Appendix A
Character Tables
Contents
A.1 Finite Point Groups ........................................................
192
C 1 and the Binary Groups C s ,C i ,C 2 ........................................
192
The Cyclic Groups C n (n = 3, 4, 5, 6, 7, 8) .................................... 192
The Dihedral Groups D n (n = 2, 3, 4, 5, 6) ...................................
194
The Conical Groups C nv (n = 2, 3, 4, 5, 6) .................................... 195
The C nh Groups (n = 2, 3, 4, 5, 6) ...........................................
196
The Rotation–Reflection Groups S 2n (n = 2, 3, 4) .............................. 197
The Prismatic Groups D nh (n = 2, 3, 4, 5, 6, 8) ................................ 198
The Antiprismatic Groups D nd (n = 2, 3, 4, 5, 6) .............................. 199
The Tetrahedral and Cubic Groups ........................................... 201
The Icosahedral Groups ..................................................... 202
A.2 Infinite Groups ............................................................. 203
CylindricalSymmetry ....................................................... 203
SphericalSymmetry ........................................................ 204
Character tables were introduced to chemistry through the pioneering work of
Robert Mulliken [1]. The book on “Chemical Applications of Group Theory” by
F. Albert Cotton has been instrumental in disseminating their use in chemistry [2].
Atkins, Child, and Phillips [3] produced a handy pamphlet of the point group character tables. 1
1 In the tables the columns on the right list representative coordinate functions that transform according to the corresponding irrep. The symbols R x ,R y ,R z stand for rotations about the Cartesian
directions.
A.J. Ceulemans, Group Theory Applied to Chemistry, Theoretical Chemistry and
Computational Modelling, DOI 10.1007/978-94-007-6863-5,
© Springer Science+Business Media Dordrecht 2013
191
Character Tables
Contents
A.1 Finite Point Groups ........................................................
192
C 1 and the Binary Groups C s ,C i ,C 2 ........................................
192
The Cyclic Groups C n (n = 3, 4, 5, 6, 7, 8) .................................... 192
The Dihedral Groups D n (n = 2, 3, 4, 5, 6) ...................................
194
The Conical Groups C nv (n = 2, 3, 4, 5, 6) .................................... 195
The C nh Groups (n = 2, 3, 4, 5, 6) ...........................................
196
The Rotation–Reflection Groups S 2n (n = 2, 3, 4) .............................. 197
The Prismatic Groups D nh (n = 2, 3, 4, 5, 6, 8) ................................ 198
The Antiprismatic Groups D nd (n = 2, 3, 4, 5, 6) .............................. 199
The Tetrahedral and Cubic Groups ........................................... 201
The Icosahedral Groups ..................................................... 202
A.2 Infinite Groups ............................................................. 203
CylindricalSymmetry ....................................................... 203
SphericalSymmetry ........................................................ 204
Character tables were introduced to chemistry through the pioneering work of
Robert Mulliken [1]. The book on “Chemical Applications of Group Theory” by
F. Albert Cotton has been instrumental in disseminating their use in chemistry [2].
Atkins, Child, and Phillips [3] produced a handy pamphlet of the point group character tables. 1
1 In the tables the columns on the right list representative coordinate functions that transform according to the corresponding irrep. The symbols R x ,R y ,R z stand for rotations about the Cartesian
directions.
A.J. Ceulemans, Group Theory Applied to Chemistry, Theoretical Chemistry and
Computational Modelling, DOI 10.1007/978-94-007-6863-5,
© Springer Science+Business Media Dordrecht 2013
191