Scaling of some chemical properties of tetrahedral and octahedral molecules plus almost spherical C and B cages

It is shown that for tetrahedral and octahedral molecules the quantity a R _e /N ^1/3 is quadratic in the ratio z/N, where R _e is the equilibrium bond length, ze is the central charge and N is the total number of electrons. Some scaling properties for the ‘breathing’ force constant k are proposed for a series of 5 tetrachlorides.     

The Effect of an Electric Field on Reaction Fronts in Autocatalytic Systems

The effects of applying a constant electric field E to an ionic autocatalytic reaction with a general power p (p≥1) are discussed through a consideration of the equations for the corresponding travelling waves. It is shown that, when the ratio of diffusion coefficients D of autocatalyst and substrate is less than some value D₀ (which depends on p), the effect of a negative electric field is to increase the wave speed of the reaction front over its field-free value. This is in contrast to previous results for cubic autocatalysis (p=2) [J.H. Merkin and H. Ševčíková. J. Math. Chem. 25 (1999) 111.] for D>D₀, where the effect is to decrease the wave speed. This feature, seen in the numerical solutions of the travelling wave equations, is confirmed by an expansion for small E and in an asymptotic analysis for p large     

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.     

Studies of viscous antagonism,excess molar volume and isentropic compressibility in aqueous mixed solvent systems at different temperatures

Using experimental data for the melting temperature T _m for four Li halides (F to I), it is demonstrated that T _m Z ^1/3 is close to constant, ? (2530 ± 250) K, where Z is the atomic number of the halogen. This formula is not appropriate for what sometimes is considered the simplest halide, LiH, and therefore alternatives are investigated which involve a characteristic electrostatic energy e ²/εs, with s the internuclear separation and ε the static dielectric constant.     

Statistical thermodynamics of networks at large deformations

A general theory of non-Gaussian elasticity is presented for real polymeric chains having fixed bond angles and restricted internal rotations. The theory contains the displacement-vector distribution given by Nagai, and the Flory-Wall-Hermans procedure is used for the calculation of network properties. Whereas the treatment is valid for all types of polymer chains, it is not totally satisfactory from a practical standpoint because of a slow series convergence if the chains are stiff. It is best utilized for flexible polymers under conditions of light crosslinking. Detailed network behavior is investigated only for polyethylene type chains having uncorrelated internal rotations. In this instance the fractional contribution f_e/f of the internal energy of the total force f is found to be a function of elongation at high degress of stretching. It may decrease, or increase, depending upon the sign of f_e/f at low elongations. Furthermore, the variation of f_e/f with elongation is independent of the fixed bond angle of the chain backbone. Stress–strain behavior and energy–strain behavior are in opposition, i.e., when the non-Gaussian contribution to the stress is greatest, it is the least for the ratio f_e/f, and vice versa. The presence of correlated internal rotations would not be expected to greatly alter these general conclusions.     

Additive moduli for crosslinked epoxies

Ultrasonic measurements were made on a series of eight crosslinked polyepoxides over the temperature range from 0 to 60°C at a frequency of 2 MHz. From these measurements the bulk (K) and shear (G) moduli were calculated. These data were then analyzed in terms of molecular component properties. Proceeding by analogy with Rao's rule for liquids, the authors found that K is not an additive property but the function U = V(K/ρ)^1/2γ is an additive property. Here V is molar volume, ρ is the density, and γ is the Gruneisen parameter (for interchain vibrations). A similar relation was found to hold for shear modulus. In particular, G is not an additive property but W = V(G/ρ)^1/2g is an additive property, where g = (1/2α) (? InG/?T)_p – 1/2 is the shear analog of the Gruneisen parameter. Using U and W, calculations were made of K and G as functions of temperature for the eight epoxies. These results agree with the measured values within the experimental uncertainty of the measurements.     

