E. A. Smolenskii

Topological Structure of the Configuration Space and the Separation of Spin and Spatial Variables for N-Electron Systems

The relationship between the topological structure of the multidimensional configuration space and the structure of the symmetrical permutation group SN is analyzed. This relationship permits to separate the spin and spatial variables during the solution of the spinless stationary Schrodinger equation. It is possible to simplify the construction of wave functions for N-electron systems and to expand the class of trial functions in the variation method. The relation of the suggested approach to the construction of wave functions by traditional methods is demonstrated by the example of three-electron systems.

The Wiener distance matrix for acyclic compounds and polymers.

The relationship between the Wiener indices and the topological structures of alkanes is analyzed. The expressions for the Wiener distances between elements of these structures are derived, and the distance matrix is constructed for them; this matrix is naturally called the Wiener distance matrix. The expressions for the Wiener indices of polymers with units of arbitrary structure are obtained.

A priori estimation of the nodal surfaces of trial wave functions of lithium atom

Some aspects of geometric interpretation of the Pauli exclusion principle in the Hartree—Fock approximation and in the framework of the many-electron wave function (MWF) method developed by the authors are discussed taking the Li (2S) ground electronic state as an example. Arguments are brought forward that indicate insufficient adequacy of the Hartree—Fock approximation for a priori estimation of the MWF nodal surfaces. It was pointed that, unlike the MWF method, the Hartree—Fock approximation can not describe the dependence of the shape of the MWF nodal surfaces on the nuclear charge of Li atom and on electron-electron correlation effects.

On applicability of optical Bloch equations to simulation of photochemical reaction dynamics

61 Recent progress in theoretical photochemistry is attributed to advances in quantum theory, which treats the chemical reaction as a non optical transition between the reagent and product states (see [1] and references therein). In this theory, the reacting system is considered a closed system. In simulation of its state population dynamics, different variants of the optical Bloch equations are used, describing the elements of the population matrix of the reacting molecular com plex and the radiation field; this matrix is reduced tak ing into account the states of secondary and spontane ous emission photons (reduced density matrix (RDM), see, e.g., [2]).

A priori determination of the nodal surfaces of trial wavefunctions of lithium hydride molecule

A comparative analysis of geometric properties of the nodal surfaces of four-electron trial wave function for LiH molecule is performed within the framework of the Hartree—Fock approximation and the method of many-electron wave functions (MWF) developed by the authors. Unlike the MWF method, the Hartree—Fock approximation fails to include the dependence of the nodal surfaces of MWF on nuclear charges of atoms in molecules and on effects of correlated motion of electrons with antiparallel spins because the nodal surfaces are specified by the mathematical properties of Slater determinants rather than physically clear and more practically valuable algebraic products of electrostatic potential differences.

Modeling of heats of combustion and shale oil yields in oil shale semicoking

15 Oil shale is a promising source for power generation and chemical production. Information on the proper ties and chemical composition of oil shale mined from various deposits has been summarized in [1]. Among the oil shale properties, heats of combustion and shale oil yields in oil shale semicoking as a function of com position, different in different deposits, are of great practical interest. In this work, we made an attempt to model these properties as a function of chemical com position of oil shale. In searching for quantitative structure–property relationships (QSPR [2–4]) for organic compounds, topological indices are commonly used [5, 6]. How ever, in our case, the structures of all compounds con stituting oil shale are unknown; therefore, only the elemental composition of oil shale was used as descriptors. Only the contents of C, H, N, S, and organic substances reported in [1] were taken into account. Table 1 presents the characteristics of oil shale samples from different deposits, and Table 2 summa rizes information on their chemical composition [1, pp. 140–143]. It is worth noting that data in [1] are expressed in different units: for S, in percentage of the CHEMISTRY

The necessary and sufficient conditions for chemical equilibrium

The article concerns a widely accepted but incorrect concept of conditions for chemical equilibrium. The authors present a mathematically rigorous derivation of the necessary and sufficient conditions for chemical equilibrium of systems of arbitrary complexity.

Time dependence of the yields of hydrocarbon fractions in visbreaking of heavy oil residues at various temperatures and chemical compositions of feedstock

The yields of gasoline, light and vacuum gas oils, and gas fraction in thermal cracking of heavy oil residues (visbreaking) were mathematically modeled. Calculation formulas with high statistical characteristics were obtained.

Mathematical simulation of the kinetics of visbreaking of tars

The results of the mathematical simulation of the thermal cracking (visbreaking) of tars are reported. The methods of plotting kinetic curves were proposed for the determination of visbreaking product concentrations in a reaction mixture under given conditions. The effectiveness of the algorithms of plotting kinetic curves on a computer with specified computational resources was compared.

Computer-aided modeling of physicochemical characteristics of various energy sources

The authors’ review presents original methodical development works and integrates the research on the modeling of processes and estimation of physicochemical characteristics of natural (hydrocarbons) and chemical (energetic materials) energy sources. A fundamentally new method of energy generation based on transition of excited helium atoms to the superstable state in superstrong magnetic fields is described. A hypothetical possibility for these states to exist was predicted by one of the authors and confirmed by calculations.