Spin-free quantum chemistry. XXVI. The Ising,small-bipolaron theory of cuprate superconductivity

The Ising, small-bipolaron (ISB ) theory is a strong-coupling theory of cuprate superconductivity which is based on the negative-U, Hubbard Hamiltonian. Its ground state is composed of (small) bipolarons and (small-bipolaron) holes with a vibronically induced, bipolaron-hole exchange interaction, J_BH, between them. The energy gap, Δ(0), is taken to be equal to the dissociation energy of a small bipolaron and which, since it is defined spectroscopically, is not an order parameter. The application of the Ising mean-field theory to the highly degenerate ground-state yields a second-order phase change with kT_C/2 = J_BH and a real order parameter, Ω(T), which is valid over the entire temperature range from zero to T_C. Near T_C, the Ising free-energy functional takes the same form as does the Landau. In the presence of an electromagnetic field, the Ising functional is a generalization of the Ginzburg-Landau functional which employs a complex order parameter and which is invariant under the electromagnetic gauge transformation. The breaking of the gauge invariance yields the London theory of superconductivity. © 1996 John Wiley & Sons, Inc.     

Lattice dynamics with second neighbor interactions. II. Green's formula

A satisfactory definition of spectral density for the normal modes of lattice dynamics problems requires the study of singular recurrence relations which is carried out in detail for one-dimensional chains with pth neighbor interactions. The relationship of transfer matrices to the dynamical matrix is explored in order to obtain Green's formula. By using Green's formula, a mapping is defined between V_n, whose basis is formed from the normal modes of vibration of an n-particle chain, and V_2p, which is the space of boundary conditions for the recurrsion equations. Most of the properties of this mapping may be deduced from a symplectic bilinear form in V_2p which is associated with the Hermitean inner product in V_n. This symplectic form defines a geometry which is invariant under the recursion relation, as well as canonical initial and boundary conditions, and a maximal isotropic subspace which may be used to determine square summability of the normal modes and the spectral density in the limit as the number of particles becomes infinite.     

4,4′‐Bipyridine as a Unidirectional Switching Unit for a Molecular Pushing Motor

A chirality switch in which the intrinsic chirality of a 4,4′‐bipyridine is combined with a metal‐ion‐induced switching principle is described. In the uncomplexed state the 4,4′‐bipyridine unit, which is linked to an S,S,S,S‐configured cyclic imidazole peptide, is P‐configured. The addition of zinc ions leads to a rotation around the C?C bond axis of the 4,4′‐bipyridine and the M isomer of the metal complex is formed. By addition of a stronger complexing agent the metal ions are removed and the switch returns to its initial position. The combination of the chirality switch with a second switching unit allows the construction of a molecular pushing motor, which is driven chemically and by light.     

Effect of Cluster Deformations in the DLCA Modeling of the Sol-Gel Process

The diffusion limited cluster-cluster aggregation (DLCA) model is modified by including cluster deformations during aggregation, with a tuning flexibility parameter F. A three-dimensional computer simulation is presented, which starts from a collection of f-functional monomers randomly distributed in a cubic box with a volumic fraction c (concentration) and which uses the highly efficient bond fluctuation algorithm to describe the cluster deformations. It is shown that, for F 0, there exists a well defined threshold value of the volumic fraction below which the realization of all intra-aggregate bonding possibilities prevents the formation of a gelling network. For c > c _g , a true sol-gel transition occurs at a characteristic time t _g , after which an infinite cluster (which is self connected via the boundary conditions) appears. In contrast to DLCA, t _g does not increase as the box size increases. The transition at c _g is characterized by a divergence of the final clusters size for c<c _g and a divergence of the gel time for c>c _g . Several other numerical results are reported.     

THE OVERALL KINETICS OF FREE RADICAL (CO)POLYMERIZATION WITH HIGHLY DIFFUSION CONTROLLED TERMINATION

The overall reaction rate kinetics of polymerization of diethyleneglycol dimethacrylate and copolymerization of it with styrene in bulk and in the presence of inert diluents were investigated. Theresults indicated that these reactions can be treated as free radical polymerization with highly diffu-sion controlled termination reaction in which the termination rate constant is an empirically derivedfunction of monomer conversion: K_t=K_(to)(1-c ln[M]/ [M_0])~(-1) in which K_(to) is the initial terminationrate constant and c is a factor related to the magnitude of diffusion co?re The following equationof monomer conversion as a function of time could then be derived: U=1-exp {1/c [1-(1+ckt/2)~2]}in which k=K_P(R_i/2K_(to))~(1/2) and t is the time of reaction. Excellent agreement between the theoreticaland experimental overall reaction kinetic curves was obtained. The equation is valid for crosslinkingand noncrosslinking free radical polymerizations in which the self-acceleration effcct is effective fromthe very beginning of the reaction. The equation can be expressed in a more generally applicableform: U=1--exp{1/e[1--(1+?t/n)~n] in which n≥0.     

