Non-steady state model for free radical polymerization

The non-steady state theory for the kinetics of free radical polymerization taking no account of gel-effect is reviewed. Considering the facts that the monomer consumption in chain propagation is much higher than that in chain initiation and the rate constant of chain termination is much larger than that of chain propagation or transfer, a few very close approximations are introduced to solve the set of kinetical differential equations of free radical polymerization. The expressions for various molecular parameters, such as the molecular size function, the number- and weight-average degrees of polymerization and the dispersity, are derived. In accord with the non-steady state theory, the curves of free radical decay with reaction time or monomer conversion and the molecular parameters mentioned can be predicted from the reaction conditions. Several numerical examples are given.     

Empirical probability-density functions for the radii of gyration of linear random-flight chains

A number of empirical equations are presented that are good approximations to computed probability density functions of the one, two and three-dimentional radii of gyration of linear random-flight chains. Equations are given that are in good agreement with the distributions over the range of the radii of most physical interest. Alternative equations are presented that give especially good fit for small values of the one and two-di-mensional radii.     

The essence of the new approach to the equation of the monolayer state

A new approach to the theory of the equation of state of the adsorption monolayer is elucidated. The approach is based on the excluded surface area. Expressions for the chemical potential are analyzed and the derivation of a master equation, which can be used to obtain equations of state in different approximations, is demonstrated. The constructed hierarchy of approximations includes both the known equations of state (Planck, van der Waals, van Laar, Frumkin) and new, more accurate equations. The new approach consists in the consideration of the three-dimensional aspect related with the orientation of anisometric particles of a monolayer. The influence of the orientational effect on the equation of the monolayer state and phase transitions is discussed.     

New theory of equation of state for surface monolayer

A novel statistical-thermodynamic approach to deriving an equation of state for a surface monolayer has been elaborated on the basis of excluded area. A master differential equation relating surface (two-dimensional) pressure to excluded area has been derived to generate equations of state for a surface monolayer. The crudest solution (the zero approximation) of the master equation reproduces the known van Laar and Frumkin equations of state. The first approximation yields the two-dimensional van der Waals equation. The second, third, and fourth approximations lead to new and more accurate equations of state. The particular result of the fourth approximation is a precise equation of state for hard disks with deviation not more than 0.46% from data obtained by Monte Carlo and molecular-dynamics simulations within the whole range of surface density. The role of the third dimension for surface equations of state is discussed. An orientation equation of state has been proposed for monolayers containing anisometric particles. It follows from the orientation equation obtained that the orientation effect creates possibility for a two-dimensional phase transition.     

A cubic perturbed hard-chain equation of state

A cubic equation of state is developed on the basis of perturbation theory. The equation is an association of three segments: the hard-sphere, the hard-chain, and the attraction. The expression for each segment was invoked from approximations of computer simulations of rigorous molecular theories of fluids, but compromised to some extent accuracy and theory for simplicity. This model equation is shown to be potentially capable of describing the PVT behavior of real fluids. As limiting cases, the new equation is reduced to expressions for the hard-sphere and the hard-body fluids. It also represents square-well fluids when the hard-chain contribution is eliminated. The square-well equation was found satisfactory in conforming with the molecular simulation results for square-well fluids and their mixtures.     

A global investigation of excited state surfaces within time-dependent density-functional response theory

This work investigates the capability of time-dependent density functional response theory to describe excited state potential energy surfaces of conjugated organic molecules. Applications to linear polyenes, aromatic systems, and the protonated Schiff base of retinal demonstrate the scope of currently used exchange-correlation functionals as local, adiabatic approximations to time-dependent Kohn-Sham theory. The results are compared to experimental and ab initio data of various kinds to attain a critical analysis of common problems concerning charge transfer and long range (nondynamic) correlation effects. This analysis goes beyond a local investigation of electronic properties and incorporates a global view of the excited state potential energy surfaces.     

