## Character table for point group D8

 D8 E 2C8 2C4 2(C8)3 C2 4C'2 4C''2 linear functions,rotations quadraticfunctions cubicfunctions A1 +1 +1 +1 +1 +1 +1 +1 - x2+y2, z2 - A2 +1 +1 +1 +1 +1 -1 -1 z, Rz - z3, z(x2+y2) B1 +1 -1 +1 -1 +1 +1 -1 - - - B2 +1 -1 +1 -1 +1 -1 +1 - - - E1 +2 +(2)½ 0 -(2)½ -2 0 0 (x, y) (Rx, Ry) (xz, yz) (xz2, yz2) [x(x2+y2), y(x2+y2)] E2 +2 0 -2 0 +2 0 0 - (x2-y2, xy) [xyz, z(x2-y2)] E3 +2 -(2)½ 0 +(2)½ -2 0 0 - - [y(3x2-y2), x(x2-3y2)]

 C2 (3) , C4 , C8 , D2 (2) , D4 (2) Number of symmetry elements h = 16 Number of irreducible representations n = 7 Abelian group no Number of subgroups 9 Number of distinct subgroups 5 Subgroups (Number of different orientations) Optical Isomerism (Chirality) yes Polar no

## Reduction formula for point group D8

Type of representation

general 3N vib

E 2C8 2C4 2(C8)3 C2 4C'2 4C''2

## Multipoles

dipole (p) A2+E1 A1+E1+E2 A2+E1+E2+E3 A1+B1+B2+E1+E2+E3 A2+B1+B2+E1+E2+2E3 A1+B1+B2+E1+2E2+2E3 A2+B1+B2+2E1+2E2+2E3 2A1+A2+B1+B2+2E1+2E2+2E3 A1+2A2+B1+B2+3E1+2E2+2E3