Twisted Form Research Articles

Intersection Numbers of Twisted Cycles and the Correlation Functions of the Conformal Field Theory

We evaluate the intersection numbers of loaded cycles and twisted forms associated with an n-fold Selberg-type integral. The result is deeply related with the geometry of the configuration space of n+3 points in the projective line.

Structural Studies on Three Plant Diterpenoids from Leonotis nepetaefolia

This paper describes the interesting structural studies on three new diterpenoids (plant products), namely, hydroxy-dialactone nepetaefolinol (9,13-epoxy-6β-hydroxy-8α-labdane-16,15 :19,20-diolactone), dehydrated nepetaefolinol (9,13-epoxylabd-5-ene-16,15:19,20-diolactone) and isomeric tetrol (15,16-epoxy-labda-13(16),14-diene-6β,9,17,19-tetrol: which is the reduction product of new diterpenoid leonotinin) isolated from Indian herbal plant Leonotis nepetaefolia (collected in the flowering season from Guindy area, Madras), and are found to be the major compounds in their extractions, so they are expected to possess the interesting pharmacological properties. In all three structures, the fused ring systems adopt distorted chair-chair, distorted chair and intermediate between 1,2-diplanar and half-chair and chair-chair conformations. In compounds 1 and 2, the twisted form of lactone rings are orthogonal to each other and make dihedral angle of 88.4(1) and 87.5(2)° with each other. The primary interaction between the molecules is van der Waal's in nature.

Crystal Structures– AManifesto for the Superiority of the Valine-Derived 5,5-Diphenyloxazolidinone as an Auxiliary in Enantioselective Organic Synthesis

The crystal structures of 32 derivatives of 4-isopropyl-5,5-diphenyl-1,3-oxazolidin-2-one (A and 1–31) are presented (Fig. 2 and Tables 1–3). In all but four structures, the Me2CH group is in a disposition that mimick a Me3C group (Figs. 3–5). The five-membered ring shows conformations from an envelope form with the Ph2C group out of the plane containing the other four atoms to the twist form with the twofold axis through the CO group (Fig. 6, and Table 2). In the entire series, the Me2CH and the neighboring trans Ph group are approximately antiperiplanar (average torsion angle 155°). The structural features are used to interpret the previously observed reactivity behavior of the diphenyl-oxazolidinone derivatives. The practical advantages of the title compound over classical Evans auxiliaries are outlined (Figs. 1 and 7, and Scheme 2): high crystallinity of all derivatives, steric protection of the CO group in the ring, excellent stereoselectivities in reactions of its derivatives, and safe preparation and easy recovery of the auxiliary.

Ab initio studies on the van der Waals complexes of polycyclic aromatic hydrocarbons. II. Naphthalene dimer and naphthalene–anthracene complex

Ab initio calculations were carried out for the naphthalene dimer and naphthalene–anthracene complex to determine their stable geometries and binding energies. Two medium-size basis sets of 6-31G*(0.25) and 6-31+G* were employed at the MP2 level. Five local minima were found for the naphthalene dimer, three of which were parallel-displaced type and the other two T-shaped type. The global minimum geometry was a parallel-displaced structure of a two-layer graphitic type (Ci point group), not the crossed form (D2d). Its energy calculated by the 6-31G*(0.25) and 6-31+G* basis sets was −7.62 and −6.36 kcal/mol, respectively. The naphthalene–anthracene complex showed four local minima, two of which were parallel-displaced type and the other two T-shaped type. The global minimum was a twisted parallel-displaced form (C2), in which the centers of both molecules lie on the same z-axis with their two long axes skewed at an angle of ≈40°. Its energy was −11.30 and −9.52 kcal/mol with the 6-31G*(0.25) and 6-31+G* basis sets, respectively. From these results a set of general rules for the stable geometry of the polycyclic aromatic hydrocarbon clusters were derived, which turned out to be the same as those previously deduced from other systems less directly relevant to polycyclic aromatic hydrocarbons: (1) a face-to-face configuration is unstable, (2) the T-shaped structure is stable, (3) the parallel-displaced structure is also stable. We also found some additional rules: (4) the energies of the T-shaped and parallel-displaced structures are quite comparable when the molecules are small, but (5) the parallel-displaced structure becomes more stable than the T-shaped one as the molecules become larger due to the nature of the π–π interaction. The interplanar distance of stable parallel-displaced structures was about 3.3–3.4 Å, while the plane-to-center distances of T-shaped structures was about 5.0–5.1 Å. We also discovered what we would call the integer rule for the binding energy of the polycyclic aromatic hydrocarbon clusters in that the binding energy varied linearly as the number of overlapping hexagons in the parallel-displaced structures. The ratio of binding energies for the benzene dimer, benzene–naphthalene complex, naphthalene dimer, and naphthalene–anthracene complex were nearly 1:2:3:4.