Relations between transport coefficients and their density and temperature dependence

Nonequilibrium statistical mechanics via density fluctuation theory predicts relations between the bulk and shear viscosity, thermal conductivity, and self-diffusion coefficient of a fluid. In this Feature Article, we discuss such relations holding for fluids over wide ranges of density and temperature experimentally studied in the laboratory. It is discussed how such relations can be used to successfully compute the density and temperature dependence on the basis of intermolecular interaction potential models with the help of the modified free volume theory and the generic van der Waals equation of state once the parameters in them are determined at a low density or at a subcritical temperature. Although some approximations have been made to derive them, they represent a reliable molecular theory of transport coefficients over the entire density and temperature ranges of fluids--namely, gases and liquids--a theory hitherto unavailable in the kinetic theory of liquids and dense gases.     

Approximate and high-accuracy equations of state of one-component normal substances

The paper presents the results of studies performed to obtain approximate and high-accuracy equations of state of one-component substances. The preferred form of such equations was established. Two-and three-parameter equations of state that described experimental data much better than the other known equations of state with a small number of parameters were obtained. A step spherically symmetrical interaction potential that correctly reproduced the behavior of the real potential was suggested. Equations for the second virial coefficient of polar and nonpolar substances over the whole temperature range studied were obtained. High-accuracy equations of state of real gases describing the thermal and caloric properties of normal polar and nonpolar fluids (regular part) at densities up to 1.5ρ_c 10 within the accuracy of experimental (tabulated) data were obtained.     

The coupled-cluster method with a multiconfiguration reference state

The coupled-cluster approach to obtaining the bond-state wave functions of many-electron systems is extended, with a set of physically reasonable approximations, to admit a multiconfiguration reference state. This extension permits electronic structure calculations to be performed on correlated closed- or open-shell systems with potentially uniform precision for all molecular geometries. Explicit coupled cluster working equations are derived using a multiconfiguration reference state for the case in which the so-called cluster operator is approximated by its one- and two-particle components. The evaluation of the requisite matrix elements is facilitated by use of the unitary group generators which have recently received wide attention and use in the quantum chemistry community.     

Adiabatic approximation of time-dependent density matrix functional response theory

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.     

Accuracy of second order perturbation theory in the polaron and variational polaron frames

In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.     

Optimum counting programs for short-lived activities

Equations describing the precision obtained when counting for periods significant compared to a half-life are derived. Optimum solutions which involve transcendental equations are obtained numerically, and convenient approximations are given.     

Singlet excitation energies of thiophene derivatives of fluorene: TD‐DFT study

Fluorene‐thiophene (FT)‐based oligomers and polymers and their derivatives are good candidates for organic blue light‐emitting diodes. In this work, the intrinsic properties of the ground and excited states of FT monomer and its derivatives are studied. The ground‐state optimized structures and energies are obtained using molecular orbital theory and density functional theory (DFT). The ground‐state potential energy curves or surfaces of FT and its derivatives are also obtained. All derivatives are nonplanar in their electronic ground states. The character and energy of the first 20 singlet–singlet electronic transitions are investigated by applying the time‐dependent density functional theory (TD‐DFT) approximations to the correspondingly optimized ground‐state geometries. The lowest singlet state is studied with the configuration interaction (singles) approach (CIS). Excitation energies are red shifted when the FT unit or its derivatives are extended longitudinally. CIS results suggest geometry relaxation in the first singlet excited state. When available, a comparison is made with experimental results. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Two- and three-parameter equations for representation of retention data in reversed-phase liquid chromatography

Two-parameter equations that describe the dependence of ln kappa upon psi, where kappa is the retention factor and psi the volume fraction of the organic modifier in the mobile phase, are examined in what concerns the underlying approximations and their performance to fit experimental data obtained from reversed-phase liquid chromatography. Using 293 experimental systems, it was found that the performance of these equations to describe ln kappa versus psi data is rather low, since the percentage of the systems that can be described satisfactorily ranges from 40 to 60% depending on the fitting equation. This percentage may be raised to 75%, if the discreteness effect is properly taken into account. A further improvement to 90% of the systems studied can be achieved only by the use of three-parameter equations, which may arise by refinements of the rough approximations of the two-parameter equations. Although the refinements do not lead always to better equations, we developed a new three-parameter expression of In kappa that works more satisfactorily, since it combines simplicity, linearity of its adjustable parameters and the highest applicability.     

