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1. Introduction

Molecular Quantum Similarity of Enantiomers: Chiral Axis vs Asymmetric Centra Janssens S., Boon G., Geerlings P. Onderzoeksgroep Algemene Chemie (ALGC), Faculteit Wetenschappen, Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium. 1. Introduction.

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1. Introduction

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  1. Molecular Quantum Similarity of Enantiomers: Chiral Axis vs Asymmetric CentraJanssens S., Boon G., Geerlings P.Onderzoeksgroep Algemene Chemie (ALGC), Faculteit Wetenschappen,Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium. Vrije Universiteit Brussel

  2. 1. Introduction • Similarity  Fundamental concept in chemistry / pharmacology • Chirality  Lots of pharmacologically important molecules • Assume: degree of chirality linked to (dis)similarity of 2 enantiomers dissimilarity = 1- similarity • How quantify molecular similarity? Vrije Universiteit Brussel

  3. 2. Objectives • Quantify dissimilarity of enantiomers • Global & local similarity indices • Orientation! • Conformations! • Illustration Mezey’s “Holographic Electron Density Theorem” sp3, sp2, sp1 carbon • chirality dissimilarity link Vrije Universiteit Brussel

  4. 3. Similarity indices • Carbó index: generalized cosine index MQSM perfect similarity • Use next to r(r) also eliminates dominant effect of core electrons Vrije Universiteit Brussel

  5. Local SI  (finite, arbitrary subdomain) • • • • • • E=E • • • • • • (r) • (r), N • Hohenberg – Kohn • Mezey: Holographic Electron Density Theorem electrons nuclei • • • • E=E • • • • • compatible • • with a single (r) (r) (r) for a given (positions & charges) ground state Vrije Universiteit Brussel

  6. Hirshfeld partitioning • Total electron density r(r)  atomic contributions rA(r) • Global index converted to local analogue: Contribution C* to total rR(r) Promolecular density Contribution C* to product rR(r) rS(r) Vrije Universiteit Brussel

  7. Orientation dependency • Translational problem • Relative orientation • Maximal similarity? • Several alignment methods • Physico-chemical features • Topological-geometrical features  TGSA • Maximize similarity  QSSA • Align backbone atoms BB QSSA BB Vrije Universiteit Brussel

  8. SI for conformers • Boltzmann weighted (BW) SI: • BW specific rotation : Vrije Universiteit Brussel

  9. 4. ApplicationsChiral axis X X C C C H H a b X H C C C X H a b • 1,3-disubstituted allenes: chiral structures without C* XHC=C=CX’H with XX’=FF, ClCl, BrBr, FCl, FBr, ClBr • No conformational flexibility Vrije Universiteit Brussel

  10. Selected alignment 7 5 7 5 1 2 3 4 1 2 3 4 6 6 X X X X X C C C C H C C H H H X H H C C C a a C C C X H H a b b X a b b 0° 180° Vrije Universiteit Brussel

  11. 5. Results: Global SI XHC=C=CX’H • BB alignment constraint BB 180° B3LYP/6-31G* •  heavy atoms at large distance  global SI  coinciding  global SI  “non-diagonal” dihalogen allenes 0° HH, FF, HCl, HCl 180° HF, HF, HH, ClCl average Vrije Universiteit Brussel

  12. Global SI XHC=C=CX’H • BB alignment constraint BB 180° B3LYP/6-31G* •  intermediate values  effect heavy halogens cancels out • ≠ due to not fully perfect sp2 character C1, C3 “diagonal” dihalogen allenes 0° HH, FF, HF, HF 180° HF, HF, HH, FF Vrije Universiteit Brussel

  13. Global SI • XHC=C=CX’H with XX’=FF, ClCl, BrBr, FCl, FBr, ClBr • SI: BrBr < ClBr ≈ FBr < ClCl < FCl < FF sequence of “size” of atoms, follows chemical intuition • In line with CHFClBr: coinciding atoms ClCBr > FCBr > HCBr > FCCl > HCCl > HCF 0.990 0.055 heavier halogens superimposed  SI  Vrije Universiteit Brussel