Structure Elucidation of 6-t-Butyl-6-phenylpentathiane Monoxides by X-ray Crystallography and DFT Calculations

Abstract 6-t-Butyl-6-phenylpentathiane was oxidized with trifluoroperacetic acid (CF3CO3H) or dimethyldioxirane (DMD) at -20 °C. Oxidation with CF3CO3H yielded pentathiane 3-oxide as the main product, whereas that of DMD gave 1- and 3-oxides. The structures of 1- and 3-oxides were finally determined by X-ray crystallographic analysis. DFT calculations of the NMR chemical shifts were performed on the chair and twist forms of the pentathiane and sixteen isomers of the monoxides with the GIAO method at the B3LYP/6-31G* level. The calculated chemical shifts were verified to be in practical agreement with the experimental data of the pentathiane and the isolated 1- and 3-oxides.

Stereochemistry of Seven-Membered Heterocycles: XLII. A Theoretical Study of Stereochemistry of H Complexes Formed by Conformationally Nonuniform 2-R-1,3-Dioxacyclohept-5-enes with Some Proton Donors

According to semiempirical AM1 calculations, the stability of the boat and twist forms of 2-R-1,3- dioxacyclohept-5-enes depends on the size of substituents at the acetal carbon atom. The twist form gives diastereomeric H complexes with chloroform and methanol of the cis and trans structure, containing monocentered hydrogen bonds, whereas the chair conformation preferably forms complexes with a two-centered hydrogen bond. Based on theoretical data (θO H, ΔH, geometry of complexes), the specific features of H complexes of the conformers in electrophilic addition and cycloaddition were revealed. Considerable preferableness of the exo attack of the diastereotopic double bond in the H complex having the chair form is due to the steric accessibility of the exo side, whereas in the complexes of the twist form the facial selectivity is appreciably lower.

Theoretical study of some bis-verdazyl diradicals: singlet–triplet energy gap

The bis-verdazyl diradical (BVD) system is closely examined by using the multiconfiguration wavefunctions as well as the density functional theory (DFT). The totally symmetric singlet ground state turns out to have strong multiconfiguration character at all levels of theory. The singlet ground state takes on the planar structure while the most stable triplet state corresponds to the twisted form. The MCSCF+MCQDPT2 calculations are shown to be sufficient to predict the singlet–triplet energy gap which is insensitive to the electronic characters of the ring substituents.

DNA rotation by a coordinated conformational change of RecA filaments.

RecA protein forms two types of filament structures in the presence or absence of nucleotide cofactors. We recently constructed two molecular models of the DNA structure, the unwound form (N-type structure) and the twisted form (S-type structure), which correspond to the helical pitches of the extended form (ATP form) and compressed form (non-nucleotide form) of the RecA filament, respectively. If ATP hydrolysis is unidirectional and cooperative, and if the extended and compressed forms of RecA filament are interconvertible, the coordinated conformational change travels along the filament. While the RecA filament undergoes this worm-like motion, the wave of conformational change between the unwound and the twisted forms of DNA travels as ATP hydrolyzes, which makes the DNA strands rotate.

Ab-Initio molecular geometry and normal coordinate analysis of pyrrolidine molecule

The molecular geometry of pyrrolidine was quantum mechanically calculated using the split valence 6-31G** basis set. Electron correlation energy has been computed employing MP2 method. The molecule showed an envelope form puckered structure with inter-plane angle of 36.4° and has a total energy of −132976.80 kcal mol −1 of which a −464.86 kcal mol −1 electron correlation energy. The twist form of the molecule showed a twist angle of 10.2° from planarity and has a total energy of −132976.05 kcal mol −1 involving −464.097 kcal mol −1 electron correlation energy. The normal coordinates of the molecule were theoretically analyzed on the basis of the Cs point symmetry of the envelope form. Using initial set of force constants obtained from the ab-initio calculations the fundamental vibrational frequencies were computed. The IR and laser Raman spectra of Pyrrolidine molecules were measured. All the observed vibrational bands including combination bands and overtones were assigned to normal modes with the aid of the potential energy distribution values obtained from normal coordinate calculations. The molecular force field was obtained by refining the initial set of force constants using the least square fit method. The molecular force field was determined by refining the initial set of force constants using the least square fit method instead of using the less accurate scaling factor methods. The determined molecular force field has produced simulated frequencies best match to the observed values. The low frequency molecular out-of-plane deformation modes were observed in both infrared and Raman spectra at 298 and 163 cm −1. The barrier of ring twisting estimated from the observed ring out-of-plane vibrational mode at 163 cm −1 was found 3.1 kcal mol −1.

