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Structure Theory (structure + theory)

Distribution by Scientific Domains

Chemistry	80%

Selected Abstracts

Between ends and fibers

JOURNAL OF GRAPH THEORY, Issue 2 2007
C. Paul Bonnington
Abstract Let , be an infinite, locally finite, connected graph with distance function ,. Given a ray P in , and a constant C , 1, a vertex-sequence is said to be regulated by C if, for all n,,, never precedes xn on P, each vertex of P appears at most C times in the sequence, and . R. Halin (Math. Ann., 157, 1964, 125,137) defined two rays to be end-equivalent if they are joined by infinitely many pairwise-disjoint paths; the resulting equivalence classes are called ends. More recently H. A. Jung (Graph Structure Theory, Contemporary Mathematics, 147, 1993, 477,484) defined rays P and Q to be b-equivalent if there exist sequences and VQ regulated by some constant C , 1 such that for all n,,; he named the resulting equivalence classes b-fibers. Let denote the set of nondecreasing functions from into the set of positive real numbers. The relation (called f-equivalence) generalizes Jung's condition to . As f runs through , uncountably many equivalence relations are produced on the set of rays that are no finer than b -equivalence while, under specified conditions, are no coarser than end-equivalence. Indeed, for every , there exists an "end-defining function" that is unbounded and sublinear and such that implies that P and Q are end-equivalent. Say if there exists a sublinear function such that . The equivalence classes with respect to are called bundles. We pursue the notion of "initially metric" rays in relation to bundles, and show that in any bundle either all or none of its rays are initially metric. Furthermore, initially metric rays in the same bundle are end-equivalent. In the case that , contains translatable rays we give some sufficient conditions for every f -equivalence class to contain uncountably many g -equivalence classes (where ). We conclude with a variety of applications to infinite planar graphs. Among these, it is shown that two rays whose union is the boundary of an infinite face of an almost-transitive planar map are never bundle- equivalent. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 125,153, 2007 [source]

Predicting New Ferromagnetic Nitrides from Electronic Structure Theory: IrFe3N and RhFe3N.

CHEMINFORM, Issue 20 2005
Joerg von Appen
Abstract For Abstract see ChemInform Abstract in Full Text. [source]

Infrared spectra of water molecule encapsulated inside fullerene studied by instantaneous vibrational analysis,

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 10 2009
Kiyoshi Yagi
Abstract Instantaneous vibrational analysis (IVA) is proposed for computing the infrared spectrum of dynamically fluctuating system, and applied to a water molecule encapsulated into fullerene (H2O@C60). A molecular dynamics simulation is first carried out to generate an ensemble of configurations averaging the rotational and translational motion of H2O inside fullerene. At each configuration, instantaneous vibrational frequencies of the water molecule are computed by the vibrational configuration interaction method, which are then employed to construct the line-shape of the spectrum. The vibrational spectrum in the OH stretching region is computed at a temperature of 10 and 100 K based on a direct potential energy surface incorporating the electronic structure theory. It is found that the vibrational frequency of the symmetric stretching mode is blue-shifted compared to that of isolated water, whereas that of the asymmetric stretching mode exhibits no shift in average. The relation between IVA and instantaneous normal mode analysis is presented, and their performances are compared. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source]

A phase-space method for arbitrary bimolecular gas-phase reactions: Theoretical description

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2001
A. Gross
Abstract A theoretical model for the calculation of rate constants for arbitrary bimolecular gas-phase reactions was developed. The method is based on the phase-space statistical method developed by Light and co-workers 1,6. In the present article this method is extended to arbitrary molecular systems. The new method requires knowledge of the molecular properties in the reaction and products channels of the chemical system. The properties are the vibrational frequencies, moments of inertia, and potential energy for the interacting species in their ground state equilibrium configuration. Furthermore, we have to calculate either the energy barrier or the long-range potential for the chemical system (if the reaction channel does not have an energy barrier). The usefulness of the method is that it can be applied to all bimolecular reactions, trimolecular reactions, and even reactions of higher orders. Therefore, it can be applied to cases where rate constants of complex chemical reactions are required, but reliable laboratory measurements or other means to estimate rate parameters are not yet possible. Even if spectroscopic data are not available for the reactants and products, it is possible to use electronic structure theory to calculate the required data. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001 [source]

Prediction of the Solubility, Activity Coefficient and Liquid/Liquid Partition Coefficient of Organic Compounds

MOLECULAR INFORMATICS, Issue 9 2004
H. Hilal
Abstract Solvation models, based on fundamental chemical structure theory, were developed in the SPARC mechanistic tool box to predict a large array of physical properties of organic compounds in water and in non-aqueous solvents strictly from molecular structure. The SPARC self-interaction solvation models that describe the intermolecular interaction between like molecules (solute-solute or solvent-solvent) were extended to quantify solute-solvent interaction energy in order to estimate the activity coefficient in almost any solvent. Solvation models that include dispersion, induction, dipole-dipole and hydrogen bonding interactions are used to describe the intermolecular interaction upon placing an organic solute molecule in any single or mixed solvent system. In addition to estimation of the activity coefficient for 2674 organic compounds, these solvation models were validated on solubility and liquid/liquid distribution coefficient in more than 163 solvents including water. The RMS deviations of the calculated versus observed activity coefficients, solubilities and liquid/liquid distribution coefficients were 0.272,log mole fraction, 0.487,log mole fraction and 0.44,log units, respectively. [source]