Simple evaluation of Franck–Condon factors and non‐Condon effects in the Morse potential

The calculation of Franck–Condon factors between different 1‐D Morse potential eigenstates using a formula derived from the Wigner function is discussed. Our numerical calculations using a simple program written in Mathematica are compared with other calculations. We show that our results have a similar accuracy as those calculations performed with more sophisticated methods. We discuss the extension of our method to include non‐Condon effects in the calculation. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 280–295, 2002     

The "invisible" 13C NMR chemical shift of the central carbon atom in [(Ph3PAu)6C]2+: a theoretical investigation

The experimental 13C NMR chemical shift of the central carbon atom in the octahedral [(Ph3PAu)6C]2+ cluster was investigated on the basis of relativistic density functional calculations. In order to arrive at independent model conclusions regarding the value of the chemical shift, a systematic study of the dependence of the cluster structure on the phosphine ligands, the chosen density functionals, and the basis set size was conducted. The best structures obtained were then used in the NMR calculations. Because of the cage-like cluster structure a pronounced deshielding of the central carbon nucleus could have been expected. However, upon comparison with the 13C NMR properties of the related complex [C{Au[P(C6H5)2(p-C6H4NMe2)]}6]2+, Schmidbaur et al. have assigned a signal at delta=135.2 ppm to the interstitial carbon atom. Our calculations confirm this value in the region of the aromatic carbon atoms of the triphenylphosphine ligands. The close-lying signals of the 108 phenyl carbon atoms can explain the difficulties of assigning them experimentally.     

Electrostatic calculation of the substituent effect: an efficient test on isolated molecules

The energy of a disubstituted molecule has often been approximated by simple electrostatic formulas that represent the substituents as poles or dipoles. Herein, we test this approach on a new model system that is more direct and more efficient than testing on acid-base properties. The energies of 27 1,4-derivatives of bicyclo[2.2.2]octane were calculated within the framework of the density functional theory at the B3LYP/6-311+G(d,p) level; interaction of the two substituents was evaluated in terms of isodesmic homodesmotic reactions. This interaction energy, checked previously on some experimental gas-phase acidities, was considered to be accurate and served as reference to test the electrostatic approximation. This approximation works well in the qualitative sense as far as the sign and the order of magnitude are concerned: beginning with the strongest interaction between two poles, a weaker interaction between pole and dipole, and the weakest between two dipoles. However, all the electrostatic calculations yield energies that are too small, particularly for weak interaction, and this fundamental defect is not remedied by some possible improvements. In particular, variation of the effective permittivity would require a physically impossible value less than unity. The explanation must lie in a more complex distribution of electron density than anticipated in the electrostatic model. It also follows that possible conclusions about the transmission of substituent effects "through space" have little validity.     

Substituent effects on the kinetics for the chemiluminescence reaction of 6-arylimidazo[1,2-a]pyrazin-3(7H)-ones (Cypridina luciferin analogues): support for the single electron transfer (SET)-oxygenation mechanism with triplet molecular oxygen

Kinetics of chemiluminescence reactions of 2-methyl-6-phenylimidazo[1,2-a]pyrazin-3(7H)-one (1c, Cypridina luciferin analogue) and substituent effects of the 6-aryl group of derivatives 1 strongly suggest that the rate-determining step is a single electron transfer from an anion derived from 1 to a triplet molecular oxygen (O₂) in the oxygenation process.     

Effects of Amplitude of the Radiofrequency Electromagnetic Radiation on Aqueous Suspensions and Solutions

The effects of radiofrequency (RF) (1–4) and magnetic fields (5–9) on the behavior of aqueous solutions and suspensions have been a popular subject in recent years. The mechanism of the magnetic “water memory” effect, though, is still largely unknown (5). In this work, we present evidence that the primary “receptor” of the electromagnetic radiation is a gas/liquid interface. Gas can be either already present in water or produced by the effects of electromagnetic fields. Perturbed gas/liquid interfaces require hours to equilibrate. Certain RF and magnetic signals also produce reactive oxygen and hydrogen species (superoxide, hydrogen peroxide, hydrogen, atomic hydrogen). The perturbed gas/liquid interface modifies the hydrogen bonding networks in water and also the hydration of ions and interfaces. Careful outgassing removes all of the effects of the electromagnetic fields, including the magnetic memory effect. The amplitude of the applied field influences the observed effects. Different amplitudes of RF radiation perturb the interfacial water in different ways and consequently affect the behavior of colloids and ions in specific manners. For instance, the bulk and template precipitation of calcium carbonate, zeta potentials of suspended colloids, rate of dissolution of colloidal silica, and attachment of colloidal silica to metal surfaces are modified in specific ways with the low amplitude or high amplitude RF treatments described in this paper. The solubility/diffusivity of gas species is also modified in a different manner, and it is probably at the core of the specificity of the RF amplitude effects.     

Optimum gas chromatographic conditions in wall-coated capillary columns. Extended and simplified forms of the Golay-equation

Band broadening in capillary columns is satisfactorily described by the Golay-equation extended to situations of appreciable pressure drop by Giddings. In practice, however, several simplifications are often made. The effect of these simplifications on the calculated values of the minimum plate height and optimum carrier gas velocity are treated systematically.     

Mechanistic aspects of the Wolff-Kishner reaction. V. The cation effect on the reaction of benzophenone hydrazone in butyl carbitol and decyl alcohol

The rate of the Wolff-Kishner reaction of benzophenone hydrazone in butyl carbitol increases as the cation of the alkoxide base is varied in the order K>Na>Li>Mg. The replacement of butyl carbitol by 1-decanol also accelerates the reaction, and an additional increase is caused by the presence of crown ether. On the basis of changes in the activation parameters, it is concluded that the reactivity of the hydrazone anion increases as the contact ion pair becomes more fully solvated and dissociated.     

Surface effects on phase transition behavior and thermal polymerization of long-chain diynoic acids in micro DSC measurements

Effects of metal surfaces, such as aluminium, silver and gold, on the melting behavior and thermal polymerization of long-chain diynoic acids having a diacetylene group at different positions were investigated by thermal analyses using DSC, TG and other methods. The surface effects of metals were significant in the order of Ag, Al and Au. These effects are attributable to the anchoring of carboxyl group on the surface by chemisorption, which leads to unfavorable condition for polymerization of heptadeca-2,4-diynoic acid. In the case of tricosa-10,12-diynoic acid, containing a flexible methylene chain, inserted between COOH and C≡C?C≡C groups, the anchoring of COOH on the metal surface causes rather favorable effect on the polymerization.     

C12-s-C12·2Br与低碳醇混合水溶液胶团化行为的温度效应和焓/熵补偿

季铵盐Gemini表面活性剂C12-s-C12·2Br(s=2,3,4,6)与丙醇、丁醇、戊醇、己醇混合水溶液的In(cmc)随温度升高而逐渐增大.计算所得热力学数据表明,C12-s-C12·2Br与醇混合胶团化过程服从熵驱动机理,也出现了焓/熵补偿现象.随着温度上升,熵驱动力增大,在指定温度时,醇分子烷烃链上碳原子数n增大使△Gm0值减小,胶团结构更加稳定;而增加s使值增大,胶团稳定性下降.