Variational calculations with unbounded operators

In a constrained variational calculation, the minimum of the expectation value of an operator H, subject to the constraint that the expectation value of an operator A have a definite value, is sought. Fonte and Schiffrer have recently noted that the Lagrange multiplier method of of determining the solution to this problem fails when the operator A is unbounded. We show that in this case, the expectation value of H can be made arbitrarily close to the unconstrained minimum, for any constrained value of 〈A〉. This result casts doubt on the validity of the results of calculations, in which an unbounded operator (such as the quadrupole moment of a nucleus) is constrained, even if these calculations are carried out using a finite-dimensional basis in which the restricted operator is bounded. Various alternatives to these calculations are discussed.     

Fluoro-containing complexes of chromium (III). II. Crystal structure oftrans-difluorodiaquo-ethylenediaminechromium(III) chloride

The results of an X-ray structure determination of one of the three possible chloride salts of [Cr(en) F₂(OH₂)₂]⁺ show the two fluoro ligands to betrans to each other. The purple crystals are monoclinic in the space groupC2/c-C _2h ⁶ , witha=11.409(3),b=9.319(2),c=10.260(3) Å,β=128.73(2)° andD _c =1.73 g cm^?3 forZ=4. Least-squares refinement based on 1341 independent observed reflections resulted in a finalR of 0.026. The molecule lies on a crystallographic two-fold axis, and the Cr-F, Cr-N, and Cr-O bond lengths are 1.885(1), 2.044(2), and 1.997(2) Å respectively. It is suggested that the ill-defined shoulder in the visible electronic spectrum of this complex is indicative of atrans dihalo geometry.     

Bestimmung von Halogen in organischem Material

Analytical and Bioanalytical Chemistry -     

Diffusion and trapping in a suspension of spheres with simultaneous reaction in the continuous phase

Much progress has been made in modeling the reaction of Brownian particles with spherical traps. Previously, work has focused on the effective reaction rate of systems of particles that diffuse freely until they are trapped by spheres in the dispersion. A particularly effective and efficient method to describe the reacting system is based on first-passage time distributions, from which an effective reaction rate coefficient of the suspension can be determined. The analysis presented here addresses reaction and diffusion in systems in which particles can undergo reaction in the continuous phase as well as reaction at the sphere surface. The first-passage method is extended to allow reaction or decay of the diffusing species in the continuous phase. The diffusion path is divided into a series of first-passage regions and is considered the probability of the particle being consumed in each of these regions. This allows the determination of the total reaction rate of the suspension (continuous phase reaction plus trapping) and the relative consumption rate in each phase. The extended method is applied to a model system of concentric spheres with a known continuum solution. It is shown to be accurate for consumption of reactant in the continuous phase from approximately 0 to approximately 100%. The method then is applied to a suspension of spheres.     

Interligand transmetallic charge-transfer transitions in mixed-ligand chelates

In chelates of divalent zinc which have two different aromatic ligands, a new absorption band is observed in the visible region. This new band is interpreted as arising from a π→π* interligand transmetallic charge-transfer (ITCT) transition. The nature of this type of charge-transfer transition in a chelate molecule, using a molecular orbital model, is examined. Experimental results for the chelates (3,4-toluenedithiolato)(1,10-phenanthroline)zinc(II), (3,4-toluenedithiolato)(2,2′-dipyridyl)zinc(II),and (3,4-toluenedithiolato)(2,2′-biquinoline)zinc(II) are presented.     

Laser desorption in transmission geometry inside a Fourier-transform ion cyclotron resonance mass spectrometer

We report here the first application of laser desorption (LD) in transmission geometry (backside irradiation of the sample through a transparent support) inside a Fourier-transform ion cyclotron resonance mass spectrometer (FT-ICR). A probe-mounted fiber optic assembly was used to simplify the implementation of this LD technique. This setup requires little or no instrument modifications, has minimum maintenance requirements, and is relatively inexpensive to build. The performance of the probe was tested by determining the molecular weight of a commercial polystyrene standard from its matrix-assisted laser desorption/ionization (MALDI) spectrum. The measured average molecular weight is comparable to that obtained for the same sample by MALDI in the conventional top-illumination arrangement (reflection geometry) and by the manufacturer of the sample by gel permeation chromatography. The average velocities measured for ions evaporated by transmission mode LD of several neat samples are about half the velocity of those obtained by using the reflection geometry. Therefore, transmission mode irradiation of the sample holds promise to desorb ions that are easier to trap in an ICR cell. An oscillating capillary nebulizer was adapted for the deposition of analytes to improve sampling reproducibility.     

Establishing Radiolanthanum Chemistry for Targeted Nuclear Medicine Applications

We report the first targeted nuclear medicine application of the lanthanum radionuclides ^132/135La. These isotopes represent a matched pair for diagnosis via the positron emissions of ¹³²La and therapy mediated by the Auger electron emissions of ¹³⁵La. We identify two effective chelators, known as DO3Apic and macropa, for these radionuclides. The 18-membered macrocycle, macropa, bound ^132/135La with better molar activity than DO3Apic under similar conditions. These chelators were conjugated to the prostate-specific membrane antigen (PSMA)-targeting agent DUPA to assess the use of radiolanthanum for in vivo imaging. The ^132/135La-labeled targeted constructs showed high uptake in tumor xenografts expressing PSMA. This study validates the use of these radioactive lanthanum isotopes for imaging applications and motivates future work to assess the therapeutic effects of the Auger electron emissions of ¹³⁵La.