Twisted Form Research Articles

Probing the structural and electronic effects to stabilize nonplanar forms of thioamide derivatives: A computational study

Density functional calculations have been performed to examine the stability of nonplanar conformations of thioamide derivatives. Electrostatic, orbital, and ring strain effects were invoked to stabilize the nonplanar conformations of thioamide systems 2-7. Electrostatic interactions helped to achieve the twisted forms of thioamide derivatives; however, pyramidal forms predicted to be the global minimum. Negative hyperconjugative type interactions enhanced the stability of the twisted form 4b when compared with the planar form 4a. The influence of ring strain effect to achieve the twisted form of thioamide was observed with azirine ring. The predictions made with B3LYP/cc-pVDZ+ level of theory was found to be in good agreement with more accurate CBS-QB3 method. The solvent calculations performed with polarized continuum solvation model suggest that the relative stabilities of the nonplanar forms of thioamide derivatives are in general similar to the gas phase results. The importance of hydrogen bonding interactions between the solvent molecules and thioamide derivatives was observed toward the enhanced stability of twisted forms using a combination of explicit solvent molecules and continuum model. The natural bond orbital analysis confirmed the participation of n(N) → π*(C=S) delocalizations in the planar forms and corroborated the earlier reports on larger delocalizations in thioamide systems. Furthermore, the influence of electrostatic and ring strain effects on the amide, natural amides, and selenoamide has also been studied.

Anomeric effect and theoretical vibrational spectra compared to the experiment in 2-chloro-1,3,2-dioxaphosphorinane-2-oxide, -sulfide, and -selenide. I. Anomeric effect and structures

2-Chloro-1,3,2-dioxaphosphorinane-2-oxide, -sulfide, and -selenide are studied at the DFT/B3LYP level and several ab initio methods using a 6-311G** basis set. Our energy optimizations by all these methods show that for oxide DFT and ab initio methods are not much different, while for the sulfide and the selenide the DFT relative energies are higher by about a kcal/mol as compared to those of MP2, MP3, MP4(SDTQ)//MP2, and CCSD(T)//MP2 (//MP2 indicates that a single-point calculation based on the MP2 optimized geometry is performed). However, regardless of rather large relative energies, that does not change the fact that in all three cases the conformational equilibrium mixture contains more than 95% of the lowest, chair-equatorial conformer (this indicates that the P=X bond is in equatorial position). This one and the next higher conformer (chair-axial) are confirmed to be real conformers (energy minima) in all cases. The energetically much higher twist and boat forms are probably just stationary states and local maxima because in many cases, geometry optimizations do not converge to them. Only for MP2 and the selenide do all optimizations converge to the desired stationary state. The relative energies could all be explained in terms of anomeric effects and ring strains. The decreasing covalent character of the P=X bond, with X changing from O to S and to Se, shows itself in the increasing bond lengths and the decreasing strength of anomeric effects.

