Perturbational and variational treatments of the Morse oscillator

The Morse oscillator hamiltonian is expressed as an infinite expansion in powers of a natural perturbation parameter, the square root of the anharmonicity constant, relative to the simple harmonic oscillator as zeroth-order hamiltonian. A transformation of variables leads to a hamiltonian which involves terms no higher than second order in this natural perturbation parameter. In both cases, the exact bound state eigenvalues of the Morse oscillator are given by second-order perturbation theory. The Schrödinger equation corresponding to the transformed Morse hamiltonian is solved variationally, via a complete set expansion in simple harmonic oscillator eigenstates. Accurate approximations to the exact eigenvalues and eigenfunctions of bound states of the Morse oscillator can be obtained for all but the very highest levels.     

Perturbational calculations of parity-violating effects in nuclear-magnetic-resonance parameters

We investigate the effects of the parity-violating electroweak interaction in the spectral parameters of nuclear magnetic resonance. Perturbational theory of parity-violating effects in the nuclear magnetic shielding is presented to the order of G(F)alpha, and in the indirect spin-spin coupling, to the order of G(F)alpha3. These leading-order parity-violating corrections are evaluated using analytical linear-response theory methods based on Hartree-Fock and density-functional theory reference states. Parity-violating contributions to spin-spin couplings are evaluated for the first time at the first-principles level. Calculations are carried out for two chiral halomethanes, bromochlorofluoromethane and bromofluoroiodomethane.     

Thermodynamic and kinetic analysis of the dimerization of aqueous glyoxal

Equilibria and rates of interconversion between monomeric and dimeric glyoxal were measured in aqueous solution. The equilibrium constant [G₂]/[G₁]² was 0.56 M^?1 at 25°C, and was hardly affected by changes of ionic strength and pH but increased rapidly with increase of temperature. The rate of depolymerization was first-order in dimer, with the pseudo first-order rate coefficient in the pH range 1.3–7.8being of the form b₁[H₃O⁺] + b₂ + b₃[OH^?]/(1 + b₄[OH^?]) + b₅[OH^?]. Coefficients b₁ and b₂ were more strongly affected by changes of temperature, though [OH^?] was much the more effective catalyst. This rate form has not previously been observed for monomer-dimer inter-conversion of α-hydroxycarbonyls and α-dicarbonyls or for related reactions such as mutarotations and hydrations. Equivalent rate forms arisefrom reactions where an intermediate at steady state and low concentration is produced.     

Theoretical analysis of the effects of reversible dimerization in size exclusion chromatography

Reversible dimer formation in size exclusion chromatography (SEC) can cause peak splitting, merging, tailing, and fronting. Such behavior can be predicted by the association rate and the dissociation rate relative to the convection rate. Slow association and dissociation result in separated monomer and dimer peaks. Fast association and slow dissociation result in one single dimer peak. Slow association and fast dissociation result in one single monomer peak. Intermediate association and dissociation result in a merged, broad peak with either fronting when monomers dominate or tailing when dimers dominate. A diagram based on the two relative rates is generated to predict general peak shape and retention behavior in SEC.     

Addressing the regioselectivity problem in organic synthesis

A screening process uncovered a heterogeneous catalytic system that hydrolyzes one of two nearly identical ketals in several diketals with a high selectivity.     

Perturbational relativistic theory of electron spin resonance g-tensor

We carry out a complete treatment of the leading-order relativistic one-electron contributions, arising from the Breit-Pauli Hamiltonian, to the g-tensor of electron spin resonance spectroscopy. We classify the different terms and discuss their interpretation as well as give numerical ab initio estimates for the F2(-), Cl2(-), Br2(-), and I2(-) series, using analytical response theory calculations with a multiconfigurational self-consistent field reference state. The results are compared to available experimental data. (c) 2004 American Institute of Physics     

Predicting the regioselectivity of nucleophilic addition to arynes using frontier molecular orbital contribution analysis

The regioselectivity of nucleophilic addition to substituted arynes was predicted using frontier molecular orbital contribution analysis. This model indicates that the percentage of the LUMO on the reacting terminus of the aryne is responsible for the observed regioselectivity; the nucleophile attacks the carbon possessing higher contribution of the LUMO.     

