特征标表

1  若干对称操作对特征标的贡献 对称操作 对特征标的贡献 对称操作 对特征标的贡献 E 3 i -3 C2 -1 σ 1 C3 0 S3 -2 C4 1 S4 -1         2 点群特征标 1. Cs点群 Cs E σh     A' 1 1 x, y, Rz x2, y2, z2, xy A" 1 -1 z, Rx, Ry yz, xz           2. Cn点群 C2 E C2     A 1 1 z, Rz x2, y2, z2, xy B 1 -1 x, y, Rx, Ry yz, xz           C6 E C6 C3 C2 C32 C65     A 1 1 1 1 1 1     B 1 -1 1 -1 1 -1     E1 1 1 ε ε* -ε* -ε 1 1 -ε -ε* ε* ε     E2 1 1 -ε* -ε -ε -ε* 1 1 -ε* -ε -ε -ε*     Γφ 6 0 0 0 0 0                       3. Cnv点群 C2ν E C2 σν(xz) σν'(yz)     A1 1 1 1 1 z x2, y2, z2 A2 1 1 -1 -1 Rz xy B1 1 -1 1 -1 x, Ry xz B2 1 -1 -1 1 y, Rx yz               C3ν E 2C3 3σν     A1 1 1 1 z x2 + y2, z2 A2 1 1 -1 Rz   E 2 -1 0 (x, y) ( Rx, Ry) (x2 – y2, xy) (xz, yz)             C4v E 2 C4 C2 2 σν 2 σd     A1 1 1 1 1 1 z x2 + y2, z2 A2 1 1 1 -1 -1 Rz   B1 1 -1 1 1 -1   x2 – y2 B2 1 -1 1 -1 1   xy E 2 0 -2 0 0 (x, y) (Rx, Ry) (xz, yz)                 4. Cnh点群 C2h E C2 i σh     Ag 1 1 1 1 Rz x2, y2, z2, xy Bg 1 -1 1 -1 Rx, Ry xz, yz Au 1 1 -1 -1 z   Bu 1 -1 -1 1 x, y                 5. Dn点群 D3 E 2 C3 3 C2     A1 1 1 1   x2 + y2, z2 A2 1 1 -1 z, Rz   E 2 -1 0 (x, y) ( Rx, Ry) (x2 – y2, xy) (xz, yz)             D4 E 2 C4 C2=C42 2 C2' 2 C2"     A1 1 1 1 1 1   x2 + y2, z2 A2 1 1 1 -1 -1 z, Rz   B1 1 -1 1 1 -1   x2 – y2 B2 1 -1 1 -1 1   xy E 2 0 -2 0 0 (x, y) (Rx, Ry) (xz, yz)                 6. Dnh点群 D2h E C2(z) C2(y) C2(x) i σ(xy) σ(xz) σ(yz)     Ag 1 1 1 1 1 1 1 1   x2, y2, z2 B1g 1 1 -1 -1 1 1 -1 -1 Rz xy B2g 1 -1 1 -1 1 -1 1 -1 Ry xz B3g 1 -1 -1 1 1 -1 -1 1 Rx yz Au 1 1 1 1 -1 -1 -1 -1     B1u 1 1 -1 -1 -1 -1 1 1 z   B2u 1 -1 1 -1 -1 1 -1 1 y   B3u 1 -1 -1 1 -1 1 1 -1 x                         D3h E 2 C3 3 C2 σh 2S3 3σv     A1' 1 1 1 1 1 1   x2 + y2, z2 A2' 1 1 -1 1 1 -1 Rz   E' 2 -1 0 2 -1 0 (x, y) (x2 – y2, xy) A1" 1 1 1 -1 -1 -1     A2" 1 1 -1 -1 -1 1 z   E" 2 -1 0 -2 1 0 (Rx, Ry) (xz, yz)                   D4h E 2 C4 C2 2 C2' 2C2" i 2S4 σh 2 σv 2 σd     A1g 1 1 1 1 1 1 1 1 1 1   x2 + y2, z2 A2g 1 1 1 -1 -1 1 1 1 -1 -1 Rz   B1g 1 -1 1 1 -1 1 -1 1 1 -1   x2 – y2 B2g 1 -1 1 -1 1 1 -1 1 -1 1   xy Eg 2 0 -2 0 0 2 0 -2 0 0 (Rx, Ry) (xz, yz) A1u 1 1 1 1 1 -1 -1 -1 -1 -1     A2u 1 1 1 -1 -1 -1 -1 -1 1 1 z   B1u 1 -1 1 1 -1 -1 1 -1 -1 1     B2u 1 -1 1 -1 1 -1 1 -1 1 -1     Eu 2 0 -2 0 0 -2 0 2 0 0 (x, y)                             D5h E 2 C5 2 C52 5C2 σh 2S5 2S53 5σv     A1' 1 1 1 1 1 1 1 1   x2 + y2, z2 A2' 1 1 1 -1 1 1 1 -1 Rz   E1' 2 2cos72? 