AM1 study of conformational properties of Z, Z-, E, E- and E, Z-cyclodeca-1,6-diene

An investigation employing the AM1 semiempirical SCF MO method to calculate structure optimization and conformational interconversion pathways for the three geometrical isomers of cyclodeca-1,6-diene has been undertaken. The Z, Z-isomer is calculated to be 10.3 kJ mol −1 more stable than the E, E-isomer, while the E, Z-isomer is 13.3 kJ mol −1 less stable than the Z, Z-isomer. A chair conformation with C 2 h symmetry is found to be the most stable geometry for Z, Z-cyclodeca-1,6-diene ( 1). The boat form, with C 2 v symmetry, is only 3.5 kJ mol −1 less stable than the chair conformer. Conformational interconversion of these forms requires 52 kJ mol −1. The crown form of the parallel family of E, E-cyclodeca-1,6-diene ( 2) is 7.4 kJ mol −1 more stable than the plane-symmetrical chair–chair–boat geometry. Two axial-symmetrical conformations are found for the crossed family of 2. The twist-boat conformation, with a nonintersecting C 2 axis, is calculated to be 10.3 kJ mol −1 less stable than the crown conformation. The unsymmetrical boat–chair ( 3-BC) conformation of E, Z-cyclodeca-1,6-diene ( 3) is calculated to be 16.6 kJ mol −1 more stable than the axial-symmetrical twist form. The interconversion of 3-TC and twist conformations take place via an unsymmetrical transition state, which is 45.6 kJ mol −1 less stable than 3-TC. The barrier for swiveling of the trans double bond through the unsaturated bridge in compounds 2 and 3 is calculated to be 102.5 and 61.9 kJ mol −1, respectively.

Spectral characteristics of 2-aminodiphenylamine in different solvents and at various pH values

The absorption and fluorescence spectra of 2-aminodiphenylamine (2ADA) have been studied as a function of solvent polarity and acid concentration. Analysis of solvatochromic and prototropic shifts of 2ADA reveals: (i) the presence of intramolecular hydrogen bonding between imino and amino groups in the ground state, (ii) dual fluorescence (360 and 430 nm) of the monocation (2ADA +) formed by the protonation of amino group; and (iii) proton-induced quenching of the monocation (2ADA +) fluorescence. In the dual fluorescence of 2ADA +, the longer wavelength emission at 430 nm is found to be from the twisted form of the monocation. The rate constants of the proton-induced quenching of 2ADA + are determined.

Ab-initio molecular geometry and normal coordinate analysis of tetrahydrothiophene molecule

The molecular geometry of tetrahydrothiophene (THT) was quantum mechanically calculated using the split valence 6–31G** basis set. Electron correlation energy has been computed employing MP2 method. The molecule showed a twist form puckered structure with a twist torsion angle of 13° and has a total energy of −347 877.514 kcal/mol of which a 436.715 kcal/mol electron correlation energy. The envelope form of the molecule showed an inter-plane angle of 22° and has a total energy of − 347 974.430 kcal/mol involving −436.558 kcal/mol electron correlation energy. The normal coordinates of the molecule were theoretically analyzed and the fundamental vibrational frequencies were calculated. The IR and laser Raman spectra of THT molecule was measured. All the observed vibrational bands including combination bands and overtones were assigned to normal modes with the aid of the potential energy distribution values obtained from normal coordinate calculations. The molecular force field was determined by refining the initial set of force constants using the least square fit method instead of using the less accurate scaling factor methods. The determined molecular force field has produced simulated frequencies which best match the observed values. The lowest-energy modes of vibration were two molecular out-of-plane deformations, observed at 114 and 166 cm −1. The barrier of ring twisting estimated from the observed ring out-of-plane vibrational mode at 114 cm −1 was estimated.

$p$-adic Fourier theory

In this paper we generalize work of Amice and Lazard from the early sixties. Amice determined the dual of the space of locally Q_p -analytic functions on Z_p and showed that it is isomorphic to the ring of rigid functions on the open unit disk over C_p . Lazard showed that this ring has a divisor theory and that the classes of closed, finitely generated, and principal ideals in this ring coincide. We study the space of locally L -analytic functions on the ring of integers in L , where L is a finite extension of Q_p . We show that the dual of this space is a ring isomorphic to the ring of rigid functions on a certain rigid variety X . We show that the variety X is isomorphic to the open unit disk over C_p , but not over any discretely valued extension field of L ; it is a “twisted form” of the open unit disk. In the ring of functions on X , the classes of closed, finitely generated, and invertible ideals coincide, but unless L=Q_p not all finitely generated ideals are principal. The paper uses Lubin–Tate theory and results on p-adic Hodge theory. We give several applications, including one to the construction of p-adic L -functions for supersingular elliptic curves.

