NMR spectra of icosahedral (Ih and I) fullerenes

By analyzing the topological structures of the three types of icosahedral fullerenes: (1) , (2) and (3) k,\;h,k = 1,2,...} \right)$$ " align="middle" border="0"> , we have obtained theoretically the ¹³C NMR spectra with natural abundance for ¹³C of all the icosahedral (I_h and I) fullerenes.     

Reaction graphs and a construction of reaction networks

Summary A general definition of reaction graphs is presented. For a pair of isomeric molecular graphs and , related by a chemical transformation , the reaction graph is determined using a maximal common subgraph defined for vertex mapping . A binary operation defined for graphs constructed over the same vertex set enables us to decompose the reaction graph into the sum of prototype reaction graphs. A decomposition of an overall reaction graph can be advantageously used for the construction of a reaction network. An oriented path in this network beginning at and ending at corresponds to a breakdown of the transformation into a sequence of intermediates.     

On the cycle index of point groups

In this brief work we express the cycle index of the molecular point groups as a function of a limited number of initial geometrical parameters. Such parameters are the number of elements composing the domain D of sites of substitutions in the molecule belonging to the point group G, and the numbers of sites of D lying on the symmetry elements for G.     

Molecular Structure and Conformation of p-Bis(trimethylsilyl)benzene: A Study by Gas-Phase Electron Diffraction and Theoretical Calculations

The molecular structure and conformation of p-bis(trimethylsilyl)benzene have been investigated by gas-phase electron diffraction, ab initio MO calculations at the HF/6-31G*, MP2(f.c.)/6-31G*, and B3LYP/6-31G* levels, and MM3 molecular mechanics calculations. The calculations indicate the syn- and anti-coplanar conformations, with two bonds in the plane of the benzene ring, to be energy minima. The perpendicular conformations, with two bonds in a plane orthogonal to the ring plane, are transition states. The two coplanar conformers have nearly the same energy with a low interconversion barrier, 0.3–0.5 kJ mol^–1. The calculated lengths of the and bonds differ by only a few thousandths of an angstrom, in agreement with electron diffraction results from molecules containing either or bonds. The geometrical distortion of the benzene ring in p-bis(trimethylsilyl)-benzene may be described by superimposing independent distortions from each of the two SiMe₃ groups. The electron diffraction intensities from a previous study (Rozsondai, B.; Zelei, B.; Hargittai, I. J. Mol. Struct. 1982, 95, 187) have been reanalyzed, imposing constraints from the theoretical calculations, and using a model based on a 1:1 mixture of the two coplanar conformers. The effective torsion angles of the SiMe₃ groups may indicate nearly free rotation. Important geometrical parameters from the present electron diffraction analysis are , and . While the mean bond lengths are virtually the same from the previous and present analyses, the new ipso angle is in better agreement with the MO calculations [HF, 116.9° MP2(f.c.), 117.1° B3LYP, 116.9°].     

Volumetric Properties of Binary Mixtures of Acetonitrile and Chloroalkanes at 25°C and Atmospheric Pressure

Excess molar volumes for binary mixtures of acetonitrile + dichloromethane, acetonitrile + trichloromethane, and acetonitrile + tetracloromethane at 25°C have been used to calculate partial molar volumes , excess partial molar volumes , and apparent molar volumes of each component as a function of composition. The V _m ^Evalues are negative over the entire composition range for the systems studied. The applicability of the Prigogine–Flory–Patterson theory was explored. The agreement between theoretical and experimental results is satisfactory for the systems with dichloromethane and tetrachloromethane. For the unsymmetrical behavior of the system with trichloromethane, however, the agreement is poor.     

Cluster Models of Co2+ at the Cation Sites of Zeolite ZSM-5

The local structure of Co₂₊ at the -, , and -cation sites of zeolite ZSM-5 was calculated in terms of density functional theory using the cluster approach. The local geometry of the oxygen environment of Co₂₊ is characterized; it is found that the ion stabilization energy increases in the series .     

Effect of solvent on the partial molal volumes and heat capacities of nonelectrolytes

Group contributions to in seven solvents and to in three solvents have been tabulated. The variation of group parameters is discussed in terms of the solvent compressibility coefficient, _T. The scaled particle theory (SPT) is used to calculate cavity contributions to and C _p2 ^o . Interaction contributions are obtained from the cavity terms and and values estimated through the additivity schemes. values are more sensitive to solute-solvent interactions than in water and less sensitive in methanol. The SPT results for heat capacities support the concept of structural promotion by hydrophobic solutes in water.     

