CU-Boulder CHEM 6321 - Isomerism with Rigid Molecular Graphs

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Isomerism with Rigid Molecular GraphsCayley (1874)Pasteur (1848)Kekule (1858)vant Hoff and LeBel (1874)Chiral ≡ Non-congruent mirror images (Kelvin in 1904)The Molecular Graph 1821-1895, England 1842 graduated Trinity Collegeas “senior wrangler” 1849 became a lawyer 1863 became chair of math atCambridge, where he diedhappy but poor - 966 papers Invented the concept of twokinds of geometry (Euclean andTopological) Invented modern matrix algebra Invented group theory Invented the molecular graphIsomerism with Rigid Molecular GraphsCayley (1874)Pasteur (1848)Kekule (1858)vant Hoff and LeBel (1874)Chiral ≡ Non-congruent mirror images (Kelvin in 1904)Lord Kelvin’s Definition of ChiralityKheir is Greek for “Hand”In 1904, Lord Kelvin delivered his famous “Baltimore Lectures onMolecular Dynamics and the Wave Theory of Light in which he stated…”Icall any geometric figure, or group of points, chiral, and say it haschirality, if its image in a plane mirror, ideally realized, cannot be broughtto coincide with itself.” Chemists did not start using the term until the1960s (Eliel’s first edition of “Streochemistry of Carbon Compounds”does not contain the term according to John C. Leffingwell, “Chirality andOdour Perception,” http://www.leffingwell.com/chirality/chirality.htmSenior wrangler (e.g. Cayley) was the student who scoredhighest on the Cambridge math Tripos exam. Kelven wasonly “Second Wrangler.” Most interesting quote: “There isnothing new to be discovered in physics now. All that remainsis more and more precise measurement.” Address to theBritish Association for the advancement of Science in 1900.Isomerism in Non-Rigid Molecular Graphs• Euclidean (Molecular Rigidity)• Topological (Non-HomeotopicMolecular GraphSome Interesting Examples of Euclidean Isomerismchiral chiral chiral chiralchiral chiral chiral chiralBr BrOHBrOHBr Br BrOHBrOHBrOHOHOHOHOHOHOHOHchiral chiral chiral chiralClBrBrBrBrClClBrBrBrBrClHomomers DiastereomersHomomersEnantiomers Conformers Enantiomers Classic problems withunambiguous solutions{“Gray Area”Topological StereoisomersTopological stereochemistry papers:Topology of Graphs All knots are homeomorphic to the unknot. All knots have an achiral embedding (theunknot and other “amphichiral” knots). Before organic chemists became involvedwith topology in the context of organicsynthesis, there was very little work on low-Dtopology of graphs.••Theta curveChiral embedding of a theta curveUncolored Möbius Ladders~*Graf, E.; Lehn, J. M. "Synthesis and Cryptate Complexes of a Spheroidal Macrotricyclic Ligandwith Octahedrotetrahedral Coordination," J. Am. Chem. Soc. 1975, 97, (17), 5022-5024.*≡ HomeotopicAchiral presentation of thethree-rung Möbius ladderThe 3-rung Möbiusladder is the KuratowskiK3,3 nonplanar graph!This famous graph hasnine edges and sixvertices3- and 4-Rung Möbius Ladders with Colored RungsSimon, J. "Topological Chirality of Certain Molecules,"Topology 1986, 25, 229-235.Flapan, E. "Symmetries of Mobius Ladders," MathematischeAnnalen 1989, 283, (2), 271-283.Chiral embeddingAchiral embedding!Odd number of rungs: Intrinsically Chiral - no achiral embeddingSpeaking of AchiralSo far, all the achiral objects we’vediscussed have rigidly achiralpresentations (conformations). Is thisnecessary for achirality?Mislow Euclidean Rubber GloveChemically achiral (≡ not resolvable), but rigidlychiral in every possible conformation.Mislow, K.; Bolstad, R. "Molecular Dissymmetry and Optical Inactivity," J. Am. Chem. Soc.1955, 77, (24), 6712-6713.OH(S)-menthol (R)-mentholHOA Topological Rubber GloveFlapan, E. "Rigid and Nonrigid Achirality," Pacific J. Math. 1 987, 129, (1), 57-66.A topologicalmeso compoundA topologicalrubber gloveTopological Hierarchy of Molecular ChiralityMost ChiralIntrinsically chiral graph : No topologically achiral embeddingsTopologically chiral embedding of an intrinsically achiral graphNominal Euclidean chirality : Rigidly chiral presentation (or set of presentations) of a topologically achiral graph with no pathway for racemizationTopological rubber glove : Topologically and chemically achiral but rigidly chiral in every presentationEuclidean rubber glove : Topologically and chemically achiral but rigidly chiral in every accessible presentation (conformation)Nominally achiral : Rigidly achiral presentation accessibleLeast ChiralResolvableNon-resolvableTable 1. Topological Hierarchy of Molecular Chirality. Walba, D. M., A Topological Hierarchy of Molecular Chirality and other Tidbits in TopologicalStereochemistry. In New Developments in Molecular Chirality: Understanding Chemical Reactivity,Mezey, P. G., Ed. Kluwer Academic Publishers: Boston, 1991; Vol. 5, pp 119-129.Lecture on Wednesday, Feb 8will be held in Ekeley M339Synthesis of Möbius LaddersThe THYME Diol-Ditosylate “Ladder”OH NaHO+NaTsOOTsO +MechanismTransformationOHTsO+NaH, DMFO****NucleophilesCH3OHNaH, DMFCH3O-Weak Nucleophile Strong NucleophileHOMO E = -12 eV HOMO E = -1 eVElectrophilesSOOOCH3TsO CH3=Weak electrophileLUMO E = 3.4 eVBimolecular Nucleophilic SubstitutionOCH3-HOMO E = -1 eVSOOOCH3H3COCH3New BondLeaving GroupSOOO+LUMO E = 3.4 eVBimolecular Nucleophilic SubstitutionOH NaHO+NaTsOOTsO +SN2 arrow-pushing mechanismSynthesis of the three rung ladder Furan and THPethers serve asorthogonal alcoholprotecting groups Furan gives THYMEdiol in the presenceof TsO groups Macrocyclization byetherification canbe accomplished atvery high dilution– Both nucleophile andelectrophile are in thesame moleculeSynthesis of the Racemic Möbius LadderHow can we prove the structures?30-membered ring formation31-membered ring formationSynthesis of the Racemic Möbius LadderHow can we prove the structures?Proof by NMR - 1 Two products separated by chromatography Products have the same hydrodynamic radius, andshow the same molecular ion in the MS Both show the qualitatively the same 1H and 13C NMRspectra in solution– An AB quartet for the allylic protons– A broad peak for the ethyleneoxy protons– Four signals in the proton-decoupled carbon spectrumProof by NMR - 2 - the Prism Symmetry dictates four signals in the 13C If the prism could turn “inside-out” on theNMR time scale, the allylic protons would beenantiotopic Observation of diastereotopic allylic protonsmeans this motion is slow– Proton NMR (250 MHz) at 443ºK in DMSO


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CU-Boulder CHEM 6321 - Isomerism with Rigid Molecular Graphs

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