Global dynamics and transition state theories: Comparative study of reaction rate constants for gas-phase chemical reactions

In this review article, we present a systematic comparison of the theoretical rate constants for a range of bimolecular reactions that are calculated by using three different classes of theoretical methods: quantum dynamics (QD), quasi-classical trajectory (QCT), and transition state theory (TST) approaches. The study shows that the difference of rate constants between TST results and those of the global dynamics methods (QD and QCT) are seen to be related to a number of factors including the number of degrees-of-freedom (DOF), the density of states at transition state (TS), etc. For reactions with more DOF and higher density of states at the TS, it is found that the rate constants from TST calculations are systematically higher than those obtained from global dynamics calculations, indicating large recrossing effect for these systems. The physical insight of this phenomenon is elucidated in the present review.     

Accelerating Kohn‐Sham response theory using density fitting and the auxiliary‐density‐matrix method

An extension of the formulation of the atomic‐orbital‐based response theory of Larsen et al., JCP 113, 8909 (2000) is presented. This new framework has been implemented in LSDalton and allows for the use of Kohn‐Sham density‐functional theory with approximate treatment of the Coulomb and Exchange contributions to the response equations via the popular resolution‐of‐the‐identity approximation as well as the auxiliary‐density matrix method (ADMM). We present benchmark calculations of ground‐state energies as well as the linear and quadratic response properties: vertical excitation energies, polarizabilities, and hyperpolarizabilities. The quality of these approximations in a range of basis sets is assessed against reference calculations in a large aug‐pcseg‐4 basis. Our results confirm that density fitting of the Coulomb contribution can be used without hesitation for all the studied properties. The ADMM treatment of exchange is shown to yield high accuracy for ground‐state and excitation energies, whereas for polarizabilities and hyperpolarizabilities the performance gain comes at a cost of accuracy. Excitation energies of a tetrameric model consisting of units of the P700 special pigment of photosystem I have been studied to demonstrate the applicability of the code for a large system.     

Equation of state for high density solid and melt polyethylene

Pressure‐volume‐temperature (PVT) measurements for high‐density linear polyethylene (LPE) are studied experimentally over a temperature range of 290 to 470 K and pressures up to 3.1 kbar. For melt, the results can be represented by the Tait equation within the precision of the data. It is noticed that for each isotherm, an abrupt departure from the Tait representation occurs at a particular pressure. This is ascribed to onset of solidification due to pressure. Further, variation of the degree of crystallinity with pressure at various temperatures has been investigated. Finally, the PVT data has been analyzed in terms of the LJD cell theory in its original form without any modifications or simplifications of the cell potential. Satisfactory agreement is obtained between experiment and theory over the entire range of PVT data both in solids and melt states. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1618–1623, 2005     

A theory of a curved vapor-liquid separation boundary: The lattice gas model

Molecular theory of curved vapor-liquid interphase boundaries was considered in terms of the lattice gas model. The theory uses the quasi-thermodynamic concept of curved layers of a separation boundary with a large radius. The transition from a rectangular lattice to such layers is performed by the introduction of a variable number of the nearest neighbors. The problems (1) of the transition from distributed molecular models to layer models reflecting macroscopic symmetry of the interphase boundary and (2) of a minimum linear size of the surface region to which thermodynamic approaches are applicable were considered. Equations for the quasi-equilibrium distribution of molecules at the vapor-liquid boundary in a metastable system were constructed in the quasi-chemical approximation taking into account direct correlations between the nearest interacting molecules. A metastable state is maintained by a pressure jump described by the macro-scopic Laplace equation on a separation surface inside the interphase region. Equations for local mean pressure values and normal and tangential pressure tensor components inside the interphase region were constructed. These equations were used to obtain microscopic difference mechanical equilibrium equations for curved boundaries of spherical and cylindrical drops in the metastable state. The relation between the micro-scopic difference mechanical equilibrium equations and similar differential equations and the macroscopic Laplace equation, which described pressure jump in a metastable system, was considered. Various definitions of surface tension are discussed.