The Full Non-Rigid Group Theory for cis- and trans-Dichlorodiammine Platinum(II) and Trimethylamine

The non-rigid molecule group theory (NRG), in which the dynamical symmetry operations are defined as physical operations, is a new field of chemistry. In a series of papers Smeyers applied this notion to determine the character table of restricted NRG (r-NRG) of some molecules. For example, Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the r-NRG of this molecule is a group of order 648, containing two subgroups of order 324 without inversions (see J. Math. Chem. 28 (2000) 377–388). In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of AH3 groups attached to a rigid framework. We have studied the full non-rigid group (f-NRG) of cis- and trans-dichlorodiammine platinum(II) and trimethylamine and we have proven that they are groups of orders 36, 72 and 1296 with 9, 18 and 28 conjugacy classes, respectively. This shows that the full non-rigid group and the restricted non-rigid group of these molecules are not isomorphic. The method can be generalized to apply to other non-rigid molecules. The f-NRG molecule group theory is shown to be used advantageously to study the internal dynamics of such molecules

Simetrijska svojstva nekih kemijskih grafova

Let G be a weighted graph with the adjacency matrix A = [aij]. A Euclidean graph associated with a molecule is defined by a weighted graph with the adjacency matrix D = [dij], where for i ≠ j, dij is the Euclidean distance between the nuclei i and j. In this matrix, dii can be taken to be zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian computed the Euclidean graphs and automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene (see Chem. Phys. Letters 232 (1995) 415–423). The present work describes a simple computational method by means of which it is possible to calculate the automorphism group of weighted graphs. We have applied this method to compute the symmetry of trimethylamine and cubane.Neka je G uteženi graf s matricom susjedstva A = [aij]. Euklidski graf pridružen molekuli definiran je kao uteženi graf s matricom susjedstva D = [dij], gdje je dij euklidska udaljenost između čvorova i i j. U toj matrici dijagonalni elementi dii jednaki su nuli, ako su svi čvorovi grafa ekvivalentni. Ako nisu, tada se uvode težine za različite čvorove. Balasubramanian je izračunao euklidske grafove i grupe automorfizama benzena, otkrivene i zasjenjene konformacije etana i ferocena (vidi Chem. Phys. Lett. 232 (1995) 415–423). U ovome radu je prikazana jednostavna računska metoda pomoću koje se mogu računati grupe automorfizama za utežene grafove. Metoda je ilustrirana na računanju simetrijskih svojstava grafova kojima su prikazani trimetilamin i kuban

The Full Non-Rigid Group Theory for Tetraammine Platinum(II)

The non-rigid molecule group theory (NRG), in which the dynamical symmetry operations are defined as physical operations, is a new field of chemistry. In a series of papers Smeyers applied this notion to determine the character table of restricted NRG of some molecules. In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of NH3 groups attached to a rigid framework. We have studied the full non-rigid group (f-NRG) of tetraammine platinum(II) with the symmetry group C2v and we have proven that it is a group of order 216 with 27 conjugacy classes. We have also computed the character table of this group

The Full Non-Rigid Group Theory for Tetraammine Platinum(II)

The non-rigid molecule group theory (NRG), in which the dynamical symmetry operations are defined as physical operations, is a new field of chemistry. In a series of papers Smeyers applied this notion to determine the character table of restricted NRG of some molecules. In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of NH3 groups attached to a rigid framework. We have studied the full non-rigid group (f-NRG) of tetraammine platinum(II) with the symmetry group C2v and we have proven that it is a group of order 216 with 27 conjugacy classes. We have also computed the character table of this group

The full nonrigid group theory for trimethylamine

The nonrigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this note, a simple method is described by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of methyl groups attached to a rigid framework. We study the full NRG of trimethylamine N(CH3)3 and prove that it is a group of order 1296 with 28 conjugacy classes. The method can be generalized to apply to other nonrigid molecules. The full nonrigid (f-NRG) molecule group theory is seen to be used advantageously to study the internal dynamics of such molecules

The Full Non-Rigid Group Theory for cis- and trans-Dichlorodiammine Platinum(II) and Trimethylamine

The non-rigid molecule group theory (NRG), in which the dynamical symmetry operations are defined as physical operations, is a new field of chemistry. In a series of papers Smeyers applied this notion to determine the character table of restricted NRG (r-NRG) of some molecules. For example, Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the r-NRG of this molecule is a group of order 648, containing two subgroups of order 324 without inversions (see J. Math. Chem. 28 (2000) 377–388). In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of AH3 groups attached to a rigid framework. We have studied the full non-rigid group (f-NRG) of cis- and trans-dichlorodiammine platinum(II) and trimethylamine and we have proven that they are groups of orders 36, 72 and 1296 with 9, 18 and 28 conjugacy classes, respectively. This shows that the full non-rigid group and the restricted non-rigid group of these molecules are not isomorphic. The method can be generalized to apply to other non-rigid molecules. The f-NRG molecule group theory is shown to be used advantageously to study the internal dynamics of such molecules

© Hindawi Publishing Corp. THE FULL NONRIGID GROUP THEORY FOR TRIMETHYLAMINE

The nonrigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this note, a simple method is described by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of methyl groups attached to a rigid framework. We study the full NRG of trimethylamine N(CH3)3 and prove that it is a group of order 1296 with 28 conjugacy classes. The method can be generalized to apply to other nonrigid molecules. The full nonrigid (f-NRG) molecule group theory is seen to be used advantageously to study the internal dynamics of such molecules. 2000 Mathematics Subject Classification: 92E10. 1. Introduction. Group theory for nonrigid molecules (NRG), developed to accommodate two distinct points of view, has grown in popularity recently. Smeyers in [8] and others in [10, 12, 13] list among the areas of applicatio

Symmetry properties of tetraammine platinum(II) with C(2v) and C(4v) point groups

Let G be a weighted graph with adjacency matrix A=[a(ij)]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[d(ij)], where for i≠j, d(ij) is the Euclidean distance between the nuclei i and j. In this matrix d(ii) can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of tetraammine platinum(II) with C(2v) and C(4v) point groups

Molecular dynamics simulation and thermo-mechanical characterization for optimization of three-phase epoxy/TiO2/SiO2 nano-composites

In this research, experimental and theoretical method are used to improve and optimized the thermo-mechanical properties of hybrid Epoxy/TiO2/SiO2 nano-Composites. For investigation of the influence of weight percentage of Silica toward Titana in TiO2–SiO2 hybrid nanoparticles on tensile properties of epoxy, the composite was optimized by surface methodology. Thirteen experiments were designed by using design expert commercial software totally. The TiO2–SiO2 hybrid nanoparticles were synthesized by sol-gel method. Then, epoxy/TiO2–SiO2 nanocomposites were prepared by direct mixing method. Four factors as elongation at break (EAB), yield strength (σy), ultimate strength (σu) and elastic modulus (E) were investigated by using tensile test device. The optimization results showed that the best (EAB), (σy), (σu) and (E) outcomes are 29.3, 17.72, 17.43 and 4.34% respectively with 14.64% weight percent of Silica in total amount of TiO2–SiO2 0.73% hybrid nanoparticles. In order to investigate the chemical and thermo-mechanical properties of nanocomposite as tensile tests, TGA, XRD, FT-IR, SEM, EDX and DRS analysis were performed. In addition, due to the high reliability in predicting the reaction among different materials and comparing with the results of experimental work, which is based on polymer-nanoparticle interaction energy, molecular dynamics simulation (MD) were used. The simulations were performed by using materials studio (MS) software. The numerical and analytical results show that the presence of small amount of Silica beside Titanium creates a strong interaction between fillers and epoxy resin