The application of strictly localized geminals to the description of chemical bonds

A theory is developed in which closed-shell molecules are viewed as systems of weakly interacting chemical bonds. Composite-particle creation operators obtained by an appropriate quasiparticle transformation are used to create the wave function of two-electron bonds. These quasiparticles are bosons, since they are composed of two electrons, but the total many-electron wave function is properly antisymmetric. The internal structure of the quasi-Bose-particles is affected by inductive interbond interactions. Delocalization and dispersion interactions between different bonds are neglected, thus the approach corresponds to a first-order many-body PT (Perturbation Theory) with a correlated, but fully localized, reference state. The whole formalism is developed ab initio. The nonorthogonality problem is handled by a biorthogonal formulation. To illustrate the effectiveness of the model, numerical calculations are reported.     

Phase diagrams of grafted molecules under external fields: A mean field model

A mean field theory is extended to investigate the phase behavior of grafted molecules under external fields. In the model, each grafted molecule contains two states, similar to the Ising model, and the applied field interacts with only one of the two states. The free energy of this model is formulated as a function of composition, field strength, and a parameter to account for the intermolecular interactions of neighboring molecules. Our calculations show that uniform fields exhibit no significant effect on phase diagrams. In contrast, linear gradient fields affect critical temperature but show no direct effect on critical composition. Under external fields with quadratic spatial gradient, both critical constants become sensitive to field direction and strength. Moreover, an analysis of field dependent critical constants suggests that quadratic fields affect miscibility and critical temperature. A brief comparison of the current model and the Ising model is also given.     

Systematic investigation of the global phase behavior of polymer-solvent systems in the density-density plane

The phase behavior of fluid mixtures is understood by the critical lines in fluid-gas diagrams. We investigated the critical lines of polymer-solvent systems at the mathematical double point, where two critical lines meet and exchange branches, and its environment within the framework of a model that combines the lattice gas model of Schouten, ten Seldam and Trappeniers with the Flory-Huggins theory. The critical lines are expressed as a function of x₁ and x₂, the density of type 1 polymer molecules and the density of type 2 polymer molecules, respectively; in this way global phase diagrams are presented and discussed in the density-density plane. Density-density plots are preferable when studying the differences in behavior of different classes, since they enable us to follow the connectivities in a systematic way. In this study the connectivity of critical lines at the mathematical double point and its around is investigated in detail. We also discuss the topology of the critical lines according to the Sadus classification scheme for ternary mixtures.     

Analysis of reduced density matrices in the co-ordinate representation. III. Electron density and correlation in the ground states of H2 and the H6 ring system within some approximations of the simple LCAO type

The electron density and spatial correlation as given by the MO , VB and AMO methods for H₂ and H₆ are studied by means of diagrams. For comparison, diagrams representing accurate wave functions for H₂ are also given. The study of model functions representing localized bonds leads to results concerning the nature of localized electron pairs in agreement with those of Lennard-Jones.     

Bent bonds, the antiperiplanar hypothesis and the theory of resonance. A simple model to understand reactivity in organic chemistry

By taking into consideration bent bonds (τ-bonds, tau-bonds), the antiperiplanar hypothesis, the classic theory of resonance, and the preference for staggered bonds over eclipsed bonds in tetrahedral systems, a simple qualitative model is presented to rationalize the conformation and reactivity for a wide range of compounds containing double bonds and/or carbonyl groups. Alkenes, carbonyl and carboxyl derivatives, conjugated systems as well as other functional groups are revisited. This also leads to a simple model to understand aromaticity, and electrocyclic reactions. The bent bond model and the antiperiplanar hypothesis provide a qualitative model for better understanding the electron delocalization and the reactivity inherent to unsaturated organic systems by an alternative view of the classic resonance theory.     

Applications of polymer rism theory to blends

Polymer RISM (reference interaction site model) theory is a theory of polymer systems in the liquid phase in which account for chemical realism can be made. Results are reported here of phase diagrams (spinodals) for blend systems calculated by means of this theory, using the mean spherical approximation as a closure. The systems investigated are an isotopic blend, a set of homopolymer/copolymer blends, and a model blend containing specific interactions.     

