Structure and properties of organic molecules. 1. Three-dimensional topological indices of alkanes

The Winer and Schultz three-dimensional topological indices of alkanes are considered and compared with ordinary two-dimensional indices. Methods of index design and details of calculations are discussed. Unlike two-dimensional indices, three-dimensional ones adequately reflect differences between both structural and rotational isomers. Regression analysis of property-index correlations for formation enthalpy, molar volume, evaporation heat, and boiling temperature is performed using various two- and three-parameter (linear, quadratic, exponential, logarithmic, and power) functions. The ability of three-dimensional indices to correlate with these properties is found to be as good as that of two-dimensional ones. Tver State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 484–492, May–June, 1998. This work was supported by RFFR grant No. 96-03-32384.     

Chain numbering and encoding of cyclic hydrocarbons

The numbering of carbon atoms in organic molecules is called chain numbering. It is suggested that bonds be classified as chain bonds (between atoms with consecutive indices) and nonchain bonds. Among atoms we distinguish the first atom (No. 1) and the last atom (having the largest index) as well as initial and final atoms (starting and finishing unbranched sections of atomic chains). Also, internal numbering of elements within these classes is proposed. For condensed cyclic hydrocarbons, formulas for deriving the number of cycles are given, and a linear-chain encoding system is worked out; in this system, nonchain bonds are assigned the indices of their atoms. Rules for unique numbering (canonical chain numbering) are developed; they involve maximization of the indices of the initial atoms and nonchain bonds. The linear-chain encoding of cyclic hydrocarbon structures ensures unification and systematization of their names. Tambov State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 4, pp. 731–736, July–August, 1995. Translated by L. Smolina     

Analysis of molecular chirality using the lattice model of spatial structure

A lattice model of the spatial structure of a molecule is suggested. A broken line is constructed to characterize atoms and molecular fragments. The line is a spiral (left or right) embracing the whole lattice containing the molecule. The mutual arrangement of molecular fragments along the broken line is described by a molecular code. The code contains all the necessary information about molecular conformation and configuration in compressed form. Comparing the codes makes it possible to evaluate the structural similarity and dissimilarity of molecules. For example, one can easily estimate the chirality level for enantiomers. Using this approach is demonstrated on various model structures. A. V. Bogatskii Physicochemical Institute, Ukrainian Academy of Sciences. Odessa State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 541–546, May–June, 1998. This work was supported by INTAS grant INTAS-UA 95-0060.     

Algorithm for estimating molecular dissymmetry

A simple criterion for estimating molecular dissymmetry and an algorithm of its calculation are suggested. Calculations are performed for compounds belonging to different point groups. The new molecular characteristic may be used to predict the magnitude and sign of optical rotation. Chelyabinsk State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 500–506, May–June, 1998.     

Isothermal compressibility and correlation radius near the critical point: Numerical analysis of the Ornstein-Zernike equation

Solution of the Ornstein-Zernike equation is analyzed numerically in the Percus-Yevick and hyperchain approximations for a system of Lennard-Jones particles in a critical region. The temperature dependences of correlation functions, isothermal compressibility η, and correlation radius of density fluctuations ζ are investigated at a critical density; the corresponding critical indices are determined. It is shown that the Percus-Yevick approximation yields satisfactory results when the correlation functions are calculated within a range corresponding to approximately 50 atomic (molecular) diameters. In this case, with ≈5% deviations from the critical temperature, the calculated and experimental values of η and critical indices are in good agreement. Tver State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 5, pp. 799–807, September–October, 1995. Translated by I. Izvekova     

Structure and properties of organic molecules. 2. Graph-theoretical study of alkenes and alcohols

Topological indices for describing organic compounds with multiple bonds and heteroatoms are treated. The Schultz indices (including modified ones) and the connectivity indices of various types are calculated for saturated alkenes and alcohols. The discriminating ability of the indices and their applicability for structure-property correlations are examined. Various functions approximating the property-index correlations are tested using regression analysis. The Schultz and connectivity indices possess nearly the same correlation ability, as shown by reference to formation enthalpy, molar volume, evaporation heat, and boiling temperature. They may be effectively used for calculating and predicting the physicochemical properties of the title compounds. Tver State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 493–499, May–June, 1998. This work was supported by RFFR grant No. 96-03-32384.     

