Quantum dynamics of H2, D2, and HD in the small dodecahedral cage of clathrate hydrate: evaluating H2-water nanocage interaction potentials by comparison of theory with inelastic neutron scattering experiments

We have performed rigorous quantum five-dimensional (5D) calculations and analysis of the translation-rotation (T-R) energy levels of one H(2), D(2), and HD molecule inside the small dodecahedral (H(2)O)(20) cage of the structure II clathrate hydrate, which was treated as rigid. The H(2)- cage intermolecular potential energy surface (PES) used previously in the molecular dynamics simulations of the hydrogen hydrates [Alavi et al., J. Chem. Phys. 123, 024507 (2005)] was employed. This PES, denoted here as SPC/E, combines an effective, empirical water-water pair potential [Berendsen et al., J. Phys. Chem. 91, 6269 (1987)] and electrostatic interactions between the partial charges placed on H(2)O and H(2). The 5D T-R eigenstates of HD were calculated also on another 5D H(2)-cage PES denoted PA-D, used by us earlier to investigate the quantum T-R dynamics of H(2) and D(2) in the small cage [Xu et al., J. Phys. Chem. B 110, 24806 (2006)]. In the PA-D PES, the hydrogen-water pair potential is described by the ab initio 5D PES of the isolated H(2)-H(2)O dimer. The quality of the SPC/E and the PA-D H(2)-cage PESs was tested by direct comparison of the T-R excitation energies calculated on them to the results of two recent inelastic neutron scattering (INS) studies of H(2) and HD inside the small clathrate cage. The translational fundamental and overtone excitations, as well as the triplet splittings of the j=0-->j=1 rotational transitions, of H(2) and HD in the small cage calculated on the SPC/E PES agree very well with the INS results and represent a significant improvement over the results computed on the PA-D PES. Our calculations on the SPC/E PES also make predictions about several spectroscopic observables for the encapsulated H(2), D(2), and HD, which have not been measured yet.     

Polarization dependence of transition intensities in double resonance experiments: unresolved spin doublets

The polarization dependence of transition intensities in multiple resonance spectroscopic experiments can provide information useful for making rotational assignments. A formalism to describe the polarization dependence of transition intensities in multiple resonance experiments, particularly for cases when two rotational/fine structure quantum numbers are needed to specify the state of the system, is presented. The formalism is presented in a form usable both when the transitions between the underlying fine structure components are experimentally resolved, as well as when they are unresolved, to form composite lines. This sort of treatment is necessary for cases when the two quantum numbers that specify the fine structure differ significantly, such as is the case at low N, when the difference between J and N becomes comparable to the value of J. Ratios of transition intensities in different experimentally convenient polarization arrangements are evaluated for the case of composite N transitions formed by combining the spin components of a doublet system. The formalism is expressed in a form easily extendable to accommodate experimental cases of more than two excitation steps, or a combination of excitation steps and an external static electric field. This polarization diagnostic has been experimentally applied to assign spectral features in double resonance Rydberg spectra of CaF.     

Theoretical study of the oxidative polymerization of aniline with peroxydisulfate: Tetramer formation

Semi‐empirical quantum chemical study of the oxidative polymerization of aniline with ammonium peroxydisulfate, in aqueous solutions without added acid, has been based on the MNDO‐PM3 computations of thermodynamic, redox, and acid–base properties of reactive species and the intermediates, combined with the MM2 molecular mechanics force‐field method and conductor‐like screening model of solvation. The main reaction routes of aniline tetramerization are proposed. The regioselectivity of the formation of aniline tetramers by redox and electrophilic aromatic substitution reactions is analyzed. It was proved that the linear N? C4 coupled tetra‐aniline is formed as a dominant product by three different pathways: comproportionation redox reaction between N‐phenyl‐1,4‐benzoquinonediimine and 4‐aminodiphenylamine, the one‐electron oxidation of aniline with its half‐oxidized N? C4 coupled trimer, and the electrophilic aromatic substitution reaction of aniline with fully oxidized N? C4 coupled trianiline nitrenium cation. The electrophilic aromatic substitution reaction of the N? C4 coupled aniline trimer with aniline nitrenium cation, as well as the oxidation of aniline with half‐oxidized branched trimer, lead to the branched aniline tetramers. The competing character of different tetramerization routes is highlighted. The oxidative intramolecular cyclization of branched oligoanilines and polyaniline, leading to the generation of substituted phenazine units, has been predicted to accompany the classical routes of the polymerization of aniline. Various molecular (branched vs. linear) oligomeric structures produced at different level of acidity during the course of polymerization and their impact on the formation of supramolecular structures of conducting polyaniline (nanorods and nanotubes vs. granular morphology), are discussed. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Formation of sodium 6-hydroxy-2-naphthoate in the <Emphasis Type="Italic">Kolbe-Schmitt</Emphasis> reaction

