Frank Weinhold Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, WI Natural Bond Orbital Picture of Valency, Bonding, and Torsional Phenomena Lise Meitner Lecture I, Hebrew University, Jerusalem, June 17, 2007

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

“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

“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)

“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)

How Does NBO Work?

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)]

2-Center QM Superposition

Pauli Restrictions Donor-AcceptorDonor-Donor General “mechanism”: 1-e donor-acceptor superposition

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

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

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

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

Rydberg Bonds e.g., 3 T 4 CH 3 CHO

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

Ethane Rotation Barrier: Sterics or Hyperconjugation?

Sterics?Hyperconjugation?

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

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) The PMO “unperturbed problem” is more mysterious than the effect it purports to explain! [V&B, pp ]

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

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

Sterics: Common Sense? H---H distances increase but  E barrier increases! [H.R. Duebal & F. F. Crim, JCP 83, 3863 (1985)]

Protein Folding: Torsional Barriers at Double Bonds

Eclipsing propensity at double bonds?

Resonance Control of Torsional “Stiffness”?

Coordinative H-Bond Modulation of Amide Rotation Barriers

Torsional “Steering” of Acetamide—X Complexes

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

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