Iranian Journal of Mathematical Chemistry
Year:2016 | Volume:7 | Issue:2|Papers Count:7

Stereoisograms of octahedral complexes are classified into five types (type I–type V) under the action of the correspondingRS -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 Oh 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 maximumRS -permutation group, a CI-CF of the maximum ligand-reflection group, and a CI-CF of theRS -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 of octahedral 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.

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 unitsubduced-cycle-index (USCI) approach, Fujita’s proligand method, and Fujita’s stereoisogram approach were developed, so as to integrate van’t Hoff’s way (asymmetry, stereogenicity) and Le Bel’s way (dissymmetry, chirality), which caused continuous confusion in the history of stereochemistry.

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.

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 RandiC (1X) (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, 1X) could be used successfully for modeling and predicting the heat capacity (CV), two descriptors (J, 1X) could be efficiently used for estimating the entropy (S) and one descriptors (1X) could be predict the thermal energy of compounds.

LetG be a finite group and C (G) be the family of representative conjugacy classes of subgroups ofG. The matrix whose H, K -entry is the number of fixed points of the set G/Kunder the action of H is called the table of marks of G where H, K run through all elements inC (G). 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.

The concept of weak algebraic hyperstructures orHv -structures constitute 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.