Crystal structure of 4,13-dimethyl-3,7,10,14,19,22,25-heptaoxapentacyclo- [25.0.0(1,6).0(6,26).0(11,16).0(11,18)]heptacosa-4,11-diene-2,15-dione.
of conjugated enones with olefins are useful for making a cyclobutane ring system. We have previously reported on the intermolecular photocycloaddition reactions of 2-pyrones with olefins,1–3 and the intramolecular photodimerization reactions of 4,4′-polymethylenedioxy-di-2-pyrones4 to clarify the reactivity involving the study of peri-, site, and stereoselectivities. As a part of an application of the cycloaddition reactions, we have planned to synthesize a macrocyclic compound possessing two cyclobutane rings using double photocycloaddition reactions of 6,6′-dimethyl-4,4′-dimethylenediox-di-2-pyrone (1) with di(ethylene glycol) divinyl ether (2). A solution of (1) (1.39 g), (2) (1.58 g), and xanthone (0.98 g) as a sensitizer in acetonitrile (500 ml) was irradiated with a 400W high-pressure mercury lamp (>350 nm ) for 20 h under a nitrogen atmosphere. After removing the solvent, an oily residue was chromatographed by silica gel (eluent: ethyl acetate–hexane) to give a solid product (3) in 20% yield, which was recrystallized from ethyl acetate. Since the usual analytical and spectroscopic techniques do not permit the identification of two types of isomers, (3) and (4) (in Fig. 1), an X-ray diffraction study of the product was carried out to determine the structure. Data collections were performed at 93 K with graphitemonochromated Mo Kα radiation on a Rigaku RAXIS-RAPID Imaging Plate diffractometer (λ = 0.71069 Å). Lorentz and polarization corrections were applied to the intensity data. The structure was solved by direct methods using SIR 92.5 The structure was refined by a full-matrix least-squares method. The non-hydrogen atoms were refined anisotropically. Hydrogen atoms were refined isotropically. All calculations were performed using the teXsan6 crystallographic software package. Table 1 gives the crystal data and experimental conditions. Figure 2 is an ORTEP diagram of the molecule, which shows the atomic-labeling scheme. The final positional parameters are given in Table 2, and selected bond lengths and angles are listed in Table 3. 1017 ANALYTICAL SCIENCES AUGUST 2001, VOL. 17 2001 © The Japan Society for Analytical Chemistry
Intramolecular photocycloadditions of 6,6′‐dimethyl‐4,4′‐polymethylenedioxy‐di‐2‐pyrones
Photosensitized reactions of 4,4′-polymethylene-di-2-pyrones 2b-e afforded [2+2]-cycloadducts 3-5, site-selectively. The selectivity depended upon the methylene chain length. Namely, the three carbon chain gave a syn head-to-head adduct 3b at the 3,4-position of the 2-pyrone ring, the four to six carbon chains gave syn head-to-head adducts 4c-e at the 5,6-position and/or anti head-to-head adducts 5d,e at the 5,6-position, respectively. The intramolecular cycloaddition mechanism was also explained from results calculated by means of PM3-CI method.
Inhomogeneous Boundary Value Problems for Compressible Navier-Stokes Equations: Well-Posedness and Sensitivity Analysis
In this paper compressible, stationary Navier–Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions that take form (1.12). The approximate solutions are determined from Stokes problem (1.11). The small perturbations are given by solutions to (1.13). The uniqueness of solutions for problem (1.13) is proved, and, in addition, the differentiability of solutions with respect to the coefficients of differential operators is shown. The results on the well-posedness of nonlinear problems are interesting on their own and are used to obtain the shape differentiability of the drag functional for incompressible Navier–Stokes equations. The shape gradient of the drag functional is derived in the classical and useful for computations form; an appropriate adjoint state is introduced to ...