Depolarization field effect on the ferroelectric behavior of polymers

The effect of the depolarization field in crystallites on the ferroelectric behavior of polymers is discussed on the assumption that the crystallite is a prolate ellipsoid with its major axis directed along the electric field. The theory relates the polarization P and the electric field E in the crystallite to the overall values P and E for the polymer. The determination of the P -E hysteresis of a crystallite from the P-E hysteresis is given with examples for poly(vinylidene fluoride) (PVDF) and vinylidene fluoride (VDF)–trifluoroethylene (TrFE) copolymer. The ratio R = J/(P_s ? P), with J the switching current density and P_s the saturation polarization of polymer, is proved to be free from the depolarization field effect and the plot of logR against logarithmic time is shown to have merit for characterization of switching behavior. Examples of the curves are given for PVDF and VDF-TrFE copolymers. The temporal change of local electric field in the unreversed domains in the crystallite in the course of polarization reversal is predicted by the theory and this change is proved to be a significant mechanism of switching acceleration.     

Axial force fluctuations in long-chain molecules

The fluctuations Δf in the axial force f acting on a long-chain molecule whose end-to-end displacement r is fixed are computed for a freely jointed model in which the covalent bonds are represented by stiff linear springs. It is found that the relative fluctuation Δf/f remains large regardless of the length of the chain. A time-dependent computer simulation of the model serves both to verify the theoretical calculation of Delta;f and to provide physical insight. The result helps to clarify the difference in behavior of the strain ensemble (r is fixed and f fluctuates) and the stress ensemble (f is fixed and r fluctuates) for which, in the absence of excluded volume, the strain ensemble predicts that f = 0 for r = 0, while for the stress ensemble with f = 0 it is found that 〈r²〉₀ > 0.     

Prediction of microstructures for polydisperse block copolymers,using continuous thermodynamics

A generalization of an earlier theory (Leary–Henderson–Williams) developed for microphase separation in monodisperse block copolymers is made for copolymers having moderate degrees of polydispersity and illustrated for the Schultz molecular weight distribution (MWD). First, an explicit study is made of molecular weight (M) effects for monodisperse poly (styrene–butadiene) diblock (SB) and triblock (SBS) copolymers. For a fixed temperature, it is shown how the critical molecular weight (M_c)—above which the copolymer is phase-separated at equilibrium —varies with molecular composition (?_S, volume fraction of S component) for both molecular architectures. Also predicted are the microstructural parameters ΔT(M) and f(M)—interphase thickness and volume fraction, respectively—and the high-M limiting functions ΔT ∝? M^α2, f ∝? M^α3, D ∝? M^α4 (D is domain repeat distance) and T_s ∝? M^α5 (T_s is separation temperature). Then, for polydisperse systems in the range 1 ? p ? 3 ( where \[ P = \bar M_w /\bar M_n \] ) corresponding predictions at constant \[ \bar M_n \] are made after identifying the mixture free-energy-minimum state with a weight average of the free energy minima of each fraction of the MWD. Calculations are made specifically for ?_S = 0.50 and T_s = 298 K. It is shown that, even when \[ \bar M_n < M_c \] , polydispersity can induce microphase separation if p is sufficiently large. Good success is obtained in comparisons of D predictions with data on blends of two polydisperse diblock samples.     

Thec logc contribution to the electrolyte conductance and Onsager's reciprocal relation

The differential equations and the boundary conditions for the nonequilibrium binary distribution function of an unsymmetrical binary electrolyte are derived from the Ebeling-Falkenhagen continuity equation. The connection between the Onsager reciprocal relation and the binary distribution functions is shown. Further, Feistel's result for thec logc contribution to the conductance is extended to unsymmetrical binary electrolytes. The reason for the difference between Feistel's and Chen'sc logc term is explained, and the significance of Onsager's reciprocal relation for the calculation ofc logc and higher-concentration contributions of the conductance is discussed.     

Ozonolysis of methyl, amino and nitro substituted ethenes: A semi-empirical molecular orbital study

The three-step ozonolysis reaction is studied for a number of methyl, amino and nitro substituted ethenes (classified as symmetrically, asymmetrically and cis/trans substituted) using the PM3 SCF-MO method. Substituent effects are predicted to generally yield the order NH₂ > Me > NO₂ for the ability to enhance facility of ozonolysis, in line with the electrophilic nature of ozone. Geometry and conformation allow for a variety of different pathways, and the lowest energy pathway is predicted for each case, with consequences for identity of the intermediates preferentially involved. Greater stability of the trans isomer of the carbonyl oxide intermediate is the main factor for its preferred involvement in the second step of the reaction. For the cis/trans substituted ethenes, the major product (the secondary ozonide) is predicted as being the cis ozonide and the trans ozonide for the cis and the trans substituted ethenes, respectively.     

