On the equivalence between the microscopic frictional theory and transition-state theory

The generalized Langevin equations are presented by considering such microscopic motions of molecules described by the microscopic Hamiltonian whose potential function is quadratic and internal degree of freedom is multidimensional. Considering the long time behavior of the reactive mode, the Grote-Hynes equation has been derived from the generalized Langevin equations. Furthermore, we have proved that solving the Grote-Hynes equation is equivalent to solving the eigenvalue problem for the whole system, and then the Grote-Hynes treatment coincides with the transition-state theory for the whole system. © 1996 John Wiley & Sons, Inc.     

Introducing the theory of relativity

A simple way of introducing the theory of relativity to chemistry students is presented. This is based on experimental observations of the variation in the mass of an electron with speed. Analysis of these generates the equations chemists use, and provides a basis for critical discussion of the theory.     

Development of the electrocrystallization theory

The problems of nucleation at electrocrystallization of metals and alloys are considered. The thermodynamics and kinetics of nucleation in stationary and nonstationary modes, the atomistic approach to the formation of nuclei and their growth (isolated and overlapped), the dependence of the nucleation rate on the adsorption of surfactants, the deposit grain size as a function of overpotential, and the grain size of eutectic alloys are discussed. Conclusions are drawn on the most important factors which should be taken into account during the analysis of processes of electrochemical nucleation and cluster growth.     

To the theory of wetting

Young’s equation is considered as applied to describe the behavior of ideal systems in thermodynamic equilibrium with the classification of the solid bodies into bodies having low-energy and high-energy surfaces. This classification verifies the validity of categorizing real systems into wetting and nonwetting ones with the wetting boundary lying at the contact angle having a value of θ = 90° and allows the nonwetting systems to be represented by three ranges of manifestation of contact angles, namely: a nonwetting range with contact angles of θ > 106°, an equilibrium wetting range (74° < θ < 106°), and a nonequilibrium incomplete wetting range (θ < 74°).     

A theory of polymer solutions without the mean-field approximation in Flory-Huggins theory

The concept of the volume fraction at chain end is proposed, which is the conditional probability for a site having been occupied, knowing that an adjacent site is occupied by polymer end. The overall entropy of polymer/solvent system is separated into two fundamentally different parts, i.e., the translational entropy and the conformational entropy. Based on these a theory of polymer solutions is established. When a mean-field approximation is introduced, Flory-Huggins (FH) theory is recovered. The FH interaction parameters and spinodal curves of the polystyrene/cyclohexane system are calculated and compared with the experimental data. The good prediction of them two is achieved.     

Performance of the density matrix functional theory in the quantum theory of atoms in molecules

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.     

Regarding the theory of the Zeno line

The line of thermodynamic states with a unit value of the compressibility factor was calculated for a Lennard-Jones system using four different approaches. We show that all four approaches give rise to a straight line on the density-temperature plane. Thus, we theoretically confirm that the Lennard-Jones system satisfies Zeno line regularity.     

On the theory of the electrochemical diode

Russian Chemical Bulletin -     

Recent advances in simple valence-bond theory and the theory of hybrid bond orbitals

The history of important developments in the theory of hybrid bond orbitals and its application in valence-bond theory is reviewed. One of the salient points, the bond strength of a hybrid orbital, is defined as the value of the angular part of the orbital along the bond direction. Characteristic bond angles corresponding to maxima in the bond strength are presented for various basis sets. In order to alleviate computational difficulties in determining the bond strength for complex systems, an approximation to it, the pair-defect-sum approximation, is described. The results of an exhaustive test of the validity of this approximation are presented. Applicaitions of these ideas to coordinate chemistry are provided. Finally, the case is made for the continued viability of valence-bond theory in this age of omnipresent computer terminals.     

On the theory of thermometric titration

The general equation defining the change in solution temperature DeltaT during a thermometric titration is DeltaT = T - T(0) = - AV 1 + BV where A and B are constants, V is the volume of titrant used to produce temperature T, and T(0) is the initial temperature. There is a linear relation between the inverse values of DeltaT and V: 1 Delta T = - a V - b where a = 1/A and b = B/A, both a and b being constants. A linear relation between DeltaT and V is usually a special case of this general relation, and is valid only over a narrow range of V. Graphs of 1/DeltaTvs. 1/V are more suitable for practical calculations than the usual graphs of DeltaTvs. V.     

