1,3-Dipolar Cycloadditions : FMO and Beyond · 1,3-Dipolar Cycloaddition Huisgen proposed a...

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1,3-Dipolar Cycloadditions

Lawrence M. Wolf

Group Meeting

Cycloadditions: FMO and Beyond

Lawrence M. Wolf

Group Meeting

Various Dipoles and MO for allylFleming, I.

Hiberty, P. C. et al. J. Am. Chem. Soc. 1983, 105, 719

Isoelectronic w/ allyl anion

Fleming, I. Molecular Orbitals and Organic Reactions, Wiley, 2010

1,3-Dipolar Cycloaddition

Huisgen proposed a concerted process on the

basis of the following observations:

(1) lack of trappable intermediates

(2) stereospecificity

(3) substituent effects favoring two-bond processes

Firestone proposes a diradical based mechanism

that is consistent with all three of the above:

Both (1) and (2) can be rationalized on the basis of

the reactivitiy of the diradical a smaller barrier of the reactivitiy of the diradical a smaller barrier of

bond rotation to reaction

Huisgen

Firestone

Huisgen, R. Angew. Chem. Int. Ed. 1963, 2, 633.

Huisgen, R. Angew. Chem. Int. Ed. 1963, 2, 565.

Firestone, R. A. J. Org. Chem. 1968, 33, 2285.

Huisgen, R. J. Org. Chem. 1968, 33, 2291

Scrambling Experiment

Firestone, R. A.; Houk, K. N. et. al. J. Am. Chem. Soc. 1985, 107

Barrier of rotation for n-propyl

radical is ~0.1-0.4 kcal/mol.

Even if barrier for cyclization (kc)

is 0.1 kcal/mol, and barrier to

rotation (kr) is 0.4, ~27% of cis

product would form from trans

and vice versa.

FMO Theory: Salem-Klopmann EquationFleming, I.

Klopman, G. J. Am. Chem. Soc. 1968, 90, 223

Salem, L. J. Am. Chem. Soc. 1968, 90 543

EquationFleming, I. Molecular Orbitals and Organic Reactions, Wiley, 2010

Sustmann, R. Tetrahedron Lett. 1971, 29, 2717

FMOs in 1,3-Dipolar Cycloadditions

HO controlled:

-Rate Acceleration

- Dipole

- R,X,C

- Dipolarophile

LU controlled:

-Rate Acceleration:

- Dipole:

- Dipolarophile:

- R,X,C

Houk, K. N.; Sims. J. et. al. J. Am. Chem. Soc. 1973, 95, 7287.

Houk K. N.; Sims, J. et. al. J. Am. Chem. Soc. 1973, 95, 7301

Cycloadditions

, 7287.

, 7301

Relative dipole FMO energies

Rates of Cycloadditions vs. HOMO

Sustmann, R.; Trill, H. Angew. Chem. Int. Ed. 1972, 11, 838

vs. HOMO-LUMO energies

Applying FMO to aryl azide [3+2]Fleming, I.

Fleming, I. Molecular Orbitals and Organic Reactions, Wiley, 2010

Other methods for Predicting Regiochemistry

Allopolarization:

- Differences in charge at potential reactive

DFT based reactivity descriptors:

- ρ(r) (electron denisty)

- µ (chemical potential)

- η (chemical hardness)

HSAB Principle

Fukui, K. et. al. J. Chem. Phys. 1972, 20, 722

Ess. D. H.; Jones, G. O.; Houk, K. N. Adv. Synth. Catal. 2006, 348

Geerlings P. et. al. J. Phys. Org. Chem. 2003, 16, 615.

- η (chemical hardness)

- S (Softness)

- s(r) (Local softness)

- f(r) (Fukui function, reactivity

index)

Regiochemistry

Differences in charge at potential reactive

348, 2337.

A New Reactivity Model

- Slopes for reactions with ethylene and acetylene are

equivalent despite significantly different FMO energies

Houk, K. N.;

Houkl, K. N.;

(acetylene)

Slopes for reactions with ethylene and acetylene are

equivalent despite significantly different FMO energies

does not fit trend

, K. N.; Ess. D. H. J. Am. Chem. Soc. 2007, 129, 10646.

Transition State Geometries

As χZ decreases, the earlier is the TS.

Houkl, K. N.;

decreases, the earlier is the TS

Activation Energy → Distortion + Interaction Activation Energy → Distortion + Interaction

Distortion energy in [3+2]

Activation, Distortion, and Interaction energies

Stepwise mechanism (diradical)

Houkl, K. N.;

H-L gap (stability):

oxide > imine > ylide

Effect of Distortion on Energy Levels

Houkl, K. N.;

Effect of Distortion on Energy Levels

Substituent Effects

(1) ∆Edǂ is nearly constant , and reactivity is

dictated by ∆Eiǂ

(2) ∆Eiǂ is similar across the series of alkenes,

and dipole, alkene, or both distortion

energies control reactivity

(3) Substituents influence both ∆Edǂ and ∆Ei

Houkl, K. N.; Ess. D. H. J. Am. Chem. Soc. 2008, 130, 10187., 10187.