  14. Local SI XHC=C=CX’H • BB alignment constraint BB 180° B3LYP/6-31G* • Extra constraint C1/C3 perfect sp2 • Numerical illustration of Mezey’s Theorem on sp2/sp1 C-atoms • Substituent values all =1 within precision considered Vrije Universiteit Brussel

  15. Local SI XHC=C=CX’H • BB alignment constraint BB 180° B3LYP/6-31G* • Extra constraint C1/C3 perfect sp2 • substituents on C at large distance  SI smaller • = (FF) or ≠ (FCl) substituents  value = or ≠ Vrije Universiteit Brussel

  16. Chiral axis vs. chiral center (Boon et al.) Halomethane CHFClBr sp3 C-atom similar values Simple amino acids: Ala, Asp, Cys, Leu, Ser, Val similar values Boltzmann weighted SI NH2 R-C*-COOH H • sp2 ≥ sp1 > sp3 • Chiral axis: less direct chirality source  Mezey’s Theorem less pronounced for allenes Vrije Universiteit Brussel

  17. “Calibration” curve • RR’C=C=CR”R’”: exp data* of molar rotation f R=CH3 R’=H R”=CH3 R’”=H R=CH3 R’=H R”=CH2OH R’”=H R=Ph R’=H R”=CH3 R’”=H R=Ph R’=CH3 R”=COOH R’”=CH3 R=Ph R’=CH3 R”=COOH R’”=H R=Ph R’=H R”=COOH R’”=H R=Ph R’=H R”=Ph R’”=H *W.Runge, In The Chemistry of Ketenes, Allenes and Related Compounds, Part 1, Editor: S.Patai, Wiley, 1980, p.99 Vrije Universiteit Brussel

  18. “Calibration” curve exp f theor f theor f reliable y = 1.5242x + 4.4695 exp. f 2000 R2 = 0.9163 y = 0.9902x - 50.862 1500 R2 = 0.9207 1000 500 theor. f 0 -500 0 500 1000 1500 2000 -500 B3LYP/6-31G* B3LYP/6-311++G (and solvent effect) Vrije Universiteit Brussel

  19. Link SI - []D XHC=C=CX’H 450 400 0.65 350 300 0.6 250 200 0.55 150 100 0.5 50 0 0.45 FF FCl FBr ClCl ClBr BrBr FF FCl FBr ClCl ClBr BrBr • Calculated specific rotation []D global SI []D SI • ‘Mirror’ image pattern, exact nature of correlation not known Vrije Universiteit Brussel

  20. 6. Outlook • 2C*, halogen substituted ethanes • X1X2X3C―CY1Y2Y3 with X1,X2,X3,Y1,Y2,Y3 = H, F, Cl, Br • Conformational flexibility  Boltzmann weighted SI • Backbone alignment with C1, C2, X, Y superimposed Vrije Universiteit Brussel

  21. 7. Conclusions • Extension similarity 1C*  0C*, 2C* sp3  sp2, sp1 • Global/local SI based on r/Dr  complementary info • Numerical illustration of Mezey’s ‘Holographic Electron Density Theorem’ • Reliable f due to comparison theory  exp • chirality dissimilarity link Vrije Universiteit Brussel

  22. Publications G.Boon, C.Van Alsenoy, F.De Proft, P.Bultinck, P.Geerlings, J. Phys. Chem. A, 107, 11120 (2003) G.Boon, C.Van Alsenoy, F.De Proft, P.Bultinck, P.Geerlings, J. Phys. Chem. A, 110, 5114 (2006) S.Janssens, G.Boon, P.Geerlings, J. Phys. Chem. A, 110, 9267 (2006) S.Janssens, G.Boon, P.Geerlings, Lecture Series in Computer and Computational Sciences, xxx (2006) Vrije Universiteit Brussel

  23. Acknowledgements Prof. Dr. P. Geerlings Dr. G. Boon Thank you for your attention! Vrije Universiteit Brussel

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