The Ising free-energy functional

We show that the Ising free-energy functional f(T, X) yields a second-order phase transition. The value of X, a generalized order parameter, which minimizes the functional is the real-order parameter, Ω = tanh[Ω(T_C/T)] where T_c = J/(2k) and J is the Ising coupling constant. The Ising theory is applicable to the second-order phase transitions in ferromagnets, ferroelectrics, and superconductors. The constant temperature slices of f(T, X) yields the Ising functional which is valid over the entire range of T and which is identical to the Landau functional for T/T_C close to unity. © 1996 John Wiley & Sons, Inc.     

Kinetics analysis of the isothermal crystallization of Cu55Zr45 metallic glass by differential scanning calorimetry

The crystallization kinetics of Cu₅₅Zr₄₅ (at%) glassy alloy is studied under isothermal condition using differential scanning calorimetry (DSC). The plot of correlation between the crystallized volume fraction α and annealing time t shows a sigmoid-type curve, which is steeper with higher annealing temperature. Furthermore, in isothermal crystallization condition, local activation energy E_α values, determined using the Arrhenius equation, range from 181.1 to 187.8 kJ/mol, which is nearly a constant. The local Avrami exponent n(α) values, obtained by the Johnson-Mehl-Avrami equation, which range from 2.2 to 4.0 at different annealing temeperatures, which indicates that the crystallization mechanism is diffusion-controlled transformation. Moreover, n(α) becomes greater with increasing annealing temperature, which indicates that annealing temperature can affect nucleation rate and growth type.     

Symmetry properties of chemical graphs. V. Internal rotation in XY⋅3XY⋅2XY3

Structures XY?₃XY?₂XY₃ of symmetry C_2v (of which propane is an example) are examined and the rearrangement due to the internal rotation of the end groups XY₃ studied. The isomerization graph is constructed, various forms of which are displayed and the symmetry of which has been determined. The order of the group is 72. There are nine prime (irreducible) representations (4A + E + 4G) with the following partitioning of the elements into classes: 1, 4², 6², 9, 12², 18. When the mechanism for rearrangement is generalized to include enantiomers, a duplex graph is produced with the order of the group 144 which is isomorphic to the group S₂(S₃,S₂) (generalized wreath product of the symmetric group S₂ and S₃). The corresponding graph has been constructed and displayed in one of more symmetrical forms. Isomorphism of groups of order 144 is discussed and a procedure is outlined in which correspondence between distinctive combinatorial objects is established by inducing permutations of m elements from available permutations of n elements. The scheme is based on selection of suitable graph invariants in one system and their labeling as m objects which form the basis for representation of the symmetry for the other system.     

Moderately concentrated solutions of polystyrene. II. Integrated-intensity light scattering as a function of concentration,temperature, and molecular weight

Integrated-intensity light scattering data are reported for moderately concentrated solutions of polystyrene in benzene and in cyclopentane. The benzene system is one for which the second virial coefficient A₂ is large; data obtained over the range 0.5 < A₂Mc < 30, with c the polymer concentration, are analyzed in terms of the (extrapolated) intensity at zero angle and the angular dependence of the intensity. The former is discussed in terms of power law representations based on scaling relations, which are found to represent the data. The latter is discussed in terms of the dependence of the chain dimensions on concentration. With cyclopentane, the behavior is similar for temperatures for which A₂ is near its maximum, but for T near either Θ_U or Θ_L, for which A₂ is zero or small, the angular dependence of the scattering is distinctly different, with the intensity exhibiting a maximum as a function of scattering angle.     

Effect of surfactant adsorption time on the observation of Newton black film in foam film

Observation of Newton black film (NBF) in foam film is possible only with a certain probability W which depends on the concentration C of surfactant in the solution and on the time t_a during which adsorption of surfactant at the solution/air interface has taken place. In the paper, the W(C,t_a) dependence is derived and used to analyze the effect of t_a on the critical surfactant concentration C_c below which NBF in foam film practically cannot be observed. An expression for the C_c(t_a) function is obtained which reveals that C_c decreases substantially with increasing t_a. This expression is found to describe well experimental C_c(t_a) data for foam films obtained from aqueous solution of the therapeutic surfactant INFASURF.     