Molecular force fields obtained using the nonempirical stabilizer of the regularizing functional

A new approach to the analysis of the force fields of polyatomic molecules is discussed. The results of quantum chemical calculations in combination with experimental data are used in a regularizing procedure, where the nonempirical matrix of the force constants determines the stabilizer of Tikhonov's functional. The use of stable numerical methods allows the specific modeling of the force fields of polyatomic molecules with due account of rotational isomerism. M. V. Lomonosov Moscow State University, Chemical Faculty. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 204–216, March–April, 1995. Translated by I. Izvekova     

Forming taxonomic groups of organic compounds for calculating gas-chromatographic retention indices from physicochemical constants

The traditional approach to calculations of gas-chromatographic retention indices from physicochemical constants of organic compounds in homologous series does not encompass all possible objects. Forming different taxonomic groups of compounds by variations in the formal unsaturation, the number of atoms of different elements within molecules, or any complex fragments of structure/composition makes it possible to calculate unknown retention indices by several independent methods from different arrays of initial data. The application of simple three-parameter equations provides an accuracy comparable to the modern interlaboratory error of determination of retention indices for any compounds. St. Petersburg State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 6, pp. 176–182, November–December, 1994. Translated by L. Smolina     

Effect of the components of the raman scattering tensor on band intensities

The Raman scattering (RS) tensor as a function of excitation radiation frequency is studied taking into account, the vibration quantum. It is shown that the corresponding asymmetric components of the tensor are described by fast converging series. Expressions are obtained for the antisymmetric and symmetric components of the RS tensor. A convenient formula is proposed for the calculation of the RS tensor and its components, where the tensor is represented as a sum of the derivative of static polarizability and the terms containing fast converging series. The formula makes it possible to avoid infinite summation. Computer experiments simulating the dependence of the intensity of RS bands and their components on the excitation frequency are carried out. Moscow State University of Building Engineering. V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 6, pp. 1006–1015, November–December, 1996. Translated by I. Izvekova     

Methods of studies on quantitative structure–activity relationships for chiral compounds

Chiral compounds are very important in drug development, organic synthesis, materials science, toxicology, or environmental chemistry. Therefore, for creating new drugs, several methods have been suggested in recent years. In several laboratories in the world, some new methods for the derivations of the parameters were constructed and used for studies on quantitative structure–activity/property relationships of chiral molecules. The algorithms reviewed in this paper involve Zargeb group chiral indices, chiral molecular connectivity index, chiral topological charge index, chiral A_m index, chiral indices based on the matrixes, chiral indices based on chiral product, conformation‐independent chirality code, conformation‐dependent chirality code, quantitative two‐dimensional chirality degrees of benzenoids, and so on. Copyright © 2012 John Wiley & Sons, Ltd.     

Structural inhomogeneity types of perovskite-like superconductors. Relation to growth conditions

Literature data and our studies are used to consider three types of structural inhomogeneity in perovskite-like superconductors. Their irregular mixed-layered structures differ in the nature and distribution of impurity layers. A three-dimensional diagram is suggested for each type of defect. A great variety of postgrowth conditions are discussed to choose optimal conditions for obtaining perfect single crystals with the desired content of oxygen and T_s. St. Petersburg State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 5, pp. 15–22, September–October, 1994. Translated by O. Kharlamova     

Separation of the vibrational,rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates

