Ring Inversion Research Articles

Synthesis of Trialkylhydroxylamines by Stepwise Reduction of O-Acyl N,N-Disubstituted Hydroxylamines: Substituent Effects on the Reduction of O-(1-Acyloxyalkyl)hydroxylamines and on the Conformational Dynamics of N-Alkoxypiperidines.

The influence of the electron-withdrawing azide group on the reduction of O-(1-acyloxy-ω-azido)hydroxylamines by triethylsilane in the presence of boron trifluoride etherate is studied and found to increase with increasing proximity to the reaction site, suggesting that the reaction proceeds by way of aminoxocarbenium ion intermediates. The ability to carry azides through the reaction sequence affords O-(ω-azidoalkyl-N,N-dialkylhydroxylamines thereby making such functionality available for use in click chemistry. A series of 4-substituted N-alkoxypiperidines were prepared and studied by variable temperature NMR spectroscopy leading to the conclusion that the rate-determining step in the stereomutation of such piperidines is the piperidine ring flip and not nitrogen inversion or rotation about the N-O bond. The process of N-O bond rotation only becomes rate determining when in the presence of pervasive steric hindrance as is the case with the N-alkoxy-2,2,6,6-tetramethylpiperidines.

Characterizations of core and dual core inverses in rings with involution

ABSTRACTLet R be a unital ring with involution. We give the characterizations and representations of the core and dual core inverses of an element in R by Hermitian elements (or projections) and units. For example, let and . Then a is core invertible if and only if there exists a Hermitian element (or a projection) p such that and is invertible. As a consequence, a is an element if and only if there exists a Hermitian element (or a projection) p such that and is invertible. We also get a new characterization for both core invertibility and dual core invertibility of a regular element by units, and their expressions are shown. In particular, we prove that for , a is both Moore–Penrose invertible and group invertible if and only if is invertible along a.

The (b, c)-Inverse in Rings and in the Banach Context

In this article, the (b, c)-inverse will be studied. Several equivalent conditions for the existence of the (b, c)-inverse in rings will be given. In particular, the conditions ensuring the existence of the (b, c)-inverse, of the annihilator (b, c)-inverse and of the hybrid (b, c)-inverse, will be proved to be equivalent, provided b and c are regular elements in a unitary ring \(\mathcal {R}\). In addition, the set of all (b, c)-invertible elements will be characterized and the reverse order law will be also studied. Moreover, the relationship between the (b, c)-inverse and the Bott–Duffin (p, q)-inverse will be considered. In the context of Banach algebras, integral, series and limit representations will be given. Finally, the continuity of the (b, c)-inverse will be characterized.

Representations of the (b,c)-inverses in rings with involution

Let R be a ring and b,c ? R. The concept of (b,c)-inverses was introduced by Drazin in 2012. In this paper, the existence and the expression of the (b,c)-inverse in a ring with an involution are investigated. A new representation of the (b,c)-inverse based on the group inverse is also presented.

A class of Drazin inverses in rings

A strongly direct sum decomposition given by a strongly nil-clean endomorphism motivates us to introduce a class of new Drazin inverses, which is called strong Drazin inverse. In this paper, some basic properties of the strong Drazin inverse are obtained. We show the Cline’s Formula and Jacobson’s Lemma for the strong Drazin inverse. Further, some additive results for the strong Drazin inverse are presented under additional conditions that ab = 0 or ab = ba.

On the Moore-Penrose inverse in rings with involution

On the Moore-Penrose inverse in rings with involution

On the pseudo drazin inverse of the sum of two elements in a Banach algebra

In this paper, some additive properties of the pseudo Drazin inverse are obtained in a Banach algebra. In addition, we find some new conditions under which the pseudo Drazin inverse of the sum a + b can be explicitly expressed in terms of a, az, b, bz. In particular, necessary and sufficient conditions for the existence as well as the expression for the pseudo Drazin inverse of the sum a+b are obtained under certain conditions. Also, a result of Wang and Chen [Pseudo Drazin inverses in associative rings and Banach algebras, LAA 437(2012) 1332-1345] is extended.

