjugation.
• Because white light is made of several frequency components, RGB, the appearance of color is the complement of what it absorbs.
• Examples include pH indicators and laundry.
• The HOMO-LUMO gap can be halved by having the Pi system interact with non-bonding electrons.

Aromaticity

• The stability of benzene over cyclohexatriene.  Resonance energy of 34 kcal/mole.
• The energy diagram of mono cyclic pi systems looks like the corresponding circumscribed polygon standing on one vertex.  The zero energy level goes directly through the center of the polygon or circle.
• Some mono cyclic pi systems are more stable than alkenes, aromatic, flat 4n+2 Pi electrons, Huckel's rule for mono cyclic pi systems.
• Some mono cyclic pi systems are less stable than alkenes, anti-aromatic, flat 4n Pi electrons, rings size 3-5.
• Some mono cyclic pi systems are just alkenes, non-aromatic, not flat with 4n+2 or 4n Pi electrons.
• Some cyclic pi systems may be charged.
• Some cyclic pi systems may not be monocyclic, benzenoid or non-benzenoid.
• Some cyclic pi systems include other atoms besides carbon and are called aromatic heterocycles,