Temperature-controlled regioselectivity in the reductive cleavage of p-methoxybenzylidene acetals

The regioselective ring opening of pyranosidic 4,6-p-methoxybenzylidene acetals with BH(3)/Bu(2)BOTf in THF can be tuned by adjusting the reaction temperature and reagent concentrations. Reductive cleavage at 0 degrees C resulted in the exclusive formation of 4-O-p-methoxybenzyl (PMB) ethers, whereas reaction at -78 degrees C produced 6-O-PMB ethers in high yields. The latter condition was observed to be compatible with a variety of acid-sensitive functional groups, including allyl and enol ethers. The presence of water does not interfere with reductive ring opening and may contribute toward in situ generation of H(+) as a catalyst for 6-O-PMB ether formation. Reductive cleavage under rigorously aprotic conditions is greatly decelerated, and yields only the 4-O-PMB ether. The temperature-dependent reductive cleavage of the 4,6-acetal can be described in terms of kinetic versus thermodynamic control: Lewis-acid coordination of the more accessible O-6 is favored at higher temperatures, whereas protonation of the more basic but sterically encumbered O-4 predominates at low temperatures.     

Sequence- and regioselectivity in the montmorillonite-catalyzed synthesis of RNA

The possible role of catalysis in forming a limited number of RNAs from activated monomers is investigated by examining the sequence- and regioselectivity in the montmorillonite-catalyzed formation of RNA dimers and trimers. The reactivity of A was similar to that of G, and C was comparable in reactivity to U. Yet the reactivity of the purine nucleotides differed from that of the pyrimidines. In the reaction of nucleotides (pN) with activated monomers (ImpN), the sequence- and regioselectivity was Pu(3')Py > Pu(3')Pu = Pu(2')Py > Pu(2')Pu. The 5'-pyrimidine initiated dimers formed less efficiently than the 5'-purine initiated dimers. Trimer formation was investigated by the synthesis of 8 dimers (pNpN) and measuring the yields of trimers formed in the reaction of each dimer with a mixture of equal molar amounts of four activated monomers. The reactivity of the dimers depended on the nucleotide attached to the 3'-end of the RNA and the regiochemistry of the phosphodiester bond. Rules based on these studies are proposed to predict the sequence- and regioselectivity of the RNAs formed in montmorillonite-catalyzed reactions. These rules are consistent with the structures of the 2-5-mers formed in the reaction of equimolar amounts of ImpA and ImpC. This research establishes that the montmorillonite catalyst limits the number of RNA oligomer isomers formed. The potential significance of these findings to the origins of life is discussed.     

Stereoselectivity and regioselectivity in the segment-coupling Prins cyclization

The scope of the segment-coupling Prins cyclization has been investigated. The method is outlined in Scheme 1 and involves esterification of a homoallylic alcohol (1), reductive acetylation to give the alpha-acetoxy ether (3), and cyclization on treatment with a Lewis acid to produce a tetrahydropyran (4). Alkene geometries dictate the product configurations, with E-alkenes leading to equatorial substituents and Z-alkenes leading to axial substituents (Table 1). Not unexpectedly, applying the method to allylic alcohols leads to fragmentation rather than a disfavored 5-endo-trig cyclization. Dienols in which one alkene is allylic and the other alkene is homoallylic cyclize efficiently and produce the tetrahydropyrans 49-54, Table 3. Dienols with two homoallylic alkenes cyclize with modest to high regioselectively, generating tetrahydropyrans 40-45, Table 2. The relative rates for cyclization decrease in the order of vinyl > Z-alkene > E-alkene > alkyne. The configurations of the products are consistent with cyclization via a chair conformation, Figure 1. The 2-oxonia Cope rearrangement may be a factor in the regioselectivity of diene cyclizations and in the erosion of stereoselectivity with Z-alkenes. This investigation establishes the stereoselectivity and regioselectivity for a number of synthetically useful segment-coupling Prins cyclizations.     