Ab initio computational study of 1-methyl-4-silatranone and attempts at its conventional synthesis

1-Methyl-4-silatranone could exhibit the structural aspects of a typical silatrane including a short N–Si bond distance reflecting a dative bond. But given the significant amide resonance in a [3.3.3] bridgehead bicyclic lactam, the lone pair could be shared with the carbonyl group leading to a very long N–Si bond, essentially a “non-silatrane.” Ab initio calculations (MP2/6-311 + G*) predict that ground state conformations of this molecule are best regarded as lactams rather than silatranes, the most stable having a calculated N–Si bond length of 2.902 A and an N–CO bond length of 1.387 A. The calculated transition state for inversion of the amide ring retains very little amide resonance (N–CO, 1.440 A). Some of this loss is compensated through tightening of the N–Si bond (2.422 A), leading to a net energy of activation of ca 8 kcal/mol. Attempts to synthesize 1-methyl-4-silatranone using conventional pathways successful for 1-methylsilatrane [condensations employing N,N-bis(2-hydroxyethyl)glycolamide in place of tris(2-hydroxyethyl)amine] were unsuccessful. This is due to the net loss in resonance energy of the amide reactant relative to that in the [3.3.3] system, the essential absence of the N–Si dative bond, and the rigidity introduced by the planar amide linkage in the starting material. A more likely pathway to successful synthesis should be formation of the amide linkage in the final step.

Bicommuting properties of generalized inverses

Let R be any associative ring and let . By making use of the bicommutant comm, Koliha and Patrício [Elements of rings with equal spectral idempotents. J Aust Math Soc. 2002;72:137–152], Wang and Chen [Pseudo Drazin inverses in associative rings and Banach algebras. Linear Algebra Appl. 2012;437:1332–1345], and Drazin [Generalized inverses: uniqueness proofs and three new classes. Linear Algebra Appl. 2014;449:402–416] have found three ways to define a unique idempotent p associated with a for increasingly general a. In this article it is shown that one can associate with a unique ‘left’ and ‘right’ idempotents p and q under much weaker conditions on a. For any semigroup S and any given , in 2012 [Drazin MP. A class of outer generalized inverses. Linear Algebra Appl. 2012;436:1909–1923] the author defined as being a (b, c)-inverse of a if , and , which hypotheses are satisfied, for suitable b and c, by essentially every known outer generalized inverse y. Here it is shown that if b and c are equivalent under J.A. Green’s equivalence relation (or, in particular, if , as holds for the Moore–Penrose inverse , for the pseudo-inverse and for the Bott-Duffin inverse), then and . This leads to weaker alternative conditions on a, b, c still sufficient for the existence of unique corresponding left and right idempotents p, q. Beyond comm, etc., a more general version is established which replaces ordinary commutativity by an intertwining property.

DFT and structural studies of 2-oxo-1,2,3,4-tetrahydropyridines

Quantum chemical calculations based on density functional theory (DFT) and X-ray crystal structure analysis of some ethyl 4-aryl-6-methyl-2-oxo-1,2,3,4-tetrahydropyridine-5-carboxylates (THPYs) were applied in order to elucidate the effect of variations of the additional substituent on the C4-aryl ring on the molecular geometry, conformation and packing of molecules in the crystalline lattice. Due to the presence of the C4 stereocenter, these compounds exist as a racemic mixture in the crystal structure. Intermolecular interactions between the potential hydrogen donor (NH) and hydrogen acceptor (2-CO) of the heterocycle in the enantiomeric pair forming a sheet like dimeric structure, which provides especial stability to the crystal packing. The existence of the short intramolecular interactions (CH⋯π) and (CH⋯O) are a key feature which imparts also additional stability to the molecular conformation in the solid state. Most computational data including conformation of the heterocycle, the values of the bond lengths and angles are well in agreement with the experimental data. Ring flip calculations for 4-phenyl substituent explain the extreme torsional strain caused by the eclipsing of the carbon-hydrogen bonds in 3-CH2 moiety with the neighboring C4Caryl and C4H bonds and also the changes of some characteristic bond lengths and angles. These calculations indicate the more favored pseudo-axial orientation of the phenyl group over the pseudo-equatorial orientation.