Quantumchemical Investigation of Unsaturated Sixmembered Heterocycles: I. Steric and Electronic Structures of 1,2-dihydro-1,2-azaphosphorin

By quantumchemical calculations of 1,2-dihydro-1,2-azaphosphorin by semiempirical and abinitio calculations we discovered that in gas phase it has twist form with planar nitrogen and pyramidal phosphorus atoms, the latter with a pseudoaxial substituent. The N-H and P-H bonds occupy anticlinal positions.

Kinetics of the Conformer Reactions: II. Significance of Media in the Electrophilic addition Reactions

The kinetics of electrophilic addition reaction of bromine to a multiple bond in a series of con-formationally unhomogenous 2-substituted 1'3-dioxa-5-cycloheptenes was studied. We found that the com-pounds with trans structure are formed. The partial reaction rate constant for chair, twist forms, thereaction susceptibility parameters to the substituent electronic effect at the C2atom are obtained. Relativereactivity of the alternative steric structures is defined by the specific solvation of the substrate. The result obtained are compared with those achieved without accounting for conformational term.

X-ray diffraction study of DL-1,4-dimethyl-2,5-dioxabicyclo[2.2.1]heptane-3,6-dione: the sense of twist and folding

The title dilactone exists in a crystalline state (110 K) as enantiomeric synchro-(+,+)-(R,R)- and synchro-(–,–)-(S,S)-twist forms (τ0 = |1.8°|) with the retention of C2 symmetry, linked by infinite zig-zag heterochiral chains (space group C2/c) by mutual H-bonds of the CH2–H‥O=C type.

Twisted forms of finite étale extensions and separable polynomials

Examples of twisted forms of finite étale extensions and separable polynomials are calculated using Mayer‐Vietoris sequences for non‐abelian cohomology.

Solvent Effects on Solute Electronic Structure and Properties: Theoretical Study of a Betaine Dye Molecule in Polar Solvents

The electronic structure of the betaine dye molecule, pyridinium- N-phenoxide [4-(1-pyridinio)phenolate] including the effects of geometry and polar solvents, has been studied at an ab initio level using the reference interaction site model self-consistent-field (RISM-SCF) method. Acetonitrile (CH3CN) and water (H2O) were selected as polar solvents. We obtain both the optimized solute geometry in solution and the total free energy profile with respect to variation in the torsion angle between the pyridinium and phenoxide rings and analyze the various electronic and solvation contributions. The betaine molecule in the gas phase has a twisted geometry, which is slightly more twisted in solution. In acetonitrile, the calculated structure shows good agreement with earlier semiempirical results for the minimum free energy structure. It is shown that the solute dipole moment is strongly enhanced in polar solution, also in accord with earlier semiempirical calculations. However, in solution, there is relatively little change in dipole moment with changes in the torsion angle, in contrast to the marked variation in the gas phase. Correspondingly, the solvation free energy is only weakly more negative with increasing twist. Electron correlation in the solute molecule is shown to play an important role in the torsional free energy, destabilizing the twisted form. This destabilization decreases by a factor of 4 from the gas phase to water, with increasing charge localization induced by the solvent. The implications of these results for interaction site models of charge-separated conjugated molecules in solution are discussed.

Cohomologie galoisienne des groupes quasi-déployés sur des corps de dimension cohomologique ≤2; Galois cohomology of quasi-split groups over fields of cohomological dimension ≤ 2

Let k be a perfect field with cohomological dimension ≤ 2. Serre's conjecture II claims that the Galois cohomology set H1(k,G) is trivial for any simply connected semi-simple algebraic G/k and this conjecture is known for groups of type 1A n after Merkurjev–Suslin and for classical groups and groups of type F4 and G2 after Bayer–Parimala. For any maximal torus T of G/k, we study the map H1(k, T) → H1(k, G) using an induction process on the type of the groups, and it yields conjecture II for all quasi-split simply connected absolutely almost k-simple groups with type distinct from E8. We also have partial results for E8 and for some twisted forms of simply connected quasi-split groups. In particular, this method gives a new proof of Hasse principle for quasi-split groups over number fields including the E8-case, which is based on the Galois cohomology of maximal tori of such groups.

Pseudorotation in tetrahydrofuran⋯HF heterodimer

Seven isotopomers of the hydrogen-bonded heterodimer tetrahydrofuran⋯HF have been investigated in the frequency range 6–18 GHz using molecular-beam Fourier transform microwave spectroscopy. The rotational spectra of C4H8O⋯HF and C4H8O⋯DF exhibit small tunneling splittings, which were not observed for C4D8O⋯HF and the four single 13C isotopomers. These observations analyzed in terms of symmetry considerations allow us to conclude that these splittings are due to pseudorotation within the tetrahydrofuran subunit of the complex and not to HF inversion. The spectroscopic parameters of the complex have been interpreted in terms of a geometry in which tetrahydrofuran has a conformation close to the twisted ring form, with HF lying on the plane bisector to the COC ring angle.