A new method is suggested for separating the vibrational, rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates that are linear with respect to the natural vibrational coordinates. It is shown that, in this case, Coriolis interactions between the vibrational and rotational motions are absent. The solutions of the anharmonic vibrational-rotational problems in the curvilinear and linear vibrational coordinates are compared. The absence of Coriolis interactions between the vibrational and rotational motions in the curvilinear vibrational coordinates is proved numerically. The same conclusion is additionally supported by calculations of the anharmonic vibrational energy levels for the H₂O, H₂S, NO₂, SO₂, and ClO₂ molecules in the linear and curvilinear vibrational coordinates using the Hamiltonian designed in the curvilinear vibrational coordinates with and without Coriolis vibrational-rotational interactions. Volgograd Pedagogical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 239–254, March–April, 1995. Translated by I. Izvekova     

Sphericities of Double Cosets,Double Coset Representations,and Fujita’s Proligand Method for Combinatorial Enumeration of Stereoisomers

The concepts of double coset representations and sphericities of double cosets are proposed to characterize stereoisomerism, where double cosets are classified into three types, i.e., homospheric double cosets, enantiospheric double cosets, or hemispheric double cosets. They determine modes of substitutions (i.e., chirality fittingness), where homospheric double cosets permit achiral ligands only; enantiospheric ones permit achiral ligands or enantiomeric pairs; and hemispheric ones permit achiral and chiral ligands. The sphericities of double cosets are linked to the sphericities of cycles which are ascribed to right coset representations. Thus, each cycle is assigned to the corresponding sphericity index (a _d , c _d , or b _d ) so as to construct a cycle indices with chirality fittingness (CI-CFs). The resulting CI-CFs are proved to be identical with CI-CFs introduced in Fujita’s proligand method (S. Fujita, Theor. Chem. Acc. 113 (2005) 73–79 and 80–86). The versatility of the CI-CFs in combinatorial enumeration of stereoisomers is demonstrated by using methane derivatives as examples, where the numbers of achiral plus chiral stereoisomers, those of achiral stereoisomers, and those of chiral stereoisomers are calculated separately by means of respective generating functions.     

Comparison of the variational and bound perturbation theories in dipole polarizability calculations of molecular complexes

For a model molecular complex, analytical expressions are obtained for the coefficients A₃ and A₆ of dipole polarizability expansion in a reciprocal power series of intermolecular distances in terms of the variational (VPT) and bound (BPT) Hartree-Fock perturbation theories. It is shown that A₃(VPT)<A₃(BPT), A₆(VPT)<A₆(BPT) for weak electron-electron interactions and A₃(BPT)<A₃(VPT), A₆(BPT)<A₆(VPT) for strong electron-electron interactions. Scientific Research Institute of Chemistry, Kharkov State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 535–540, May–June, 1998.     

Evaluating molecular asymmetry

A method for calculating the asymmetry parameters of molecules based on Avnir’s CSM approach combined with the “dissymmetry function” method is suggested. The performance of the approach is demonstrated on various geometrical models — high-symmetry antiprisms of S₁₀ and D₅ symmetry groups, helices, and molecular objects. It is shown that the MCSM method unambiguously determines the symmetry element or estimates the degree of asymmetry for molecules from different structural classes. A. V. Bogatskii Physiocochemical Institute, Ukrainian Academy of Sciences. Odessa State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 547–552, May–June, 1998.     

Orthogonal contacts between benzene rings: A special type of specific intermolecular interactions

The crystal structures of benzene and some of its derivatives are analyzed in detail. The structures are characterized by orthogonal contacts between the benzene cycles (OBzC). Although the orthogonal contacts conflict with the close packig law, they are an important structure-forming factor, being thus a specific type of intermolecular interactions. The OBzC system, which is inherent in the orthorhombic crystals of benzene, remains invariable in 2-aminophenol and 2-amino-4-chlorophenol crystals, notwithstanding other specific interactions (H-bonding and halogen...halogen contacts). OBzC are also observed in para- and ortho-cresol crystals. A classification of OBzC is given, and an especially effective projection method (rectangular projection) is suggested. M. V. Lomonosov Moscow State University, Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 5, pp. 775–789, September–October, 1995. Translated by L. Smolina     

