1H, 13C, 17O NMR and quantum‐chemical study of the stereochemistry of the sulfoxide and sulfone derivatives of 3‐arylidene‐1‐thioflavan‐4‐one epoxides

The oxidation of the trans,cis‐( 2 ) and trans,trans‐epoxides ( 3 ) of differently substituted (Z)‐3‐arylidene‐1‐thioflavan‐4‐ones ( 1 ) with dimethyldioxirane (DMD) yielded the appropriate sulfoxides ( 4, 5 ) and sulfones ( 6, 7 ). The structures were elucidated by the extensive application of one‐ and two‐dimensional ¹H, ¹³C and ¹⁷O NMR spectroscopy. The conformational analysis was achieved by the application of ³J(C,H) coupling constants, NOESY responses and ab initio calculations. The preferred ground‐state conformers (twisted envelope‐A, twisted envelope‐B for 6 and twisted envelope‐A, envelope‐B for 7 ) were obtained as global minima of the theoretical ab initio MO study and also the examination of the ¹⁷O and ¹³C chemical shifts, calculated for the global minima structures of the sulfone isomers by the GIAO method. Analogous results, obtained for the sulfoxide isomers ( 4, 5 ), not only led to the preferred conformers but also gave evidence for the trans arrangement of the 2‐Ph group and the oxygen atom of the S?O group. Chemical shift differences between the isomers, sulfoxides and sulfones were corroborated by ab initio calculations of the anisotropic effects of the oxirane ring and the S?O and SO₂ groups. Copyright © 2003 John Wiley & Sons, Ltd.     

Asymptotic arc-components of unimodal inverse limit spaces

We consider the inverse limit space (I,f) of a unimodal bonding map f as fixed bonding map. If f has a periodic turning point, then (I,f) has a finite non-empty set of asymptotic arc-components. We show how asymptotic arc-components can be determined from the kneading sequence of f. This gives an alternative to the substitution tiling space approach taken by Barge and Diamond [Ergodic Theory Dynamical Systems 21 (2001) 1333].     

1D and 2D solid state NMR investigations of the framework structure of As-synthesized AlPO4-14

The framework structure of As-synthesized A1PO₄-14 has been investigated with a combination of different one-dimensional ²⁷Al and ³¹P solid state NMR techniques and ²⁷Al/³¹P double resonance methods. The results are found to be fully consistent with the assumed structural model. ²⁷Al MAS and DOR experiments at three different magnetic field strengths together with simulations show the presence of two tetrahedral sites, one pentacoordinated and one octahedral aluminum site. The ²⁷Al quadrupolar coupling constants and the ³¹P isotropic chemical shifts of the tetrahedral sites correlate well with tetrahedral shear-strain parameters and mean P-O-A1 bond angles, respectively. These correlations allow one to assign all of the NMR resonances to specific T-sites in the proposed framework structure. The assignments are then further confirmed by the application of three different two-dimensional heteronuclear correlation methods (i.e., ²⁷Al → ³¹P TEDOR, CP, and INEPT) which reveal the connectivities between AlO_x and PO₄ polyhedra. The two-dimensional INEPT experiment is applied here for the first time in the solid state.     

Electronic excitation and singlet-triplet coupling in uracil tautomers and uracil-water complexes

Electronic spectra of uracil in its diketo (lactam) form and five enol (lactim) tautomeric forms have been investigated by means of combined density functional and configuration interaction methods. We have simulated the effects of hydrogen bonding with a protic solvent by recomputing the spectrum of uracil in the presence of two, four, or six water molecules. Geometries of the electronic ground state and several low-lying excited states have been optimized. Spin-orbit coupling has been determined for correlated wavefunctions employing a non-empirical spin-orbit mean-field approach. In accord with experiment, we find the diketo tautomer to be the most stable one. The calculations confirm that the first absorption band arises from the ¹( π↦π^*) S ₀↦S ₂ excitation. The experimentally observed vibrational structure in this band originates from a breathing mode of the six ring. Complexation with water molecules is seen to cause a significant blue shift of n↦π^* excitations while leaving π↦π^* excitations nearly uninfluenced. Computed radiative lifetimes are presented for the experimentally known weak phosphorescence from the π↦π^* excited T₁ state. Among the uracil lactim tautomers, one is particularly interesting from a spectroscopic point of view. In this tautomer, the π↦π^* excitation gives rise to the S₁ state. Received 18 February 2002 / Received in final form 5 June 2002 Published online 13 September 2002     

Jordan Structures in Harmonic Functions and Fourier Algebras on Homogeneous Spaces

We study the Jordan structures and geometry of bounded matrix-valued harmonic functions on a homogeneous space and their analogue, the harmonic functionals, in the setting of Fourier algebras of homogeneous spaces.Supported by EPSRC grant GR/G91182 and NSERC grant 7679.     

Class field theory for strictly quasilocal fields with Henselian discrete valuations

The paper establishes a relationship between finite separable extensions and norm groups of strictly quasilocal fields with Henselian discrete valuations, which yields a generally nonabelian one-dimensional local class field theory.     

NOTE ON A BOUNDARY VALUE PROBLEM OF POISSON＇S EQUATION

This note shows that fur a BVP of Poisson‘s equation with Qm(u,v) as its source function, a direct evaluation of some integrals yields the same exact results as obtained by similarity analysis.     

Extremal holomorphic diffusion processes

Extremal holomorphic diffusion processes are studied. We formulate a stochastic control problem for the extremal function of a set. We then characterize the extremal holomorphic diffusion processes as the optimal diffusion processes of the problem. By making use of SDE representation for the processes, we show that they move on an integral submanifold of the coefficients vector fields of the SDE passing through the starting point.     

Handling of intrinsic divergence in the orthogonal gradient method of orbital optimization in an MC-SCF framework and geometry optimization in pathological cases: I (propynal in excited states)

It is demonstrated that a generalized version of the orthogonal gradient method of orbital optimization may sometimes encounter a specific divergence problem which may be termed intrinsic to the first order method. Instead of switching over to a more sophisticated second order method one can cure the divergence problem at the first order level itself by suitably tailoring the MC-SCF operator or the MC-SCF energy matrix. Results of complete geometry optimization of propynal in^l,3nπ* and³ππ* states (pathological cases) are reported to demonstrate the usefulness of the method at an INDO-MCSCF level of approximation. The results of structure calculations are further rationalized from generalized quantum chemical bond order indices.     

Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation

Two embeddings of a homogeneous endpoint Besov space are established via the Hausdorff capacity and the heat equation. Meanwhile, a co-capacity formula and a trace inequality are derived from the Besov space.