On the parametrisation of unitary matrices by the moduli of their elements

The parametrisation of ann×n unitary matrix by the moduli of its elements is not a well posed problem, i.e. there are continuous and discrete ambiguities which naturally appear. We show that the continuous ambiguity is (n–1)(n–3)-dimensional in the general case and in the symmetric caseS _ij=S_ij. We give also lower bounds on the number of discrete ambiguities, the number of solutions being at least in the first case and for the symmetric one, where [r] denotes the integral part ofr.     

Cu2+ in liquid ammonia—The impact of solvent flexibility and electron correlation in ab initio quantum mechanical charge field molecular dynamics

The impact of solvent flexibility and electron correlation on the simulation results of Cu²⁺ in liquid ammonia has been investigated via an ab initio quantum mechanical charge field molecular dynamics (QMCF MD) simulation approach. To achieve this, three different simulation systems were considered in this study, namely Cu²⁺ in rigid and flexible ammonia at Hartree-Fock (HF) level of theory, as well as resolution of identity second order Møller-Plesset (MP2) perturbation theory in the rigid body case. In all cases, a stable octahedral [Cu(NH₃)₆]²⁺ complex subject to dynamic Jahn-Teller distortions without the occurrence of ligand exchange was observed. The Cu²⁺ − NH₃ distance in the first shell agrees well with the experimental and other theoretical data. In all three cases, the structural data shows that the rigid-body ammonia model in conjunction with the HF level of theory provides accurate data for the first solvation shell, while at the same time, the computational demand and thus the achievable simulation time are much more beneficial. The vibrational analysis of the Cu²⁺ − NH₃ interaction yields similar force constants in the three investigated systems indicating that there is no distinct difference on the dynamical properties of the first solvation shell. In addition to the QMCF MD simulations, a number of natural bond orbital (NBO) analyses were carried out, confirming the strong electrostatic character of the Cu²⁺ − NH₃ interaction.     

Brownian motion near an absorbing sphere

The spherically symmetric solution of the Fokker-Planck equation with absorbing boundary is given in terms of a solution of an equivalent integral equation whose explicit form is found.     

Synthesis of enantiomerically pure inherently chiral calix[4]arenes using the meta-substitution strategy

A meta-substituted aminocalix[4]arene 4 immobilized in the cone conformation was prepared via mercuration of the starting tetra-propoxy derivative, followed by nitrosation and reduction reactions. Acylation of the amino group by chiral amino acid residues ((S)-N-trifluoroacetyl-Ala or (S)-N-trifluoroacetyl-Phe) allowed for the preparation of diastereomeric amides that were separated by preparative TLC on silica gel. Subsequent cyclization under Bischler-Napieralski reaction conditions yielded calixarenes 7b and 7c bearing an oxazole moiety in the meta position instead of the expected upper rim-bridged compounds. The reaction sequence represents a straightforward approach towards enantiomerically pure inherently chiral calix[4]arene derivatives (without HPLC separation steps). The absolute configuration of the enantiomers were confirmed by single crystal structure determination (X-ray).     

Discovery of Potent, Selective and Reversible Caspase-3 Inhibitors

Recent studies towards understanding the molecular mechanisms of apoptosis have revealed the importance of a group of cysteinyl aspartate specific proteases, the caspases, in the programmed cell death process (Hengartner, M.O. Nature 2000, 407, 770). Caspase-3, in particular, has been characterized as the dominant effector caspase involved in the proteolytic cleavage of a variety of protein substrates including cytoskeletal proteins, kinases and DNA repair enzymes during apoptosis (Nicholson…