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

Abstract

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.

New computer program to calculate the symmetry of molecules

“…In this paper, we freely use these functions and the reader is encouraged to consult the GAP manual [20] and Refs. [14][15][16]21].…”

“…The motivation for this study is outlined in Refs [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the reader is encouraged to consult these papers for background material as well as for basic computational techniques. Our notation is standard and taken mainly from Refs.…”

Q-conjugacy character and markaracter tables of tetraammineplatinum(II)

“…19,20 Let G be the symmetry group of tetraammineplatinum(II) (see Fig. 1), then by the following program in GAP: gap>G:=Group((2,3,4,5) (6,9,12,15,7,10,13,16,8,11,14,17), (2,3,4,5) (6,9,12,15,7,10,13,17,8,11,14,16),(2,5)(3,4)(6,15)(7,17)(8,16)(9,12)(10,14)(11,13)); gap> t:=TableOfMarks(G); Sort("t"); gap> c:=CharacterTable(G); gap>Display(t); Display(c); one obtains the mark and the character tables of tetraammineplatinum(II), hence its SCSG G can be calculated as follows: …”