Relativistic spin-orbit coupling effects on secondary isotope shifts of (13)C nuclear shielding in CX(2) (X = O, S, Se, Te)

Rovibrational corrections, temperature dependence, and secondary isotope shifts of the (13)C nuclear shielding in CX(2) (X = O, S, Se, Te) are calculated taking into account the relativistic spin-orbit (SO) interaction. The SO effect is considered for the first time for the secondary isotope shifts. The nuclear shielding hypersurface in terms of nuclear displacements is calculated by using a density-functional theory method. Ab initio multiconfiguration self-consistent field calculations are done at the equilibrium geometry for comparison. (13)C NMR measurements are carried out for CS(2). The calculated results are compared with both present and earlier experimental data on CO(2), CS(2), and CSe(2). The heavy-atom SO effects on the rovibrational corrections of (13)C shielding are shown to be significant. For CSe(2) and CTe(2), reliable prediction of secondary isotope effects and their temperature dependence requires the inclusion of the SO corrections. In particular, earlier discrepancies of theory and experiment for CSe(2) are fully resolved by taking the SO interactions into account.     

Conformations and energetics of sulfur and selenium diimides

The geometries and energetics of different conformations of sulfur and selenium diimides E(NR)(2) (E = S, Se; R = H, Me, (t)Bu, C(6)H(3)Me(2)-2,6, SiMe(3)) have been studied by using various ab initio and DFT molecular orbital techniques. The syn,syn conformation is found to be most stable for parent E(NH)(2), but in general, the preferred molecular conformation for substituted chalcogen diimides is syn,anti. In the case of E(NH)(2) the present calculations further confirm that syn,syn and syn,anti conformations lie energetically close to each other. From the three different theoretical methods used, B3PW91/6-31G proved to be the most suitable method for predicting the geometries of chalcogen diimides. The optimized geometrical parameters are in a good agreement with all available experimental data. While qualitative energy ordering of the different conformations is independent of the level of theory, the quantitative energy differences are dependent on the method used. The performance and reliability of higher level ab initio calculations and DFT methods using large basis sets were tested and compared with experimental information where available. All of the higher level ab inito methods give very similar results, but the use of large basis sets with the B3PW91 method does not increase the reliability of the results. The combination of CCSD(T)/cc-pVDZ with the B3PW91/6-31G-optimized geometries is found to be the method of choice to study energetic properties of chalcogen diimides.     

Rapid LC-MS detection of cyanobacterial hepatotoxins microcystins and nodularins—Comparison of columns

Eight reversed-phase columns intended for rapid HPLC were assessed for the separation of thirteen microcystins and nodularins, cyclic peptidic hepatotoxins. The instrumentation consisted of an Agilent Technologies 1200 Rapid Resolution high performance liquid chromatography system coupled to a mass spectrometer, Bruker Daltonics Ultra Performance High Capacity Ion Trap MS (HCT Ultra) with electrospray ionisation (RRLC-ESI-IT-MS). The columns tested were 2-2.1 mm × 50 mm in diameter and length, and contained small particles (1.8-2.7 μm), or monolithic silica supports for fast performance. The shortest total run time achieved was 3 min 15 s including equilibration and injection. Critical microcystin pairs were still resolved. Several columns showed excellent performance.     

On finite rank perturbations of definitizable operators

It was shown by P. Jonas and H. Langer that a selfadjoint definitizable operator A in a Krein space remains definitizable after a finite rank perturbation in resolvent sense if the perturbed operator B is selfadjoint and the resolvent set ρ(B) is nonempty. It is the aim of this note to prove a more general variant of this perturbation result where the assumption on ρ(B) is dropped. As an application a class of singular ordinary differential operators with indefinite weight functions is studied.     

Electronic spectroscopy of I(2)-Xe complexes in solid Krypton

In the present work, we have studied ion-pair states of matrix-isolated I(2) with vacuum-UV absorption and UV-vis-NIR emission, where the matrix environment is systematically changed by mixing Kr with Xe, from pure Kr to a more polarizable Xe host. Particular emphasis is put on low doping levels of Xe that yield a binary complex I(2)-Xe, as verified by coherent anti-Stokes Raman scattering (CARS) measurements. Associated with interaction of I(2) with Xe we can observe strong new absorption in vacuum-UV, redshifted 2400 cm(-1) from the X → D transition of I(2). Observed redshift can be explained by symmetry breaking of ion-pair states within the I(2)-Xe complex. Systematic Xe doping of Kr matrices shows that at low doping levels, positions of I(2) ion-pair emissions are not significantly affected by complexation with Xe, but simultaneous increase of emissions from doubly spin-excited states indicates non-radiative relaxation to valence states. At intermediate doping levels ion-pair emissions shift systematically to red due to change in the average polarizability of the environment. We have conducted spectrally resolved ultrafast pump-probe ion-pair emission studies with pure and Xe doped Kr matrices, in order to reveal the influence of Xe to I(2) dynamics in solid Kr. Strikingly, relaxed emission from the ion-pair states shows no indication of complex presence. It further indicates that the complex escapes detection due to a non-radiative relaxation.     

Selfadjoint Schrödinger operators on the half-space with compactly supported Robin boundary conditions

Schrödinger differential operators on a half-space with compactly supported Robin boundary conditions are studied. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary triples and quasi boundary triples for elliptic operators

The abstract concepts of boundary triples and their recent generalizations are useful tools to parametrize the self-adjoint and maximal dissipative/maximal accumulative extensions of formally symmetric elliptic differential expressions with the help of explicit boundary conditions. In the present note the parametrizations induced by the “natural” quasi boundary triple with the Dirichlet and Neumann trace as boundary maps are compared with the parametrizations induced by a “classical” ordinary boundary triple, where a regularized Neumann trace is used for one of the boundary maps. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation

Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz.     

A note on the Pauli problem in light of approximate joint measurements

We show that there exist informationally incomplete phase space observables such that the Cartesian margins are informationally equivalent with position and momentum. This shows that it is possible to reconstruct the position and momentum distributions of a quantum system from the statistics of a single observable, and thus a single measurement, even though the state of the system is not uniquely determined by the statistics.