The determination of the past and the future of a physical system in quantum mechanics

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with using unsharp measurements.This work was partly supported by the Bundesministerium für Forschung und Technologie, Bonn, the Research Institute for Theoretical Physics, Helsinki, and the University of Turku Foundation, Turku.     

Coherent States and Number-Phase Uncertainty Relations

The number-phase uncertainty relations arerevisited in view of the recent discovery of a propercovariant phase observable. The high-amplitude limits ofthe coherent-state expectations of the moment operators of the phase observable are determined and thebehavior of the number-phase uncertainty product in thatlimit is investigated.     

Hardy's inequality and the boundary size

We establish a self-improving property of the Hardy inequality and an estimate on the size of the boundary of a domain supporting a Hardy inequality.

     

Quantum-chemical gas-phase calculations on the protonation forms oftrans- andcis-urocanic acid

The neutral, cationic, and anionic structures of both prototropic tautomers oftrans- andcis-urocanic acid [(E)- and (Z)-3-(1H-imidazol-4(5)-yl)propenoic acid, respectively] were studied by using semiempirical andab initio gas-phase calculations. Potential energy surfaces of the structures were calculated by using the semiempirical AM1 method, and the geometries corresponding to global minima on these surfaces were optimized up to the MP2/6-31G^* level of theory. The calculated protonation forms of each urocanic acid isomer have a planar molecular structure due to a delocalized -electron system, and all of them prefer thes-trans conformation with respect to the bond between the imidazole and the propenoic acid moieties. Thecis-urocanic acid structures are stabilized by an intramolecular hydrogen bond. The chargedcis-urocanic acid isomers have a lower molecular energy than the correspondingtrans-isomers, whereas the neutral molecules have, after inclusion of thermodynamic corrections, approximately the same energy. The cationic urocanic acid structures have about 2500 kJ mol^–1 lower energy than the anionic ones and about 1000 kJ mol^–1 lower energy than the neutral ones. The nonzwitterionic forms of the neutral urocanic acid isomers have about 200 kJ mol^–1 lower energy than the zwitterionic ones. These energy differences are explained by the proton affinities of the imidazole and the propenoic acid moieties of the urocanic acid structures.     

Molecular recognition in a uradinyl-functionalized stable radical

Stable radical 2-(6-uradinyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-1-oxyl (1) binds to hydrogen-bonding complement 2,6-di(propylamido)pyridine (DAP) in chloroform with Ka=220 M(-1) at 33 degrees C; ESI-MS shows not only 1:DAP complementary dyad formation, but also 1:(DAP)2 formation at higher concentrations of DAP.     

Molecular dynamics simulations of conserved Hox protein hexapeptides. I. Folding behavior in water solution

Molecular dynamics simulations of hexapeptides TFDWMK and LFPWMR; the highly conserved regions of Hox proteins Hox B1 and Hox B8, respectively, are carried out starting from extended structures to investigate their conformational space in water solution. In addition, we have studied TADWMK and TADAMK, where the aromatic residues Phenylalanine and Tryptophan were successively substituted for Alanine to investigate effects from the presence/absence of aromatic amino acids and interactions between them to folding behavior. The backbone of the hexapeptides in all simulations folds to a similar conformation found in experimental studies in solution. Intramolecular, hydrophobically driven interactions between the aromatic residues and internal hydrogen bonds are found to stabilize the conformations.     

Synthesis and catalytic activity of new chiral unsymmetrical Mn(III)-Schiff-base complexes containing salicylaldehyde and 1-(2-hydroxyphenyl)ketone units

Two new chiral unsymmetrical (non-C₂-symmetric) Schiff-base ligands containing salicylaldehyde and 1-(2-hydroxyphenyl)ketone units were synthesized from (R,R)-1,2-diphenylethylenediamine as the chiral diamine using a stepwise approach. The Mn(III) complexes of the ligands were subsequently used as catalysts in asymmetric epoxidation of unfunctionalized alkenes and the results were compared with those obtained using typical C₂-symmetric Mn(III)–salen complexes. Possible reasons for the differences in reactivity and selectivity between the two types of catalysts are briefly discussed.     

Manganese(II) and copper(II) hexafluoroacetylacetonate 1:1 complexes with 5-(4-[N-tert-butyl-N-aminoxyl]phenyl)pyrimidine: regiochemical parity analysis for exchange behavior of complexes between radicals and paramagnetic cations

Mn(hfac)(2) and Cu(hfac)(2) form coordination complexes with 5-(4-[N-tert-butyl-N-aminoxyl]phenyl)pyrimidine, PyrimPh-NIT. (Mn[PyrimPh-NIT](hfac)(2))(2) and (Cu[PyrimPh-NIT](hfac)(2))(2), 1 and 2, respectively, are cyclic M(2)L(2) dimers that exhibit strong exchange coupling between the coordinated paramagnetic dication (M) and nitroxide (NIT) unit. The M-NIT exchange is strongly antiferromagnetic (AFM) in 1 and strongly ferromagnetic (FM) in 2. Magnetic susceptibility measurements for 1 were fitted to an AFM spin pairing model with J/k = -0.25 K between Mn-NIT spin sites units. Complex 2 also exhibits AFM spin pairing between S = 1 Cu-NIT spin units that is somewhat field dependent at low temperature. The fit of corrected paramagnetic susceptibility chi(T) to an AFM spin pairing model at 200 Oe yields J/k = (-)3.8 K, quite similar to earlier measurements at 1000 Oe yielding J/k = (-)5.0 K. At 1.40 K, the magnetization of 2 does not approach saturation until somewhat above 170 kOe, giving an S-shaped curve; at 0.55 K, the magnetization curve shows steps characteristic of field-induced crossover between the S = 0 ground state and excited spin states. From the steps in the 0.55 K data, we estimate J/k = (-)3.8-4.0 K for 2, in good agreement with the analysis of chi(T).