Chapter 8. π- MO Diagrams

Transcription

1 Pericyclic Reac/ons and Tools to determine Reac/on Mechanisms The goal of this chapter: draw molecular orbital diagrams of simple organic molecules determine whether a pericyclic reac/on is thermally or photochemically allowed using molecular orbital theory gain an understanding of ine/c isotope effects and how they and other tools can be used in determining reac/on mechanisms π- MO Diagrams π- orbitals are simple : Construct the symmetry allowed combina/ons of atomic p z - orbitals ubs/tuents are treated as perturba/ons : Ø Increase/decrease the lobes of the unsubs/tuted hydrocarbon The fron/er molecular orbitals (FMOs, i.e., OMO and LUMO) are sufficient FMOs are powerful: Predict the reac/on condi/ons (thermal, photochemical) and stereoselec/vity! Recall: Energy of the MOs increases with the number of nodes Example: lenes are straighyorward General ücel solu+on for acyclic systems n= number of atoms =, 2,3 π E = α + 2β cos (n +)

2 π- MO Diagrams of Cyclic lenes Rule of thumb (or of symmetry, see later): Draw the seleton structure with a vertex on the bo^om Ø The posi/ons of the carbon atoms indicate the spacing of the MOs π- MO Diagrams of Cyclic lenes General ücel solu+on for cyclic systems E = α + 2β cos 2π (n) n= number of atoms = 0, ±, ±2 ±l for even n n=2l = 0, ±, ±2 ±l for odd n n=2l+ α β α 2β α α+2β α+2β α 2β α.6 β α β α+0.68 β α+2β α+2β α+ β 2

3 π- MO Diagrams of Cyclic lenes Group theory gives the shapes (rela/ve signs and sizes) by: ymmetry adapted linear combina/on (LC) of atomic orbitals Example: π- MO of C Use the pure cyclic groups, i.e., C 5 symmetry and not the full symmetry (D 5h ) The character table is: E C 5 (C 5 ) 2 (C 5 ) 3 (C 5 ) 4 E E 2 e e * e 2 e 2* e 2 e 2* e * e e 2* e 2 e e * e=exp(2πi/5) = cos(2π/5)+i sin(2π/5) (Euler rela/on) Therefore: e i; e* i; e i; e 2 * i e * e e 2* e 2 ϕ 4 z ϕ 3 ϕ 5 ϕ 2 ϕ Pic one p z (φ ) orbital and perform the symmetry opera/ons E C 5 (C 5 ) 2 (C 5 ) 3 (C 5 ) 4 φ φ φ 2 φ 3 φ 4 φ 5 π- MO Diagrams of Cyclic lenes ymmetry adapted linear combina/ons is simple (the first factor is the normaliza/on): π =(/ 5)( φ + φ 2 + φ 3 + φ 4 + φ 5 ) This is the fully symmetric π- orbital (lowest in energy) The degenerate e and e components of E are: e = φ +(0.3+.0i) φ 2 +( i) φ 3 +( i) φ 4 +(0.3-.0i) φ 5 e = φ +(0.3-.0i) φ 2 +( i) φ 3 +( i) φ 4 +(0.3+.0i) φ 5 when rounding all numerical values to decimal place. The linear combina/ons allow for real valued MOs: e + e (2 ϕ ϕ2.6ϕ3. 6ϕ ϕ5) e - e pplying the same principle to E 2 leads to: e 2 + e e 2 e 2 (2 ϕ.6 ϕ2 +.6 ϕ3+.6ϕ4.6 ϕ5) ( ) E C 5 (C 5 ) 2 (C 5 ) 3 (C 5 ) 4 E E 2 e e e 2 e ( ) net ( ) ( ) (.9ϕ +.2ϕ.2ϕ.9 ϕ ) (.2ϕ.9ϕ +.9ϕ.2 ϕ ) e e * e 2 e 2* e 2 e 2* e * e e 2* e 2 e e * e * e e 2* e 2 Γφ φ φ 2 φ 3 φ 4 φ 5 bonding interac/on 2 net an/- bonding interac/on ϕ 5 ϕ 4 z ϕ 3 ϕ ϕ 2 3

4 General Defini/ons for Pericyclic Reac/ons upra- /ntarafacial and Con- /Disrotatory supra- antara- antara- supra supra antara The components for a reac/on are the parts of the molecule that undergo a change during a pericyclic reac/on. Which pericyclic reac/ons occur in the ground state? Reac/ons formally allowed might be geometrically unfavourable R.B. Woodward and R. offmann, ngew. Chem. Int. Ed. 969, 8, 78. General Rules for Pericyclic Reac/ons Pericyclic reac/ons are concerted and hence do not show any (radical) intermediates. ground- state pericyclic change is symmetry- allowed when the total number of (4q+2)supra and (4r)antara components is odd. q and r are integers Reac/ons allowed in the ground state are forbidden in the excited state and vice versa. Condi/ons: a) The geometry must be physically realizable b) Non- par/cipa/ng bonds do not interfere Viola/ons? There are none! 4