New characterizations for core inverses in rings with involution

The core inverse for a complex matrix was introduced by Baksalary and Trenkler. Raki\'c, Din\v{c}i\'c and Djordjevi\'c generalized the core inverse of a complex matrix to the case of an element in a ring. They also proved that the core inverse of an element in a ring can be characterized by five equations and every core invertible element is group invertible. It is natural to ask when a group invertible element is core invertible, in this paper, we will answer this question. We will use three equations to characterize the core inverse of an element. That is, let $a, b\in R$, then $a\in R^{\tiny\textcircled{\tiny\#}}$ with $a^{\tiny\textcircled{\tiny\#}}=b$ if and only if $(ab)^{\ast}=ab$, $ba^{2}=a$ and $ab^{2}=b$. Finally, we investigate the additive property of two core invertible elements. Moreover, the formulae of the sum of two core invertible elements are presented.

Controlling Proton Delivery through Catalyst Structural Dynamics

AbstractThe fastest synthetic molecular catalysts for H2 production and oxidation emulate components of the active site of hydrogenases. The critical role of controlled structural dynamics is recognized for many enzymes, including hydrogenases, but is largely neglected in designing synthetic catalysts. Our results demonstrate the impact of controlling structural dynamics on H2 production rates for [Ni(PPh2NC6H4R2)2]2+ catalysts (R=n‐hexyl, n‐decyl, n‐tetradecyl, n‐octadecyl, phenyl, or cyclohexyl). The turnover frequencies correlate inversely with the rates of chair–boat ring inversion of the ligand, since this dynamic process governs protonation at either catalytically productive or non‐productive sites. These results demonstrate that the dynamic processes involved in proton delivery can be controlled through modification of the outer coordination sphere, in a manner similar to the role of the protein architecture in many enzymes. As a design parameter, controlling structural dynamics can increase H2 production rates by three orders of magnitude with a minimal increase in overpotential.

Controlling Proton Delivery through Catalyst Structural Dynamics.

The fastest synthetic molecular catalysts for H2 production and oxidation emulate components of the active site of hydrogenases. The critical role of controlled structural dynamics is recognized for many enzymes, including hydrogenases, but is largely neglected in designing synthetic catalysts. Our results demonstrate the impact of controlling structural dynamics on H2 production rates for [Ni(PPh2 NC6H4R2 )2 ]2+ catalysts (R=n-hexyl, n-decyl, n-tetradecyl, n-octadecyl, phenyl, or cyclohexyl). The turnover frequencies correlate inversely with the rates of chair-boat ring inversion of the ligand, since this dynamic process governs protonation at either catalytically productive or non-productive sites. These results demonstrate that the dynamic processes involved in proton delivery can be controlled through modification of the outer coordination sphere, in a manner similar to the role of the protein architecture in many enzymes. As a design parameter, controlling structural dynamics can increase H2 production rates by three orders of magnitude with a minimal increase in overpotential.

Conformational Dynamics of the Single Lipopolysaccharide O-Antigen in Solution.

The O-antigen is the most variable and highly immunogenic part of the lipopolysaccharide molecule that covers the surface of Gram-negative bacteria and makes up the first line of cellular defense. To provide insight into the details of the O-antigen arrangement on the membrane surface, we simulated its behavior in solution by molecular dynamics. We developed the energetically favorable O-antigen conformation by analyzing free-energy distributions for its disaccharide fragments. Starting from this conformation, we simulated the behavior of the O-antigen chain on long timescales. Depending on the force field and temperature, the single molecule can undergo reversible or irreversible coil-to-globule transitions. The mechanism of these transitions is related either to the rotation of the carbohydrate residues around O-glycosidic bonds or to flips of the pyranose rings. We found that the presence of rhamnose in the O-antigen chain crucially increases its conformational mobility.

Chairs!: A Mobile Game for Organic Chemistry Students To Learn the Ring Flip of Cyclohexane

The hallmark of game-based learning is that students discover concepts through trial and error as they play. With the digital landscape in higher education shifting to mobile-first, new tools for learning chemistry are both possible and needed. Interactive games for chemistry bring intuitive content directly to students through their devices. The game Chairs! was created to teach the ring flip of cyclohexane. The development of this new mobile learning tool for organic chemistry and its implementation in classrooms are described.

40]π Fused and Nonfused Core-Modified Nonaphyrins: Syntheses and Structural Diversity.

The synthesis of fused and nonfused core-modified 40π nonaphyrins are reported. Spectroscopic and X-ray structural studies reveal a twisted figure-eight conformation in the freebase form that is nonaromatic. Structural changes occur, from figure-eight to open extended conformation, upon protonation, thereby adopting 4nπ Hückel antiaromatic character, which is reflected in spectroscopic and theoretical studies. Such a structural change also induces ring inversions of specific heterocyclic rings by 180°.

