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

E3i-3 C2-1σ1 C 30S 3-2 C 41S 4-1

2点群特征标表

1.C s 点群

CsE σh A'11x,y,R z x

2

,y 2,z 2

,xy

A"1-1z,R x ,R y yz,xz

2.C n 点群

C2EC2 A11z,R z x

2

,y 2,z 2

,xy

B1-1x,y,Rx,Ryyz,xz

2C 65

C 6EC 6C 3C 2C 3 A111111 B1-11-11-1

E 11

ε * -ε 1-ε * ε 1

* ε -ε 1 *

-ε ε

E21

1 * -ε -ε

-ε * -ε

1 1

* -ε -ε

-ε * -ε

Γφ600000 3.C nv 点群

C2νEC2σν(xz)σν'(yz) 222

A11111zx,y,z A 211-1-1R z xy B 11-11-1x,R y xz B21-1-11y,Rxyz

C3νE2C33σν A1111zx

2

+y 2,z 2

A211-1Rz

2 E2-10(x,y)(R x ,R y )(x

–y 2

,xy)(xz,yz) 2

,xy)(xz,yz )

C4vE2C4C22σν2σd

2 A111111zx 22

+y,z 1

B 11-111-1x

2

–y 2

B 21-11-11xy

E20-200(x,y)(Rx,Ry)(xz,yz)

4.C nh 点群

C 2h EC 2i σh Ag1111Rzx

2

,y 2,z 2

,xy

B g 1-11-1R x ,R y xz,yz A u 11-1-1z Bu1-1-11x,y

5.D n 点群

D 3E2C 33C 2 A 1111x

2

+y 2,z 2

A211-1z,Rz

2 E2-10(x,y)(Rx,Ry)(x

–y 2

,xy)(xz,yz) 2

,xy)(xz,yz )

22C 2'2C 2"D 4E2C 4C 2=C 4 A111111x

2

+y 2,z 2

A2111-1-1z,Rz

2 B 11-111-1x 2 –y

B 21-11-11xy

E20-200(x,y)(Rx,Ry)(xz,yz)

6.D nh 点群

D2hEC2(z)C2(y)C2(x)i σ(xy)σ(xz)σ(yz) A g 11111111x

2

,y 2,z 2

B 1g 11-1-111-1-1R z xy B 2g 1-11-11-11-1R y xz B3g1-1-111-1-11Rxyz A u 1111-1-1-1-1 B 1u 11-1-1-1-111z B2u1-11-1-11-11y B3u1-1-11-111-1x D 3h E2

C 33C 2σh 2S 33σv

2+y2,z2 A2'11-111-1Rz

2

2 E'2-102-10(x,y)(x 2 –y,xy)

A 1"111-1-1-1 A 2"11-1-1-11z

E"2-10-210(Rx,Ry)(xz,yz)

D 4h E2C 4C 22C 2'2C 2"i2S 4σh 2σv 2σd A 1g 1111111111x

2

+y 2,z 2

A2g111-1-1111-1-1Rz

2 B1g1-111-11-111-1x 2 –y

B 2g 1-11-111-11-11xy

E g 20-20020-200(R x ,R y )(xz,yz) A1u11111-1-1-1-1-1 A2u111-1-1-1-1-111z B 1u 1-111-1-11-1-11 B 2u 1-11-11-11-11-1 E u 20-200-20200(x,y)

25C 2σh 2S 52S 53

5σv D 5h E2C 52C 5 A1'11111111x

2

+y 2,z 2

A2'111-1111-1Rz

E 1'22cos72?2cos144?022cos72?2cos144?0(x,y)

2 E 2'22cos144?2cos72?022cos144?2cos72?0(x –y 2

,xy) 2

,xy)

A1"1111-1-1-1-1 A2"111-1-1-1-11z

E 1"22cos72?2cos144?0-2-2cos72?-2cos144?0(R x ,R y )(xz,yz) E 2"22cos144?2cos72?0-2-2cos144?-2cos72?0

D 6h E2C 62C 3C 23C 2'3C 2"i2S 32S 6σh 3σd 3σv Γπ6000-20000-620

7.D nd 点群

D 2dE2S4C22C2'2σd A 111111x

2

+y 2,z 2

A 2111-1-1R z

2 B11-111-1x 2

–y

B21-11-11zxy

E20-200(x,y)(R x ,R y )(xz,yz)

3

D3dE2C33C2i2S63σd A 1g 111111x

2

+y 2,z 2

A 2g 11-111-1R z

2 Eg2-102-10(x,y)(x –y 2

,xy)(xz,yz) 2

,xy)(xz,yz)

A1u111-1-1-1 A 2u 11-1-1-11z E u 2-10-210(R x ,R y )

2i2S1032S105σdD5dE2C53C22C5 A 1g 11111111x

2

+y 2,z 2

A 2g 111-1111-1R z

E1g22cos72?2cos144?022cos72?2cos144?0(Rx,Ry)(xz,yz)

2 E2g22cos144?2cos72?022cos144?2cos72?0(x 2

–y,xy)

A 1u 1111-1-1-1-1 A 2u 111-1-1-1-11z

E 1u 22cos72?2cos144?0-2-2cos72?-2cos144?0(x,y) E2u22cos144?2cos72?0-2-2cos144?-2cos72?0

8.T d 点群

TdE8C33C26S46σd A 111111x

2

+y 2+z 2

A 2111-1-1

2 E2-1200(2z

2 –x –y 2,x 2–y 2)

2,x 2–y 2)

T130-11-1(Rx,Ry,Rz) T 230-1-11(x,y,z)(xy,xz,yz)

9.O h 点群

O h E8C 36C 26C 4

3C2 2i6S 48S 63σh 6σd =C 4

A 1g 1111111111x

2

+y 2+z 2

A2g11-1-111-111-1 E g 2-100220-120(z

2

,x 2–y 2

)

T 1g 30-11-1310-1-1(R x ,R y ,R z ) T 2g 301-1-13-10-11(xy,xz,yz) A1u11111-1-1-1-1-1 A2u11-1-11-11-1-11 E u 2-1002-201-20 T 1u 30-11-1-3-1011(x,y,z) T2u301-1-1-3101-1

10.

4

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