5 Pericyclic Reac/ons ground- state pericyclic change is symmetry- allowed when the total number of (4q+2) s and (4r) a components is odd. This means that any 2-, 6-, 0-, 4- electron, etc. suprafacial component is considered, and any 0-, 4-, 8-, 2- electron, etc. antarafacial component is considered when determining if there are an odd number for the reac/on under considera/on. Examples: 4s. Cycloaddi8ons, e.g. Diels- lder reac8ons are 4π s + 2π s applying the general rule: 2s 2s component 0 4a component um is the reac/on is symmetry- allowed in the ground state For the 2π s + 2π s cycloaddi/on: 2 2s component um is 2 the reac/on is symmetry- forbidden in the ground state but the 2π a + 2π s cycloaddi/on: The Rare Case of Thermal [2+2] Cycloaddi/ons The 2 π s +2 π a reac/on is symmetry allowed - but does not readily occur: 2s component, sum is. The product would be highly strained, as the two reactants are perpendicular to each other Ketenes have considerably less steric hindrance and a low lying quasi- empty p- orbital perpendicular to the reac/ng double bond. The 2π s +2π a reac/ons of etenes are indeed observed experimentally supra partially-empty π-orbital O O Δ O antara Rac 5

6 Pericyclic Reac/ons ground- state pericyclic change is symmetry- allowed when the total number of (4q+2)s and (4r)a components is odd. 2. igmatropic rearrangements are denoted by [i,j], where i and j refer to the posi/on of the new σ- bond rela/ve to the old one LUMO Which fron/er orbitals to set up? One way is to consider a 4s+2s reac/on. OMO MOs at the Origin of the Woodward- offmann Rules 3) Electrocyclic Ring- opening/closing of cycloalenes: 4n π conrotatory in the ground- state (consider the OMO) 4n+2 π disrotatory in the ground- state supra Rac Δ antara supra Δ supra new σ-bond Rac [2πs +2σa] [2πs +2πa] 4n π disrotatory in the excited state (consider the LUMO) [4πs +2πs] [4πs +2σs] 4n+2 π conrotatory in the excited state supra hν supra Rac [2πs +2σs] [2πs +2πs] ll the reac/ons are highly stereoselec/ve! [4πs +2πa] supra antara hν new σ-bond Rac [4πs +2σa] 6

7 Pericyclic Reac/ons ground- state pericyclic change is symmetry- allowed when the total number of (4q+2)s and (4r)a components is odd. pplying the general rule to [m+n] cycloaddi/ons, sigmatropic and electrocyclic reac/ons (where m and n indicate the number of par/cipa/ng (π) electrons) leads to 4 categories: m+n 4q allowed in the ground state conrotatory m s +n a m a +n s 4q+2 disrotatory m s +n s m a +n a allowed in the excited state disrotatory m s +n s m a +n a conrotatory m s +n a m a +n s MOs at the Origin of the Woodward- offmann Rules Consider a model Diels- lder Reac/on The OMO of the diene matches in symmetry with the LUMO of the dienophile formally, Diels- lder Reac/ons are 4π s + 2π s and therefore occur disrotatory O O O equal to Rac ince the reac/on occurs disrotatory, trans, trans (or E,E) dienes convert into cis- subs/tuted cyclohexanes, while trans- cis (or E,Z) dienes convert into trans- subs/tuted cyclohexanes. 7

8 [2+2] Cycloaddi/ons: correla/on diagram MO diagrams give a more complete picture than the simple FMO picture Example: Why is the 2 π s, 2 π s cycloaddi/on of ethene forbidden in the ground state but allowed in the excited state? No direct connec/on between the two ground states direct connec/on between the two excited states exists but is energe/cally unfavorable Quiz on correla/on diagrams Develop an orbital symmetry correla/on diagram for the hexatriene- cyclohexadiene interconversion by considering both conrotatory and disrotatory processes. conrotatory σ disrotatory 8