Strained multiple bonds

Houk, K. N.; Ess. D. H.; Jones, G. O.; Schoenebeck, F. J. Am. Chem. Soc. J. Am. Chem. Soc. 2009, 131, 8121

Cycloalkynes

Better fit with distortion model over strain-

release modelHouk, K. N.; Ess. D. H.; Jones, G. O.; Schoenebeck, F. J. Am. Chem. Soc. J. Am. Chem. Soc. 2009, 131, 8121

Problem

Houk, K. N.; Arndsten, B. A. J. Am. Chem. Soc. 2008, 130, 10052.

Houk, K. N.; Arndsten, B. A. et. al. J. Org. Chem. 2010, ASAP

, 10052.

, ASAP

Solution

Houk, K. N.; Arndsten, B. A. J. Am. Chem. Soc. 2008, 130, 10052.

Houk, K. N.; Arndsten, B. A. et. al. J. Org. Chem. 2010, ASAP

, 10052.

, ASAP

Nature of reactive state: Valence Bond Theory

3 Remaining Questions:

(1) Why does reactivity follow that of the H-L gap

dipoles but not dipolarophiles?

(2) Why does ∆Edǂ correlate with ∆Eǂ while this is not

general for many other reactions?

(3) Why are the geometries of the distorted dipoles so

strikingly similar whether added to ethylene or

acetylene?

Hiberty, P. C.;

Nature of reactive state: Valence Bond Theory

while this is not

Why are the geometries of the distorted dipoles so

Ψ: valence bond wavefunction of 1,3 dipole

WK: weight of HLSP functions (closed and

open shell representations Ф)

Example: Diazonium Betaines

, P. C.; Braida, B. et. al. J. Am. Chem. Soc. 2010, 132, 7631.

Proposal

ΨreactantHypothesis:

∆Eǂ = C1E(ζc) + C2

Hiberty, P. C.; Braida, B. et. al. J. Am. Chem. Soc. 2010,

(ααααa+ζa) •

(ααααb+ζb) •

(ααααc+ζc) •

ααααa•

ααααb•

ααααc•

, 132, 7631.

Weights of Limiting Valence Bond Representations

, 132, 7631.

Correlations with bi-radical character

∆Eǂ

(kcal/mol)

weights of equilibrium geometries

(kcal/mol)

weights of equilibrium geometries

∆Eǂ

(kcal/mol)

E(ζc)

radical character

(kcal/mol)

(i) A critical weight of the diradical

resonance form

Linear dipoles: 0.34

Bent dipoles: 0.426

(ii) A critical energy gap between

ground state and diradical

Linear dipoles: 91 kcal/mol

Bent dipoles: 76 kcal/mol

, 132, 7631.

Dynamics: Early and Late Barriers

Xu, L.; Doubledar, C. E.; Houk, K. N. J. Am. Chem. Soc. 2010, 132, 3029, 3029

Transition Vectors and Bending Mode Contributions

Xu, L.; Doubledar, C. E.; Houk, K. N. J. Am. Chem. Soc. 2010, 132, 3029

Transition Vectors and Bending Mode Contributions

Start from TS with 0.6

kcal in the reactant

direction

, 3029

Energy Partitioning

Acetylene

Ethylene

Xu, L.; Doubledar, C. E.; Houk, K. N. J. Am. Chem. Soc. 2010, 132, 3029

Erc = 0.6 kcal/mol

, 3029

Trajectory Analysis

Xu, L.; Doubledar

Decrease in amplitude is in

accord with %V to Eavl

Doubledar, C. E.; Houk, K. N. J. Am. Chem. Soc. 2010, 132, 3029

Following a TrajectoryXu, L.; , L.; Doubledar, C. E.; Houk, K. N. J. Am. Chem. Soc. 2010, 132, 3029

Snapshots continued

Xu, L.;

Importance of dipole vibration is Importance of dipole vibration is

apparent for dipoles 1-3

Importance of rotation is apparent

for dipoles 4-6

, L.; Doubledar, C. E.; Houk, K. N. J. Am. Chem. Soc. 2010, 132, 3029

Time Gaps between bond formations (concerted Xu, L.;

Gaps between bond formations (concerted vs stepwise), L.; Doubledar, C. E.; Houk, K. N. J. Am. Chem. Soc. 2010, 132, 3029

C-C, C-N, C-O

Vibrational

period=30 fs

Inconsistent w/ a

cyclodiradical

intermediate

Conclusions

• The energy required for distortion was discovered to correlate well with activation energy while not being general among other reactions

• The correlation held constant when FMO theory was insufficient (vs alkyne; nitrilium ylide)

• Alternatively, the reactivity can be explained in terms of the difference in • Alternatively, the reactivity can be explained in terms of the difference in energy between the ground state and pure

• The diradicaloid model can be interpreted as being a special case of the distortion model

• Dynamics simulations revealed the important contribution of energy to the total distortion energy and the relative roles of all three forms of energy (vib., rot., trans.)

The energy required for distortion was discovered to correlate well with activation energy while not being general among other reactions

The correlation held constant when FMO theory was insufficient (alkene

Alternatively, the reactivity can be explained in terms of the difference in Alternatively, the reactivity can be explained in terms of the difference in energy between the ground state and pure diradical reactive state (TS)

model can be interpreted as being a special case of the

Dynamics simulations revealed the important contribution of vibrationalenergy to the total distortion energy and the relative roles of all three

1,3-Dipolar Cycloadditions : FMO and Beyond · 1,3-Dipolar Cycloaddition Huisgen proposed a...

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