Intrinsic invariants of cross caps

It is classically known that generic smooth maps of \(\varvec{R}^2\) into \(\varvec{R}^3\) admit only isolated cross cap singularities. This suggests that the class of cross caps might be an important object in differential geometry. We show that the standard cross cap \(f_{\mathrm{std }}(u,v)=(u,uv,v^2)\) has non-trivial isometric deformations with infinite-dimensional freedom. Since there are several geometric invariants for cross caps, the existence of isometric deformations suggests that one can ask which invariants of cross caps are intrinsic. In this paper, we show that there are three fundamental intrinsic invariants for cross caps. The existence of extrinsic invariants is also shown.     

(R)-(+)-[VCD(+)945]-4-Ethyl-4-methyloctane, the simplest chiral saturated hydrocarbon with a quaternary stereogenic center

Enantiopure (R)-(+)-[VCD(+)945]-4-ethyl-4-methyloctane, the simplest chiral saturated hydrocarbon with a quaternary stereogenic center, was synthesized by the use of MαNP acid method, and its absolute configuration was first unambiguously determined by the ¹H NMR anisotropy, X-ray crystallography, and VCD methods.     

Electrochemical electron-transfer process of polymers containing N-methylphenothiazine

For a fundamental study of the electrochemical behavior of electroactive polymers a series of poly(3-vinyl-10-methylphenothiazine) (polyMPT), copolymers of 3-vinyl-10-methylphenothiazine and methyl methacrylate (MMA) (copolyMPT), and 3-ethyl-10-methylphenothiazine (EMPT) (a related monomer model) were prepared. The methylphenothiazine groups in these compounds showed reversible, one-electron oxidation waves in the triangular-were voltammograms. From a detailed comparison of the voltammograms between these polymers and EMPT it was revealed that the electroactive groups in poly MPT were not the “noninteracting” centers in the strict sense, whereas those in copolyMPT, in which the centers are spaced with the MMA segments, were typically noninteracting in nature; that is, in polyMPT the oxidation takes place at the potential 40 m V lower than that of EMPT and copolyMPT exhibited a wave identical to that of EMPT in shape and potential. The exhaustive electron transfer occurred from polyMPT to the electrode. On the other hand, a significant number of centers remained unoxidized in copolyMPT. The self-exchange electron transfer within the polymer coil facilitates the exhaustive oxidation. For this event the proximity of the centers was an essential factor.     

Stereochemical study of chiral tautomeric flavorous furanones by vibrational circular dichroism

2-Substituted-3(2H)-furanone derivatives are industrially significant aroma compounds possessing a unique keto-enol tautomeric feature causing their racemization. Absolute configurations of two flavorous furanones, which have remained unclear for the past 40 years since their discovery, were clarified by the vibrational circular dichroism technique as well as chemical relay reactions. Odor evaluation of each enantiomer revealed relationships between their configurations and their odor activities.     

Effects of central metal ions on vibrational circular dichroism spectra of tris-(beta-diketonato)metal(III) complexes

Vibrational circular dichroism (VCD) spectra of a series of [M(III)(acac)3] (acac = acetylacetonato; M = Cr, Co, Ru, Rh, Ir, and Al) and [M(III)(acac)2(dbm)] (dbm = dibenzoylmethanato; M = Cr, Co, and Ru) have been investigated experimentally and/or theoretically in order to see the effect of the central metal ion on the vibrational dynamics of ligands. The optical antipodes give the mirror-imaged spectra in the region of 1700-1000 cm(-1). The remarkable effect of the central metal ion is observed experimentally on the VCD peaks due to C-O stretches (1500-1300 cm(-1)) for both [M(III)(acac)3] and [M(III)(acac)2(dbm)]. In the case of Delta-[M(III)(acac)3], for example, the order of frequency of two C-O stretches (E and A2 symmetries) is dependent on the kind of a central metal ion as follows: E (-) > A2 (+) for M = Co, Rh, and Ir, while A2 (+) > E (-) for M = Cr and Ru. In the case of Delta-[M(III)(acac)2(dbm)], the order of frequency of three C-O stretches (A, B, and B symmetries) is as follows: A (-) > B (+) > B (+) for Co(III), B (+) > A (-) > B (-) for Cr(III), and A (-) > B (+) > B (-) for Ru(III). These results imply that the energy levels of C-O stretches are delicately affected by the kind of central metal ion. Since such detailed information is not obtained from the IR spectra alone, the VCD spectrum can probe the effect of the central metal ion on interligand cooperative vibration modes.     

Stereochemical studies of sialic acid derivatives by vibrational circular dichroism

Systematic VCD studies of N-acetylneuraminic acid (Neu5Ac), a recognition-related unique carbohydrate, were performed for the first time. Two pairs of anomeric isomers regarding a quaternary C2 asymmetric carbon of Neu5Ac derivatives were synthesized. VCD spectral patterns around the ester carbonyl region, as well as other Mid-IR regions, would be practical markers to distinguish the C2 stereochemistry.     

Salvileucalin C, a novel rearranged neoclerodane diterpene from Salvia leucantha

Salvileucalin C (1), a novel neoclerodane diterpene having an unprecedented carbon framework and a structurally closely related salvileucalin D (2) were isolated and their absolute structures were elucidated by the vibrational circular dichroism (VCD) spectra.