Subduction of Q-conjugacy representations and characteristic monomials for combinatorial enumeration

A new method of combinatorial enumeration is presented. The subduction of Q-conjugacy representations gives a characteristic subduction table and a characteristic monomial table. A cycle index is defined on the basis of such monomials and used for combinatorial enumeration of isomers. Received: 10 October 1997 / Accepted: 13 February 1998 / Published online: 17 June 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     

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 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     

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     

Anodic oxidation of 2-aminofluorene in CH2Cl2 + 0.2 M Bu4NBF4: electrochemical behaviour of the derived oxidation products

The physicochemical properties and electrochemical behaviour of products obtained by anodic oxidation of 2-aminofluorene in CH₂Cl₂ + 0.2 M Bu₄NBF₄ are presented together with the oxidation conditions. Received: 8 January 1998 / Accepted: 21 September 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     

Electron affinities, excitation energies and ionization potentials of the transition metals (I) Sc and Ti

The electron affinities of the Sc and Ti atoms have been obtained by configuration interaction calculations. Energy convergence with respect to the systematic expansion of both the one-electron basis set and the configuration space was investigated for valence electrons, and the inclusion of correlation contributions from core electrons and relativistic effects gave the electron affinities of 0.181 eV and 0.163 eV for Sc and Ti, respectively. These are in excellent agreement with the observed values of 0.189 ± 0.020 eV and 0.080 eV. The same approach was applied for the first excited states and positive ions of both atoms. Excellent agreement with the experimental results was also obtained for these states. Received: 16 February 1998 / Accepted: 2 April 1998 / Published online: 23 June 1998     

Theoretical study of the valence π → π* excited states of polyacenes: anthracene and naphthacene

The valence π → π ^* excited states of anthracene and naphthacene are studied with multireference perturbation theory with complete active space self-consistent field reference functions. The predicted spectra provide a consistent assignment of all one- and two-photon spectra and T-T spectra of low-lying valence π → π ^* excited states of anthracene and naphthacene. The present theory predicts the valence π → π ^* excitation energies with an accuracy of 0.15 eV for anthracene and of 0.25 eV or better for naphthacene. The excited states of anthracene and naphthacene are compared with those of benzene and naphthalene studied previously. The present calculations predict that, going from anthracene to naphthacene, there is a symmetry reversal of the two lowest singlet state transitions, but not for the triplet, just as indicated by the experimental data. Some general trends of polyacene excited states are discussed based on the calculated results for benzene to naphthacene. Conclusive results obtained for anthracene and naphthacene can be used as a model for understanding the excited states of larger polyacenes. Received: 22 April 1998 / Accepted: 6 July 1998 / Published online: 28 September 1998     

Structure and stabilities of (HA1NH)n (n = 2–4)

Ab initio molecular electronic structure methods have been used to study the relative stability of the planar inorganic ring (HAlNH)_n (n = 2–4) during homodesmotic and monomer polymerization reactions. Optimized geometries, frequencies and energies through restricted Hartree-Fock/6-31G* are reported, and energies at the self-consistent field optimized geometries including M?ller-Plesset fourth perturbation theory with single, double and quadruple excitation (MP4SDQ) corrections are also reported for both reactions. Homodesmotic reactions with MP4SDQ −28.5 kcal/mol for (AlN)₂, 1.9 kcal/mol for (AlN)₃ and −0.97 kcal/mol for (AlN)₄. On analysing a π-molecular orbitals diagram, only one, three and three strongly bonding π-molecular orbitals exist for the planar four-, six- and eight-membered AlN rings, respectively. Received: 9 March 1998 / Accepted: 19 March 1998 / Published online: 23 June 1998     

Examining ligand-protein interactions with binding-energy landscapes

Binding-energy landscapes are used to investigate the thermodynamics of molecular recognition for the pteridine ring, a recognition anchor in binding with dihydrofolate reductase, and two molecules with the same shape but different heteroatom substitutions. The relative importance of hydrogen bonding and hydrophobic interactions in this system is analyzed by comparing these three different decorations of the pteridine scaffold. Received: 5 May 1998 / Accepted: 3 September 1998 / Published online: 17 December 1998     

RISM-SCF study of the free-energy profile of the Menshutkin-type reaction NH3+CH3Cl→NH3CH3++Cl− in aqueous solution