Heuristic lipophilicity potential for computer-aided rational drug design: Optimizations of screening functions and parameters

In this research we test and compare three possible atom-basedscreening functions used in the heuristic molecular lipophilicity potential(HMLP). Screening function 1 is a power distance-dependent function, b , screening function 2is an exponential distance-dependent function, b_iexp( , and screening function 3 is aweighted distance-dependent function, For every screening function, the parameters ( ,d₀, and are optimized using 41 common organic molecules of 4 types of compounds:aliphatic alcohols, aliphatic carboxylic acids, aliphatic amines, andaliphatic alkanes. The results of calculations show that screening function3 cannot give chemically reasonable results, however, both the powerscreening function and the exponential screening function give chemicallysatisfactory results. There are two notable differences between screeningfunctions 1 and 2. First, the exponential screening function has largervalues in the short distance than the power screening function, thereforemore influence from the nearest neighbors is involved using screeningfunction 2 than screening function 1. Second, the power screening functionhas larger values in the long distance than the exponential screeningfunction, therefore screening function 1 is effected by atoms at longdistance more than screening function 2. For screening function 1, thesuitable range of parameter d₀ is 1.5 < d₀ < 3.0, and d₀ = 2.0 is recommended. HMLP developed in this researchprovides a potential tool for computer-aided three-dimensional drugdesign.     

Dissociation Constants of Protonated Cysteine Species in NaCl Media

The sulfur-containing biomolecule, cysteine has a role in physiological and natural environment because of its strong interactions with metals. To understand these interactions of metals with cysteine, one needs reliable dissociation constants for the protonated cysteine species [ CH(CH₂SH)COOH; H₃B⁺]. The values of dissociated constants, p , for protonated cysteine species (H₃B⁺ H⁺ + H₂B, K ₁; H₂B H⁺ + HB^–,K ₂; HB^– H⁺ + B^2–,K ₃) were determined from potentiometric measurements in NaCl solutions as a function of ionic strength, 0.5–6.0 mol-(kgH₂O)^–1 and between 5, and 45°C. The equations

On the Pressure and Electric Field Dependencies of the Relative Permittivity of Liquids

The dependencies of the relative permittivity of over 50 liquids on the pressure P, as , and of some 40 liquids on the (square of the) electric field E at ambient conditions, as were obtained from literature data. The function was fitted to a simple expression in and the compressibility, _T. These data were used to obtain the limiting slope for the partial molar volumes and the electrostriction of electrolytes in various solvents.     

Electronic Energy Structure of a Series of Chalcopyrite-Like Compounds AgGaS2–CdGa2S4–InPS4

The effect of pseudovacancies on the density of electronic states of valence electrons in AgGaS₂, CdGa₂S₄, and InPS₄ is studied both experimentally, by means of X-ray spectroscopy, and theoretically, by calculating the partial densities of electronic states using the local coherent potential. The compounds under study are the derivatives of the sphalerite structural type (doubled cell) with gradually increasing deficiency of metals from to and further to , where is a vacancy. The environment of the metal atoms remains tetrahedral, while that of the sulfur atoms changes with increasing number of vacancies from four (AgGaS₂) to three (CdGa₂S₄) and two (InPS₄). For the compounds under study, SK and PK X-ray emission and absorption spectra were recorded at a resolution of about 0.2 eV, and the local partial densities of states were calculated for all components of the compounds. The theoretical curves practically coincide in shape and energy position of fine structure elements with the corresponding experimental curves. This allowed reliable conclusions about the energy positions of electronic states at the top of the valence band and about the dependence of the SK emission and absorption spectra in the series of compounds under study on variation of the crystal structure and on the chemical composition of the nearest surroundings of sulfur atoms.     

Effect of charge on the standard partial molar volumes and heat capacities of organic electrolytes in methanol and water

Previously developed additivity schemes for nonelectrolytes have been used to estimate and for tetraalkyl and tetraphenyl methanes in methanol and water. Corrections have been applied to the thermodynamic values of these model compounds to account for a variation in size of the central atom, and these were used to ascertain the effect of charge on and of alkyl and phenyl quaternary ions having N, P and B as central atoms. Investigations of R₄NBr, (R=methyl to heptyl) salts show that the charge effect on and of R₄N⁺ ions is large and relatively independent of ion size suggesting that the solvent molecules penetrate the ions. The ability to estimate and of the quaternary ions in the bromide salt solutions has made it possible to make ionic assignments with some confidence; (Br^–) has been evaluated as 19.7±2 and 30.2±7 cm³-mol^–1 and (Br^–) as –83±7 and –68±30 J-K^–1-mol^–1 in methanol and water, respectively. The use of organic ions for making ionic assignments of and is critically examined and comparisons with other assignments are made. The scaled particle theory is employed to divide the heat capacities of electrolytes into cavity and interaction contributions.     

Two Algorithms for Computing the Randles–Sevcik Function from Electrochemistry

We derive two expansions of the Randles–Sevcik function : an asymptotic expansion of for x and its Taylor expansion at any x ₀ . These expansions are accompanied by error bounds for the remainder at any order of the approximation.     

