Non-adiabatic transitions near avoided crossings: theory and numerics

We present a review of rigorous mathematical results about non-adiabatic transitions in molecular systems that are associated with avoided crossings of electron energy level surfaces. We then present a novel numerical technique for studying these transitions that is based on expansions in semiclassical wavepackets.     

Template synthesis and crystal structure of an asymmetric square-planar complex: Pyridine-2,6-dicarbaldehyde-bis(<Emphasis Type="Italic">S</Emphasis>-methylisothiosemicarbazonato)nickel(II) iodide

The asymmetric complex [Ni(HL)]I (where H₂L is pyridine-2,6-dicarbaldehyde-bis(S-methylisothiosemicarbazone)) is synthesized by the [2 + 1] template condensation of S-methylisothiosemicarbazide hydroiodide with pyridine-2,6-dicarbaldehyde in the presence of nickel(II) acetate. The crystal structure of the [Ni(HL)]I complex (where HL is C₁₁H₁₄N₇S₂) is determined using X-ray diffraction. The square-planar coordination of the nickel(II) central atom is provided by four N donor atoms of the chelating ligand, namely, one N atom of the pyridine residue and three N atoms of the isothiosemicarbazide fragments. The deprotonated isothiosemicarbazide fragment in the imino form and the neutral ammonium isothiosemicarbazide fragment differ in the degree of deprotonation, the mode of coordination to the central atom (N¹N³ and N², respectively), and the conformation (E and Z, respectively). The structural features of the ammonium isothiosemicarbazide fragment are associated with the formation of zwitterions. It is established that the crystal structure of the compound under investigation contains centrosymmetric dimers. These dimers participate in the formation of the second coordination sphere N₄S of the central atom.     

Alkane hydroperoxidation with peroxides catalysed by copper complexes

Various copper(I) and copper(II) derivatives, both "simple" ones (copper acetate, perchlorate and a complex with CH3CN) and compounds containing N,O-chelating ligands, catalyse very efficient (turnover numbers attain 2200) oxidation of saturated hydrocarbons with peroxyacetic acid (PAA) or tert-butyl hydroperoxide (TBHP) in acetonitrile solution at 60 degrees C. Alkyl hydroperoxide, alcohol and ketone are formed, the main product being an alkyl hydroperoxide in the oxidation with PAA and an alcohol for the case of TBHP. It has been proposed that the oxidation with PAA is induced via the attack of species r* [HO* or CH3C(=O)O*] on the alkane, RH. A competitive attack of r* on the solvent, CH3CN, also occurs. It has been assumed that in the case of the reaction catalysed by complex Cu(CH3CN)4BF4, copper is present mainly in the form of Cu+ cation, and the rate-limiting step of the oxidation process is the formation of r* via reaction (1): CH3C(=O)OOH + Cu+ --> CH3C(=O)O* + HO- + Cu2+ or/and CH3C(=O)OOH + Cu+ --> CH3C(=O)O- + HO* + Cu2+ with initial rate W1 = k1[PAA][Cu(CH3CN)4BF4] and k1 = 1.7 mol(-1) dm3 s(-1) at 60 degrees C. The activity of the Cu-catalyst is dramatically changed on a small modification of N,O-chelating ligands in the catalyst.     

Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation

We propose a new algorithm for solving the semiclassical time-dependent Schrödinger equation. The algorithm is based on semiclassical wavepackets. The focus of the analysis is only on the time discretization: convergence is proved to be quadratic in the time step and linear in the semiclassical parameter $\varepsilon $ .     

Mixed finite elements on sparse grids

Summary. This paper generalizes the idea of approximation on sparse grids to discrete differential forms that include )- and -conforming mixed finite element spaces as special cases. We elaborate on the construction of the spaces, introduce suitable nodal interpolation operators on sparse grids and establish their approximation properties. We discuss how nodal interpolation operators can be approximated. The stability of -conforming finite elements on sparse grids, when used to approximate second order elliptic problems in mixed formulation, is investigated both theoretically and in numerical experiments. Received November 2, 2000 / Revised version received October 23, 2001 / Published online January 30, 2002 This work was supported by DFG. This paper is dedicated to Ch. Zenger on the occasion of his 60th birthday.