On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Über die quantitative Bestimmung von Quecksilber(II)ionen durch katalytische Zersetzung von Ferrocyanid.

Zusammenfassung Die unter katalytischer Wirkung von Quecksilber(II)ionen ablaufende Umsetzung von Ferrocyanid zu Berlinerblau wurde als quantitative kolorimetrische Methode zur Bestimmung von Quecksilber(II) in Konzentrationen von 5 bis 50g/ml ausgearbeitet.

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Summary The partial oxidation of ferrocyanide to Prussian blue accomplished under the catalytic action of mercury(II) ions has been developed into a quantitative method for the determination of mercury(II) in concentrations of 5 to 50g/ml.

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Résumé L'oxydation partielle du ferrocyanure en bleu de Berlin sous l'influence catalytique des ions Hg(II) a été mise au point comme méthode de dosage des ions Hg(II) à des concentrations de 5 à 50g/ml.

     

Photoredox‐Catalyzed Alkenylation of Benzylsulfonium Salts

Visible light‐mediated radical alkenylation of benzylsulfonium salts was achieved by means of fac‐Ir(ppy)₃ as a photocatalyst, giving allylbenzenes as products. A variety of functional groups, such as halogen, ester, and cyano, were well tolerated in this transformation. Starting benzylsulfonium salts could be readily prepared from benzyl alcohols by an acid‐mediated substitution, increasing the synthetic utility of this transformation.     

Disappearing Polymorphs in Metal–Organic Framework Chemistry: Unexpected Stabilization of a Layered Polymorph over an Interpenetrated Three-Dimensional Structure in Mercury Imidazolate

The “disappearing polymorph” phenomenon is well established in organic solids, and has had a profound effect in pharmaceutical materials science. The first example of this effect in metal-containing systems in general, and in coordination-network solids in particular, is here reported. Specifically, attempts to mechanochemically synthesize a known interpenetrated diamondoid (dia) mercury(II) imidazolate metal–organic framework (MOF) yielded a novel, more stable polymorph based on square-grid (sql) layers. Simultaneously, the dia-form was found to be highly elusive, observed only as a short-lived intermediate in monitoring solvent-free synthesis and not at all from solution. The destabilization of a dense dia-framework relative to a lower dimensionality one is in contrast to the behavior of other imidazolate MOFs, with periodic density functional theory (DFT) calculations showing that it arises from weak interactions, including structure-stabilizing agostic C−H⋅⋅⋅Hg contacts. While providing a new link between MOFs and crystal engineering of organic solids, these findings highlight a possible role for agostic interactions in directing topology and stability of MOF polymorphs.     

Photophysics of Fluorescent Contact Sensors Based on the Dicyanodihydrofuran Motif

Fluorescent molecular rotors have been used for measurements of local mobility on molecular length scales, for example to determine viscosity, and for the visualization of contact between two surfaces. In the present work, we deepen our insight into the excited-state deactivation kinetics and mechanics of dicyanodihydrofuran-based molecular rotors. We extend the scope of the use of this class of rotors for contact sensing with a red-shifted member of the family. This allows for contact detection with a range of excitation wavelengths up to ∼600 nm. Steady-state fluorescence shows that the fluorescence quantum yield of these rotors depends not only on the rigidity of their environment, but – under certain conditions – also on its polarity. While excited state decay via rotation about the exocyclic double bond is rapid in nonpolar solvents and twisting of a single bond allows for fast decay in polar solvents, the barriers for both processes are significant in solvents of intermediate polarity. This effect may also occur in other molecular rotors, and it should be considered when applying such molecules as local mobility probes.     

Stereoelectronic Basis for the Kinetic Resolution of N‐Heterocycles with Chiral Acylating Reagents

The kinetic resolution of N‐heterocycles with chiral acylating agents reveals a previously unrecognized stereoelectronic effect in amine acylation. Combined with a new achiral hydroxamate, this effect makes possible the resolution of various N‐heterocycles by using easily prepared reagents. A transition‐state model to rationalize the stereochemical outcome of this kinetic resolution is also proposed.     

Tuning Thiophene with Phosphorus: Synthesis and Electronic Properties of Benzobisthiaphospholes

1,4‐Dimercapto‐2,5‐diphosphinobenzene and 3,6‐bis(hexyloxy)‐1,4‐dimercapto‐2,5‐diphosphinobenzene were synthesized and combined with various acid chlorides to obtain a series of benzobisthiaphospholes. Electrochemical and photophysical properties of the substituted benzobisthiaphospholes have been evaluated, and the observed reductions are more facile than the related benzothiaphospholes and 2,6‐diphenylbenzobisthiazole. A benzobisthiaphosphole with C₆H₄‐p‐CN substituents was reduced at E_1/2=?1.08 V (vs. saturated calomel electrode (SCE)). X‐ray diffraction data for several of these phosphorus heterocycles has been obtained, and DFT calculations at the B3LYP level have been performed.