Structural study of copper and chromium poly[3,3′-dithiobis(2,4-pentanedionates)]

The structures of copper poly[3,3′-dithiobis(2,4-pentanedionate)], obtained from 3,3′-dithiobis(2,4-pentanedione) and copper chloride, and chromium oligo-3,3′-dithiobis(2,4-pentanedionate), obtained by treating chromium tris(3-chlorosulfenyl-2,4-pentanedionate) with butyl magnesium bromide, are studied by comparing the calculated and experimental X-ray scattering functions. Optimal models for the copper and chromium polychelate structures are suggested. The structure of the macromolecular chain depends on the mutual arrangement of metallochelate nuclei, which is similar to that in a crystal matrix of a monomer, rather than on the stereochemistry of the disulfide bond. Far-East State University, Vladivostok. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 1, pp. 152–156, January–February, 1995. Translated by I. Izvekova     

Structure and thermodynamics of hydrocarbon liquids: Computer simulation based on rism theory

A system of Ornstein-Zernike integral equations is solved numerically to determine the heats of vaporization ΔH_V of liquid ethane, propane, and n-butane. It is shown that the calculations (the deformations of valence bonds and bond angles in the liquid-phase molecules are ignored) give rather accurate values of ΔH_V, which are in agreement with the corresponding experimental data. On the other hand, it is established that if there are intramolecular rotational degrees of freedom, ΔH_V depends on the angle of internal rotation ϕ. The function ΔH_V(ϕ) is minimum for trans-conformations (ϕ=0) and maximum for cis-conformations (ϕ=180°). Hence, intermolecular interactions stabilize compact (convolute) conformations. The energy of this effect is of the order of 1 kJ/mole. Tver State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 5, pp. 808–813, September–October, 1995. Translated by I. Izvekova     

Simple One-electron Invariants of Molecular Chirality

Pseudoscalar measures of electronic chirality for molecular systems are derived using the spectral moment theory applied to the frequency-dependent rotational susceptibility. In this scheme a one-electron chirality operator naturally emerges as a quantum counterpart of the triple scalar product, involving velocity, acceleration and second acceleration. Averaging over an electronic state vector gives rise to an additive chirality invariant (κ-index), considered as a quantitative measure of chirality. A simple computational technique for quick calculation of the κ-index is developed and various structural classes (cyclic hydrocarbons, cage-shaped systems, etc.) are studied. Reasonable behaviour of the chirality index is demonstrated. The chirality changes during the β-turn formation in Leu-Enkephalin is presented as a useful example of the chirality analysis for conformational transitions.     

Phase transitions,conformational lability,and intermolecular interactions in alkoxycyanobiphenyls

Vibrational spectroscopy methods (IR absorption, Raman scattering, calculations) were used to study changes in molecular structures of alkoxycyanobiphenyls during phase transitions. The spectra were measured in the 33–3500 cm⁻¹ region at temperatures of 100–450 K. The temperature dependences of the IR bands that correspond to the noncharacteristic vibrations of molecular fragments between the phenyl rings and the alkyl radicals point to the conformational polymorphism of these molecules. An analysis of the Raman bands corresponding to the characteristic vibrations of the C−H bonds of alkyl radicals [q(CH)], the C−H and C−C bonds of phenyl rings [q(CH) and Q(CC)], and the CN bonds of the cyano groups [Q(CN)] suggests significant intermolecular interactions. The conformational lability and intermolecular interactions are associated with differences in molecular packing in the substances of this homologous series. Saratov State University. Institute of Solid State Physics, Rostov State University. Institute of Physics, Uzbekistan Academy of Sciences. Samarkand State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 5, pp. 814–822, September–October, 1995. Translated by I. Izvekova