Enhanced regioselectivity of Yang photocyclization in the crystalline state

[reaction: see text] In contrast to the solution state, where Yang photocyclization of ketones of general structure 1 leads to equal amounts of cyclobutanols 2 and 3 (by abstraction of HA and HB, respectively), irradiation in the crystalline state is much more regioselective, favoring either 2 or 3 depending on the nature of the substituent X. X-ray crystallography and molecular mechanics calculations reveal the source of this remarkable solid-state regioselectivity.     

Novel anti-Markovnikov regioselectivity in the Wacker reaction of styrenes

The Wacker reaction is one of the longest known palladium-catalysed organic transformations, and in the vast majority of cases proceeds with Markovnikov regioselectivity. Palladium(II)-mediated oxidation of styrenes was examined and in the absence of reoxidants was found to proceed in an anti-Markovnikov sense, giving aldehydes. Studies on the mechanism of this unusual transformation were carried out, and indicate the possible involvement of a eta(4)-palladium-styrene complex. With a heteropolyacid as the terminal oxidant, oxidation of styrene to give the anti-Markovnikov aldehyde as the major product was found to be catalytic.     

Perturbational calculation of the exchange forces in the two lowest states of the hydrogen molecule

The interaction energies in the ground (X¹Σ) and the first excited (b³Σ)states of the hydrogen molecule were calculated using the modified Jansen and Byers Brown perturbation method. Calculations were performed for nine values of the internuclear distance R in the range 5 a.u. ≦ R ≦ 9 a.u. The present results were compared with the interaction energies calculated by four other perturbation methods as the expectation values of the H – E⁰ operator with the function accurate up to the first order. The results show that the method can give satisfactory values of the interaction energies.     

On the regioselectivity of elimination reactions in terpene derivatives

Tertiary alcohols with prenyl or geranyl moities, bearing a second oxygen. function in the 3, 4 or 5 position were dehydrated under various conditions : the composition of the olefinic mixture obtained was accounted for, by an intramolecular base relay effect.Basic elimination of analogous dimethylsutfonium salts gave results that could be related to the inductive effect : a correlation between regioselectivity and the Taft constantσ_I of the second oxygen function was found, except for the very basic alkoxide groups where an alternative regioselective elimination took place.     

Chemo- and regioselectivity in the reactions of polyfunctional pyrroles

The chemo- and regioselectivity of the reduction, oxidation and Wittig reaction of polyfunctional pyrroles, containing a variety of reactive centres was investigated. The reaction of 3,5-dichloropyrrole-2,4-dicarboxaldehydes with potassium permanganate leads to regioselective oxidation of the 2-formyl group, while the Wittig reaction with 1 equiv of a triphenylphosphorane produced the 2-alkenyl substituted pyrroles.     

Structure-based evaluation of the regioselectivity in bifurcated hydrogen bonds

Unsymmetrical phenolic (thio)urea molecules are investigated and compared to evaluate the regioselectivity of the bifurcated hydrogen bonds. The supramolecular aggregation can feature self-sorting homomeric α-networks through recognition between N–H···O(S) and O–H···O intermolecular hydrogen bonds. The regioselectivity of bifurcated hydrogen bond was investigated using single crystal X-ray diffraction studies, DFT calculations and Cambridge Structural Database analysis. The influence of several key variables on the fidelity of regioselectivity was described.     

Structure of the trimer of acrolein diethyl acetal

Summary The product formed by the condensation of acrolein diethyl acetal under the influence of BF₃ etherate is a trimer of composition C₂₁H₄₂O₆ and is 2-ethoxy-4-(1-ethoxyallyl)glutaraldehyde diethyl acetal. A mechanism is proposed for its formation via a quasi-aromatic complex with subsequent cyclic electron transfer.