Excited-state properties of Rh(2)(O(2)CCH(3))(4)(L)(2) (L = CH(3)OH, THF, PPh(3), py)

The photophysical properties of Rh(2)(O(2)CCH(3))(4)(L)(2) (L = CH(3)OH, THF = tetrahydrofuran, PPh(3) = triphenylphosphine, py = pyridine) were explored upon excitation with visible light. Time-resolved absorption shows that all the complexes possess a long-lived transient (3.5-5.0 micros) assigned as an electronic excited state of the molecules, and they exhibit an optical transition at approximately 760 nm whose position is independent of axial ligand. No emission from the Rh(2)(O(2)CCH(3))(4)(L)(2) (L = CH(3)OH, THF, PPh(3), py) systems was detected, but energy transfer from Rh(2)(O(2)CCH(3))(4)(PPh(3))(2) to the (3)pipi excited state of perylene is observed. Electron transfer from Rh(2)(O(2)CCH(3))(4)(PPh(3))(2) to 4,4'-dimethyl viologen (MV(2+)) and chloro-p-benzoquinone (Cl-BQ) takes place with quenching rate constants (k(q)) of 8.0 x 10(6) and 1.2 x 10(6) M(-1) s(-1) in methanol, respectively. A k(q) value of 2 x 10(8) M(-1) s(-1) was measured for the quenching of the excited state of Rh(2)(O(2)CCH(3))(4)(PPh(3))(2) by O(2) in methanol. The observations are consistent with the production of an excited state with excited-state energy, E(00), between 1.34 and 1.77 eV.     

Structure of a surfactant-templated silicate framework in the absence of 3d crystallinity

The structure of a novel molecularly ordered two-dimensional (2D) silicate framework in a surfactant-templated mesophase has been established by using a combination of solid-state nuclear magnetic resonance (NMR) spectroscopy, X-ray diffraction, and quantum chemical and empirical force-field modeling. These materials are unusual in their combination of headgroup-directed 2D crystalline framework ordering, zeolite-like ring structures within the layers, and long-range mesoscopic organization without three-dimensional (3D) atomic periodicity. The absence of registry between the silicate sheets, resulting from the liquidlike disorder of the alkyl surfactant chains, has presented significant challenges to the determination of framework structures in these and similar materials lacking 3D crystalline order. Double-quantum (29)Si NMR correlation experiments establish the interactions and connectivities between distinct intra-sheet silicon sites from which the structure of the molecularly ordered inorganic framework is determined.     

Off-Diagonal hypervirial relations

A generalization of a theorem on off-diagonal hypervirial relations is obtained and is used to demonstrate when to expect exact solutions of eigenvalue problems using the hypervirial method. Links are established between the hypervirial method and other approximation methods. The harmonic oscillator and hydrogen atom problems are given as examples.     

A limiting absorption principle for Schrödinger operators with Von Neumann-Wigner type potentials

In this paper we prove the main step in establishing a limiting absorption principle for von Neumann-Wigner type Schrödinger Hamiltonians of the form –+csinb|x|/|x|+V(x), whereV(x) is a short range potential. The first fundamental step is to obtain a limiting absorption principal for the free operator –+csinb.|x|/|x|. The free operator is unitarily equivalent to a direct sum of ordinary differential operators. We obtain uniform estimates for the resolvents of these ordinary differential operators. by obtaining uniform estimates for the Weyl-Green kernels of these resolvents. In turn, these latter estimates require uniform estimates on the Wronskians of certain generalized eigen-solutions of these differential operators.This paper is dedicated to the memory of the late Professor Charles C. Conley.