1. Natural Bond Orbital Picture of Valency, Bonding, and Torsional Phenomena Frank Weinhold Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, WI 53706 (weinhold@chem.wisc.edu) Lise Meitner Lecture I, Hebrew University, Jerusalem, June 17, 2007

2. Outline • How NBO Works Why Concepts/Analysis? NAO/NBO/NLMO/NRT Overview • How Chemical Bonding Works Donor-Acceptor Superposition Some Exotic Species • How Rotation Barriers Work Ethane Proteins

3. “The Nature of the Chemical Bond is the problem at the heart of all chemistry.” Bryce Crawford, Jr. (1953) “If you look at the great controversies in organic chemistry, They were interesting because in most of them you had to decide what it is that you have to write down on paper to represent chemical structures…They had problems with benzene and resonance hybrids of various kinds.” John D. Roberts, Chem. Intelligencer, Apr. 1998, p. 29

4. “The more accurate the calculations become, the more the concepts tend to vanish into thin air.” R. S. Mulliken, J. Chem. Phys. S2, 43 (1965) “It is at least arguable that, from the point of view of quantum chemistry as usually practiced, the supercomputer has dissolved the bond.” B. T. Sutcliffe, Int. J. Quantum Chem. 58, 645 (1996)

5. “It is nice to know that the computer understands the problem. But I would like to understand it too.” E. P. Wigner (quoted in Physics Today, July 1993, p. 38)

6. How Does NBO Work?

11. www.chem.wisc.edu/~nbo5

12. What is Chemical Bonding? (A1) Thermally robust atom-atom attraction (A2) Exchange-type “valence” attraction (Pauli; “overlap”) vs. (A3) Donor-Acceptor Superposition (1-e and composites) [F. Weinhold, “Chemical Bonding as a Superposition Phenomenon,” J. Chem. Educ.76, 1141 (1999)]

13. 2-Center QM Superposition

14. Pauli Restrictions Donor-Acceptor Donor-Donor 1-e donor-acceptor superposition General “mechanism”:

15. Unit (“half-bond”) Covalent reciprocal complementary 2-c symmetry types Dative/Coordinate uni-directional competitive

19. 3-center/2-electron Hypovalent “Tau bonds” (Lipscomb, Longuet-Higgins) e.g., diborane

20. 3-center/4-electron Hypervalent “Omega bond” (Pimentel-Rundle-Coulson) e.g., bifluoride ion

21. 2-center/2-electron “Nu bonds” e.g., N2+ radical cation

22. Rydberg Bonds e.g., 3T4 CH3CHO

23. High-Order Metal-Metal Bonds: W-W Quintuple Bond

26. Ethane Rotation Barrier: Sterics or Hyperconjugation?

27. Sterics? Hyperconjugation?

28. T. K. Brunck & FW, J. Am. Chem. Soc. 101, 1700 (1979); FW, Nature 411, 539 (2001)

29. PMO Theory (Dewar): Mathematical Consistency? • Q1. What’s the “unperturbed” H(0)? • non-Hermitian (unphysical!) • imaginary eigenvalues • non-orthogonal eigenstates • (non-conservation of probability • and other overlap pathologies) [V&B, pp. 229-234] The PMO “unperturbed problem” is more mysterious than the effect it purports to explain!

30. Q2. Why were the s* (acceptor) orbitals ignored? [FW, Angew. Chem. 115, 4320 (2003)] Conclusion: s-s* hyperconjugation better “explains” the PMO diagram!

31. Sterics: Common Sense? Steric size increases but DEbarrierdecreases! [E. B. Wilson, Adv. Chem. Phys. 2, 367 (1959)]

32. Sterics: Common Sense? H---H distances increase but DEbarrierincreases! [H.R. Duebal & F. F. Crim, JCP 83, 3863 (1985)]

33. Protein Folding: Torsional Barriers at Double Bonds

34. Eclipsing propensity at double bonds?

36. Resonance Control of Torsional “Stiffness”?

37. Coordinative H-Bond Modulation of Amide Rotation Barriers

38. Torsional “Steering” of Acetamide—X Complexes

39. Residue(R-X)-Modulated “Folding Code” Mechanism? (Current MM/MD potentials oblivious to these effects!)

40. Summary • Only the hyperconjugatives-s* picture • of torsional barriers satisfies reasonable • criteria for • mathematical consistency • common sense • predictive utility with respect to • conjugative and H-bonding phenomena Many thanks!