What to Learn from a Comparative Genomic Sequence Analysis of <Emphasis Type="Italic">L</Emphasis>-Carnitine Dehydrogenase

Summary. In contrast to eukaryotic cells certain eubacterial strains have acquired the ability to utilize L-carnitine (R-(–)-3-hydroxy-4-(trimethylamino)butyrate) as sole source of energy, carbon and nitrogen. The first step of the L-carnitine degradation to glycine betaine is catalysed by L-carnitine dehydrogenase (L-CDH, EC 1.1.1.108) and results in the formation of the dehydrocarnitine. During the oxidation of L-carnitine a simultaneous conversion of the cofactor NAD⁺ to NADH takes place. This catabolic reaction has always been of keen interest, because it can be exploited for spectroscopic L-carnitine determination in biological fluids – a quantification method, which is developed in our lab – as well as L-carnitine production.Based on a cloned L-CDH sequence an expedition through the currently available prokaryotic genomic sequence space began to mine relevant information about bacterial L-carnitine metabolism hidden in the enormous amount of data stored in public sequence databases. Thus by means of homology-based and context-based protein function prediction is revealed that L-CDH exists in certain eubacterial genomes either as a protein of approximately 35 kDa or as a homologous fusion protein of approximately 54 kDa with an additional putative domain, which is predicted to possess a thioesterase activity. These two variants of the enzyme are found on one hand in the genome sequence of bacterial species, which were previously reported to decompose L-carnitine, and on the other hand in gram-positive bacteria, which were not known to express L-CDH. Furthermore we could not only discover that L-CDH is located in a conserved genetic entity, which genes are very likely involved in this L-carnitine catabolic pathway, but also pinpoint the exact genomic sequence position of several other enzymes, which play an essential role in the bacterial metabolism of L-carnitine precursors.     

Rhombohedral boron subnitride,B13N2, by X‐ray powder diffraction

The structure of the title compound consists of distorted B₁₂ icosahedra linked by N—B—N chains. The compound crystallizes in the rhombohedral space group Rm (No. 166). The unit cell contains four symmetry‐independent atom sites, three of which are occupied by boron [in the 18h, 18h (site symmetry m) and 3b (site symmetry m) Wyckoff positions] and one by nitrogen (in the 6c Wyckoff position, site symmetry 3m). Two of the B atoms form the icosahedra, while N atoms link the icosahedra together. The main feature of the structure is that the 3b position is occupied by the B atom, which makes the structure different from those of B₆O, for which these atom sites are vacant, and B_4+xC_1−x, for which this position is randomly occupied by both B and C atoms.     

Synthesis of Glycosyl Azides by the Addition of Phenylselenenyl Azide to Glycals

Abstract

The addition of phenylselenenyl azide to glycals is carried out under conditions that give 2-deoxy-2-phenylselenoglycosyl azides. This regiochemistry is opposite to that obtained under free-radical conditions, which are known to produce 2-azido-2-deoxyselenoglycosides. The addition reaction is carried out with phenylselenenyl chloride and sodium azide in dimethylformamide, and is stereoselective for trans addition. Tri-O-benzyl-d-glucal and di-O-benzyl-l-rhamnal each gave two addition products, in which the phenylselenyl and azido groups were either trans diaxial or trans diequatorial. Tri-O-benzyl-d-galactal gave only the trans diaxial addition product.     

Neutron scattering by liquid crystals. A new analysis

Abstract

This paper presents a new analysis of all (old and new) quasi-elastic neutron scattering results obtained for seven members of the PAA series (n = 1,…, 7). The analysis is based upon a discussion of the parameter p, which is the deviation of the intensity of the elastic component from the intensity demanded by a reorientational model. If the value of this parameter is negative, it may be interpreted as an indication of an additional motion which has not been taken into account in the model. The first model analysed in this way for all seven substances in the nematic phase was that of the rotational diffusion of the whole molecule in its stretched (trans) conformation, around the long axis. A very large negative values of p (p ? -60 per cent) was obtained, clearly showing that some motions have been neglected. The second model was that of the rotational diffusion of moieties consisting of benzene rings plus alkoxy side-chains. The diffusion occurs around the benzene para-axes, and the alkoxy side-chains are assumed to be in their trans conformations. Less negative values of p (p ? -10 per cent) were obtained, indicating that other motions still exist. Since these must take place in the alkyl chains, we make a third step in the analysis, in which we retain the second model but now take substances which are alkyl-deuterated (which means masking for the neutron incoherent scattering method). Now values of p which are nearly zero are obtained which means that the motions previously ignored indeed exist in the alkyl chains. An even-odd effect observed in the dependence of p on n indicates that even molecules are more mobile than odd ones, probably due to less steric hindrance in more ordered, even substances.

A critical discussion on reorientational correlation times is also presented.     

