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A simplified method of plane trajectory calculation is proposed for solving the problem of planning the path defined by a sequence of turning points. The trajectory consists of oriented segments of straight lines joined by clothoids (Cornu spirals). The efficiency of the method is validated by means of numerical simulations in the MATLAB/Simulink environment.

Various aspects of mathematical modeling of the inclination parameter converter based on two double-axis accelerometers in a single integrated design are considered. Possible variants of design patterns of such a converter are presented. Additional turns of the accelerometer sensors mounted in the transducer body are considered. Generalized static mathematical models for two double-axis accelerometers as part of the inclination parameter converter are obtained, which ensure accurate determination of the spatial orientation angles of an object: zenith and sighting (apsidal) angles.

A new method of solving the many-body Schredinger equation is proposed. It is based on the use of constant particle-particle interaction potential surfaces (IPSs) and the representation of the many-body wave function in a configuration interaction form with coefficients depending on the total interaction potential. For these coefficients the corresponding set of linear ordinary differential equations is obtained. A hierarchy of approximations is developed for IPSs. The solution of a simple exactly solvable model and He-like ions proves that this method is more accurate than the conventional configuration interaction method and demonstrates a better convergence with increasing basis set.

The conformational properties of p-n-propyloxybenzoic acid and p-n-propyloxy- p'-cyanobiphenyl molecules, which can exhibit liquid crystalline properties in the formation of Н-complexes, are studied (DFT/B3LYP)/cc-pVTZ method). It is found that a molecule of p-n-propyloxybenzoic acid has 16 conformers that can be divided into four groups with respect to relative energies (0 kcal/mol, 1.6 kcal/mol, 6.5 kcal/mol, and 8.1 kcal/mol), and a molecule of p-n-propyloxy-p'-cyanobiphenyl has six conformers with relative energies of 0 kcal/mol (two conformers, φ(С_ph-O-C-C)=180°) and 1.6 kcal/mol (four conformers, φ(С_ph-O-C-C)=64.4°). In all conformers of the 3-AOCB molecule, phenyl rings are turned at 35° relative to each other. A conformation with the planar arrangement of two rings has a higher energy by 1.5 kcal/mol. Barriers to the internal rotation of different groups are determined and it is established that the structural nonrigidity of the molecules is mainly due to the possible rotation of the -C₂Н₅ moiety about the C-C bond. It is shown that with increasing temperature the vibrational amplitudes of the OC₃H₇ substituent, which enhance the probabilities of transitions between the conformers, become appreciably larger. It is found that p-n-propyloxybenzoic acid and p-n-propyloxy-p'-cyanobiphenyl can form Н-complexes with the medium hydrogen bond. Two types of the structural organization of Н-complexes are considered: linear and angular. The similarity of energies of Н-complexes with different structures (NBO analysis) can be the reason for the occurrence of two liquid crystalline subphases of p-n-propyloxybenzoic acid and p-n-propyloxy-p'-cyanobiphenyl system.

The formation of structures obtained during the hydration and non-exchangeable absorption of phenylalanine by a low-basic AN-221 ion exchanger in the НСl form is modeled in the work. Quantum chemical calculations are made using the Gaussian 03 program implementing the B3LYP hybrid density functional with the 6-31G++(d,p) basis set. The sequence of hydration and dissociation of functional groups of the ion exchanger is determined, the structure is optimized, and its formation energy during the non-exchangeable sorption of phenylalanine by the AN-221 (НСl) anion exchanger is estimated.

The structural characteristics of micelles from our previous work (Part I) are used to calculate the electrostatic energy of ions in the electric double layer on the surface of spherical ionic micelles in solutions of sodium n -alkyl sulfate homologues with the following number of carbon atoms in the molecule: n_C = 8, 10, 12, and 14. This energy is found to depend on the thickness of the electric double layer and its average radius on the surface of a micelle, the aggregation number, the degree of binding of counterions, and the dielectric constant. The developed semi-empirical method is used to calculate interfacial tensions in spherical micelles for the said homologues in solutions at their critical micellar concentrations and T = 303 K. These values are split into the contributions from the hydrophobic and electrostatic components. The electrostatic component of the interfacial tension in spherical micelles is compared with the expression for the ion-ion repulsion energy to obtain the values of static permittivity (dielectric constant) in the surface layer of micelles.