9 Determina/on of reac/on mechanisms To understand and improve chemical reac/ons, chemists need to now their mechanisms. Mechanisms indicate the detailed path followed by all atoms of the species involved in going from reactants to products. The only way to validate a mechanism or to pic among mechanis/c hypothesis is to probe its consistency with respect to experiments; however the en/re hypothesized mechanism is not the ul/mate truth! Two of the most common methods to probe reac/on mechanisms are described herea}er. Kine/c tudies First tool to determine reac/on mechanisms: ine/c studies Monitor rate of reac/on as a func/on of: - concentra/ons of reactants - solvent - temperature Obtain reac/on order, first indica/on on how many and which molecules are involved in the rate- determining step. Using appropriate ine/c studies, insight can be gained on the number of reac/on steps, of species involved, on ac/va/on parameters 9

10 Kine/c Isotope Effects Kine/c studies: no informa/on on which bond is broen or formed. Use ine/c isotope effects! Isotopic subs/tu/on can influence reac/on ine/cs: D 6 Reac/on with proceeds 6 /mes faster than with D! Large effect = direct par/cipa/on of in the reac/on Primary ine/c isotope effect Kine/c Isotope Effects Isotopes differ in principle only by their mass and have the same chemical reac/vity. owever, X- and X- D bonds have different lengths and dissocia/on energies! Different mass for D: different vibra/onal frequency and hence different zero- point energies. 0

11 Kine/c Isotope Effects Difference in ZPE is bigger for larger force constants. Lower force constant for T Difference in ac/va/on energy for D and Generally: D D D > Force constant of the bond lower for T than for reactant Force constant of the bond higher < for T than for reactant Force constant of the bond does = not change Kine/c Isotope Effects Kine/c isotope effects are not only observed for reac/ons implying directly: D =. maller ine/c isotope effect because is not directly involved. econdary ine/c isotope effect ere, D is in α posi/on to the reac/on center: α- deuterium isotope effect.

12 Kine/c Isotope Effects Transi/on state in this example is similar to carboca/on: Force constant for out- of- plane bending vibra/on smaller in T (sp 2 ) than in reactant (sp 3 ): origin of this α- deuterium isotope effect. Kine/c Isotope Effects Example of inverse ine/c isotope effect: D = 0.74 Force constant for the indicated bending is higher in the T: ine/c isotope effect lower than! Change of hybridiza/on at a carbon between T and reactant can be monitored by isotopic subs/tu/on on this C. 2

13 Kine/c Isotope Effects Kine/c isotope effects also occur for D in β posi/on: D =.9 β- deuterium isotope effect C- D bond weaened at the T due to hyperconjuga/on For norbornane above, conforma/on is fixed so that hyperconjuga/on is maximal. Kine/c Isotope Effects Primary ine/c isotope effects can be greatly enhanced by quantum mechanical tunneling. = Qe E/RT Q = eα β α (βe α αe β ) α = E / RT β = 2aπ 2 (2mE) /2 / h Tunneling rate depends exponen/ally on mass and on barrier width D can reach 50 or more! 3

14 Kine/c Isotope Effects Kine/c isotope effects also occur for heavier atoms. Much more difficult to measure: going from to D increase mass by 00%, going from 2 C to 3 C increase mass by only 8%! clever way to measure mul/ple ine/c isotope effects was devised by ingleton and Thomas. Reactants naturally possess some amount of heavy isotopes lie D or 3 C. During the reac/on, specific molecules do not react at the same rate depending on which isotopes are present. Consequently, le}over reactants are enriched in some isotopes. Measure of isotopic enrichment of reactants for each posi/on gives access to all ine/c isotopic effects! D.. ingleton,.. Thomas, J. m. Chem. oc., 995, 7, 9357 Linear Free Energy Rela/onships Instead of subs/tu/ng an atom by a heavier isotope, en/re fragments (subs/tuents) can be added or substracted to a molecular system. ubs/tuents influence reac/on rates through: Field effects (for charged, dipolar subs/tuents) Induc/ve effects (for electronega/ve subs/tuents, etc.) Resonance effects (for π subs/tuents, etc.) Polarizability effects teric effects olva/on effects 4

15 Linear Free Energy Rela/onships To quan/fy the subs/tuent effects, Linear Free Energy Rela/onships (LFER) can be used. First, subs/tuents should be characterized. amme^ defined a scale measuring subs/tuent ability to influence acidity of benzoic acid: X= is taen as a reference, and all other subs/tuent effects (in meta or para posi/on) are measured rela/ve to it: σ K = σ = X m/ p meta / para log K Linear Free Energy Rela/onships During the reference reac/on, a nega/ve charge builds up on the acid. σ m/p measures subs/tuent ability to donate or a^ract electrons and hence to destabilize or stabilize the nega/ve charge. σ m/p < 0: electron dona/ng group, destabilize nega/ve charge σ m/p > 0: electron withdrawing group, stabilize nega/ve charge Values for a number of subs/tuents are tabulated. Note that σ m/p reflects the total electron dona/ng/a^rac/ng ability, by induc/on or resonance, but not the direct stabiliza/on by resonance of a nega/ve charge! In the reference reac/on, nega/ve charge cannot be stabilized directly by resonance. ee for example: D.. McDaniel,. C. Brown, J. Org. Chem., 958, 23,

