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H.B. Bürgi Department of Chemistry and Biochemistry, University of Bern,
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H.B. Bürgi Department of Chemistry and Biochemistry, University of Bern,

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  1. Retrieving, assessing, analysing and interpreting information on chemical bonding from structural data bases H.B. Bürgi Department of Chemistry and Biochemistry, University of Bern, Organic Chemistry Institute, University of Zürich ChemKrist-Workshop 2009, Freiburg

  2. Primary Crystallographic Databases Acta Cryst., volume B58, Part 3, Number 1 (June 2002) Metal and Intermetallic Structures The Pauling File (Structures, Phases, physical properties of Binaries) Inorganic Crystal Structure Database Cambridge Structural Database of organic and metal-organic structures Nucleic Acid Database Protein Data Bank

  3. Overview • 0. AXIOM: Interatomic distance is a convenient and reliable probe to gauge the strength of chemical bonds • 1. Assessment of bond lengths,comparison to reference values (push-pull acetylene, Cr CaF5) • Correlated distance changes in groups of related compounds, principal component analysis (in a Au2Ru3 cluster) • 3. Correlations between structure and activation energies • 4. A flatlander's look at 3D- and 12D-data, cluster analysis (five-coordinationMX5) • Summary

  4. Assessment of bond lengths in a ‘push-pull’ acetylene • reasonably mirror symmetric (s.u. 0.002-3 Å), • R(F) = 0.031, wR(F2) = 0.088 • effect of ‘electron pushing-pulling’ on bond lengths? P. Wilhelm et al., Acta Cryst. C52 (1996) 2004

  5. Int tables Unweighted sample mean d = Σi di / n Sample standard deviation σ = Σi [(di – d)/(n-1)]1/2 Sample median m Lower, upper quartile ql, qu Number of observations n (p. 788-803)

  6. Complete distribution • Distribution for planar N, mean valence angle > 117.6o • Distribution for pyramidal N, mean valence angle in the range 108-114o • d m σ ql qu n • overall 1.390 1.385 0.030 1.366 1.420 69 • planar 1.371 1.370 0.016 1.363 1.382 41 • pyramidal 1.426 1.425 0.011 1.421 1.431 22 Digression I: bimodal distribution Resolution of bimodal distribution of C-N bond lengths in Car-N(Csp3)2 fragments

  7. Digression II: outlier removal • Effect of removing outlier in Car - CN (< 4σ) • d m σ ql qu n • Before 1.455 1.444 0.012 1.436 1.448 32 • After 1.443 1.444 0.008 1.436 1.448 31

  8. BF4– PF6– Digression III: skewed distribution Skewed distributions of X – F bond lengths in BF4– and PF6– ions. International Tables, vol. C and A.G. Orpen, M.G. Quayle, Dalton Trans. (2001) 1601 d m σ ql qu n BF4– 1.365 1.372 0.029 1.352 1.390 84 PF6– 1.551 ~1.56 0.037 2703 Note that d m and that ql, qu are asymmetrically disposed about the mean d. Short distances probably due to high thermal motion or unresolved disorder

  9. Observed – Reference Alternatingdifferences! Dipolar Lewis structure (s.u. 0.002-3 Å), Bond lengths in a ‘push-pull’ acetylene Observed vs. Reference

  10. 221 185 239 192 229 194 250 A robust restraint on bond lengths in multinary phases Example Cr Ca F5: bipartite bond graph, (bond distance in pm) Network equations Vi: Valence of atom i (oxidation state) sij: Theoretical bond valence between atoms i and j (M-L: +, L-M: –) Valence sum rule Equal bond valence rule Empirical correlation between ln sij and observed distances Rij with parameters Ro and B. Empirical bond valence VCr= +3, VCa= +2, VF = –1 I.D. Brown, The ChemicalBond in Inorganic Chemistry, Oxford (2002)

  11. 3 1 2 3 1 0.39 0.61 1 0.26 0.48 2 0.26 0.41 0.17 Comparison of observed and calculated bond lengths • Decrease of bond valence and increase in bond length with increasing coordination number • Testing for missing atoms in crystal structure (poor scatterers, e.g. H) • Strain in structure and hydrogen bonding

  12. Au(2) Au(1) Ru(2) Ru(1) Ru(3) Correlated distance changes in metal clustercontaining Au2Ru3 fragments A.G. Orpen, I.D. Salter, Organometallics 10 (1991) 111

  13. Au(2) Au(1) Ru(2) Ru(1) Ru(3) (Å2) Variance-covariance matrix of metal-metal distances

  14. An observation Center of data cloud (mean) prin1 Δi Digression IV: Finding the principal axes of a data cloud (principal component analysis) obs2 prin2 - The direction of prin1 is chosen in such a way that ΣΔi2 becomes a minimum. - Technically this implies diagonalization of the covariance matrix cov(i,j) obs1

  15. A B C (TBP)(SP) (TBP) AB C (TBP)(SP) (TBP) % of total 92.3 2.9 1.6 1.4 variance explained Principal components and cluster rearrangement A B C (TBP) (SP) (TBP)

  16. Acetal hydrolysis: structure correlation Principal component analysis shows correlated changes of structural parameters P.G. Jones, A.J. Kirby, JACS106 (1984) 6207 H.B. Bürgi, K.C. Dubler-Steudle, JACS110 (1988) 7291

  17. Acetal hydrolysis: structure-energy correlation E = k2*q2 /2 – k3(Eo‡)*q3 – k1*q ΔE‡ / Δq = – (6 Eo‡ * k2)1/2 E = k2*q2 /2 – k3(Eo‡)*q3 Eo‡ Calc: 320 kcal (mol Å)-1 Exp: 300 kcal (mol Å)-1 H.B. Bürgi, K.C. Dubler-Steudle, JACS110 (1988) 7291

  18. Acetal hydrolysis: model of enzymatic catalysis 1 2 Structural data from 1: No COOH with COOH CH2-OCH3 1.398 1.383 Å CH2-OBCO 1.4081.424 Å Relative rates of hydrolysis from 2 1 1010 A.D. Bond, A.J. Kirby, E. Rodriguez, Chem. Commun (2001) 2266 E. Hartwell, D.R.W. Hodgson, A.J. Kirby, JACS122 (2000) 9326

  19. Bowl depth and inversion barrier in corannulenes E = x4 – a * x2 xeq = ± (a / 2)1/2 ΔE = – xeq4 small a large a T.J. Seiders, K.K. Baldrige, G.H. Grube, J.S. Siegel, JACS123 (2001) 517

  20. 11 12 8 10 7 9 5 1 6 2 3 4 distance Digression V: A flatlander’s look at nD-data, cluster analysis 3D: 2D: • Single linkage • Centroid linkage • Complete linkage T.P.E. Auf der Heyde, J. Chem. Ed. 67 (1990) 461

  21. A flatlander’s look at 12D-data (analysed by cluster analysis)

  22. (deg) T1 T4 T2 ‘Cluster centrotype‘ or ‘archetypal configuration‘ Mean and variance of the internal angles for clusters T1 to T4

  23. Au(2) Au(1) Ru(2) Ru(1) Ru(3) Summary • 1. Assessment of bond lengths: Comparison to standard distances (International Tables, vol. C; valence sum rule) • 2. Correlated distance changes: Covariance, Principal component analysis, Reaction paths • 4. Too many parameters: • Clusteringthe data in • principal component • space 3. Correlations between structure and activation energies