This work is an extension of our investigation of the mechanism of the Kolbe-Schmitt reaction of sodium 2-naphthoxide. The carboxylation reaction of sodium 2-naphthoxide in the position 6 is examined by means of the B3LYP/LANL2DZ method. After the initial formation of sodium 2-naphthoxide-CO₂ complex, the carbon of the CO₂ moiety performs an electrophilic attack on the naphthalene ring in position 8. Further transformations lead to the formation of sodium 6-hydroxy-2-naphthoate. Our findings are in good agreement with the experimental results on the carboxylation reaction of sodium 2-naphthoxide. Correspondence: Svetlana Marković, Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia.     

<Emphasis Type="Italic">p</Emphasis>-Adic probability logics

This paper represents an comprehensive overview of the results from three papers where we developed several propositional logics for reasoning about p-adic valued probability.Each of these logics is a sound, complete and decidable extension of classical propositional logic.     

Pyridyl‐Endcapped Polyynes: Stabilized Wire‐like Molecules

A 4‐ethynylpyridyl derivative with sterically shielding phenyl groups in the 3‐ and 5‐positions has been synthesized and used to terminate a series of polyynes. This approach allows for the synthesis of stable polyynes up to an octayne, twice as long as previous accessible for “unstabilized” pyridyl‐endcapped polyynes. The potential of these polyynes as wire‐like linkers to metal centers is demonstrated by axial coordination of pyridyl groups to zinc‐ and ruthenium‐metalloporphyrins.     

Hydrogen Bonding between Metal‐Ion Complexes and Noncoordinated Water: Electrostatic Potentials and Interaction Energies

The hydrogen bonding of noncoordinated water molecules to each other and to water molecules that are coordinated to metal‐ion complexes has been investigated by means of a search of the Cambridge Structural Database (CSD) and through quantum chemical calculations. Tetrahedral and octahedral complexes that were both charged and neutral were studied. A general conclusion is that hydrogen bonds between noncoordinated water and coordinated water are much stronger than those between noncoordinated waters, whereas hydrogen bonds of water molecule in tetrahedral complexes are stronger than in octahedral complexes. We examined the possibility of correlating the computed interaction energies with the most positive electrostatic potentials on the interacting hydrogen atoms prior to interaction and obtained very good correlation. This study illustrates the fact that electrostatic potentials computed for ground‐state molecules, prior to interaction, can provide considerable insight into the interactions.     

Generalization of Popoviciu-Type Inequalities Via Fink’s Identity

We obtained useful identities via Fink’s identity, by which the inequality of Popoviciu for convex functions is generalized for higher order convex functions. We investigate the bounds for the identities related to the generalization of the Popoviciu inequality using inequalities for the ?eby?ev functional. Some results relating to the Grüss- and Ostrowski-type inequalities are constructed. Further, we also construct new families of exponentially convex functions and Cauchy-type means by looking at linear functional associated with the obtained inequalities.     

Functional weak convergence of partial maxima processes

For a strictly stationary sequence of nonnegative regularly varying random variables (X _n ) we study functional weak convergence of partial maxima processes \(M_{n}(t) = \bigvee _{i=1}^{\lfloor nt \rfloor }X_{i},\,t \in [0,1]\) in the space D[0, 1] with the Skorohod J ₁ topology. Under the strong mixing condition, we give sufficient conditions for such convergence when clustering of large values do not occur. We apply this result to stochastic volatility processes. Further we give conditions under which the regular variation property is a necessary condition for J ₁ and M ₁ functional convergences in the case of weak dependence. We also prove that strong mixing implies the so-called Condition \(\mathcal {A}(a_{n})\) with the time component.