Direct subduction of Q-conjugacy representations to give characteristic monomials for combinatorial enumeration

Characteristic monomials for a finite group are obtained by direct subductions of Q-conjugate representations. They are shown to give a generating function that is capable of solving enumeration problems. Received: 1 May 1998 / Accepted: 16 July 1998 / Published online: 18 September 1998     

Möbius function and characteristic monomials for combinatorial enumeration

After the definitions of amplified representations and number-theoretical vectors, the markaracter table of a cyclic subgroup is converted into the corresponding Q-conjugacy character table. The conversion is shown to necessitate an interconversion matrix that contains M?bius functions as elements. Since the interconversion matrix gives characteristic monomials for cyclic groups, all the powers appearing in each of the characteristic monomials are shown to be integers. Characteristic monomials for finite groups are then built up by starting from those of cyclic groups. This procedure clarifies the fact that all the powers appearing in each characteristic monomial for finite groups are integers. The relationship between characteristic monomial tables and unit-subduced-cycle-index tables is discussed with respect to their application to isomer enumeration. Received: 15 July 1998 / Accepted: 16 December 1998 / Published online: 16 March 1999     

Isomer combinatorics for acyclic conjugated polyenes: enumeration and beyond

A combinatorial approach to fully conjugated acyclic polyenes (C _N H _{N +2}) is considered with a view to the extension of standard enumeration techniques to treat a widened range of chemically interesting features. As a first step, enumerations are made respecting: placement of single and double bonds, the occurrence of cis/trans isomers, and the degree (and type) of “radicality” of such conjugated networks. As a further extension, several structural (graph-theoretic) invariants averaged over various types of isomer classes and sub-classes are made, and then these invariants are utilized to estimate several physicochemical properties averaged over these same classes or sub-classes. The properties currently so considered are heats of formation, indices of refraction, and magnetic susceptibilities. Finally, the asymptotic behaviors of isomer counts and isomer properties in the many-atom limit is elaborated. Received: 10 August 1998 / Accepted: 17 November 1998 / Published online: 16 March 1999     

Subduction of dominant representations for combinatorial enumeration

Summary A new method for giving cycle indices is presented for combinatorial enumeration. Thus, cyclic groups are characterized by markaracter tables, the elements of which are determined by the orders of their subgroups. A set of such cyclic groups (defined as dominant subgroups) is used to characterize a group G of finite order, where the markaracter table for the group G is constructed with respect to dominant representations (DRs), which are defined as coset representations corresponding to the dominant subgroups. By starting from the markaracter table, we propose an essential set of subdominant markaracter tables and a magnification set for the group G; the latter concept clarifies the relationship between each subdominant markaracter table and the markaracter table of a dominant subgroup. The subduction of DRs is obtained by the markaracter table to produce a dominant subduction table and a dominant USCI (unit-subduced cycle index) table. The latter is used to evaluate a cycle index to be applied to combinatorial enumeration. The cycle index is shown to be equivalent to the couterpart of our previous approach concerning both cyclic and non-cyclic subgroups. The latter, in turn, has been proved to be equivaltent to the cycle index obtained by the Redfield-Pólya theorem.     

Sequence dependence of DNA radioprotection by the thiols WR-1065 and WR-151326

Sequence-dependent variations of DNA structure modulate radiation-induced strand breakage. Thiols reduce breakage by scavenging damaging radiolytic OH ^. and repairing sugar radicals. As shown by sequencing gel electrophoresis, WR-1065 radioprotection is modulated by sequence, whereas that of WR-151326, a larger thiol, is more evenly distributed. Molecular modelling was performed on complexes of a 53 bp oligonucleotide (belonging to a natural restriction fragment) with one molecule of WR-1065 or WR-151326. Energy minimised structures exhibit a broadening of the minor groove of an AAATT motif upon WR-1065 binding, and a narrowing of the groove upon WR-151326 binding. Consequently, the accessibility to OH^˙ of H4′ (whose abstraction leads to strand breakage) increases near WR-1065, whereas it decreases near WR-151326. This modifies locally the otherwise homogeneous radioprotection. The effect of WR-151326 strengthens the protection at all tested binding sites, whereas that of WR-1065 diminishes it in some regions, in good agreement with the observed radioprotection distribution. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 11 November 1998     

