Investigation of the center intensity of first- and second-order Laguerre-Gaussian beams with linear and circular polarization

The vectorial Debye integral shows that tightly focused Laguerre-Gaussian (LG) beams have a residual intensity at the focal point for linear polarization, for a topological charge of m=1 and 2. We measured the shapes of linearly and circularly polarized LG beams and found that a central intensity appeared at m=1 and 2 for linear and right-handed circular polarization, however, it is completely canceled for left-handed circular polarization. In general, when the orbital angular momentum of the LG beam is parallel to the spin angular momentum of the photons, zero intensity is always achieved at the focus.     

High-Energy Collision-Induced Dissociation by MALDI TOF/TOF Causes Charge-Remote Fragmentation of Steroid Sulfates

A method for structural elucidation of biomolecules dating to the 1980s utilized high-energy collisions (~10 keV, laboratory frame) that induced charge-remote fragmentations (CRF), a class of fragmentations particularly informative for lipids, steroids, surfactants, and peptides. Unfortunately, the capability for high-energy activation has largely disappeared with the demise of magnetic sector instruments. With the latest designs of tandem time-of-flight mass spectrometers (TOF/TOF), however, this capability is now being restored to coincide with the renewed interest in metabolites and lipids, including steroid-sulfates and other steroid metabolites. For these metabolites, structure determinations are required at concentration levels below that appropriate for NMR. To meet this need, we explored CRF with TOF/TOF mass spectrometry for two groups of steroid sulfates, 3-sulfates and 21-sulfates. We demonstrated that the current generation of MALDI TOF/TOF instruments can generate charge-remote fragmentations for these materials. The resulting collision-induced dissociation (CID) spectra are useful for positional isomer differentiation and very often allow the complete structure determination of the steroid. We also propose a new nomenclature that directly indicates the cleavage sites on the steroid ring with carbon numbers.

Singularities of Blaschke normal maps of convex surfaces

We prove that the difference between the numbers of positive swallowtails and negative swallowtails of the Blaschke normal map for a given convex surface in affine space is equal to the Euler number of the subset where the affine shape operator has negative determinant.     

The first halogen-substituted cyclotrigermenes: a unique halogen walk over the three-membered ring skeleton and facial stereoselectivity in the Diels-Alder reaction

Dark red crystals of the halogen-substituted cyclotrigermenes [(tBu3Si)3Ge3X; X = Cl, Br, I] were obtained in good yields by the reaction of [(tBu3Si)3Ge3]+.TTFPB- (TTFPB- = tetrakis(2,3,5,6-tetrafluorophenyl)borate) with potassium halides (KCl, KBr, or KI) in diethyl ether. The crystal structures of the halogen-substituted cyclotrigermenes reveal a cis-bent Ge=Ge double bond, caused by the introduction of the electronegative halogen atom on the sp3 germanium atom of cyclotrigermene. In solution, an intramolecular halogen migration over the three-membered ring skeleton was observed. Facial stereoselectivity in the Diels-Alder reaction of new cyclotrigermenes with 2,3-dimethyl-1,3-butadiene is also reported.     

Structure of dichlorine monoxide as studied by microwave spectroscopy. Determination of equilibrium structure by a modified mass dependence method

The microwave spectra of four isotopic species of dichlorine monoxide (OCl₂) have been observed, and the rotational constants have been obtained. The r_m structure for each isotopic species has been determined by Watson's method. The equilibrium structure has been estimated by taking proper averages of r_m structures to be $\text{r}{}_{\mathrm{e}}\text{(OCl) = 1.69587(7)}\text{A}\text{?}$ and ∠_eClOCl = 110.886(6)°. The general applicability and the merit of the present method for estimating the equilibrium structure are pointed out.