On the Rabinowitz Floer homology of twisted cotangent bundles

Let (M, g) be a closed connected orientable Riemannian manifold of dimension n ≥ 2. Let ω: = ω0 + π*σ denote a twisted symplectic form on T*M, where \({\sigma\in\Omega^{2}(M)}\) is a closed 2-form and ω0 is the canonical symplectic structure \({dp\wedge dq}\) on T*M. Suppose that σ is weakly exact and its pullback to the universal cover \({\widetilde{M}}\) admits a bounded primitive. Let \({H:T^{*}M\rightarrow\mathbb{R}}\) be a Hamiltonian of the form \({(q,p)\mapsto\frac{1}{2}\left|p\right|^{2}+U(q)}\) for \({U\in C^{\infty}(M,\mathbb{R})}\). Let Σk: = H−1(k), and suppose that k > c(g, σ, U), where c(g, σ, U) denotes the Mane critical value. In this paper we compute the Rabinowitz Floer homology of such hypersurfaces. Under the stronger condition that k > c0(g, σ, U), where c0(g, σ, U) denotes the strict Mane critical value, Abbondandolo and Schwarz (J Topol Anal 1:307–405, 2009) recently computed the Rabinowitz Floer homology of such hypersurfaces, by means of a short exact sequence of chain complexes involving the Rabinowitz Floer chain complex and the Morse (co)chain complex associated to the free time action functional. We extend their results to the weaker case k > c(g, σ, U), thus covering cases where σ is not exact. As a consequence, we deduce that the hypersurface Σk is never (stably) displaceable for any k > c(g, σ, U). This removes the hypothesis of negative curvature in Cieliebak et al. (Geom Topol 14:1765–1870, 2010, Theorem 1.3) and thus answers a conjecture of Cieliebak, Frauenfelder and Paternain raised in Cieliebak et al. (2010). Moreover, following Albers and Frauenfelder (2009; J Topol Anal 2:77–98, 2010) we prove that for k > c(g, σ, U), any \({\psi\in\mbox{Ham}_{c}(T^{*}M,\omega)}\) has a leaf-wise intersection point in Σk, and that if in addition \({\dim\, H_{*}(\Lambda M;\mathbb{Z}_{2})=\infty}\), dim M ≥ 2, and the metric g is chosen generically, then for a generic \({\psi\in\mbox{Ham}_{c}(T^{*}M,\omega)}\) there exist infinitely many such leaf-wise intersection points.

Conformational stability, ab initio calculations and vibrational assignment for 1,1-difluoro- and 1,1-dichloro-1-silacyclopentane

The infrared spectrum (3200–400 cm −1) of the gas and the Raman spectrum (3200–50 cm −1) of liquid and solid 1,1-difluoro-1-silacyclopentane and 1,1-dichloro-1-silacyclopentane have been recorded. In all of these physical states only the twisted (C 2) conformer was detected. The conformational energies have been calculated with the Moller–Plesset perturbation method to the second order; MP2(Full) as well as the density functional theory by the B3LYP method utilizing a variety of basis sets up to 6-311 + G(2df,2pd). All the calculations predict only the twisted form as the stable conformer of 1,1-difluoro-1-silacyclopentane with the average barrier to planarity of 2548 cm −1 (30.49 kJ/mol) from the MP2 calculations and a significantly lower value of 1422 cm −1 (17.01 kJ/mol) from the density functional calculations. Neither calculation was significantly affected by the inclusion of diffuse functions. The C s conformer has a lower energy of 1703 cm −1 (MP2) and 1334 cm −1 (B3LYP) than the planar form. Thus the path between the two identical C 2 conformers is by pseudorotational motion rather than through the planar form. Similar results obtain for 1,1-dichloro-1-silacyclopentane. The optimized geometry calculated with the 6-311 + G(2df,2pd) basis is given together with a complete vibrational assignment for the twisted (C 2) conformer. These assignments are supported by normal coordinate calculations with scaled force constants from MP2(Full)/6-31G(d) calculations. The results of these spectroscopic and theoretical studies are discussed and compared to the corresponding results for silacyclopentane.

Automorphisms and twisted forms of the $N=1,2,3$ Lie conformal superalgebras

We classify the N = 1, 2, 3 superconformal Lie algebras of Schwimmer and Seiberg by means of differential non-abelian cohomology, and describe the general philosophy behind this new technique. The structure of the group (functor) of automorphisms of the corresponding Lie conformal superalgebra is a key ingredient of the proof.

Thin Severi-Brauer Varieties

Severi-Brauer varieties are twisted forms of projective spaces (in the sense of Galois cohomology) and are associated in a functorial way to central simple algebras. Similarly quadrics are related to algebras with involution. Since thin projective spaces are finite sets, thin Severi-Brauer varieties are finite sets endowed with a Galois action; they are associated to etale algebras. Similarly, thin quadrics are etale algebras with involution. We discuss embeddings of thin Severi-Brauer varieties and thin quadrics in Severi-Brauer varieties and quadrics as geometric analogues of embeddings of etale algebras into central simple algebras (with or without involution), and consider the geometric counterpart of the Clifford algebra construction.

