1. Correlation Between the Diradical Character of 1,3-Dipoles and their Reactivity Toward Ethylene and Acetylene P.C. Hiberty, Laboratoire de Chimie Physique Université de Paris-Sud, 91405 Orsay, France An application of ab initio valence bond theory Dedicated to Prof. T.H. Dunning

2. Some families of 1,3-dipoles Azomethine betaines : Nitrilium betaines : Diazonium betaines :

3. Dipolar cycloadditions Example: Azomethine betaines :

4. Cycloaddition on ethylene (azomethine oxide) :

5. Cycloaddition on acetylene (azomethine oxide) : We expect :

6. We observe : (accurate ab initio) Cycloaddition on acetylene (azomethine oxide) :

7. Nitrilium ylide + ethylene or acetylene : Still two identical barriers …

8. Nitrilium imine + ethylene or acetylene (aromatic product !) Still two identical barriers, idem for the 9 1,3-dipoles

9. Frontier Orbital Theory (FMO) 1,3-dipole Ethylene HOMO LUMO HOMO LUMO Small HOMO-LUMO gap: => Low reaction barrier

10. Frontier Orbital Theory (FMO) 1,3-dipole Ethylene HOMO LUMO HOMO LUMO Let ’ s focus on the dipole ’ s HOMO The higher this HOMO, the lower the reaction barrier

11. Frontier Orbital Theory (FMO) E(HOMO) ∆H ≠ Z = OZ = NHZ = CH 2 diazonium betaines N-N-Z From: DH Hess, KN Houk, JACS 2008, 130, 10187

12. Frontier Orbital Theory (FMO) E(HOMO) ∆H ≠ Z = OZ = NHZ = CH 2 diazonium betaines N-N-Z From: DH Hess, KN Houk, JACS 2008, 130, 10187 azomethine Betaines

13. Frontier Orbital Theory (FMO) E(HOMO) ∆H ≠ Z = OZ = NHZ = CH 2 diazonium betaines N-N-Z nitrilium betaines HN-N-Z azomethine Betaines From: DH Hess, KN Houk, JACS 2008, 130, 10187

14. Dipole-1,3 BV HO BV HO acetylene FMO predicts higher barriers for reaction with acetylene than with ethylene (at variance with experiment) Now, taking the FMOs of the dipolarophile into account … ethylene

15. Geometries of transition states Falsifies Hammond ’ s principle ~ same geometries (the more exothermic the reaction, the earlier the transition state) It looks like the kinetics depend on only one of the two reactants: the 1,3-dipole. True for the 9 reactions (more exothermic)

16. Ess and Houk ’ s Distortion/Interaction model ∆E ≠ = ∆E ≠ + ∆E ≠ di 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 C 2 H 4 and C 2 H 2 ? - why does ’ nt matter at all ??? - How to relate the barrier to properties of reactants ?

17. Try to see things from a different perspective => Valence Bond theory What is the difference between 1,3-dipoles and other reactants ? Combination of three resonance structures: Not reactive Reactive

18. R é actant ’ 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

19. R é actant ’ s geometry : 48.4%18.0%33.7% Transition state ’ s geometry : 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

20. Same calculations, for all 1,3-dipoles: 33.7 38.0 41.3 Geometry: Reactants :Transition state: 21.3 26.5 26.3 21.6 25.1 27.7 38.6 43.2 46.6 32.1 35.7 35.4 31.6 34.4 36.4 What if the distortion would serve mainly to increase the diradical character ?

21. Proposed mechanism : 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

22. If this mechanism is the right one, prediction : 33.7 38.0 41.3 21.3 26.5 26.3 21.6 25.1 27.7 The higher the diradical character of the reactant, the easier the reaction Probable correlation diradical weight vs barrier

23. Reaction barrier vs diradical weight of the 1,3-dipole : Diradical weight (acetylene) (ethelène)

24. Diradical weight (acetylene) (ethylene) Reaction barrier vs diradical weight of the 1,3-dipole :

25. Diradical weight (acetylene) (ethylene) Reaction barrier vs diradical weight of the 1,3-dipole :

26. An alternative measure of diradical character : Transition energy ∆E Ground state Pure diradical ∆E Strong diradical character => Small ∆E Correlation between ∆E and reaction barrier ?

27. Reaction barrier vs transition energy ∆E : Ground state pure diradical (kcal/mol) ∆E kcal/mol R 2 = 0.99

28. Transition energies ∆E (reactants ’ geometries) État fondamental pur diradical (kcal/mole) ∆E ∆E ( ) rather scattered ∆E (Ground Diradical)

29. Transition energies ∆E ( = transition states ’ geometries) État fondamental pur diradical (kcal/mole) ∆E ∆E ( ) much less scattered The dipoles have  the same diradical character (∆E) once they have reached their TS geometry ∆E (Ground Diradical)

30. Proposed mechanism : 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 :

31. « 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 … )

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

33. 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 Chemie 97074 Würzburg, Germany Thanks to :