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.     

A second-order scheme for the “Brusselator” reaction–diffusion system

A second-order method is developed for the numerical solution of the initial-value problems , , and , , , in which the functions and , where A and B are positive real constants, are the reaction terms arising from the mathematical modelling of chemical systems such as in enzymatic reactions and plasma and laser physics in multiple coupling between modes. The method is based on three first-order methods for solving u and v, respectively. In addition to being second-order accurate in space and time, the method is seen to converge to the correct fixed point ( , V* = A/B) provided . The approach adopted is extended to solve a class of non-linear reaction–diffusion equations in two-space dimensions known as the “Brusselator” system. The algorithm is implemented in parallel using two processors, each solving a linear algebraic system as opposed to solving non-linear systems, which is often required when integrating non-linear partial differential equations (PDEs). This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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.     

Handling multicomponent systems in \mathbb{R}^n. I: Theoretical results

The phases of multicomponent systems (mixtures, states, etc.) containing the compounds are , where and . For (quaternary or higher dimensional systems), the displaying methods and visual investigations in the dimensional Euclidean space are tangentially or not at all described in the literature. In this paper we first develop the theoretical (both mathematical and computational) background in any dimension in . We focus not only on the important points, lines, surfaces of these systems, and computing method of the states of some processes in such systems, but also on the approximating methods of the above mentioned lines and surfaces, and, finally, on the question which is the region where a state (a point) falls into. Using the above results a computer program for PC's was created for evaluating and displaying the approximated surfaces. This program is described in I. Szalkai, SALT3DIM.exe – A program for handling 4 component mixtures, Preprint No. 047, University of Veszprém (1996), and the computing results are planned to be published in a forthcoming paper (I. Szalkai, Handling multicomponent systems in . II: Computational results, J. Chem. Inf. Comput. Sci., submitted).     

Dimension‐dependent two‐electron Hamiltonian matrix elements

Since the birth of quantum mechanics the ground state electronic energy of the twoelectron atom has received special attention. This is because the twoelectron system is the simplest atom to include electron–electron interactions. These interactions are key to understanding manyelectron systems. This paper adds to the knowledge of twoelectron atoms by presenting closed form solutions for Hamiltonian matrix elements at arbitrary spatial dimension, . The basis functions are the dependent hydrogenic wavefunctions: . The electron–electron repulsion integrals are solved by the Fourier integral transform.     

Symmetry breaking in HF wave functions of Fe(CH)2

HF and CAS calculations for linear geometry of Fe(CH)₂ with symmetry have been performed. The basis sets used were DZ and DZ + P with ECP on the iron atom. Two closedshell and one quintet RHF wave functions have been found, and . All of them are singlet and triplet unstable in the wide range of Fe–CH distances. Singlet instability leads to the Charge Density Wave (CDW) brokensymmetry wave function with two electrons on carbon or orbital in the dissociation limit. Triplet instabilities lead to two brokensymmetry HF wave functions of Axial Spin Density Wave (ASDW) type, ASDW₁ and ASDW₂. In the dissociation limit they give carbon atoms with two electrons on and orbitals coupled to singlet and triplet, respectively. The stability conditions for CDW, ASDW₁ and ASDW₂ instabilities have been derived. Other HF wave functions with spin symmetry unrestricted have been also found. CAS(8,8), CAS(10,10) and CAS(12,12) calculations for singlet, triplet and quintet states of Fe(CH)₂ have been carried out. In all CAS calculations the singlet state has the lowest energy. The Fe–CH equilibrium distances obtained from closedshell RHF wave functions are much shorter and from brokensymmetry wave functions are much longer than those obtained from CAS calculations.     

