The full nonrigid group theory for trimethylamine

Abstract

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(CH 3 ) 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.

The full non-rigid group theory for TBA (tert-butyl alcohol)

“…For example, he computed the full non-rigid group for 1,3,5-triamino-2,4,6-trinitrobenzene [10], water pentamer [13] and extended aromatic C 48 N 12 azafullerene [14]. Also Ashrafi and coauthors [16][17][18][19][20][21][22][23][24][25] computed full non-rigid group of some molecules. For example they computed the full non-rigid group of tetraammine platinum(II) [16], cis-and transdichloro-diammine platinum(II) and trimethylamine [17], tetraammine platinum(II) with C 2v and C 4v point group [19], tetraamine platinum(II) as wreath product [21], tetra-tertbutyltetrahedrane [22], tetramethylethylene [23], hexamethylbenzene [24] and melamine [25].…”

“…The motivation for this study is outlined in previous publications [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and the readers are encouraged to consult these papers for background material as well as basic computational techniques.…”

Full non-rigid group theory and symmetry of melamine

“…The character table of full non-rigid groups of trimethylamine, cis-and trans-dichloro diammine platinum(II) and tetraammine platinum(II) with C 2v and C 4v point groups was computed [8][9][10].…”

“…(2,6)(3,5)(7,8)(11,13)(10,12).Then |(a 1 ) G | = 8 and |(a 2 ) G | = |(a 3 ) G | = 6. The point group of melamine can be generated by the set V 1 = {a 1 , a 2 , a 3 }, and if (a) 2,4,6-triamino-1,3,5-triazine molecule (melamine) with D 3h point group.…”

Symmetry properties of tetraammine platinum(II) with C2v and C4v point groups

“…In (Ashrafi and Hamadanian, 2003;2004;Hamadanian and Ashrafi, 2003a;2003b), the full non-rigid group of trimethylamine with C 3v point group and tetraammine platinum(II) with C 2v and C 4v point groups are computed. In this paper we compute the symmetry of these molecules.…”