Correlation Between the Diradical Character of 1,3-Dipoles and their Reactivity Toward Ethylene and Acetylene

P.C. Hiberty, Laboratoire de Chimie PhysiqueUniversité de Paris-Sud, 91405 Orsay, France

An application of ab initio valence bond theory

Some families of 1,3-dipoles

H2C

HN

Z Z

HN

H2C H2C

HN

Z Z = O, NH, CH2

HC N Z HC N Z HC N Z Z = O, NH, CH2

N N Z N N Z N N Z Z = O, NH, CH2

Azomethine betaines :

Nitrilium betaines :

Diazonium betaines :

Dipolar cycloadditions

H2C

HN

Z Z

HN

H2C H2C

HN

Z Z = O, NH, CH2

Example: Azomethine betaines :

H2C CH2

+

HC CH

+

HC CH

H2C

HN

Z

H2C CH2

H2C

HN

Z

Cycloaddition on ethylene (azomethine oxide) :

H2C

HN

O

H2C CH2+

H2C CH2

H2C

HN

O

0

10

20

30

-10

-20

-30

-40

-50

-60

E(kcal/mole)

Cycloaddition on acetylene (azomethine oxide) :

We expect :

H2C

HN

O

H2C CH2+

H2C CH2

H2C

HN

O

HC CH+

HC CH

H2C

HN

O

0

10

20

30

-10

-20

-30

-40

-50

-60

E(kcal/mole)

15.1

We observe :(accurate ab initio)

Cycloaddition on acetylene (azomethine oxide) :

H2C

HN

O

H2C CH2+

H2C CH2

H2C

HN

O

HC CH+

HC CH

H2C

HN

O

0

10

20

30

-10

-20

-30

-40

-50

-60

E(kcal/mole)

15.1

Nitrilium ylide + ethylene or acetylene :

N N CH2

H2C CH2+

H2C CH2

NN

CH2

HC CH+

HC CH

NN

CH2

0

10

20

30

-10

-20

-30

-40

-50

-60

E(kcal/mole)

17.3

Still two identical barriers…

N N NH

H2C CH2+

H2C CH2

NN

NH

HC CH+

HC CH

NN

NH

0

10

20

30

-10

-20

-30

-40

-50

-60

E(kcal/mole)

41.8

Nitrilium imine + ethylene or acetylene (aromatic product !)

Still two identical barriers, idem for the 9 1,3-dipoles

Frontier Orbital Theory (FMO)

1,3-dipole Ethylene

HOMO

LUMO

HOMO

LUMO

Small HOMO-LUMO gap:=> Low reaction barrier

Frontier Orbital Theory (FMO)

1,3-dipole Ethylene

HOMO

LUMO

HOMO

LUMO

Let’s focus on thedipole’s HOMO

The higher this HOMO, the lower the reaction barrier

Frontier Orbital Theory (FMO)

E(HOMO)

∆H≠

Z = O Z = NH Z = CH2

diazonium betaines N-N-Z

From: DH Hess, KN Houk, JACS 2008, 130, 10187

Frontier Orbital Theory (FMO)

E(HOMO)

∆H≠

Z = O Z = NH Z = CH2

diazonium betaines N-N-Z

From: DH Hess, KN Houk, JACS 2008, 130, 10187

azomethine Betaines H2C

NHZ

Frontier Orbital Theory (FMO)

E(HOMO)

∆H≠

Z = O Z = NH Z = CH2

diazonium betaines N-N-Z

nitrilium betaines HN-N-Z

azomethine Betaines

From: DH Hess, KN Houk, JACS 2008, 130, 10187

H2CNH

Z

Dipole-1,3

BV

HO

BV

HO

acetylene

FMO predicts higher barriers for reaction with acetylenethan with ethylene (at variance with experiment)

Now, taking the FMOs of the dipolarophile into account…

ethylene

Geometries of transition states

Falsifies Hammond’s principle

H2C CH2

+HC CH

+

~ samegeometries

(the more exothermic the reaction,the earlier the transition state)

C

HN

Z

H2C CH2

C

HN

Z

HC CH

It looks like the kinetics depend on only one ofthe two reactants: the 1,3-dipole.

True for the9 reactions

(more exothermic)

Ess and Houk’s Distortion/Interaction model

∆E≠ = ∆E≠ + ∆E≠

C

HN

Z

H2C CH2

d i

Distortion energies of the isolated fragments

Interaction energy of the fragments in the TS

∆E≠i

d

∆E≠ is found to be proportional to ∆E≠

Pending questions:

- why is the dipole’s distortion the same with C2H4 and C2H2? - why does’nt matter at all ???- How to relate the barrier to properties of reactants ?

Try to see things from a different perspective=> Valence Bond theory

H2C

HN

O O

HN

H2C H2C

HN

O

What is the difference between 1,3-dipoles and other reactants ?