IR spectroscopic and quantum chemical methods are used to study the competition between water and methanol molecules in the formation of the simplest stable proton disolvates and their subsequent solvation in the case of solutions of KOH in CH₃OH and CH₃OK in H₂O with similar stoichiometries (~1:3-3.5). The complexes found in these solutions are analysed to determine their composition and structure: they are found to be heteroions (CH₃O⋯H⋯OH)^- solvated by two similar solvent molecules. In both cases, there are virtually no complexes of the second possible type (CH₃OH×(CH₃O⋯H⋯OCH₃)^-×H₂O or CH₃OH×(HO⋯H⋯OH)^-×H₂O), which appears to be due to the stoichiometric compositions of the solutions. It is shown that a DFT calculation (B3LYP/6-31++G(d,p)) of linear complexes with strong (~15-30 kcal/mol) H bonds reproduces, with good accuracy, the IR spectra of the solutions, which consist mainly of these complexes.

Based on thermodynamic simulation data on the deposition of condensed phases with the complex composition in the Si-C-N-O-H system in a wide temperature range, using initial gas mixtures of 1,1,3,3-tetramethyldisilazane (HSi(CH₃)₂)₂NH (TMDS), TMDS with a variable mixture of oxygen and nitrogen (O₂+ xN₂), a method is developed to obtain SiC_xN_yO_z:H nanocomposite films by the plasma chemical decomposition of this gas mixture in the temperature range of 373-973 K. By FTIR and energy dispersive X-ray spectroscopy the structure of chemical bonds and the elemental composition of the obtained silicon oxycarbonitride films are studied. The in situ composition of the initial gas phase in PECVD processes is examined by optical emission spectroscopy.

Isostructural fluorooxalate complex compounds of indium(III) M₂[InF₃(C₂O₄)H₂O] (M = K, Rb), being the first representatives of a new class of mixed-ligand fluoro-containing complex compounds of indium(III) are synthesized for the first time and structurally studied. The crystal structures of M₂[InF₃(C₂O₄)H₂O] (M = K, Rb) are formed of K⁺ cations (Rb⁺ respectively) and complex [InF₃(C₂O₄)H₂O]^2- anions. The indium atom in the complex anion is surrounded by four F atoms, two of which are bridging, the oxygen atom of the coordinated H₂O molecule, and two oxygen atoms of the bis-bidentate (tetradentate) oxalate group. The coordination polyhedron of the indium atom (CN 7) is a pentagonal bipyramid. Via alternating double bridging F atoms and tetradentate bridging C₂O₄ group, the In(III) atom polyhedra are arranged in polymer chains. Via hydrogen O-H⋯F bonds the chains are organized in layers. Between the layers, the K⁺ or Rb⁺ cations are located, which strengthen the crystal structure.

The salt 1-(4-trifluoromethyl-2,3,5,6-tetrafluorophenyl)-3-benzylimidazolium bromide [(CF₃C₆F₄)NC₃H₃N(CH₂Ph)]⁺×Br^- is crystallized from methanol in the space group P-42₁c of the tetragonal crystal system with unit cell parameters a = b = 21.6531(3) Å, c = 8.1968(2) Å, V = 3843.13(13) ų, Z = 8, d_calc = 1.5732 g/cm^-3. The structure possesses square channels with a width of ca. 5.2 Å, which accounts for 14 % of the volume, and contains one methanol molecule per ion pair. The cation interacts with three bromide ions through an anion - π interaction and two C-H⋯Br^- interactions. These interactions are investigated by DFT calculations.