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Conjugated Systems When the P Orbitals of Double Bonds Are On

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Conjugated Systems When the P Orbitals of Double Bonds Are On Conjugated Systems When the p orbitals of double bonds are on adjacent atoms, the double bonds are said to be conjugated This conjugation leads to differences in the properties of conjugated dienes Due to the conjugation the electrons can resonate between all conjugated p orbitals This resonance cannot occur between isolated double bonds Energy Differences in Conjugated Systems As seen with other structures that can resonate, the extra resonance forms lead to a more stable system Conjugated systems are thus more stable than isolated double bonds stability Remember from discussion of alkene stability, more substituted double bonds are more stable due to stability offered by hyperconjugation Therefore the stability of diene isomers can also be predicted due to conjugation and amount of substitution on the double bonds Energy Differences in Conjugated Systems Can measure stability by hydrogenation H2 catalyst The energy required for this hydrogenation indicates the stability of the alkene 2 Kcal/mol Conjugation stability 57.4 Kcal/mol Almost double in energy 55.4 Kcal/mol 28.6 Kcal/mol Conjugated systems are thus always lower in energy than isolated double bonds Structural Differences in Conjugated Systems Due to the resonance in conjugated double bonds, the bond distances are not strictly “single” or “double” bond lengths 1.47 Å 1.53 Å 1.32 Å In order for the double bonds to resonate, however, the p orbitals must be aligned H H H H H H H H H H H H s-trans s-cis s-trans is more stable due to sterics with hydrogens with the s-cis conformation Allenes The shortest possible diene system would be propadiene (called “allene”) H2C C CH2 The two double bonds of allene though are not conjugated H H H H The central carbon of allene must form a π bond with both adjacent carbons, thus the p orbitals used must be orthogonal Allenes are thus less stable than either conjugated or isolated double bonds Alkyne Isomerization using Allenes When internal alkynes are reacted with strong base, they isomerize to terminal alkynes NaNH2 NH3 The mechanism for this isomerization is first to abstract a hydrogen adjacent to the alkyne which resonates to an allene anion H NaNH2 NH3 C CH2 C CH2 NH3 NaNH2 NaNH2 NH3 H H C CH The generated allene can then react again with base to generate another allene anion The important point is that once the terminal alkyne is formed, it is quantitatively deprotonated with strong base to drive equilibrium Molecular Orbitals We can understand, and predict, many properties of conjugated systems by considering the molecular orbitals Remember when we discussed bonding in organic compounds we formed bonds by combining atomic orbitals Either sigma (σ) or pi (π) bonds were formed depending upon the symmetry of the resultant bond upon addition of the atomic orbitals The same process occurs when considering conjugated dienes Rules for combining orbitals: 1) Always get the same number of molecular orbitals as number of atomic orbitals used to combine 2) As the number of nodes increase, the energy of the molecular orbital increases 3) The molecular orbitals obtained are the region of space where the electrons reside (on time average) Molecular Orbitals First consider an isolated alkene Simplest is ethylene We can separate the sigma and pi framework With alkenes, we are interested in the pi framework since this is what controls the reactivity Energy First combine two p orbitals to form a π bond Upon addition, Instead of + and -, often will obtain two MOs represent phases with color Each p orbital has two lobes with different energy with opposite phase Molecular Orbitals The molecular orbitals obtained computationally appear same as the approximation used by combining atomic p orbitals π bond π* bond Molecular Orbitals Can draw electronic configuration for the π system Again consider ethylene Since there are 2 π electrons in this molecule, will place 2 electrons in MO diagram Always place electrons in lowest energy orbital first, each orbital can accommodate two electrons E Molecular Orbitals Can obtain molecular orbitals for larger conjugated systems using the same procedure Consider butadiene, 2 double bonds in conjugation corresponding to overlap of 4 adjacent p orbitals By combining 4 atomic p orbitals, will obtain 4 molecular orbitals that differ in phase of orbitals 0 nodes 1 node 2 nodes 3 nodes As the number of nodes increases, the energy of the orbital increases Molecular Orbitals for Butadiene Lowest unoccupied MO (LUMO) E Highest occupied MO (HOMO) 4 electrons are placed in these molecular orbitals by pairing the lowest energy MO’s until all electrons are placed in orbitals The molecular orbital that is highest in energy that