On the theory of polarographic maxima

The theory of polarographic maxima is presented taking into account the interaction of momentum transport, the electrostatic potential field, the adsorption—desorption and the faradaic processes. Several earlier results are generalised. The systems approach employed here is also extended to quasi-linear situations.     

On the theory of steady-state electrodiffusion

The problem of the electrical field strength distribution outside the boundary layer under on passing of steady-state current through electrolyte is considered. The solution is obtained as a small-parameter reciprocal-power expansion; however, the expansion of the solution in terms of positive powers of this parameter, by using of the method of splicing of asymptotic solutions, is divergent. For the region under consideration, an expression for the field strength is obtained, which differs from the corresponding expression obtained from the electrical neutrality conditions.     

On the theory of solvent effects

A simple electrostatic analysis is given of the virtual charge (solvaton) model to represent the environment effect on the electronic wave function of a solute immersed in a polarizable surrounding. New features of this model are found. The classical aspects are discussed and secondly the quantal implications are considered. A correct Hartree-Fock-like operator is derived which represents an electron in a molecular orbital subjected to the average effect of the other electrons and to the reaction field produced by the virtual charges on the atomic centers.A general formalism based on the preceding model is presented in appendix. The final equations have a form similar to Newton's equation to represent a solvated electron. Unlike some other theories in this field, there is no cut-off involved in the evaluation of the molecular integrals.     

Extension of the separated pair theory

Assuming that the separated pair ground state wave function of a 2N-electron system is already known a method is given for constructing a suitable orthogonal complement to the set of product functions built up from strongly orthogonal geminals. All terms are explicitly given which may have nonzero matrix element with the separated pair ground state. Using perturbational techniques a second order correction is calculated. In the case of Be atom the magnitudes of contributions from terms omitted in the generalized separated pair theory are estimated and found to be appreciable.

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Zusammenfassung Unter der Annahme, daß der Grundzustand eines 2N-Elektronensystems in der Methode der getrennten Elektronenpaare bekannt ist, wird eine Methode angegeben, wie man den Basissatz von Produktfunktionen aus streng orthogonalen Geminalen geeignet vervollständigen kann. Alle mit dem Grundzustand kombinierenden Terme werden explizit angegeben. Mit Hilfe der Störungsrechnung wird eine Korrektur zweiter Ordnung berechnet. Im Falle des Be-Atoms wird die Größe der in der Theorie der getrennten Elektronenpaare vernachlässigten Beiträge abgeschätzt und als beträchtlich erwiesen.

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Résumé Si l'on suppose connue la fonction d'onde à paires séparées pour l'état fondamental d'un système à 2N électrons, une méthode décrite ici permet de construire convenablement un complément orthogonal à l'ensemble des fonctions produits de géminales fortement orthogonales. Tous les termes ayant un élément dematrice non nul avec l'état fondamental sont donnés explicitement. Une correction du second ordre est calculée au moyen des techniques de perturbation. Dans le cas de l'atome de beryllium, la grandeur des contributions des termes omis dans la théorie généralisée des pair es séparées est estimée et trouvée non négligeable.

     

Concerning the theory of chirality functions

Within the scope of the theory of chirality functions, qualitatively complete chirality functions are subject to restrictions concerning both generality and applicability. In contrast thereto, the concept of qualitative supercompleteness results in less restrictive requirements for chirality functions. Consequently, the applicability of qualitatively supercomplete chirality functions is unlimited with respect to the number of ligand kinds. Given this concept, a group theoretical treatment is performed supplying the formal conditions of qualitative supercompleteness. Subsequently a construction rule for qualitiatively supercomplete chirality functions is presented, which is elaborated in detail in the appendix. On combining physical considerations with the requirement of qualitative supercompleteness the resulting chirality functions appear to include all the possible interactions within and/or between ligands and skeleton. From both a mathematical and a physical point of view these chirality functions should be adequate for describing the chiroptical properties of molecules belonging to a given skeletal class. Nevertheless, all the other critical objections to the theory of chirality functions remain.