16 Linear Free Energy Rela/onships Using amme^ constants, the amount of nega/ve or posi/ve charge building up during a reac/on can be probed. For this, the reac/on should be performed with different subs/tuents and its ine/cs measured. Then, log( X / ) is plo^ed versus σ m/p. Usually, a straight line is obtained and the slope ρ can be determined. X log = ρσ m/ p If ρ >, the reac/on is more sensi/ve to subs/tuent effects than benzoic acid and more nega/ve charge is building up. If 0 < ρ <, the reac/on is less sensi/ve than benzoic acid but s/ll builds nega/ve charge. If ρ = 0, the reac/on show no subs/tuent effect. If ρ < 0, the reac/on builds posi/ve charge. Linear Free Energy Rela/onships Cau/on: ρ directly indicates the sensi/vity of a reac/on to subs/tuent effects and not the charge! The molecular structure and the distance between the subs/tuents and the hypothe/c loca/on of the charge should always be considered. Moreover, building up nega/ve charge at T also corresponds to decrease of posi/ve charge at the T, and vice- versa. The above reac/on gives ρ = The reac/on does not build posi/ve charge but reduce nega/ve charge on O. Value of ρ can help discriminate between mechanis/c hypothesis with different charges. 6

17 Linear Free Energy Rela/onships ssign the following amme^ plots to the following reac/ons Linear Free Energy Rela/onships The linearity of X log = f ( σ m/ p) is o}en observed, but not always. Devia/ons from linearity can indicate: that the amount of charge in the T depends on the subs/tuent (gradual curvature of the plot) that subs/tuents induce a change of rate- determining step or of mechanism (abrupt change, curve can be fi^ed by two straight lines) that direct resonance stabiliza/on of a charge is involved (o}en corresponds to sca^ered data in amme^ plot) If direct resonance stabiliza/on is thought to have a role, σ + and σ - amme^ values can be used instead of σ m and σ p. 7

18 Linear Free Energy Rela/onships σ + and σ - are determined with reference reac/ons by comparison with X= lie σ m/p. amme^ plots with σ + or σ - can be more linear, indica/ng resonance stabiliza/on plays a role in the reac/on under study. Reference reac/on Index Interpreta/on σ bility to stabilize a nega/ve charge by resonance σ + bility to stabilize a posi/ve charge by resonance Linear Free Energy Rela/onships Different schemes aim at decomposing the amme^ constants to extract informa/on about polarizability, sterics, induc/on For example, - the Ta} parameters are also based on reference reac/ons to characterize polar and steric effects of subs/tuents - wain- co^ parameters characterize nucleophilicity These parameters (and many more) can all be used in ine/c studies to assess the sensi/vity of the reac/on barrier to different subs/tuent effects. 8

19 Outloo Exploring reac/on mechanisms is experimentally and computa/onally challenging except for the simplest reac/ons. imple ine/c studies may help gather basic informa/on about the reac/on steps. Isotope subs/tu/on can provide precious and detailed informa/on regarding bonds being broen and formed. The changes undergo by the molecular system are very small and will unliely change the mechanism, but measurements may be difficult. Linear Free Energy Rela/onships (LFER) allow to assess subs/tuent effects on the barrier heights and may discriminate between different mechanisms, but they imply significant modifica/ons of the molecular system, which may be prac/cally difficult and influence the mechanism under inves/ga/on. Many more techniques may be used to inves/gate a mechanism, notably to capture hypothe/cal intermediates. Only chemists imagina/on is a limit! Note that the above techniques probe only the rate- determining step. Mini Quiz 9. Examine the following pericyclic reac8on and characterize it using the electron count and suprafacial/antarafacial terminology. tate if the reac8on is allowed or forbidden based upon the generalized orbital symmetry rules. 2. The following isotope effects are found for the ozonolysis of various deuterium- subs8tuted propenes. What do these isotope effects tell you about the mechanism? (D) (D) KIE=0.88 KIE=0.88 9

20 Mini Quiz 9. Examine the following pericyclic reac8on and characterize it using the electron count and suprafacial/antarafacial terminology. tate if the reac8on is allowed or forbidden based upon the generalized orbital symmetry rules. Chapter 7 20