Chemical applications of topology and group theory

This paper characterizesforbidden polyhedra, which are polyhedra with fewer than 9 vertices which cannot be formed using only the 9s,p, andd atomic orbitals. In this connection polyhedra are of particular interest if their symmetry groups are direct product groups of the typeR × C′ _s in whichR is a group containing only proper rotations andC′ _s is eitherC _s orC _i in which the non-identity element is an inversion center or a reflection plane which is called theprimary plane of the groupR ×C′ _s . Using this terminology polyhedra of the following types are shown always to be forbidden polyhedra: (1) Polyhedra having 8 vertices, such direct product symmetry point groups, and either an inversion center or aprimary plane fixing either 0 or 6 vertices; (2) Polyhedra having a 6-fold or higherC _n rotation axis. However, these conditions are not necessary for a polyhedron to be forbidden since in addition to one 7-vertex polyhedron and ten 8-vertex polyhedra satisfying one or both of the above conditions there are two forbiddenC _3v 8-vertex polyhedra which satisfy neither of the above conditions. For part 15 of this series see reference 1.     

On the evaluation of the characteristic polynomial of a chemical graph

The evaluation of the characteristic polynomial of a chemical graph is considered. It is shown that the operation count of the Le Verrier–Faddeev–Frame method, which is presently considered to be the most efficient method for the calculation of the characteristic polynomial, is of the order n⁴. Here n is the order of the adjacency matrix A or equivalently, the number of vertices in the graph G. Two new algorithms are described which both have the operation count of the order n³. These algorithms are stable, fast, and efficient. A related problem of finding a characteristic polynomial from the known eigenvalues λ_i of the adjacency matrix is also considered. An algorithm is described which requires only n(n ? 1)/2 operations for the solution of this problem.     

What to Learn from a Comparative Genomic Sequence Analysis of L-Carnitine Dehydrogenase

In contrast to eukaryotic cells certain eubacterial strains have acquired the ability to utilize L-carnitine (R-(–)-3-hydroxy-4-(trimethylamino)butyrate) as sole source of energy, carbon and nitrogen. The first step of the L-carnitine degradation to glycine betaine is catalysed by L-carnitine dehydrogenase (L-CDH, EC 1.1.1.108) and results in the formation of the dehydrocarnitine. During the oxidation of L-carnitine a simultaneous conversion of the cofactor NAD⁺ to NADH takes place. This catabolic reaction has always been of keen interest, because it can be exploited for spectroscopic L-carnitine determination in biological fluids – a quantification method, which is developed in our lab – as well as L-carnitine production.Based on a cloned L-CDH sequence an expedition through the currently available prokaryotic genomic sequence space began to mine relevant information about bacterial L-carnitine metabolism hidden in the enormous amount of data stored in public sequence databases. Thus by means of homology-based and context-based protein function prediction is revealed that L-CDH exists in certain eubacterial genomes either as a protein of approximately 35 kDa or as a homologous fusion protein of approximately 54 kDa with an additional putative domain, which is predicted to possess a thioesterase activity. These two variants of the enzyme are found on one hand in the genome sequence of bacterial species, which were previously reported to decompose L-carnitine, and on the other hand in gram-positive bacteria, which were not known to express L-CDH. Furthermore we could not only discover that L-CDH is located in a conserved genetic entity, which genes are very likely involved in this L-carnitine catabolic pathway, but also pinpoint the exact genomic sequence position of several other enzymes, which play an essential role in the bacterial metabolism of L-carnitine precursors.     

All-electron SCF LCAO MO calculations on various conformations of cis- and trans-stilbene

Ab initio SCF calculations of cis- and trans-stilbene at different conformations were performed using two program systems. Minimal energy is obtained for cis-stilbene when the phenyl rings are rotated by 52 ° out of the molecular plane. The deviation from planarity due to steric hindrance is smaller for the trans isomer yielding a rotational angle of 19 °. The trans isomer is calculated to be more stable by 5.7 kcal/mole than the cis isomer, confirming the experimental estimate according to which the energy of isomerization is about 3 kcal/mole. This is an improvement over semiempirical calculations which predict a lower energy for the trans configuration.     

Adiabatic perturbation theory for the degenerate case. III. Adiabatic formalism by Gell-Mann and low with an arbitrary switching function

An adiabatic formalism in the degenerate or quasidegenerate subspaces, which does not depend on the particular form of the switching function g(α, t), is outlined. A general factorization theorem for the dynamic operator S_α(t, t₀ | g) is proved. This theorem enables one to formulate the perturbation expansion for the effective Hamiltonian and the wave operator which is free from the adiabatic divergencies.