Formula omitted]-invariant decomposition of ten-dimensional Yang–Mills supersymmetry

The N=1, d=10 super Yang–Mills action is constructed in a twisted form, using SU(5) invariant decomposition of spinors in 10 dimensions. The action and its off-shell closed twisted scalar supersymmetry operator Q is derived from a Chern–Simons term. The action can be decomposed as the sum of a term in the cohomology of Q and of a term that is Q-exact. The first term is a fermionic Chern–Simons term for a twisted component of the Majorana–Weyl gluino and it is related to the second one by a twisted vector supersymmetry with 5 parameters. The cohomology of Q and some topological observables are defined from descent equations. In this SU(5)⊂SO(10) invariant decomposition, the N=1, d=10 theory is determined by only 6 supersymmetry generators, as in the twisted N=4, d=4 theory. There is a superspace with 6 twisted fermionic directions, with solvable constraints.

Infrared and Raman spectra, conformational stability and vibrational assignment of 1-chloro-1-silacyclopentane

Infrared and Raman spectra (3500–60cm−1) of gas and/or liquid and solid 1-chloro-1-silacyclopentane (c-C4H8SiClH) have been recorded and the vibrational data indicate the presence of a single conformer with no symmetry which is consistent with the twisted form. Ab initio calculations with a variety of basis sets up to MP2(full)/aug-cc-pVTZ predict the envelope-axial and envelope-equatorial conformers are saddle points with nearly the same energies but much lower in energy than the planar conformer. Density functional theory calculations by the B3LYP method predicts slightly lower energies for the two envelope forms and considerably lower for the planar form. By utilizing the MP2(full)/6–31G(d) calculations the force constants, frequencies, infrared intensities, band contours, Raman activities, and depolarization values have been obtained to support the vibrational assignment. Estimated r0 structural parameters have been obtained from adjusted MP2(full)/6–311+G(d, p) calculations. These experimental and theoretical results are compared to the corresponding quantities of some other five-membered rings.

STABILITY OF ANOSOV HAMILTONIAN STRUCTURES

Let (Mn, g) denote a closed Riemannian manifold (n ≥ 3) which admits a metric of negative curvature (not necessarily equal to g). Let ω1 := ω0 + π*σ denote a twisted symplectic form on TM, where σ ∈ Ω2(M) is a closed 2-form and ω0 is the symplectic structure on TM obtained by pulling back the canonical symplectic form dx ∧ dp on T*M via the Riemannian metric. Let Σk be the hypersurface [Formula: see text]. We prove that if n is odd and the Hamiltonian structure (Σk, ω1) is Anosov with C1 weak bundles, then (Σk, ω1) is stable if and only if it is contact. If n is even and in addition the Hamiltonian structure is 1/2-pinched, then the same conclusion holds. As a corollary, we deduce that if g is negatively curved, strictly 1/4-pinched and σ is not exact then the Hamiltonian structure (Σk, ω1) is never stable for all sufficiently large k.

Synthesis and conformational analysis of 1,2-cis fused bicyclic α- d-galactofuranosyl thiocarbamate from per- O- tert-butyldimethylsilyl-β- d-galactofuranosyl isothiocyanate

Per- O- tert-butyldimethylsilyl-α,β- d-galactofuranosyl isothiocyanate ( 4) was synthesized by the reaction of per- O-TBS-β- d-galactofuranose ( 1) with KSCN, promoted by TMSI. Upon O-desilylation (1,2-dideoxy-α- d-galactofuranoso)[1,2 d]-1,3-oxazolidine-2-thione ( 6), the cis-fused bicyclic thiocarbamate was obtained as the only product. Conformational analysis, aided by molecular modelling, showed two stable twist forms ( 3T 4 and 4T O) for the five-membered sugar ring in 6. In aqueous solution, the equilibrium favours the first conformation (3:1 ratio). On the other hand, this ratio decreases for less polar solvents.

Rac-2-Hydroxy-2-(2-oxocyclopentyl)-1H-indene-1,3(2H)-dione

In the title compound, C14H12O4, the indene unit is essentially planar [r.m.s. deviation = 0.0309 (1) Å] and the cyclo­penta­none ring adopts a twist form. In the crystal, mol­ecules are joined via pairs of O—H⋯O hydrogen bonds into centrosymmetric dimers.

