Synthesis of 3-hexahelicenol and its transformation to 3-hexahelicenylamines,diphenylphosphine, methyl carboxylate,and dimethylthiocarbamate

A nonphotochemical synthetic route to 3-hexahelicenol is reported. It involves a key [2+2+2] cycloisomerization of CH(3)O-substituted triyne that is readily available from 1-methoxy-3-methylbenzene and 1-bromo-2-(bromomethyl)naphthalene. Further functional group transformations led to 3-CO(2)CH(3), 3-NH(2), 3-PPh(2), and 3-SC(O)N(CH(3))(2) substituted hexahelicenes.     

Structure of Aqueous Gallium(III) Bromide Solutions Over a Temperature Range 80–333 K by Raman Spectroscopy, X-ray Absorption Fine Structure, and X-ray Diffraction

The structure and complex formation of concentrated aqueous gallium(III) bromide (GaBr₃) solutions have been investigated over a temperature range 80–333 K by Raman spectroscopy, X-ray absorption fine structure (XAFS), and X-ray diffraction. The Raman spectra obtained at various [Br^?]/[Ga³⁺] molar ratios and temperatures have shown that complex formation between Ga³⁺ and Br^? occurs as a predominant species, with [GaBr₄]^? at [Ga³⁺] as high as 1～2 M (M = mol?dm ^?3) and [Br^?]/[Ga³⁺] ratios > ～2, and that cooling of the solutions favors the formation of the aqua Ga³⁺. The intermediate species were not seen in the Raman spectra. The XAFS data have revealed that the aqua complex has a sixfold coordination as [Ga(H₂O)₆]³⁺ with a Ga³⁺–H₂O distance of (1.96 ± 0.02) Å, whereas the [GaBr₄]^? complex has a Ga³⁺–Br^? distance of (2.33± 0.02) Å, and that vitrification of the aqueous GaBr₃ solution at liquid nitrogen temperature shifts the equilibrium toward the aqua complex. The X-ray diffraction data at different subzero temperatures have shown a tendency of decreasing Ga³⁺–Br^? and increasing Ga³⁺–H₂O interactions with lowering temperature, confirming the preference of aqua Ga³⁺ in the supercooled liquid state as well as in the glassy state. The Ga³⁺–H₂O distance of ～1.8 Å for the tetrahedral coordination was found in a 2.01 M gallium(III) bromide solution with a [Br^?]/[Ga³⁺] ratio of 3.7 and gradually increased to a value of 1.92 Å for octahedral geometry with decreasing temperature, suggesting that equilibrium shifts from [GaBr₄]^? to [Ga(H₂O)₆]³⁺ through intermediate species, [GaBr _n ]^(3?n)+ (n = 2 and 3). The Ga³⁺–Br^? and Br^?–Br^? distances within [GaBr₄]^? with an almost tetrahedral symmetry are (2.35± 0.02) and (3.82± 0.03) Å, respectively. The Ga³⁺ has the second hydration shell at (4.03± 0.03) Å and the hydration of Br^? is characterized with a Br^?–H₂O distance of (3.35± 0.02) Å at all temperatures investigated.     

Electron binding energies of aqueous alkali and halide ions: EUV photoelectron spectroscopy of liquid solutions and combined ab initio and molecular dynamics calculations

Photoelectron spectroscopy combined with the liquid microjet technique enables the direct probing of the electronic structure of aqueous solutions. We report measured and calculated lowest vertical electron binding energies of aqueous alkali cations and halide anions. In some cases, ejection from deeper electronic levels of the solute could be observed. Electron binding energies of a given aqueous ion are found to be independent of the counterion and the salt concentration. The experimental results are complemented by ab initio calculations, at the MP2 and CCSD(T) level, of the ionization energies of these prototype ions in the aqueous phase. The solvent effect was accounted for in the electronic structure calculations in two ways. An explicit inclusion of discrete water molecules using a set of snapshots from an equilibrium classical molecular dynamics simulations and a fractional charge representation of solvent molecules give good results for halide ions. The electron binding energies of alkali cations computed with this approach tend to be overestimated. On the other hand, the polarizable continuum model, which strictly provides adiabatic binding energies, performs well for the alkali cations but fails for the halides. Photon energies in the experiment were in the EUV region (typically 100 eV) for which the technique is probing the top layers of the liquid sample. Hence, the reported energies of aqueous ions are closely connected with both structures and chemical reactivity at the liquid interface, for example, in atmospheric aerosol particles, as well as fundamental bulk solvation properties.     