The structure and energetics of cryolite melts

A method of solvation energy computation is proposed for ions and molecules in the environment of an ionic melt, based on the approximation of the ionic melt as an ideal conductor. The method is used to compute equilibrium constants of some equilibria in cryolite melt. Theoretically obtained results predict that aluminium is bound in tetrafluorocomplexes AlF₄ ⁻. Received: 16 March 1998 / Accepted: 19 June 1998 / Published online: 7 October 1998     

Peptides in membranes: assessment of environmental effects via simulations using an implicit solvation model

A recently developed implicit solvation model is applied to Monte Carlo simulations of peptides in bilayer-mimetic and polar environments. The model employs the formalism of atomic solvation parameters and reproduces experimental data. Solvent effects on the␣structure of the following peptides were studied: 20-residue poly-Leu and poly-Val, transmembrane helix A of bacteriorhodopsin, magainin2. It was shown that a␣membrane-like environment considerably promotes α-helix formation (all the peptides were found to be α-helical), while simulations in water reveal helix distortion. Consistency of the results with experimental data and further implications of the model are discussed. Received: 24 April 1998 / Accepted: 3 September 1998 / Published online: 10 December 1998     

Study of flexible joints and permanent bends in DNA fragments by brownian dynamics simulations

The use of Brownian dynamics simulations to investigate the presence of structural (kinks) and dynamic (bulges) anomalies in short DNA stretches is analyzed in connection with a string-of-beads model. A scaling method to choose the hydrodynamic translational and rotational parameters of the beads is proposed and tested on straight, kinked and bulged DNA fragments 17 nm long. The model reproduces the rigid-body rotational diffusion for the straight DNA and for the fluorescence polarization anisotropy decay of the kinked and bulged DNAs the model predicts a different behavior which is found experimentally. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 23 November 1998     

Weighted HOMO-LUMO energy separation as an index of kinetic stability for fullerenes

A very simple but general index of kinetic stability, T, is proposed for π-electron systems, which is defined as a highest occupied molecular orbital (HOMO)- lowest unoccupied molecular orbital (LUMO) energy separation multiplied by the number of conjugated atoms. This new index can be justified by relating it to the approximate form of the superdelocalizability, an index of chemical reactivity defined by Fukui et al. It is best suited for predicting the kinetic stability of fullerenes. All isolable fullerene isomers have T values larger than 13. Received: 24 June 1998 / Accepted: 3 September 1998 / Published online: 17 December 1998     

Prediction of protein structure using a knowledge-based off-lattice united-residue force field and global optimization methods

A united-residue model of polypeptide chains developed in our laboratories with united side-chains and united peptide groups as interaction sites is presented. The model is designed to work in continuous space; hence efficient global-optimization methods can be applied. In this work, we adopted the distance-scaling method that is based on continuous deformation of the original rugged energy hypersurface to obtain a smoothed surface. The method has been applied successfully to predict the structures of simple motifs, such as the three-helix bundle structure of the 10-58 fragment of staphylococcal protein A in de novo folding simulations and more complicated motifs in inverse-folding simulations. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

The topology of catchment regions of potential energy hypersurfaces

A simple proof is presented for a fundamental topological property of catchment regions of potential energy hypersurfaces: each catchment region C(λ,i), representing a chemical species and its conformational range on the potential energy hypersurface, is simply k-connected for each dimension k=1,2,…3N−6−λ, where λ is the index of the catchment region. The consequences of this property on the structure of the fundamental group of reaction mechanisms (the one-dimensional homotopy group of reaction paths) is discussed. Received: 8 July 1998 / Accepted: 6 October 1998 / Published online: 23 February 1999     

The saddle point of the nucleophilic substitution reaction Cl− + CH3Cl: results of large-scale coupled cluster calculations