Molecular dynamics simulation to investigate anhydrous phosphoric acid-doped polybenzimidazole

The study conducted a molecular dynamics simulation based on a condensed-phase optimised molecular potentials for atomistic simulation studies force field model to investigate an anhydrous system of phosphoric acid-doped polybenzimidazole (poly[2,2′-(m-phenylene)-5,5′-bibenzimidazole], PBI). Intermolecular pair correlation functions and corresponding coordination numbers were calculated to research the strengths for various types of hydrogen bonding. The results display that the strengths of the hydrogen bonding interactions are in the order of o1–h pair > o2–h pair > n2a–h pair > n3a–h pair, and most protons are located around the neighbourhood of H2PO4– rather than that of PBI. The proton conductivities are 3.86 × 10−3 S cm−1 at 298 K and 8.50 × 10−3 S cm−1 at 413 K. Moreover, the value obtained from our simulation system at 413 K is within the same order of magnitude as the experimentally measured value 0.012 S cm−1 at 420% doping level. The distribution of proton displacement exhibits that the displacement of most protons is about 1.25–2.5 Å. The displacement is over 3.0 Å only for a fraction of protons. In addition, the greatest displacement can approach 4.595 Å. The trajectory analyses of protons show that the most possible mechanisms of proton transfer come from three ways: (a) between two H2PO4– anions, (b) between H2PO4– anions and benzimidazole moieties and (c) between two benzimidazole moieties. The dynamics of polymer motion was studied by the trajectory analyses of ring flips. The large amplitude flips of rings in the polymer chains were found in the system. The flips between benzene and benzimidazole are more frequent than that between benzimidazole moieties.

Saddle-Shaped Cyclic Indole Tetramers: 3D Electroactive Molecules.

We present a joint theoretical and experimental study of a series of cyclic indole tetramers aimed at understanding the fundamental electronic properties of this 3D platform and evaluating its potential in the construction of new semiconductors. To this end, we combined absorption and Raman spectroscopy, cyclic voltammetry, and spectroelectrochemistry with DFT calculations. Our results suggest that this platform can be easily and reversibly oxidized. Additionally, it has a HOMO that matches very well with the workfunction of gold, therefore charge injection from a gold electrode is expected to occur without significant barriers. Interestingly, the cyclic tetraindoles allow for good electron delocalization in spite of their saddle-shaped structures. The steric constraints introduced by N-substitution significantly inhibits ring inversion of the central cyclooctatetraene unit, whereas it only barely affects the optical and electrochemical properties (a slightly higher oxidation potential and a blueshifted absorption upon alkylation are observed).

Mixed-type reverse order laws for the group inverses in rings with involution

We investigate some equivalent conditions for the reverse order laws (ab)# = b†a# and (ab)# = b#a† in rings with involution. Similar results for (ab)# = b#a* and (ab)# = b*a# are presented too.

Per-Substituted [8]Circulene and Its Non-Planar Fragments: Synthesis, Structural Analysis, and Properties.

The syntheses, structures, and physical properties of a full series of benzannulated tetraphenylenes are reported. The palladium-catalyzed annulation of tetraiodo-substituted 2,3,6,7,10,11,14,15-octamethyltetraphenylene with insufficient di(4-anisyl)ethyne yielded a mixture of per-substituted [8]circulene and its non-planar fragments, including mono-, para-di-, ortho-di-, and triannulated products. Their structures were unambiguously verified by X-ray crystallography. Successive benzannulations significantly affect the molecular geometries, dynamic behaviors, and physical properties of the compounds. In this series of compounds, [8]circulene is the most strained one, as reflected by the significant deplanarization of the phenanthrene moieties (ca. 63° in the bay region) and the fact that it has the highest strain energy (120.6 kcal mol(-1) ). The dynamic behaviors of these compounds were examined both experimentally and theoretically. The ring flipping of per-substituted [8]circulene is confirmed to proceed through pseudorotation with a barrier of around 21 kcal mol(-1) , whereas its non-planar fragments require much more energy for the ring inversion. The photophysical and electrochemical properties of the investigated compounds depend strongly on the extent of efficient π conjugation. The successive benzannulations red-shift both the absorption and the emission bands, and reduce the first oxidation potential.