2cos144? 0 2 2cos72? 2cos144? 0 (x, y)   E2' 2 2cos144? 2cos72? 0 2 2cos144? 2cos72? 0   (x2 – y2, xy) A1" 1 1 1 1 -1 -1 -1 -1     A2" 1 1 1 -1 -1 -1 -1 1 z   E1" 2 2cos72? 2cos144? 0 -2 -2cos72? -2cos144? 0 (Rx, Ry) (xz, yz) E2" 2 2cos144? 2cos72? 0 -2 -2cos144? -2cos72? 0                           D6h E 2C6 2C3 C2 3C2' 3C2" i 2S3 2S6 σh 3σd 3σv Γπ 6 0 0 0 -2 0 0 0 0 -6 2 0     7. Dnd点群 D2d E 2 S4 C2 2 C2' 2 σd     A1 1 1 1 1 1   x2 + y2, z2 A2 1 1 1 -1 -1 Rz   B1 1 -1 1 1 -1   x2 – y2 B2 1 -1 1 -1 1 z xy E 2 0 -2 0 0 (x, y) (Rx, Ry) (xz, yz)                 D3d E 2 C3 3 C2 i 2S6 3σd     A1g 1 1 1 1 1 1   x2 + y2, z2 A2g 1 1 -1 1 1 -1 Rz   Eg 2 -1 0 2 -1 0 (x, y) (x2 – y2, xy) (xz, yz) A1u 1 1 1 -1 -1 -1     A2u 1 1 -1 -1 -1 1 z   Eu 2 -1 0 -2 1 0 (Rx, Ry)                     D5d E 2 C5 3 C2 2C52 i 2S103 2S10 5σd     A1g 1 1 1 1 1 1 1 1   x2 + y2, z2 A2g 1 1 1 -1 1 1 1 -1 Rz   E1g 2 2cos72? 2cos144? 0 2 2cos72? 2cos144? 0 (Rx, Ry) (xz, yz) E2g 2 2cos144? 2cos72? 0 2 2cos144? 2cos72? 0   (x2 – y2, xy) A1u 1 1 1 1 -1 -1 -1 -1     A2u 1 1 1 -1 -1 -1 -1 1 z   E1u 2 2cos72? 2cos144? 0 -2 -2cos72? -2cos144? 0 (x, y)   E2u 2 2cos144? 2cos72? 0 -2 -2cos144? -2cos72? 0                           8. Td点群 Td E 8C3 3C2 6S4 6σd     A1 1 1 1 1 1   x2 + y2 + z2 A2 1 1 1 -1 -1     E 2 -1 2 0 0   (2z2 – x2 – y2, x2 – y2) T1 3 0 -1 1 -1 (Rx, Ry, Rz)   T2 3 0 -1 -1 1 (x, y, z) (xy, xz, yz)                 9. Oh点群 Oh E 8C3 6C2 6C4 3C2 =C42 i 6S4 8S6 3σh 6σd     A1g 1 1 1 1 1 1 1 1 1 1   x2 + y2 + z2 A2g 1 1 -1 -1 1 1 -1 1 1 -1     Eg 2 -1 0 0 2 2 0 -1 2 0   (z2, x2 – y2) T1g 3 0 -1 1 -1 3 1 0 -1 -1 (Rx, Ry, Rz)   T2g 3 0 1 -1 -1 3 -1 0 -1 1   (xy, xz, yz) A1u 1 1 1 1 1 -1 -1 -1 -1 -1     A2u 1 1 -1 -1 1 -1 1 -1 -1 1     Eu 2 -1 0 0 2 -2 0 1 -2 0     T1u 3 0 -1 1 -1 -3 -1 0 1 1 (x, y, z)   T2u 3 0 1 -1 -1 -3 1 0 1 -1                               10.