contains electrons is called the highest occupied molecular orbital (HOMO) The molecular orbital that is lowest in energy that does not contain electrons is called the lowest unoccupied molecular orbital (LUMO) Reactivity of Conjugated Systems The π bonds of conjugated systems can react in similar reactions as isolated alkenes Br HBr While the products are similar (H and Br in this case adding to a π bond), the rate is different When considering a nucleophile adding to an electrophile, the higher in energy the HOMO of the nucleophile, the faster is the rate As learned in UV-vis spectroscopy, as the conjugation increases the HOMO-LUMO gap is smaller Due to the higher energy HOMO E of butadiene versus an isolated alkene, butadiene will react faster ΔE in an electrophilic alkene addition Reactivity of Conjugated Systems The difference in rate between conjugated and isolated alkenes can also be explained by the difference in energy for the intermediate in the rate determining step Br HBr Br Secondary cation in resonance Br HBr Br Isolated secondary cation A cation in resonance is more stable than an isolated cation, therefore the reaction of butadiene will have a lower energy of activation than 1-butene and thus the rate will be faster Thermodynamic Versus Kinetic Control Another difference between π reactions of conjugated systems versus isolated alkenes are the possibility of different products When an isolated alkene reacts, only the product from the most stable carbocation intermediate is formed Br HBr Br When conjugated alkenes react, however, the carbocation intermediate can resonate HBr Br Br Br Br 1, 2 Product 1, 4 Product Each resonance structure can react to form different products Thermodynamic Versus Kinetic Control Which product is favored (1, 2 versus 1, 4 product) can be controlled by reaction conditions The electrophile will first add to the double bond to create a resonance stabilized cation Br !+ Br !+ In positive charged species, The more stable !+ the more substituted form !+ transition state thus is more stable leads to the faster rate (kinetically favored) The more stable product (thermodynamically Br favored) In the product isomers, however, the more substituted double bond is more favored Br 1, 2 Product (Kinetic) 1, 4 Product (Thermodynamic) The resonance forms can react with the nucleophile to generate two transition state structures that have partial positive charges as the new bonds are forming A convenient experimental condition to control thermodynamic product is to run the reaction at higher temperature The kinetic product is favored at lower temperature Molecular Orbitals for Allylic Systems An allylic system refers to 3 conjugated p orbitals Allyl cation Allyl radical Allyl anion All allylic systems have 3 p orbitals in conjugation, but the number of electrons conjugated changes Molecular Orbitals for Allylic Systems With 3 conjugated p orbitals, must obtain 3 molecular orbitals 2 nodes (with odd number of carbons, nodes can occur at nucleus E 1 node unlike systems with even number of carbons) 0 nodes Depending upon number of π electrons the electronic configuration can be determined Allyl cation has 2 π electrons Allyl radical has 3 π electrons Allyl anion has 4 π electrons Implies that excess negative charge of anion is located on the terminal carbons (size of coefficients correlates with probability of electron density) Similar to resonance description Reactions with Allylic Systems An allyl system is observed as an intermediate or transition state in many reaction mechanisms Consider an SN1 mechanism: H O Cl 2 OH Generates allyl cation intermediate The relative rates for this reaction with different structures correspond to the stability of intermediate in reaction mechanism Cl Cl Cl Cl Cl Intermediate: 1˚ cation 2˚ cation 1˚/1˚ cation 1˚/2˚ cation 1˚/3˚ cation (resonance) (resonance) (resonance) Relative rate: 1 1.7 14.3 1300 1900000 Reactions with Allylic Systems Consider an SN2 mechanism: In an SN2 reaction, there is not an intermediate but rather a transition state structure for the rate-determining step Cl !- nucleophile Cl NUC Cl !- NUC nucleophile When reacting an allyl halide, Cl the transition state has an allyl structure which is more stable NUC Relative rate of SN2 reaction with ethoxide: Cl Cl Cl Electrophilic carbon in Transition state: 1˚ 1˚ in resonance 2˚ in resonance Relative rate: 1 37 1.9 (SN2) Reactions with Allylic Systems Consider pKa for allyl systems: base pKa = 50-60 Very unstable anion base pKa = 43 Anion stabilized by allyl resonance Allylic positions are much more acidic than unactivated carbons due to the resonance stabilization of anion formed after deprotonation Pericyclic Reactions Reactions involving concerted bond formation, or bond breakage, with a ring of interacting orbitals Ring of interacting orbitals -Orbitals must form a continuous
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