Electrolyte system strategies for anionic isotachophoresis with electrospray‐ionization mass‐spectrometric detection. 2. Isotachophoresis in moving‐boundary systems

This contribution is the second part of the project on strategies used in the selection of electrolyte systems for anionic ITP with ESI‐mass spectrometric detection. It presents ITP as a powerful tool for selective stacking of anionic analytes, performed in a nonconventional way in moving‐boundary systems where two co‐anions are present in both the leading and terminating zones. The theoretical background is given to substantiate the conditions for the existence and migration of ITP boundaries in moving‐boundary systems and stacking of analytes at these boundaries. The practical aspects of the theory are shown in form of stacking‐window diagrams that bring immediate information about which analytes are stacked in a given system. The presented theory and strategy are illustrated and verified on the example of analysis of a model mixture of salicylic acid, ibuprofen and diclofenac, and comparison of regular and free‐acid ITP with moving‐boundary ITP systems formed by formic and propionic acids and ammonium as counterion.     

Twist-grain-boundary phase diagrams in chiral liquid crystals

The experimental phase diagrams of several chiral systems are compared with a theoretical diagram based on the chiral Chen-Lubensky model, which predicts at least two kinds of twist-grain-boundary phase, TGBA and TGBC. Also shown for comparison are typical nonchiral phase diagrams that exhibit a nematic-smectic A-smectic C multicritical point. Several aspects of experiment and theory agree, but there appear to be common experimental features that differ from those predicted by current theory.     

Ab initio correlation corrections to the Hartree-Fock quasi band-structure of periodic systems employing Wannier-type orbitals

A size-consistent ab initio formalism to calculate correlation corrections to ionization potentials as well as electron affinities of periodic systems is presented. Our approach is based on a Hartree-Fock scheme which directly yields local orbitals without any a posteriori localization step. The use of local orbitals implies non-zero off-diagonal matrix elements of the Fock operator, which are treated as an additional perturbation and give rise to localization diagrams. Based on the obtained local orbitals, an effective Bloch Hamiltonian is constructed to second order of perturbation theory with all third-order localization diagrams included. In addition, the summation of certain classes of diagrams up to infinite order in the off-diagonal Fock elements as well as the Epstein-Nesbet partitioning of the full Hamiltonian are discussed. The problem of intruder states, frequently encountered in many-body perturbation theory, is dealt with by employing the theory of intermediate Hamiltonians. As model systems we have chosen cyclic periodic structures up to an oligoethylene ring in double-zeta basis; however, the theory presented here straightforwardly carries over to infinite periodic systems. Received: 30 April 1998 / Accepted: 27 July 1998 /  Published online: 7 October 1998     

Huckel-hubbard相关图

Huckel模型和Heisnberg-Dirac模型考虑了两种不同的相互作用,前者为单电子作用,而后者仅考虑了电子相关作用,它们是 Hubbard 模型的两种极限情形.本文以四轨道四电子体系为例讨论了三种模型,所得到的Huckel-Hubbard相关图展示了它们的适用范围及其相互关系,这样处理具有代表性,可以推广到较大的共轭体系.     

A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. IV. The short time behavior of the memory function

Using a recently developed diagrammatic formulation of the kinetic theory of fluctuations in liquids, we investigate the short time behavior of the memory function for density fluctuations in a classical atomic fluid. At short times, the memory function has a large contribution that is generated by the repulsive part of the interatomic potential. We introduce a small parameter that is a measure of the softness of the repulsive part of the potential. The diagrams in the memory function that contribute to lowest order in that small parameter are identified and summed to give an explicit expression for the dominant contribution to the memory function at short times. The result leads to a theory for fluids with continuous potentials that is similar to the Enskog theory for hard sphere fluids.     