On the basis of large-scale coupled cluster calculations including connectedz triple substitutions in a perturbative way, the geometrical parameters of the D _{3 h} saddle point of the Walden inversion reaction Cl⁻ + CH₃Cl′→ ClCH₃ + Cl′⁻ are predicted to be R _s (C—Cl) = 2.301 ? and r _s (C—H) = 1.069 ?. The barrier height with respect to the reactants is recommended to be 11.5 ± 1.0 kJ mol⁻¹. Connected triple substitutions lower the barrier height by almost a factor of 2, but have very little influence on the geometric structure of the saddle point. Received: 26 June 1998 / Accepted: 15 July 1998 / Published online: 28 September 1998     

Bis-periazulene: a simple Kekulé biradical with a triplet ground state

B3LYP/6-31G* calculations on bis-periazulene (cyclohepta[def]-fluorene) predict a triplet ground state for this molecule. The singlet has an aromatic 14π-electron periphery but is 2 kcal/mol higher in energy. The results agree with earlier predictions by Heilbronner. Received: 19 August 1998 / Accepted: 6 October 1998 / Published online: 23 February 1999     

Diatomic potential well depths from analyses of high-resolution electron energy spectra for autoionizing collision complexes

High-resolution energy spectra of electrons released in Penning ionization collisions of metastable rare gas atoms Rg*(ns) (Rg = He, Ne, Ar, Kr, Xe) with several open-shell and closed-shell atoms are analyzed to determine the well depth of the potential energy curve which describes the respective autoionizing collision complex. We thereby elucidate trends in the chemical interaction of Rg* with closed-shell target atoms A(ns ²) and establish a basis for detailed comparison with the respective interactions involving open-shell, ground state alkali atoms A(ns). From electron energy spectra due to␣associative ionization (RgH⁺ formation) in Rg* + H(1s) collisions, we determine binding energies for the RgH⁺(¹Σ) ground state potential (Rg = Ne, Ar, Kr, Xe) with uncertainties around 0.03 eV. Received: 30 June 1998 / Accepted: 5 August 1998 / Published online: 28 October 1998     

Nafion-based solid-state gas sensors: Pt / Nafion electrodes prepared by an impregnation-reduction method in sensing oxygen

The influences of the reductant concentration of NaBH₄ and the quantity of Pt loading on the active surface area and the sensitivity of the Pt/Nafion electrodes prepared by an impregnation-reduction method in detecting oxygen were investigated in this study. The Pt/Nafion electrodes with a Pt loading of 4.99 mg/cm², obtained at 0.0107 M Pt(NH₃)₄Cl₂ and 0.06 M NaBH₄, show maximum sensitivities of 0.0528 A/ppm and 0.0538 A/ppm obtained in O₂ concentration regions of 0–5000 and 5000–50 000 ppm, respectively. A sensing model was also proposed to illustrate the sensing phenomenon. Received: 21 January 1998 / Accepted: 10 March 1998     

Reactive groups on polymer-covered electrodes

Polythiophene films containing ester groups on the surface of electrodes are interesting potential carrier materials for reagents. Methyl thiophene-3-acetate (3) can be copolymerized with 3-methylthiophene (1) and 3-butylthiophene (2) by means of cyclic voltammetry (CV) at potentials of 0–2.2 V. Higher potentials (0–2.4 V) lead to overoxidation of the copolymers. The ester groups were confirmed by FTIR spectra. Electrochemical investigations of 2,2′-bithiophene (6) and 3 at equimolar ratios showed no successful copolymerization at potentials of 0–1.3 V. If the copolymerization experiments of 6 with 1 or 3 were carried out at molar ratios of 1:50 at 1.3 V, 6 with its low oxidation potential was polymerized without copolymerization of the other monomers. However, if the oxidation potential was increased stepwise from 1.3 V, the oxidation of 1 or 3 occurred, forming copolymers containing both monomer components. HPLC investigations of solutions containing mixtures of 6 and 3 and also 6 and 1 in acetonitrile/TEABF₄ showed, after exhaustive oxidation at a potential of 1.3 V, the complete absence of 6; 1 and the ester 3 were not oxidized and copolymerized at these potentials. From the results of the copolymerization experiments, as well as the HPLC investigations, it can be concluded that the dominant mechanism of the electrochemical polymerization is radical cation dimerization. Received: 21 August 1998 / Accepted: 11 January 2000     

