Character table for point group C5

=exp(2i/5)
C5 E C5 (C5)2 (C5)3 (C5)4
linear functions,
rotations
quadratic
functions
cubic
functions
A +1 +1 +1 +1 +1 z, Rz x2+y2, z2 z3, z(x2+y2)
E1 +1
+1
+
+*
+2
+2*
+2*
+2
+*
+
x+iy, Rx+iRy
x-iy, Rx-iRy
(yz, xz) (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2 +1
+1
+2
+2*
+*
+
+
+*
+2*
+2
- (x2-y2, xy) [xyz, z(x2-y2)] [y(3x2-y2), x(x2-3y2)]

Information for point groups with fivefold rotational axis


Additional information

Number of symmetry elements h = 5
Number of irreducible representations n = 5
Number of real irreducible representations n = 3
Abelian group yes
Optical Isomerism (Chirality) yes


Reduction formula for point group C5

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E C5 (C5)2 (C5)3 (C5)4




Multipoles

dipole (p) A+E1
quadrupole (d) A+E1+E2
octopole (f) A+E1+2E2
hexadecapole (g) A+2E1+2E2
32-pole (h) 3A+2E1+2E2
64-pole (i) 3A+3E1+2E2
128-pole (j) 3A+3E1+3E2
256-pole(k) 3A+3E1+4E2
512-pole (l) 3A+4E1+4E2

First nonvanishing multipole: dipole

Literature



Character tables for chemically important point groups Computational Laboratory for Analysis, Modeling and Visualization Jacobs University Bremen