## Character table for point group D5d

(x axis coincident with C'2 axis)
 D5d E 2C5 2(C5)2 5C'2 i 2(S10)3 2S10 5d linear functions,rotations quadraticfunctions cubicfunctions A1g +1 +1 +1 +1 +1 +1 +1 +1 - x2+y2, z2 - A2g +1 +1 +1 -1 +1 +1 +1 -1 Rz - - E1g +2 +2cos(2/5) +2cos(4/5) 0 +2 +2cos(2/5) +2cos(4/5) 0 (Rx, Ry) (xz, yz) - E2g +2 +2cos(4/5) +2cos(2/5) 0 +2 +2cos(4/5) +2cos(2/5) 0 - (x2-y2, xy) - A1u +1 +1 +1 +1 -1 -1 -1 -1 - - - A2u +1 +1 +1 -1 -1 -1 -1 +1 z - z3, z(x2+y2) E1u +2 +2cos(2/5) +2cos(4/5) 0 -2 -2cos(2/5) -2cos(4/5) 0 (x, y) - (xz2, yz2) [x(x2+y2), y(x2+y2)] E2u +2 +2cos(4/5) +2cos(2/5) 0 -2 -2cos(4/5) -2cos(2/5) 0 - - [xyz, z(x2-y2)] [y(3x2-y2), x(x2-3y2)]

Information for point groups with fivefold rotational axis

 Cs , Ci , C2 , C5 , D5 , C5v , C2h , S10 Number of symmetry elements h = 20 Number of irreducible representations n = 8 Abelian group no Number of subgroups 8 Subgroups Optical Isomerism (Chirality) no Polar no

## Reduction formula for point group D5d

Type of representation

general 3N vib

E 2C5 2(C5)2 5C'2 i 2(S10)3 2S10 5d

## Multipoles

dipole (p) A2u+E1u A1g+E1g+E2g A2u+E1u+2E2u A1g+2E1g+2E2g A1u+2A2u+2E1u+2E2u 2A1g+A2g+3E1g+2E2g A1u+2A2u+3E1u+3E2u 2A1g+A2g+3E1g+4E2g A1u+2A2u+4E1u+4E2u