Deformations of algebroid stacks

In this paper we consider deformations of an algebroid stack on an étale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions we show that this DGLA is quasiisomorphic to the twist of the DGLA of Hochschild cochains on the algebra of functions on the groupoid by the characteristic class of the corresponding gerbe.

전라남도 한옥보존마을 및 행복마을 한옥의 평면유형에 관한 연구

This study examines and analyzes plan of Hanok which has been newly built at rural areas in Jeollanam-do province and is to present the direction in setting architectural plan of Hanok at rural areas. For the purpose of this study, analyzed the types of Hanok based on the topological characteristics of main house and main spaces including room, living room and kitchen. Five types of 105 Hanoks, type-I, type-II, type-III, type-IV and type-V were drawn on the based of the shape of main house and topological characteristics of main rooms including room, living room and kitchen. Type-I had spatial composition of main rooms in a row and showed similar shape of main house with traditional private houses in Honam region, type-II showed placement of living room in center and main rooms beside it, type-III showed change of type-II and placed kitchen and annex behind living room and similar plan composition with type-III and secured the area of living room and rooms by enlarging the number of rooms, and type-V had the shape of main house with twisted form and placed living room in the center and each room at side or twisted part to ensure openness of living room.

Ab initio study of the polymerisation of cyclopentasilane

The molecular structures and vibration modes of cyclopentasilane (Si5H10) have been examined by employing ab initio and density-functional methods. Three different structures of Si5H10 with different symmetries are analysed, and the results show that the envelope (C s ) and the twist (C2) forms have similar energies and that the planar form (D5h ) is about 50 meV less stable than the C s and C2 forms. The excited-state potential energy surface of Si5H10 is performed using the CIS electronic energy calculation. The ring-open reaction of Si5H10 is investigated in detail by using the first-principles molecular-dynamics simulation for screening the reaction pathways. The formation of Si–H–Si is found to play an important role in the ring-open reaction.

Reply to da Rocha and Rodrigues' comments on the orientation congruent algebra and twisted forms in electrodynamics

AbstractThe recent claim by da Rocha and Rodrigues that the nonassociative orientation congruent algebra (𝒪𝒞 algebra) and native Clifford algebra are incompatible with the Clifford bundle approach is false. The new native Clifford bundle approach, in fact, subsumes the ordinary Clifford bundle one. Associativity is an unnecessarily too strong a requirement for physical applications. Consequently, we obtain a new principle of nonassociative irrelevance for physically meaningful formulas. In addition, the adoption of formalisms that respect the native representation of twisted (or odd) objects and physical quantities is required for the advancement of mathematics, physics, and engineering because they allow equations to be written in sign‐invariant form. This perspective simplifies the analysis of, resolves questions about, and ends needless controversies over the signs, orientations, and parities of physical quantities.

Diaqua(1,4,8,11-tetraazacyclotetradecane)nickel(II) fumarate tetrahydrate

The asymmetric unit of the title complex salt, [Ni(C10H24N4)(H2O)2](C4H2O4)·4H2O, comprises half of a nickel(II) complex dication, half of a fumarate dianion and two water mol­ecules. Both the NiII cation and fumarate anion lie on a crystallographic inversion center. The NiII ion in the cyclam complex is six-coordinated within a distorted N4O2 octa­hedral geometry, with the four cyclam N atoms in the equatorial plane and the two water mol­ecules in apical positions. The six-membered metalla ring adopts a chair conformation, whereas the five-membered ring exists in a twisted form. In the crystal packing, inter­molecular O—H⋯O hydrogen bonds between the water molecules and the carboxyl groups of the fumarate anions lead to the formation of layers with R 4 2(8) ring motifs. NiII complex cations are sandwiched between two such layers, being held in place by O—H⋯O, N—H⋯O and C—H⋯O hydrogen bonds, consolidating a three-dimensional network.

