On the molecular structure of cycloheptadiene

Molecular mechanics calculations on cycloheptadiene indicate that the molecule has a structure which undergoes a wide pseudorotational motion between two C₁ forms, and a C₁ form, and this structure is in equilibrium with the C₂ form. It is shown that this equilibrium mixture is consistent with all of the available experimental data.     

The hydroazocine route to highly functionalized pyrrolizidines

Studies of the preparation of 1,8-dihydroazocines and transannular cyclization of hydroazocines to produce functionalized pyrrolizidines are described. Results are presented which demonstrate that unsymmetrically substituted acetylenes bearing at least one electron withdrawing groups undergo efficient cycloaddition to 1 - β - styryl - 1,2 - dihydropyridine producing in a regio-selective fashion 3,4 - disubstituted - 1,8 - dihydroazocines. The dihydroazocines generated in this manner can be converted to 1 - formyl - Δ^4,5 - epoxyazocines which undergo interesting rearrangement reactions to form pyrrolizidines when subjected to methoxide deformylation followed by acid treatment. In addition, 1,6,7,8 - tetrahydroazocines can be converted to pyrrolizidines under bromination conditions. The intriguing chemical process which occur under the conditions outlined above are described.     

OVID and SUPER: Two overlap programs for drug design

Summary Two programs, OVID and SUPER, for exploring the similarity of molecules with respect to their action at a receptor are described. OVID accepts two molecules as input and optimizes the three-dimensional overlap of specified atoms in one molecule with specified atoms in the second molecule. The result is expressed as a percent of the theoretical maximum. OVID gives a quantitative measure of the extent of a guessed correspondence between two molecules based on volume overlap of selected atoms. The Achilles' heel of OVID is that the correspondence between the two molecules has to be guessed. We realized that it would be better to systematically examine all possible correspondences of two structures to minimize the chance of overlooking a superior correspondence. We created SUPER to satisfy this need. SUPER accepts two molecules as input and finds the top twenty correspondences of their surfaces and charge distributions, giving a quantitative measure of the extent of each correspondence. An instructive example of the application of OVID and SUPER to the design of leukotriene D₄ receptor antagonists is described. SUPER appears to be a practical brainstorming tool for the medicinal chemist trying to understand how molecules whose structures may not resemble one another in an obvious way can bind to the same site.     

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     

Infrared investigation of aluminum- and chromium-substituted magnetites and of the lacunar spinels resulting from their oxidation

When Fe³⁺ ions are substituted by aluminum or chromium on magnetite octahedral sites, the ir spectrum shows the conversion of an inverse spinel to a normal spinel. Both broad bands of magnetite are gradually replaced by the four characteristic bands of normal spinels II–III. They are also observed for solid solutions, FeCr₂O₄FeAl₂O₄, with, however, a further band at 780 cm^?1 which may be assigned to Al³⁺ ions on tetrahedral sites. Low-temperature (<400°C) oxidation of these compounds whose sizes are less than 2000 Å results in lacunar spinels III–III. The ir spectrum of these solids is characterized by two absorption bands (as for inverse spinels II–III) except for compounds close to pure γFe₂O₃ in which an order of vacancies could be put in evidence.     

NMR investigation on the conformational properties of N-[2-pyridyl-N-oxide]-amino derivatives

The proton NMR spectra of N-[2-pyridyl-N-oxide]-derivatives of primary and secondary ethylamines, containing a substituent R on the C atom bearing the amino function, have been completely analysed in terms of the fundamental NMR parameters. The preferred conformations of the compounds investigated were established by the indications from NOE experiments as well as: (1) the long range coupling across the five bond between the aminic hydrogen and the proton in 4-position of the pyridine-N-oxide ring (⁵J_m^H,NH ～ 0·5 c/s), (2) the value of the vicinal coupling constant in the fragment CHNH (³J_NHCH ～ 7–9 c/s), (3) the large deshielding (Δτ ～ 1–1·5 ppm) observed for the resonance position of the proton on the asymmetric C atom in secondary amine derivatives with respect to the corresponding primary ones, and (4) the diamagnetic shielding produced on protons in position 3 and 4 of the pyridine-N-oxide ring by different aromatic groups introduced in the R substituent.The NMR data confirmed the preferred rotamers previously suggested on the basis of ORD and CD measurements.     

AlSiP3, a compound with a novel wurtzite-pyrite intergrowth structure

AlSiP₃ is formed by heating aluminum and silicon powder with red phosphorus and adding small amounts of iodine or AlCl₃. Small, black crystals with metallic lustre grow at 1200°K. The compound crystallizes in the orthorhombic space group Pmnb (No. 62) with a = 987.2 pm, b = 586.1 pm, c = 608.8 pm and four formula units. In the structure isolated P atoms as well as P₂ pairs are present (PP = 218.2 pm). Silicon is tetrahedrally bonded (SiP = 224.2 ? 228.2 pm) whereas aluminum has octahedral coordination (AlP = 244.2 – 260.8 pm). The structure can be described as an intergrowth structure of wurtzite and pyrite type.     

Self-similar vortex reconnection

As shown by Crow in 1970, the evolution of two almost parallel vortex filaments with opposite circulation exhibits a long-wave instability. Ultimately, the symmetric mode increases its amplitude reconnecting both filaments and ending into the formation of an almost periodic structure of vortex rings. This is a universal process, which appears in a wide range of scales: from the vortex trails behind an airplane to a microscopic scale of superfluids and Bose–Einstein condensates. In this paper, I will focus on the vortex reconnection for the latter case by employing Gross–Pitaevskii theory. Essentially, I focus on the well-known laws of interaction and motion of vortex filaments. By means of numerical simulations, as well as theoretically, I show that a self-similar finite-time dynamics manifests near the reconnection time. A self-similar profile is selected showing excellent agreement with numerical simulations.     

Properties of G-martingales with finite variation and the application to G-Sobolev spaces

As is known, if $B={\left(B_t\right)}_{t\in [0,T]}$ is a $G$-Brownian motion, a process of form ${\int }_0^t{\eta }_{s}d{〈B〉}_s?{\int }_0^{t}2G\left({\eta }_s\right)ds$, $\eta \in M_G^1(0,T)$, is a non-increasing $G$-martingale. In this paper, we shall show that a non-increasing $G$-martingale cannot be form of ${\int }_0^t{\eta }_{s}ds$ or ${\int }_0^t{\gamma }_{s}d{〈B〉}_s$, $\eta ,\gamma \in M_G^1(0,T)$, which implies that the decomposition for generalized $G$-Itô processes is unique: For arbitrary $\zeta \in H_G^1(0,T)$, $\eta \in M_G^1(0,T)$ and non-increasing $G$-martingales $K,L$, if ${\int }_0^t{\zeta }_{s}d{B}_s+{\int }_0^t{\eta }_{s}ds+K_t=L_t,t\in [0,T],$then we have $\eta \equiv 0$, $\zeta \equiv 0$ and$K_t=L_t$. As an application, we give a characterization to the $G$-Sobolev spaces introduced in Peng and Song (2015).