فهرست مطالب

Mathematical Chemistry - Volume:7 Issue:2, 2016
  • Volume:7 Issue:2, 2016
  • تاریخ انتشار: 1395/04/31
  • تعداد عناوین: 7
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  • S. Fujita Pages 111-112
  • S. Fujita* Pages 113-153
    Stereoisograms of octahedral complexes are classified into five types (type I--typeV) under the action of the corresponding RS-stereoisomeric group. Their enumeration is accomplished in a type-itemized fashion, where Fujita's proligand method developed originally for combinatorial enumeration under point groups (S. Fujita, Theor. Chem. Acc., 113, 73--79 (2005)) is extended to meet the requirement of Fujita's stereoisogram approach. The cycle index with chirality fittingness (CI-CF) of the point group O_h is modulated by taking account of the CI-CF for calculating type-V quadruplets contained in stereoisograms. The modulated CI-CF is combined with a CI-CF of the maximum chiral point group (O), a CI-CF of the maximum RS-permutation group, a CI-CF of the maximum ligand-reflection group, and a CI-CF of the RS-stereoisomeric group, so as to generate CI-CFs for evaluating type-I to type-V quadruplets. By introducing ligand-inventory functions into the CI-CFs, the numbers of quadruplets ofoctahedral complexes are obtained and shown in tabular forms. Several stereoisograms for typical complexes are depicted. Their configuration indices and C/A-descriptors are discussed on the basis of Fujita's stereoisogram approach.
    Keywords: Enumeration, stereoisogram, octahedral complex, RS, stereoisomeric group
  • S. Fujita* Pages 155-221
    My half-century journey started from synthetic organic chemistry. During the first stage of my journey, my interest in stereochemistry was initiated through the investigation on the participation of steric effects in reactive intermediates, cylophanes, strained heterocycles, and organic compounds for photography. In chemoinformatics as the next stage of the journey, I proposed the concept of imaginary transition structures (ITSs) as computer-oriented representation of organic reactions. My interest was stimulated to attack combinatorial enumeration through the investigation on enumeration of subgraphs of ITSs. Stereochemistry and combinatorial enumeration was combined in my interest, so that I reached mathematical stereochemistry as the final stage of my journey. Fujita's unit-subduced-cycle-index (USCI) approach, Fujita's proligand method, and Fujita's stereoisogram approach were developed, so as to integrate vant Hoff's way (asymmetry, stereogenicity) and Le Bel's way (dissymmetry, chirality), which caused continuous confusion in the history of stereochemistry.
    Keywords: sphericity, combinatorial enumeration, stereoisogram, stereochemistry
  • H. Sakiyama*, K. Waki Pages 223-234
    Conformers of [M(ABC)6] complex have been enumerated on the basis of computational group theory, where M is the central metal, and ABC is the ligand, bound to M through A. Based on the 16 conformers of the M(AB)6 core unit, 7173 conformers have been found for the [M(ABC)6] complex, which are assigned to nine point groups, 1 D3d, 4 D3, 4 S6, 5 C2h, 7 C3, 182 C2, 15 Cs, 23 Ci, and 6932 C1.
    Keywords: Enumeration, Conformer, Octahedral [M(ABC)6] Complex, Computational Group Theory
  • F. Shafiei*, A. Alaghebandi Pages 235-251
    Quantitative Structure-Property Relationship (QSPR) models are useful in understanding how chemical structure relates to the physicochemical properties of natural and synthetic chemicals. In the present investigation the applicability of various topological indices are tested for the QSPR study on 24 aldehydes. The topological indices used for the QSPR analysis were Randić (1) (the first order molecular connectivity), Balaban (J), Wiener (W) and Harary (H) indices. In this study, the relationship between the topological indices to the thermal energy (Eth), heat capacity (Cv) and entropy(S) of 24 aldehydes are established. The thermodynamic properties are taken from HF level using the ab initio 6-31 G basis sets from the program package Gussian 98. For obtaining appropriate QSPR model we have used multiple linear regression (MLR) techniques and followed Back ward regression analysis. The results have shown that combining the three descriptors (J, W, 1) could be used successfully for modeling and predicting the heat capacity (CV), two descriptors (J, 1) could be efficiently used for estimating the entropy (S) and one descriptors (1) could be predict the thermal energy of compounds.
    Keywords: Topological indices, Aldehydes, QSPR, MLR method
  • M. Ghorbani* Pages 253-266
    Let G be a finite group and C(G) be the family of representative conjugacy classes ofý ýsubgroups of Gý. ýThe matrix whose H,K-entry is the number of ýfixed points of the set G/K under the action of H is called theý ýtable of marks of G where H,K run through all elements iný C(G)ý. Shinsaku Fujita for the first time introduced the term “markaracter” to discuss marks for permutation representations and characters for linear representations in a common basis. In this paper, we compute these tables for some classes of finite groups.
    Keywords: group action, automorphism group, mark table, markaracter table
  • B. Davvaz* Pages 267-283
    The concept of weak algebraic hyperstructures or Hv-structures constitutes a generalization of the well-known algebraic hyperstructures (semihypergroup, hypergroup and so on). The overall aim of this paper is to present an introduction to some of the results, methods and ideas about chemical examples of weak algebraic hyperstructures.
    In this paper after an introduction of basic definitions
    and results about weak algebraic hyperstructures, we review:(1) Weak algebraic hyperstructures associated with chain reactions.
    (2) Weak algebraic hyperstructures associated with dismutation reactions
    (3) Weak algebraic hyperstructures associated with redox reactions.
    Keywords: Weak algebraic hyperstructure, chain reaction, dismutation reaction, redox reaction