Bile-Acids in Asymmetric-Synthesis.2. Cholic-Acid Derived Novel Chiral Auxiliaries For Asymmetric Diels-Alder Reactions

Cholic acid-based chiral acrylate 5 yields a Diels-Alder adduct with cyclopent

Chiral polyhydroxylated tetrahydrothiophene derivatives: novel synthesis and structural elucidation by X-ray crystallography, NMR spectroscopy and molecular mechanics calculations

The dideoxygenation reaction of 1,3;4,6-di-O-alkylidene-2,5-di-S-methylthiocarbonyl-D-mannitol derivatives under Barton-McCombie reaction conditions gave the hexahydrodipyranothiophenes 4 and 7 instead of the expected 2,5-dideoxy products. Structural and conformational information on these novel derivatives has been obtained by NMR spectroscopy, single-crystal X-ray crystallography and molecular mechanics calculations.

Radical Annulation Strategy to Chiral Pupukeanones: Total Synthesis of (+)-10-ex&l(- Naphthyl)pupukean-9-onea nd (+)-lO-exo-l(- Naphthyl)-5-epipupukean-9-ones1

Intramolecular alkylation reaction of the bromoenone 12, obtained from S-carvone in three steps, furnished the bicyclo[2.2.2]octenone 13. Contrary to the anticipated radical annulation reaction, the bicyclic bromides 14 and 15, obtained from the enone 13, generated exclusively the cyclopropane product 18 via a 3-exo-trig radical cyclization on reaction with nBu3SnH and AIBN, even in the presence of a large excess of a radicophile. On the other hand, bromoenone 24, synthesized from R-carvone via S-naphthylcarvone 21, underwent radical annulation reaction in the presence of radicophiles to furnish the isotwistanes 25-28 in a regio- and stereospecific manner. Hydrogenation of the olefin 34, obtained from the diketone 27 via a regiospecific Wittig reaction, furnished the naphthyl-5-epipupukean-9-one 33, whereas stereoselective hydrogenation of the enone 36, prepared from the keto ester 25 via a Grignard reaction and dehydration sequence, generated the naphthylpupukeanone 32.

Symmetry adaptation of correlated states in the valence bond basis

Symmetry?adapted linear combinations of valence?bond (VB) diagrams are constructed for arbitrary point groups and total spin S using diagrammatic VB methods. VB diagrams are related uniquely to invariant subspaces whose size reflects the number of group elements; their nonorthogonality leads to sparser matrices and is fully incorporated into a binary integer representation. Symmetry?adapated linear combinations of VB diagrams are constructed for the 1764 singlets of a half?filled cube of eight sites, the 2.8 million ??electron singlets of anthracene, and for illustrative S?0 systems.

E. C. G. Sudarshan and Symmetry in Classical Dynamics, Optics and Quantum Mechanics

We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.

Crystal structures of fluorinated aryl biscarbonates and a biscarbamate: a counterpoise between weak intermolecular interactions and molecular symmetry

Conformational features and supramolecular structural organization in three aryl biscarbonates and an aryl biscarbamate with rigid acetylenic unit providing variable spacer lengths have been probed to gain insights into the packing features associated with molecular symmetry and the intermolecular interactions involving `organic' fluorine. Four structures but-2-yne-1,4-diyl bis(2,3,4,5,6-pentafluorophenylcarbonate), 1; but-2-yne-1,4-diyl bis(4-fluorophenylcarbonate), 2; but-2-yne-1,4-diyl bis(2,3,4,5,6-pentafluorophenylcarbamate), 3 and hexa-2,4-diyne-1,6-diyl bis(2,3,4,5,6-pentafluorophenylcarbonate), 4 have been analyzed in this context. Compound 1 adopts a non-centrosymmetric ``twisted'' (syn) conformation, whereas 2, 3 and 4 acquire a centrosymmetric ``extended'' (anti) conformation. Weak intermolecular interactions and in particular those involving fluorine are found to dictate this conformational variation in the crystal structure of 1. A single-crystal neutron diffraction study at 90 K was performed on 1 to obtain further insights into these interactions involving `organic' fluorine.

Chiral Synthons from Carvone. Part 10. Synthesis of (+)-(1S,3S,4S,7S, 8R)-5,7-Dimethyl-10-oxatetracyclo-(5.3.0.03,5,04,8)decan-9-one.

Degradation of the tolyl group in the tricyclic ketone 1b followed by stereospecific reduction of the resultant ketoester (6) furnishes the title compound (4) containing a new tetracyclic framework, establishing the stereochemistry of the aryl group in 1.

A regiospecific radical annulation strategy to functionalised chiral bicyclo[3.3.l]nonanes

A radical annulation, i.e. an intermolecular radical Michael addition followed by an intramolecular Michael addition of the resultant radical (radical cyclisation) has been employed for the construction of chiral functionalised bicyclo[3.3,1]-nonanes. Thus reaction of carvone hydrohalides 7 with (n)Bu(3)SnH and AIBN in the presence of excess of radicophiles 4 furnished, regiospecifically bicyclo[3.3.1]nonanes 8-14, introducing three new chiral centres in a stereoselective manner. Analogously the bromide 18 generated the bridgehead substituted bicyclo[3.3.1]-nonanes 19-21.

