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

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. Cycloadditionon ethylene (azomethine oxide) :

5. Cycloadditionon acetylene (azomethine oxide): We expect :

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

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) LUMO LUMO 1,3-dipole Ethylene HOMO Small HOMO-LUMO gap: => Low reaction barrier HOMO

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

11. From: DH Hess, KN Houk, JACS 2008, 130, 10187 Frontier Orbital Theory (FMO) diazonium betaines N-N-Z ∆H≠ E(HOMO) Z = O Z = NH Z = CH2

12. From: DH Hess, KN Houk, JACS 2008, 130, 10187 Frontier Orbital Theory (FMO) diazonium betaines N-N-Z ∆H≠ azomethine Betaines E(HOMO) Z = O Z = NH Z = CH2

13. From: DH Hess, KN Houk, JACS 2008, 130, 10187 Frontier Orbital Theory (FMO) diazonium betaines N-N-Z ∆H≠ nitrilium betaines HN-N-Z azomethine Betaines E(HOMO) Z = O Z = NH Z = CH2

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

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

16. Ess and Houk’s Distortion/Interaction model ∆E≠ = ∆E≠ + ∆E≠ d i Interaction energy of the fragments in the TS Distortion energies of the isolated fragments ∆E≠ is found to be proportional to ∆E≠ d • 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 ? ∆E≠ i

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 Not reactive Reactive

18. 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 Réactant’s geometry : 48.4% 18.0% 33.7% • the diradical character is not marginal

19. 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 Réactant’s geometry : 48.4% 18.0% 33.7% Transition state’s geometry : 41.7% 19.7% 38.6% • the diradical character is not marginal • It increases from reactant’s geometry to transition state’s one

20. Same calculations, for all 1,3-dipoles: Geometry: Reactants : Transition state: 33.7 38.0 41.3 38.6 43.2 46.6 21.3 26.5 26.3 32.1 35.7 35.4 21.6 25.1 27.7 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 : The higher the diradical character of the reactant, the easier the reaction 33.7 38.0 41.3 21.3 26.5 26.3 21.6 25.1 27.7 Probable correlation diradical weight vs barrier

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

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

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

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

27. Reaction barrier vs transition energy ∆E : kcal/mol R2 = 0.99 ∆E Ground state pure diradical (kcal/mol)

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

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

30. Proposed mechanism : ∆E (ground state pure diradical) Critical value for ∆E : • linear 1,3-dipoles: ∆E = 91 ± 10 kcal/mol • bent 1,3-dipoles: ∆E = 76 ± 10 kcal/mol

31. « Give me insight, not numbers »(Charles Coulson) 1,3-dipolar cycloadditions • 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 Valence bond vs Molecular Orbitals; 2 exact theories • VB is more insightful in this case • VB vs OM: describe reality with two different languages 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) Thanks to : 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