Lantern-Type Divanadium Complexes with Bridging Ligands: Short Metal−Metal Bonds with High Multiple Bond Orders

Vanadium forms binuclear complexes with a variety of ligands often containing V≡V triple bonds. Many tetragonal divanadium paddlewheel complexes with bridging bidentate ligands have been experimentally characterized. This research exhaustively treats model tetragonal, trigonal, and digonal paddlewheel-type divanadium complexes V₂L_x (L=formamidinate, guanidinate, and carboxylate; x=2, 3, 4), each in the three lowest-energy spin states. The V−V formal bond orders are obtained from metal−metal MO diagrams for representative structures. A number of short V−V multiple bonds of order 3, 3.5, and 4 are found in these model complexes. The short V≡V triple bonds and singlet ground state predicted here for the model tetragonal complexes correspond well with the limited experimental results for the series of known tetragonal paddlewheels. Digonal divanadium lanterns with very short V−V quadruple bonds are predicted as interesting synthetic targets. The V−V bond distances are categorized into distinct ranges according to the formal bond order values from 0.5 to 4. These bond length ranges are compared with the ranges compiled for other divanadium complexes including carbonyl complexes.     

Super-fermion representation of quantum kinetic equations for the electron transport problem

We discuss the use of super-fermion formalism to represent and solve quantum kinetic equations for the electron transport problem. Starting with the Lindblad master equation for the molecule connected to two metal electrodes, we convert the problem of finding the nonequilibrium steady state to the many-body problem with non-hermitian liouvillian in super-Fock space. We transform the liouvillian to the normal ordered form, introduce nonequilibrium quasiparticles by a set of canonical nonunitary transformations and develop general many-body theory for the electron transport through the interacting region. The approach is applied to the electron transport through a single level. We consider a minimal basis hydrogen atom attached to two metal leads in Coulomb blockade regime (out of equilibrium Anderson model) within the nonequilibrium Hartree-Fock approximation as an example of the system with electron interaction. Our approach agrees with exact results given by the Landauer theory for the considered models.     

A simple statistical mechanical theory for the mutual solubility of fluid mixtures of water and organic solvents under high pressure

A simple statistical mechanical theory is presented to explain phase diagrams of fluid mixtures with both a lower critical solution temperature and an upper critical solution temperature under pressure. By postulating a temperature dependence for the interaction free energy parameter of the constituent molecules and a pressure dependence for the excess volume, phase diagrams with both lower critical solution temperature, and upper critical solution temperature and their pressure dependence can be reproduced by quadratic surfaces in temperature-concentration-pressure space. The topological aspects of the observed phase diagrams in this space have been related to our theoretical model, and the thermodynamical meaning of the topologies has been interpreted based on our model. Experimental data for the mutual solubility of water and 2-butanol under pressure and that of water and 3-methylpyridine with added salts have been analyzed quantitatively and theoretical parameters are determined.     

Crystal-liquid crystal binary phase diagrams

We propose a new theoretical scheme for the binary phase diagrams of crystal-liquid crystal mixtures by a combination of a phase field model of solidification, the Flory-Huggins theory for liquid-liquid mixing and Maier-Saupe-McMillan (FH-MSM) model for nematic and smectic liquid crystal orderings. The phase field theory describes the crystal phase transition of anisotropic organic crystal and/or side chain liquid crystalline polymer crystals while the FH-MSM model explains isotropic, nematic and smectic-A phase transitions. Self-consistent calculations reveal several possible phase diagram topologies of the binary crystal-liquid crystal mixtures. The calculated phase diagrams were found to accord well to the reported experimental results.     

BSA denaturation in the absence and the presence of urea studied by the iso-conversional method and the master plots method

The effect of cure temperature and modifier proportion on the miscibility of an epoxy–amine system with a thermoplastic modifier was studied by analysis of phase diagrams, morphologies, and glass transitions. Phase diagrams for the system before and during reaction were obtained from a thermodynamic analysis of phase separation using a model based on Flory–Huggins theory. Different types of morphologies were observed and analyzed in function of cure temperature and modifier proportion. The validity of the thermodynamic model was checked by comparing with observed morphologies. Two glass transitions were observed for most of the modified systems indicating that a phase separation was occurred.     