Symmetry Properties of the Large-Deviation Function of the Velocity of a Self-Propelled Polar Particle

A geometrically polar granular rod confined in 2D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large-deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase-space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.

Diacetylenic lipid tubules:experimental evidence for a chiral molecular architecture

Molecular self-assembly is of key importance for the rational design of advanced materials. To investigate the causal relation between molecular structure and the consequent self-assembled microstructure, self-assembled tubules of diacetylenic lipids were studied. Circular-dichroism studies give experimental evidence that the formation of tubules is driven by chiral molecular packing, in agreement with recent theories of tubules. On the basis of these results, a molecular mechanism for the formation of tubules is proposed.

Combining Bayes Classification and Point Group Symmetry under Boolean Framework for Enhanced Protein Quaternary Structure Inference

Our ability to infer the protein quaternary structure automatically from atom and lattice information is inadequate, especially for weak complexes, and heteromeric quaternary structures. Several approaches exist, but they have limited performance. Here, we present a new scheme to infer protein quaternary structure from lattice and protein information, with all-around coverage for strong, weak and very weak affinity homomeric and heteromeric complexes. The scheme combines naive Bayes classifier and point group symmetry under Boolean framework to detect quaternary structures in crystal lattice. It consistently produces >= 90% coverage across diverse benchmarking data sets, including a notably superior 95% coverage for recognition heteromeric complexes, compared with 53% on the same data set by current state-of-the-art method. The detailed study of a limited number of prediction-failed cases offers interesting insights into the intriguing nature of protein contacts in lattice. The findings have implications for accurate inference of quaternary states of proteins, especially weak affinity complexes.

Symmetry-breaking transition in a two-level system coupled to an Ohmic bath: A squeezed-state approach

Displaced squeezed states are proposed as variational ground states for phonons (Bose fields) coupled to two-level systems (spin systems). We have investigated the zero-temperature phase diagram for the localization-delocalization transition of a tunneling particle interacting with an Ohmic heat bath. Our results are compared with known existing approximate treatments. A modified phase diagram using the displaced squeezed state is presented.

Target space of an asymmetric chiral gauged wzw model

It is shown that the asymmetric chiral gauging of the WZW models give rise to consistent string backgrounds. The target space structure of the chiral gauged SL(2,R) WZW model, with the gauging of subgroups SO(1, 1) in the left and U(1) in the right moving sector, is obtained. We then analyze the symmetries of the background and show the presence of a non-trivial isometry in the canonical parametrization of the WZW model. Using these results, the equivalence of the asymmetric models with the symmetric ones is demonstrated.

Asymmetric Diels-Alder Reactions of Chiral Acrylates of Cholic Acid Derivatives

New steroid-based chiral auxiliaries 6, 9, and 12 have been synthesized from readily available cholic acid. These new chiral auxiliaries place the reactive and the shielding sites in a 1,5 relationship to each other. Diels-Alder reaction of cyclopentadiene with corresponding acrylate esters (7, 10, and 13) have been examined. Acrylates 7 and 10 yielded cycloadducts with 29-88% diastereomeric excess with excellent endo selectivity in the presence of an excess of Lewis acids such as AlCl3, BF3.OEt(2), FeCl3, SnCl4, TiCl4, and ZnCl2. Treatment of acrylate 7 with cyclopentadiene in the presence of BF3.OEt(2) at -80 degrees C gave the endo adduct (>99%) with 88% de. Lewis acid catalyzed and uncatalyzed reactions of acrylates 7 and 10 with cyclopentadiene yielded cycloadducts with opposite stereochemistry. The chiral auxiliary was recovered in a nondestructive manner only via iodolactonization. Acrylate ester of alcohol 12 did not show any selectivity in either catalyzed and uncatalyzed reactions with cyclopentadiene. The presence of a flat aromatic surface at C-7 of the steroid was found to be essential to effect high diastereoselection.

Levitation Effect: Role of Symmetry and Dependence of Diffusivity on the Bond Length of Homonuclear and Heteronuclear Diatomic Species

Molecular dynamics investigation of model diatomic species confined to the alpha-cages of zeolite NaY is reported. The dependence of self-diffusivity on the bond length of the diatomic species has been investigated. Three different sets of runs have been carried out. In the first set, the two atoms of the diatomic molecule interact with the zeolite atoms with equal strength (example, O-2, the symmetric case). In the second and third sets which correspond to asymmetric cases, the two atoms of the diatomic molecule interact with unequal strengths (example, CO). The result for the symmetric case exhibits a well-defined maximum in self-diffusivity for an intermediate bond length. In contrast to this, the intermediate asymmetry leads to a less pronounced maximum. For the large asymmetric case, the maximum is completely absent. These findings are analyzed by computing a number of related properties. These results provide a direct confirmation at the microscopic level of the suggestion by Derouane that the supermobility observed experimentally by Kemball has its origin in the mutual cancellation of forces. The maximum in diffusivity from molecular dynamics is seen at the value predicted by the levitation effect. Further, these findings suggest a role for symmetry in the existence of a diffusivity maximum as a function of diameter of the diffusant often referred to as the levitation effect. The nature of the required symmetry for the existence of anomalous diffusivity is interaction symmetry which is different from that normally encountered in crystallography.