Some conjectures on S n -derived nuclear permutational(or NMR) spin encodings

On existence of limiting ‐module decompositional sets for weak ‐branching at high n; on Voronoi polyhedral dual as geometric analogues to Cayley’s SU2 embedding theorem; and on SU dual group with retention of self‐associacy over subduced irrep set, as being the sufficient further condition to ensure the determinacy of SU embeddings. In the context of structures arising from nuclear permutation (NP) or NMR dual‐group spin algebras, the first conjecture sets out the high‐index n, and thus weak‐branching limit (WBL), aspects of module decompositions as giving rise to a set of numerical values for the associated Kostka coefficients which are invariant to further incrementation in the index; the existence of such combinatorial limit properties, implicit in sst tableaux enumerations, has not been addressed in the mathematics literature to date. Conjectures 2 and 3 are concerned with the questions of geometric and sufficient algebraic realisations of the determinacy of natural finite group embeddings in specific SU permutation groups. In conjecture 2, the Voronoi dual‐structures to the regular polyhedra for NP/NMR automorphic SU2 embedded spin symmetries hold the key to physical insight. Specifically, they provide a novel combinatorial geometric view of Cayley’s theorem; the mid‐face intersecting ‐axes of the initial NMR automorphic solids become (vertex) body‐diagonal axes of the specific‐dual Voronoi polyhedra, where a distinctness condition from the spin‐sites gives raise to a geometric statement of Cayley’s theorem. Conjecture 3 is concerned with SU embeddings for which the simple Cayley criterion alone is an insufficient condition to guarantee determinacy. The self‐associacy property and its retention over the subduced irrep‐subset(s) (i.e., comparable to studies of system‐invariants via Yamanouchi–Gel’fand subduction chains) is now seen as indicative of retention of determinacy for such SU group embeddings through the above sufficiency condition. This revised version was published online in July 2006 with corrections to the Cover Date.     

Comprehensive Investigation of Yttrium and Rare Earth Element Complexation by Carbonate Ions Using ICP–Mass Spectrometry

Carbonate stability constants for yttrium and all rare earth elements have been determined at 25°C and 0.70 molal ionic strength by solvent exchange and inductively coupled plasma–mass spectrometry (ICP–MS). Measured stability constants for the formation of and from M³⁺ are in good agreement with previous direct measurements, which involved the use of radio-chemical techniques and trivalent ions of Y, Ce, Eu, Gd, Tb, and Yb. Direct ICP–MS measurements of and formation constants are also in general agreement with modeled stability constants for the metals La, Pr, Nd, Sm, Dy, Ho, Er, Tm, and Lu, based on linear-free energy relationship (LFER). The experimental procedures developed in this work can be used for assessing the complexation behavior of other geochemically important ligands such as phosphate, sulfate, and fluoride.     

Thermodynamics of Solutions of Trimethyl Aluminum and Trimethyl Gallium with Tetramethyl Tin

The enthalpies and entropies of evaporation of Al(CH₃)₃–Sn(CH₃)₄and Ga(CH₃)₃–Sn(CH₃)₄solutions were determined. It was established that solvates are formed in these systems and that the dissociation energies of specific interactions in them change in the following order: (10.3) > > > (4.08 kJ mol^–1), (6.52) > (5.14) > > (4.08 kJ mol^–1).     

Ionic Mobility, Structure, Phase Transition, and Conductivity in (NH4)3Sb4F15

Fluoride and ammonium ion dynamics in (NH₄)₃Sb₄F₁₅ was studied by ¹H and ¹⁹F NMR spectroscopy in the range 180-440 K. Types of ionic motion were determined, and their activation energies were estimated. The crystal structure of a single crystal of (NH₄)₃Sb₄F₁₅ (space group ) was solved. In the range K, a reversible phase transition has been found. Based on the experimental values of conductivity of (NH₄)₃Sb₄F₁₅ ( S/cm at T = 440 K), this antimony(III) fluoride is classified as a superionic conductor.     

Geometric and computational aspects of polymer reconfiguration

We examine a few computational geometric problems concerning the structures of polymers. We use a standard model of a polymer, a polygonal chain (path of line segments) in three dimensions. The chain can be reconfigured in any manner as long as the edge lengths and the angles between consecutive edges remain fixed, and no two edges cross during the motion. We discuss preliminary results on the following problems.Given a chain, select some interior edge , defining two subchains which are adjacent to . We keep the two subchains individually rigid and rotate one around while leaving the other fixed in space, while maintaining the vertex-angles at . We call this motion an edge spin at . An O(n ²) algorithm for this problem is given as well as an (nlogn) lower bound on the time complexity.In determining whether a chain can be reconfigured from one conformation to another, it is useful to consider reconfiguring through some canonical conformation. In our three-dimensional case, the most obvious choice is to flatten a chain into the plane. However, we demonstrate that determining if a given chain can be reconfigured into the plane without self-intersecting is NP-hard, even if the restriction that it must lie monotonically is added. We then provide an O(n) algorithm to decide if a chain has a non-crossing convex coil conformation (where all angles turn in the same direction), although we cannot yet decide if a sequence of motions to reconfigure a chain into a convex coil conformation exists.     

A Class of Orthogonal Polynomials Suggested by a Trigonometric Hamiltonian: Symmetric States

A new subclass of the Jacobi polynomials arising in the exact analytical solution of the one-dimensional Schrödinger equation with a trigonometric potential has been introduced. The polynomials which consist of a free parameter are not ultraspherical polynomials and have been simply named the -polynomials since they are generated by a trigonometric Hamiltonian. In certain sense, it is shown that the -polynomials can be regarded as a generalisation of the airfoil polynomials or the Chebyshev polynomials of the third kind. This paper is intended to discuss the basic properties of the polynomials so defined.