Energy bands and bond alternation potential in poly(para-phenylene vinylene): a comparative ab initio quantum chemical and density functional theory study

We present calculations of the total energy per unit cell for different bond alternations of the C-C bonds bridging the distance between two aromatic rings in poly(para-phenylene vinylene) (PPV), using two different parametrizations of the energy functional in the local density approximation (LDA) and the ab initio Hartree-Fock (HF) method. For the application of correlation corrections to the HF results the system is already too large. We find that even simple LDA methods are reliable alternatives to the ab initio HF method for the calculation of potential surfaces in polymers with large unit cells. The results in turn can be used to determine parameters for model Hamiltonians necessary for theoretical studies of the dynamics of nonlinear quasiparticles in the polymers. We further present the LDA band structures of PPV together with their HF and correlation (many body perturbation theory of 2^nd order in Møller-Plesset partitioning, MP2) corrected counterparts. We find that the fundamental gap obtained is too large both with HF and with the correlation corrected band structure compared to experiment. However, we use only a modest correlation method and a small basis set, which already brings us to the limits of the computers available to us. The LDA gaps on the other hand are too small which, however, could be corrected with the help of self interaction corrections. None of the latter methods would lead to exceedingly large computation times.     

Liquid-liquid equilibria of polymer solutions: Applicability of extended Redlich-Kister expansion

We developed a simple and improved expression for the Helmholtz energy of mixing which uses a Taylor series of an exponential function based on extending the Redlich-Kister expansion. This model incorporates the chain-length dependence of polymers and specific interactions such as hydrogen bonds. The proposed model can accurately predict most phase diagrams of various binary polymer solutions including upper critical solution temperature (UCST), lower critical solution temperature (LSCT), both UCST and LCST, and closed miscibility loops. Our model fits experimental data of the complex phase behavior of polymer solutions well.     

Coherent third-order spectroscopic probes of molecular chirality

The third-order optical response of a system of coupled localized anharmonic vibrations is studied using a Green's function solution of the nonlinear exciton equations for bosonized excitons, which are treated as interacting quasiparticles. The explicit calculation of two-exciton states is avoided and the scattering of quasiparticles provides the mechanism of optical nonlinearities. To first-order in the optical wave vector we find several rotationally invariant tensor components for isotropic ensembles which are induced by chirality. The nonlocal nonlinear susceptibility tensor is calculated for infinitely large periodic structures in momentum space, where the problem size reduces to the exciton interaction radius. Applications are made to alpha and 3(10) helical infinite peptides.     

Multiparameter equations of state for siloxanes: [(CH3)3-Si-O1/2]2-[O-Si-(CH3)2]i=1,…,3, and [O-Si-(CH3)2]6

This article presents the continuation of the work on the development of technical equations of state for linear and cyclic siloxanes already documented in this journal. The fluids considered herewith are octamethyltrisiloxane (MDM, C₈H₂₄Si₃O₂), decamethyltetrasiloxane (MD₂M, C₁₀H₃₀Si₄O₃), dodecamethylpentasiloxane (MD₃M, C₁₂H₃₆Si₅O₄), dodecamethylcyclohexasiloxane (D₆, C₁₂H₃₆Si₆O₆). The 12-parameter functional form proposed by Span and Wagner has been selected because of its positive characteristics. Siloxanes are produced in bulk quantities and are mostly utilized in the cosmetics industry and, mixed, as high-temperature heat transfer fluids. Furthermore, they are used as working fluids in high-temperature organic Rankine cycle power plants. The available property measurements are carefully evaluated and selected for the optimization of equation of state parameters. For some of the fluids, experimental values are scarce, therefore ad hoc estimation methods have been used to supply more information to the procedure for the optimization of the parameters of the equation of state. In addition, saturated liquid density and vapor pressure measurements are correlated with the equations proposed by Daubert and Wagner–Ambrose, respectively, to provide short, simple, and accurate equations for the computation of these properties. The recently developed isobaric ideal-gas heat capacity correlation for the selected siloxanes is included in the thermodynamic models. The performance of the newly developed equations of state is tested by comparison with experimental data and also with predictions calculated with the Peng–Robinson–Stryjek–Vera cubic EoS, as this model was adopted in previous technical studies. The new thermodynamic models perform significantly better than cubic equations of state. T–s and P  – v$v$ diagrams for all the substances are also reported.