Determination of theoretical plates in gel permeation chromatography by using polydisperse materials (polymers)

The need for an improved method of expressing performance of GPC columns and operating conditions is discussed. It is shown that theoretical plates can be calculated from chromatograms of high molecular weight materials (polymers) if the curve widths are normalized for polydispersity. The resulting value N, where N = 16d²(v/W)², is a useful measure of the real plate count afforded by the columns to polymers and is useful for comparison purposes. Since N does not provide absolute data on separation, it is better to use formulas for resolution and fractionation when such data are needed.     

Many-electron theory in the Waller–Hartree spin-free method

A many-electron theory is developed for the determination of pure spin state wave-functions and energies to avoid the difficulties in doing integration. The Waller–Hartree pure spin state wave-functions are very convenient for this purpose. The required explicit formulas for the values of the Waller–Hartree wave-functions Y(S, M) and ??Y(S, M) at some physical points are produced, where local orthonormal orbitals are used to simplify the calculation of ??Y(S, M). A method for the construction of these orbitals is given, and a transformation formula is also given to show the interchangability between the local energy expression and the conventional expectation energy integral.     

Some properties of the structure factor S(q) in two-dimensional classical liquids near freezing

We explore general properties of the main peak of the structure factor S(q) near the melting temperature T _melt in liquids confined in two dimensions, especially for the one component plasma model and for monatomic liquids interacting through inverse twelfth-power potentials. Those properties are the height of the peak, S(q _m), where q _m is the position of maximum in the peak, and the ratio between S(q _m) and q _m/Δq, where 2Δq is the width of the peak. The results obtained are then compared with those for similar systems in three dimensions. Other magnitude that we use to compare two-dimensional and three-dimensional simple liquids is r _m/Δr, where r _m is the position of the main peak in the pair distribution function g(r) and 2Δr is the width of that peak.     

Investigating the performance of parallel eigensolvers for large processor counts

Summary Eigensolving (diagonalizing) small dense matrices threatens to become a bottleneck in the application of massively parallel computers to electronic structure methods. Because the computational cost of electronic structure methods typically scales asO(N ³) or worse, even teraflop computer systems with thousands of processors will often confront problems withN 10,000. At present, diagonalizing anN×N matrix onP processors is not efficient whenP is large compared toN. The loss of efficiency can make diagonalization a bottleneck on a massively parallel computer, even though it is typically a minor operation on conventional serial machines. This situation motivates a search for both improved methods and identification of the computer characteristics that would be most productive to improve.In this paper, we compare the performance of several parallel and serial methods for solving dense real symmetric eigensystems on a distributed memory message passing parallel computer. We focus on matrices of sizeN=200 and processor countsP=1 toP=512, with execution on the Intel Touchstone DELTA computer. The best eigensolver method is found to depend on the number of available processors. Of the methods tested, a recently developed Blocked Factored Jacobi (BFJ) method is the slowest for smallP, but the fastest for largeP. Its speed is a complicated non-monotonic function of the number of processors used. A detailed performance analysis of the BFJ method shows that: (1) the factor most responsible for limited speedup is communication startup cost; (2) with current communication costs, the maximum achievable parallel speedup is modest (one order of magnitude) compared to the best serial method; and (3) the fastest solution is often achieved by using less than the maximum number of available processors.Pacific Northwest Laboratory is operated for the U.S. Department of Energy (DOE) by Battelle Memorial Institute under contract DE-AC06-76RLO 1830     

Compact contracted basis sets for third-row atoms: Ga–Kr

The (14s11p5d) primitive basis set of Dunning for the third-row main group atoms Ga-Kr has been contracted [6s4p1d]. The core functions have been relatively highly contracted while those which represent the valence region have been left uncontracted to maintain flexibility. Calculations with the [6s4p1d] contraction are reported for a variety of molecules involving third-row atoms. This basis set is found to satisfactorily reproduce experimental properties such as geometric configurations, dipole moments, and vibrational frequencies for a range of molecules. Comparisons are made with the performance of the uncontracted basis set. Polarization functions for the contracted basis set are reported and performance of the basis set with and without polarization functions is examined. A relaxation of the [6s4p1d] contraction to [9s6p2d] for higher level evergy calculations is also presented.     