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 perturbation theoretical method for determination of the dependence of the intramolecular X–H(D) potential on the hydrogen bond strength

A perturbation theoretical method is proposed that allows determination of the function describing the dependence of the intramolecular XH(D) potential on the hydrogen bond strength. Treating the XH(D) oscillators as mixed cubic–quartic oscillators in which the stretch–stretch couplings of the ν(X–H(D)) mode with the internal modes of the radical X may be neglected, and introducing the hydrogen bonding influence through the changes in the harmonic diagonal force constants (as proposed by Sceats and Rice [41]), it is possible to extract the analytical form of the function ) from the experimental versus correlations. The other parameters obtained by the empirical correlations, within this model, also have an exact physical meaning. The method is applicable to weak hydrogen bonds as well as to hydrogen bonds of intermediate strength, and, strictly speaking, to linear X– systems. However, extension to arbitrary geometry may be easily done. This revised version was published online in July 2006 with corrections to the Cover Date.     

Preferential solvation in three component systems: Evaluation of Kirkwood-Buff parameters

The extent of local excess or deficiency of a component solvent near the solute in a mixed binary solvent has been calculated using the Hall formalism for the Kirkwood-Buff equation. The possibility of calculation of the two solute-solvent Kirkwood-Buff parameters using the values is discussed. A model calculation using literature data for preferential solvation in mixed binary solvents is presented. The solute-solvent and solvent-solvent interactions and the relative size of the solvents are also shown to be relevant factors in determining the values.     

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.     

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).     

A generalized self‐consistent‐field procedure in the improved BCS theory

The basic ideas of the Improved Bardeen–Cooper–Schrieffer (IBCS) approach to the first and secondorder Reduced Density Matrices (1 and 2RDM) are briefly reviewed. The molecular orbital occupations are expressed by means of new quantities , which, satisfying a trigonometric relation, guarantee the nonidempontent condition. Thus, a variational method is introduced to determine , involving only an unconstrained minimization which may be performed using a conjugate gradient technique. A new effective Hamiltonian which is composed of the Coulomb, exchange and exchangetime inversion operators is also presented. It leads exactly to equations of Hartree–Fock type, however, the electronic field includes now an arbitrary number of orbitals and fractional occupation numbers. Accordingly, a generalized selfconsistentfield method is proposed: the iterative procedure is repeated until convergence is reached for the actual density matrix.     

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.     

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 .     

Surface Fluorination of Carboxylated Nitrile Butadiene Rubber: An XPS Study

Because of their exceptional reactivity, fluorine and fluorinated gases are of primary importance for the modification of the surface properties of materials. This study is devoted to surface treatment of thin nitrile gloves, made of carboxylated nitrile butadiene rubber latex, using either direct fluorination (10% F₂gas diluted in N₂) or plasma-enhanced fluorination in radio-frequency cold plasmas using fluorinated gases (CF₄, CHF₃). Mechanisms of fluorination of these co-elastomers have been proposed on the basis of the assignment of the different components of the XPS spectra. Several mechanisms have been observed depending on the fluorination conditions. Although the modification of nitrile gloves is already effective for fluorination reactions at room temperature, an important activation is observed for experiments carried out at 90°C. When the treatments are carried out at room temperature, a gradual fluorination occurs: in the case of 10% diluted F₂ gas, monofluorinated C—F groups are the species most found at the surface and perfluoro groups CF _n are present in lower amount. An addition reaction takes place at the CH=CH double bonds of the polybutadiene entities, leading to CHF=CHF units. Whatever the fluorination method, thermal activation yields a more massive fluorination of the surface that finally leads to perfluorinated CF₂ groups and terminal —CF₃ groups.     

Interpolation of parameters of solutions expressed as functions of composition

The number of parameters in the polynomial is discussed for N components and a polynomial extending up to power n. This number is found to be but may be N less for relative thermodynamic functions. The equation of degree n for an N-component system requires the use of data for each of the i-component systems. Data on the n-component systems suffice if n相似文献   

Vibrational spectra and structure of sulfonium nitroimides

Vibrational spectroscopy and x-ray structure analysis have been used to investigate three new types of sulfonium nitroimides: N-nitrosulfylimides, N-nitrosulfoximides, and N,N-dinitrosulfodiimides. Structural parameters have been determined for the molecules , , and .Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2489–2496, November, 1991.     

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°].     

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