Transition-state structures for describing the enzyme-catalyzed mechanisms of rubisco

The carboxylation and oxygenation processes of a model substrate, 3,4-dihydroxy-2-pentanone, have been theoreticaly characterized as a set of steps, mimicking the corresponding reactions of D-ribulose-1,5-bisphosphate catalyzed by rubisco. A theoretical characterization is carried out of transition-state structures and possible molecular intermediates represented as saddle points of index 1 and minimum energy structures, respectively. The quantum chemical characterization, at the HF/3-21G calculation level, of these stationary points is used to rationalize and to discuss both catalyzed sequences. The reported set of these stationary points maps out most experimental aspects of the reaction pathways for the real system. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 10 December 1998     

Ab initio MO study of ethylene insertion into the Sm–C bond of H2SiCp2SmCH3

Ethylene insertion into the Sm–C bond of H₂SiCp₂SmCH₃, a model reaction of an olefin polymerization propagation step, has been studied by ab initio molecular orbital methods. The small electronegativity of the Sm atom makes the Sm–C bond ionic, the methyl group being negatively charged by −0.75. The reaction passes through a loose ethylene complex with a binding energy of 15 kcal/mol and then a tight four-centered transition state with an agostic interaction between the Sm atom and one of the methyl CH bonds. A small activation energy of 14 kcal/mol is required to pass through this transition state, indicating that this is an easy reaction. Compared with the reactions with group 4 cationic silylene-bridged metallocenes the activation energy is higher and the reaction is less exothermic. The origin of these differences is discussed. The results of molecular mechanics calculations on regio- and stereoselectivities in the insertion reaction of propylene are also reported. Received: 13 July 1998 / Accepted: 28 August 1998 / Published online: 2 November 1998     

X-Ray Diffraction and Raman Spectroscopic Study of Bis-(Pyridine Base) Complexes of Cadmium(II) Halogenides

Summary.  The molecular structures of bis-(pyridine base) complexes of cadmium(II) chloride and bromide, where the pyridine base is pyridine ( py), 3-methylpyridine (3-Me-py), 4-methylpyridine (4-Me-py), and 4-ethylpyridine (4-Et-py), were investigated by means of single-crystal X-ray diffraction and Raman spectroscopy. The crystal structures of CdCl₂ py ₂ (1), CdCl₂(3-Me-py)₂ (2), and CdCl₂(4-Me-py)₂ (3) were determined. All crystals are monoclinic; 1: a = 17.784(2), b = 8.666(1), c = 3.8252(7) ?, β = 91.54(1)°, space group: P2₁/n; 2: a = 11.89(1), b = 14.41(1), c = 3.874(6) ?, β = 92.3(1)°, space group: P2₁/a; 3: a = 21.091(2), b = 3.8884(5), c = 18.2317(3) ?, β = 113.64(1)°, space group: C2/c. The structures were refined to R/R _w values (%) of 3.2/5.5, 3.0/5.0, and 3.4/5.1 for 1–3. All cadmium atoms are octahedrally coordinated with the chloride ions forming infinite di-μ-chloro polymeric linear chains and the nitrogen atoms of the pyridine base in trans configuration. The Cd chains are oriented along the c-axis in 1 and 2 and along the b-axis in 3. The crystal structures indicate the absence of a peculiar interaction between the polymeric chains. The Raman spectra of eight complexes were measured in the range of 550–50 cm⁻¹, and the Raman peaks originating from cadmium-halogen vibrations were assigned. The Raman spectra of 1 and 2 are quite alike in the lattice mode vibration region. The resemblance of the cadmium-halogen vibration peaks indicates the same halogenide ion bridged octahedral structure for all complexes. Received March 27, 2001. Accepted (revised) June 19, 2001