The free-energy profile for the Menshutkin-type reaction NH₃ + CH₃Cl → NH₃CH₃ ⁺ + Cl⁻ in aqueous solution is studied using the RISM-SCF method. The effect of electron correlation on the free-energy profile is estimated by the RISM-MP2 method at the HF optimized geometries along the reaction coordinate. Solvation was found to have a large influence on the vibrational frequencies at the reactant, transition state and product; these vibrational frequencies are utilized to calculate the zero-point energy correction of the free-energy profile. The computed barrier height and reaction exothermicity are in reasonable agreement with those of experiment and previous calculations. The change of solvation structure along the reaction path is represented by radial distribution functions between solute-solvent atomic sites. The mechanisms of the reaction are discussed from the view points of solute electronic and solvation structures. Received: 26 June 1998/Accepted: 28 August 1998 / Published online: 2 November 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     

A theoretical study on the first ionic states of vinyl fluoride, vinyl chloride, trifluoroethylene, and trichloroethylene with an analysis of the vibrational structures of the photoelectron spectra

Ab initio calculations have been performed to study the molecular structures and the vibrational levels of the first ionic states of vinyl fluoride, vinyl chloride, trifluoroethylene, and trichloroethylene. The equilibrium molecular structures and vibrational modes of these states are presented. The theoretical ionization intensity curves including the vibrational structures are also presented and compared with the photoelectron spectra. Received: 11 September 1998 / Accepted: 13 October 1998 / Published online: 1 February 1999     

Possible long-lived quartet resonance states of CO−

Two states of CO⁻ which are expected to live longer than the well-known ²Π shape resonance are examined and the results obtained are compared with the analogous states of the isoelectronic N₂ ⁻ system. The ⁴Σ⁻ and ⁴Π states are found to be stable with respect to dissociation. The latter state is also stable with respect to single-electron loss to its parent neutral state. The lifetime of this state is supposed to be long, but not necessarily long enough to allow detection in a mass spectrometer. Received: 28 May 1998 / Accepted: 23 July 1998 / Published online: 9 October 1998     

A new “hydrophobic template” method detects segments forming transmembrane α-helical bundles in ion channels

We present a “hydrophobic template” method enabling recognition of α-helix bundles in membrane channels from sequence analysis. Inspection of hydrophobic properties of pore-forming helices in proteins with known structure (A-B₅ toxins) permits delineation of a common polarity motif: two hydrophobic surface stretches separated by polar areas. The bundles are stabilized by nonpolar interhelical contacts. A number of transmembrane segments were checked for presence of this motif, and it was detected for pore-forming helices of several ion transporters (segments M2 of acetylcholine and GABA_A receptors, α5 peptide of δ-endotoxin), which reveal five α-helix bundle architecture. Applications of the method to modeling of membrane channels are discussed. Received: 24 April 1998 / Accepted: 3 September 1998 / Published online: 7 December 1998     

A theoretical study of substituent effects on the structure of isolated and condensed three-membered rings. A comparison between radicals and parent hydrocarbons

Substituent effects on the structure of radicals and parent hydrocarbons formed by isolated or condensed three-membered rings have been investigated by Hartree-Fock, post-Hartree-Fock and density functional methods. The trends of structural parameters computed for the hydrocarbon systems are in agreement with available experimental data. Substituent effects can be rationalized in terms of interactions between localized orbitals obtained by natural bond analysis. The effects are even larger in free radicals and can be analyzed using the same model. Received: 13 March 1998 / Accepted: 13 July 1998 / Published online: 9 October 1998     

The catalyzed hydrosilation reaction: substituent effects

Ab initio electronic structure calculations using MP2 wavefunctions have been used to investigate a reaction path for the hydrosilation reaction catalyzed by divalent titanium [modeled by TiH₂, TiCl₂, and Ti(C₅H₅)₂]. Optimized structures and energies are presented. All model reactions predict a barrierless reaction path compared to a barrier of 78 kcal/mol for the uncatalyzed reaction. Received: 11 August 1998 / Accepted: 3 September 1998 / Published online: 23 February 1999     

A theoretical investigation of (−)-deprenyl (selegiline) as a radical scavenger

The chemical reactions between (−)-deprenyl and ·OH or ·OOH were studied using molecular orbital theory, with N,N-dimethylpropargylamine as a model. (−)-Deprenyl was confirmed to be a good radical scavenger. The active site was the acetylenic part and ·OH- or ·OOH was trapped on either acetylenic carbon. The activation energies were about 10–20 kcal/mol. The resulting ·OH- or ·OOH-adducts, still radicals, trapped further radicals on the remaining carbon of the acetylenic part. The final double trapping products were at extraordinarily lower energy levels than the original reactants by 50–70 kcal/mol. The secondary transition states were not detected, suggesting that the reactions occurred at once or in a cascade. Some results with the model system were verified by the results with the real (−)-deprenyl system. Received: 6 October 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000