H-quadrupolar coupling-based analysis of stereochemical and regiochemical memory in the Pd-catalysed allylic alkylation of iso-cinnamyl type substrates employing the chiral monophosphine ligands ‘MOP’ and ‘MAP’

The reaction of iso-cinnamyl acetate with NaC(Me)(CO₂Me)₂, catalysed by Pd-‘MOP’ (MOP=2-methoxy-2′-diphenylphosphino-1,1′-binaphthalene) is known to proceed with a regiochemical memory effect that results in the predominant generation of the branched alkylation product. The analogous reaction employing ‘MAP’ as ligand (MAP=2-N,N-dimethylamino-2′-diphenylphosphino-1,1′-binaphthalene) proceeds with ‘normal’ regioselectivity to generate predominantly the linear isomer of product. A ²H-NMR based analysis, employing quadrupolar coupling in a chiral liquid crystal matrix, has been developed to facilitate the simultaneous study of the regiochemical and stereochemical outcome of the reaction of both enantiomers of iso-cinnamyl ester substrates in ²H-labelled but racemic samples. The analysis allows the comparison of relative rates of two competing isomerisation processes occurring in the π-allyl intermediates in the Pd-catalysed reaction, one of which facilitates asymmetric induction, the other resulting in loss of regiochemical memory. It is demonstrated that the two processes are partially coupled and that this then limits the attainment of high global enantiomeric excess in the branched product to reactions that proceed with low regiochemical retention. A key factor for the observation of high regiochemical memory is found to be the nucleophilicity of the malonate anion and the electrophilicity of the Pd-π-allyl intermediate with reduction in the reactivity of either partner resulting in the onset of substantial loss of memory.     

Counterpoise-corrected potential energy surfaces of simple H-bonded systems

Geometries and stabilization energies of various simple H-bonded complexes (water dimer, hydrogen fluoride dimer, formamide dimer, formic acid dimer) have been determined by a gradient optimization that eliminates the basis set superposition error (BSSE) by the counterpoise (CP) method in each gradient cycle as well as by the standard gradient optimization. Both optimization methods lead to different potential energy surfaces (PES). The difference depends on the theoretical level used and is larger if correlation energy is considered. Intermolecular distances from the CP-corrected PES are consistently longer, and this difference might be significant (∼0.1 ?); also angular characteristics determined from both surfaces differ significantly. Different geometries were obtained even when passing to larger basis sets (aug-cc-pVDZ). The standard optimization procedure can result in a completely wrong structure. For example, the “quasi-linear” structure of the (HF)₂ (global minimum) does not exist at the standard MP2/ 6-31G** PES (where only cyclic structure was detected) and is found only at the CP-corrected PES. Stabilization energies obtained from the CP-corrected PES are always larger than these from the standard PES where the BSSE is added only a posteriori for the final optimized structure; both energies converge only when passing to a larger basis set (aug-cc-pVDZ). Received: 11 March 1998 / Accepted: 19 June 1998 / Published online: 4 September 1998 RID=" ID=" <E6>Acknowledgements.</E6> The project was supported by the Grant Agency of the Czech Republic (Grant No. 203/98/1166). RID=" ID=" <E5>Correspondence to</E5>: P. Hobza     

Selecting an agricultural technology package based on the flexible and interactive tradeoff method

Annals of Operations Research - The aim of this paper is to solve an agricultural technology packages selection problem by considering multiple dimensions which influence a maize producer’s...     

Perpetual American Double Lookback Options on Drawdowns and Drawups with Floating Strikes

We present closed-form solutions to the problems of pricing of the perpetual American double lookback put and call options on the maximum drawdown and the maximum drawup with floating strikes in the Black-Merton-Scholes model. It is shown that the optimal exercise times are the first times at which the underlying risky asset price process reaches some lower or upper stochastic boundaries depending on the current values of its running maximum or minimum as well as the maximum drawdown or maximum drawup. The proof is based on the reduction of the original double optimal stopping problems to the appropriate sequences of single optimal stopping problems for the three-dimensional continuous Markov processes. The latter problems are solved as the equivalent free-boundary problems by means of the smooth-fit and normal-reflection conditions for the value functions at the optimal stopping boundaries and the edges of the three-dimensional state spaces. We show that the optimal exercise boundaries are determined as either the unique solutions of the associated systems of arithmetic equations or the minimal and maximal solutions of the appropriate first-order nonlinear ordinary differential equations.

     

Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions

Methodology and Computing in Applied Probability - We present closed-form solutions to some double optimal stopping problems with payoffs representing linear functions of the running maxima and...     

Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae

We consider the Weyl asymptotic formula

Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations

We study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S¹. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data in H¹(S¹), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0], T*) is a maximal half open interval of existence for a positive solution of the equation, with T* < ∞, then lim_tT* w(t,·) exists in C¹(S¹) but vanishes at some point. We show further that if T* > (1 + √3)/16π² √3 then T* = ∞ and lim_t∞ w(t,.) exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wiley & Sons, Inc.