Carbon-13 NMR studies of quinolines and isoquinolines. II. Chlorine–nitrogen interactions and N-oxide effects

Carbon-13 chemical shift assignments are reported for four chloroquinolines, six chloroisoquinolines, one dichloroquinoline, four dichloroisoquinolines, four methylchloroquinolines, two methylchloroisoquinolines, quinoline N-oxide, isoquinoline N-oxide, five methylquinoline N-oxides, two methylisoquinoline N-oxides and three chloroisoquinoline N-oxides. Chlorine substituent chemical shift (SCS) effects are reported for the alpha, ortho, meta, para and peri positions. Consistent patterns are observed for the para and peri positions, a vinylogous ortho pattern is reported and the additivity of these SCS effects is demonstrated. Alpha SCS effects vary widely from 1.1 ppm upfield in 1-chloroisoquinoline to 6.7 ppm downfield in 4-chloroquinoline. These results, together with those in the literature, permit the definition of steric and nitrogen lone-pair contributions which modify the ‘normal’ chlorine SCS effect, and these modifying contributions are shown to be roughly additive. Large (6–16 ppm) upfield shifts are observed for the carbons ortho and para to the N-oxide group. The individual magnitudes of these shifts and their sum are constant and the effects are additive in substituted systems. A 9.5 ppm upfield shift is also observed for C-8 in quinoline N-oxides which is attributed to a space–charge interaction. Substituent chemical shift (SCS) effects for the chloro and methyl groups and the chemical shifts of the methyl carbons are essentially the same in the N-oxides as in the parent heterocycles and are additive, except for those molecules where the substituent is adjacent to the N-oxide moiety, in which cases substantial interactions are observed.     

Acid Dissociation Behaviour and Complexation with Nickel(II), Copper(II) and Zinc(II) for Two Conformational Isomers of Dicyclohexylcyclam

Abstract

Acid dissociation constants for two conformational isomers of dicyclohexylcyclam, cis-anti-cis, (P) and cis-syn-cis, (N) have been determined at 25, 35 and 40°C, and thermodynamic data are estimated. It was found that (N) shows very different behaviour from (P). Stability constants of (P) and (N) toward Ni(II), Cu(II) and Zn(II) have been determined by pH-titration at 25°C by using a ligand exchange reaction. It is found that the (P) complex is more stable for Ni(II) and the (N) complex is more stable for Cu(II). Contributions of the cyclohexyl group to the macrocyclic effect (ME) have been also estimated by considering basicity corrections. It is found that substitution of the cyclohexyl group in cyclam increases ME only for the Ni(II) complex of (P).     

Rényi and Tsallis entropies of the Dirichlet and Neumann one-dimensional quantum wells

A comparative analysis of the Dirichlet and Neumann boundary conditions (BCs) of the one-dimensional (1D) quantum well extracts similarities and differences of the Rényi R(α) as well as Tsallis T(α) entropies between these two geometries. It is shown, in particular, that for either BC the dependences of the Rényi position components on the parameter α are the same for all orbitals but the lowest Neumann one, for which the corresponding functional R is not influenced by the variation of α. Lower limit α _TH of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where momentum entropies exist crucially depends on the position BC and is equal to 1/4 for the Dirichlet requirement and 1/2 for the Neumann one. At α approaching this critical value, the corresponding momentum functionals do diverge. The gap between the thresholds α _TH of the two BCs causes different behavior of the Rényi uncertainty relations as functions of α. For both configurations, the lowest energy level at α = 1/2 does saturate either type of the entropic inequality, thus confirming an earlier surmise about it. It is also conjectured that the threshold α _TH of ½ is characteristic of any 1D non-Dirichlet system. Other properties are discussed and analyzed from the mathematical and physical points of view.