Frontier orbital control in hydrazino bridged [14]annulenes

[10b.10c]Diazapyraceheptylenes 1b and 1c were obtained from olefinic precursors 6. Treatment of 7 under the same conditions does not allow a synthesis of the parent compound 1a which may be explained by frontier orbital considerations.     

An investigation of the reliability of the Galerkin-Petrov method with a special study of the helium atom ground state

A convergence characterization of the Galerkin-Petrov method by means of quantities characterizing pairs of subspaces is presented. The usefulness of our approach for setting up reliable computational schemes is demonstrated for the He atom ground state. Several methods of constructing pairs of subspaces for use in quantum chemistry are suggested.     

Cores,cutsets and the fixed point property

The purpose of this paper is the analysis and application of the concepts of a core (a pair of chains) and cutset in the fixed point theory for posets. The main results are:

1. (Theorem 3) If P is chain-complete and (*), it contains a cutset S such that every nonempty subset of S has a join or a meet in P, then P has the fixed point property (FPP),
2. (Theorem 5) If P or Q is chain-complete, Q satisfies (*) and both P and Q have the FPP, then P x Q has the FPP.
3. (Theorem 6) Let P or Q be chain-complete and there exist p∈P and a finite sequence f ₁, f ₂, ..., f _n of order-preserving mappings of P into P such that $$\left( {\forall x\varepsilon P} \right)x \leqslant f_1 \left( x \right) \geqslant f_2 \left( x \right) \leqslant \cdots \geqslant f_n \left( x \right) \leqslant p$$ If P and Q have the FPP then P x Q has the FPP.
4. (Theorem 7) If T is an ordered set with the FPP and {P _t :t∈T} is a disjoint family of ordered sets with the FPP then its ordered sum ∪{P _t :t∈T} has the FPP.

     

Disconnected Ordered Sets are Max-Reconstructible

Every finite disconnected set P is determined (up to automorphism) by the family {P − {a}:a ∈ Max _P }.     

Proximal primal–dual best approximation algorithm with memory

We propose a new modified primal–dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates computed in previous steps in the formulas defining current iterate. To this end we consider projections onto intersections of halfspaces generated on the basis of the current as well as the previous iterates. To calculate these projections we are using recently obtained closed-form expressions for projectors onto polyhedral sets. The resulting algorithm with memory inherits strong convergence properties of the original best approximation proximal primal–dual algorithm. Additionally, we compare our algorithm with the original (non-inertial) one with the help of the so called attraction property defined below. Extensive numerical experimental results on image reconstruction problems illustrate the advantages of including memory into the original algorithm.     

Understanding relativistic effects of chemical bonding

To elucidate the physical origin of relativistic changes of molecular properties, exact theorems, perturbation theory, and Hartree-Fock-Slater-Pauli calculations are exploited. The relativistic molecular virial theorem offers insight into the relativistic and nonrelativistic, kinetic, and potential energy contributions to the bond energy. In general, there exist two contributions to the relativistic correction of a molecular property: the relativistic change at the nonrelativistic equilibrium geometry and the change of the nonrelativistic property due to the relativistic change of the equilibrium geometry. Sometimes the first and sometimes the second contribution is the dominant one. Accurate numerical results for H⁺₂-like systems are obtained using direct relativistic double perturbation theory. In some cases, near-degenerate perturbation theory is mandatory. Relativistic changes of chemical bond energies are often proportional to the density change in the K-shell when the bond is formed. Relativistic corrections to many properties (and also to the 1s²-correlation energy) are often proportional to Z²α². © 1996 John Wiley & Sons, Inc.     

Dimension two,fixed points and dismantlable ordered sets

When does the fixed point property of a finite ordered set imply its dismantlability by irreducible elements? For instance, if it has width two. Although every finite ordered set is dismantlable by retractible (not necessarily irreducible) elements, surprisingly, a finite, dimension two ordered set, need not be dismantlable by irreducible elements. If, however, a finite ordered set with the fixed point property is N-free and of dimension two, then it is dismantlable by irreducibles. A curious consequence is that every finite, dimension two ordered set has a complete endomorphism spectrum.     

FTIR Cryospectroscopic Study of Fermi Resonance Polyads νs ≈ 2νb in CHF3

Optics and Spectroscopy - The sequences of Fermi resonances νs ≈ 2νb in the IR spectrum of a fluoroform solution (CHF3) in liquefied krypton have been studied. Here, νs is the...     

Complexes of lasalocid 2-naphthylmethyl ester with monovalent metal cations studied by mass spectrometry, spectroscopic and semiempirical methods

Lasalocid acid is an ionophore able to carry protons and cations through the cell membrane. Its 2-naphthylmethyl ester (NAFB) and its complexes with Li⁺, Na⁺ and K⁺ cations were synthesized and their structures were studied by ESI-MS, ¹H NMR, ¹³C NMR, FTIR and PM5 methods. The ESI-MS spectra indicate that NAFB forms stable complexes with Li⁺, Na⁺ and K⁺ cations of exclusively 1:1 stoichiometry and that the complexation of Li⁺ cations by NAFB is favoured. The NMR and FTIR spectra indicate that the oxygen atom of the ketone group of the NAFB molecule is involved in the coordination of the cations, and the strength of this process is dependent on the type of cation. We find that the intramolecular O(3)?CH···O(2) hydrogen bond in NAFB and its complexes is partially broken in acetonitrile solution and that this process is independent of the type of cation. The PM5 semiempirical calculations allow visualisation of all structures and determination of the hydrogen bond parameters.