First-principles study of the thermally induced polymerization of cyclopentasilane

The molecular structures and vibration modes of cyclopentasilane (Si 5H 10) have been examined by employing ab initio and density-functional methods. Three different structures of Si 5H 10 with different symmetries are analyzed, and the results show that the envelope (C s ) and the twist (C 2) forms have similar energies and that the planar form (D 5 h ) is about 50 meV less stable than the C s and C 2 forms. The ring-open reaction of Si 5H 10 is investigated in detail by using the first-principles molecular-dynamics simulation for screening the reaction pathways. The formation of Si–H–Si is found to play an important role in the ring-open reaction.

Three-Dimensional Structure of Twinned and Zigzagged One-Dimensional Nanostructures Using Electron Tomography

Electron tomography and high-resolution transmission electron microscopy were used to characterize the unique three-dimensional (3D) structures of twinned Zn(3)P(2) (tetragonal) and InAs (zinc blende) nanowires synthesized by the vapor transport method. The Zn(3)P(2) nanowires adopt a unique superlattice structure that consists of twinned octahedral slice segments having alternating orientations along the axial [111] direction of a pseudo cubic unit cell. The apexes of the octahedral slice segment are indexed as six equivalent <112> directions at the [111] zone axis. At each 30 degrees turn, the straight and zigzagged morphologies appear repeatedly at the <112> and <011> zone axes, respectively. The 3D structure of the twinned Zn(3)P(2) nanowires is virtually the same as that of the twinned InAs nanowires. In addition, we analyzed the 3D structure of zigzagged CdO (rock salt) nanowires and found that they include hexahedral segments, whose six apexes are matched to the <011> directions, linked along the [111] axial direction. We also analyzed the unique 3D structure of rutile TiO(2) (tetragonal) nanobelts; at each 90 degrees turn, the straight morphology appears repeatedly, while the in-between twisted form appears at the [011] zone axis. We suggest that the TiO(2) nanobelts consist of twinned octahedral slices whose six apexes are indexed by the <011>/<001> directions with the axial [010] direction.

An electric charge has no screw sense – a comment on the twistfree formulation of electrodynamics by da Rocha and Rodrigues

AbstractDa Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and superfluous, and (ii) that they can derive the Lorentz force equation from Maxwell's equations. As to (i), we point out that the distinction of polar/axial and twisted/untwisted derives from the property of the electric charge of being a pure scalar, that is, not carrying any screw sense. Therefore, the mentioned distinctions are necessary ingredients in any fundamental theory of electrodynamics. If one restricted the allowed coordinate transformations to those with positive Jacobian determinants (or prescribed an equivalent constraint), then the RR scheme could be accommodated; however, such a restriction is illegal since electrodynamics is, in fact, also covariant under transformations with negative Jacobians. As to (ii), the “derivation” of the Lorentz force from Maxwell's equations, we point out that RR forgot to give the symbol F (the field strength) in Maxwell's equations an operational meaning in the first place. Thus, their proof is empty. Summing up: the approach of RR does not bring in any new insight into the structure of electrodynamics.

An electric charge has no screw sense - a comment on the twistfree formulation of electrodynamics by da Rocha and Rodrigues

Da Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and superfluous, and (ii) that they can derive the Lorentz force equation from Maxwell's equations. As to (i), we point out that the distinction of polar/axial and twisted/untwisted derives from the property of the electric charge of being a pure scalar, that is, not carrying any screw sense. Therefore, the mentioned distinctions are necessary ingredients in any fundamental theory of electrodynamics. If one restricted the allowed coordinate transformations to those with positive Jacobian determinants (or prescribed an equivalent constraint), then the RR scheme could be accommodated; however, such a restriction is illegal since electrodynamics is, in fact, also covariant under transformations with negative Jacobians. As to (ii), the "derivation" of the Lorentz force from Maxwell's equations, we point out that RR forgot to give the symbol F (the field strength) in Maxwell's equations an operational meaning in the first place. Thus, their proof is empty. Summing up: the approach of RR does not bring in any new insight into the structure of electrodynamics.