Combination of three resonance structures:

Not reactive Not reactive Reactive

H2C

HN

O O

HN

H2C H2C

HN

O

Réactant’s geometry : 48.4% 18.0% 33.7%

Valence Bond theory

Ab initio calculation of the weights for each VB structure.Method: « breathing orbital valence bond »:

• Orbitals are pure atomic orbitals• each VB structure has its specific set of orbitals

• the diradical character is not marginal

H2C

HN

O O

HN

H2C H2C

HN

O

Réactant’s geometry : 48.4% 18.0% 33.7%

Transition state’sgeometry :

41.7% 19.7% 38.6%

Valence Bond theory

• the diradical character is not marginal• It increases from reactant’s geometry to transition state’s one

Ab initio calculation of the weights for each VB structure.Method: « breathing orbital valence bond »:

• Orbitals are pure atomic orbitals• each VB structure has its specific set of orbitals

Same calculations, for all 1,3-dipoles:

33.738.041.3

Geometry:

Reactants : Transition state:

21.326.526.3

21.625.127.7

H2C

HN

Z Z = O Z = NH Z = CH2

HC N Z Z = O Z= NHZ = CH2

N N Z Z = OZ = NHZ= CH2

38.643.246.6

32.135.735.4

31.634.436.4

What if the distortion would serve mainlyto increase the diradical character ?

Proposed mechanism :

barrierless

critical diradical

character

1) dipole distortion 2) barrierless reaction

X ZY

X Y Z

X Y Z

X Y Z

a

b

c

XY

Z

E

• The 1,3-dipole distorts until it has reached a critical diradical character (definition to be specified)• It attacks !

This mechanism would explain why dipolarophile doesn’t matter

If this mechanism is the right one, prediction :

33.738.041.3

21.326.526.3

21.625.127.7

H2C

HN

Z Z = O Z = NH Z = CH2

HC N Z Z = O Z= NHZ = CH2

N N Z Z = OZ = NHZ= CH2

The higher the diradical characterof the reactant, the easier the reaction

Probable correlationdiradical weight vs barrier

Reaction barrier vs diradical weight of the 1,3-dipole :

Diradical weight

H2C

HN

ZZ = O Z = NH Z = CH2

N N Z

Z = OZ = NHZ= CH2

HC N ZZ = O Z= NHZ = CH2

(acetylene)(ethelène)

Diradical weight

H2C

HN

ZZ = O Z = NH Z = CH2

N N Z

Z = OZ = NHZ= CH2

HC N ZZ = O Z= NHZ = CH2

(acetylene)(ethylene)

Reaction barrier vs diradical weight of the 1,3-dipole :

Diradical weight

H2C

HN

ZZ = O Z = NH Z = CH2

N N Z

Z = OZ = NHZ= CH2

HC N ZZ = O Z= NHZ = CH2

(acetylene)(ethylene)

Reaction barrier vs diradical weight of the 1,3-dipole :

An alternative measure of diradical character : Transition energy ∆E

H2C

HN

Z

H2C

HN

Z

Z

HN

H2C

H2C

HN

Z

Ground state

Pure diradical

∆E

Strong diradical character=> Small ∆E

Correlation between ∆Eand reaction barrier ?

Reaction barrier vs transition energy ∆E :

Ground state pure diradical (kcal/mol)∆E

kcal/molR2 = 0.99

Transition energies ∆E (reactants’ geometries)

État fondamental pur diradical (kcal/mole)∆E

0

50

100

150

200

250

Gap

diazonium betaines nitrilum betaines azomethine betaines

78

9

4

5 6

1

23

∆E ( ) rather scattered

∆E(Ground Diradical)

Transition energies ∆E ( = transition states’ geometries)

État fondamental pur diradical (kcal/mole)∆E

0

50

100

150

200

250

Gap

diazonium betaines nitrilum betaines azomethine betaines

78

9

4

5 6

1

23

∆E ( ) much less scatteredThe dipoles have the same diradical character (∆E) once they have reached their TS geometry

∆E(Ground Diradical)

Proposed mechanism :

barrierless

critical diradical

character

1) dipole distortion 2) barrierless reaction

X ZY

X Y Z

X Y Z

X Y Z

a

b

c

XY

Z

E

• linear 1,3-dipoles: ∆E = 91 ± 10 kcal/mol• bent 1,3-dipoles: ∆E = 76 ± 10 kcal/mol

∆E (ground state pure diradical)

Critical value for ∆E :

« Give me insight, not numbers » (Charles Coulson)

• 1,3-dipoles are special reactants (violate ordinary laws)• The diradical character is the correlating quantity• A mechanism is proposed, consistent with accurate ab initio data• Reaction barriers estimated from reactants’ properties

1,3-dipolar cycloadditions

• VB is more insightful in this case • VB vs OM: describe reality with two different languages

Valence bond vs Molecular Orbitals; 2 exact theories

Valence bond, just seing things from a different perspective(as Prof. Keating would say…)

Try to see things from a different perspective (Prof. Keating, Dead Poet Society)

Try to see things from a different perspective (Prof. Keating, Dead Poet Society)

B. Braida, Laboratoire de Chimie Théorique,Université de Paris 6, 75252 Paris, France

C. Walter and B. Engels, Institut für Organische Chemie97074 Würzburg, Germany

Thanks to :