线形分子点群与各种子群的对应关系

说明：线形分子的分子轴选为z轴。轴点群假定与主对称轴一致，但是对点群D2h，C2v，C2h，和Cs给出了线形轴相对位置与几种分子轴的关系。

D∞h aD6h (D6 a)C6vD4h (D4 a)D3h (D3 b,c)C3vD2d

D2h

C2v

C2h

Cs
z --> zz --> xz --> zz --> yz --> xz --> zz --> x,yσh --> σσv --> σ
Σg+A1gA1A1gA1'A1A1AgAgA1A1A1AgAgA'A'
Σu+A2uA1A2uA2"A1B2B1uB3uA1B2B1AuBuA"A'
Σg-A2gA2A2gA2'A2A2B1gB3gA2B1B2AgBgA'A"
Σu-A1uA2A1uA1"A2B1AuAuA2A2A2AuAuA"A"
ΠgE1gE1EgE"EEB2g + B3gB1g + B2gB1 + B2A2 + B2A2 + B12BgAg + Bg2A"A' + A"
ΠuE1uE1EuE'EEB2u + B3uB1u + B2uB1 + B2A1 + B1A1 + B22BuAu + Bu2A'A' + A"
ΔgE2gE2B1g + B2gE'EB1 + B2Ag + B1gAg + B3gA1 + A2A1 + B1A1 + B22AgAg + Bg2A'A' + A"
ΔuE2uE2B1u + B2uE"EA1 + A2Au + B1uAu + B3uA1 + A2A2 + B2A2 + B12AuAu + Bu2A"A' + A"
ΦgB1g + B2gB1 + B2EgA1" + A2"A1 + A2EB2g + B3gB1g + B2gB1 + B2A2 + B2A2 + B12BgAg + Bg2A"A' + A"
ΦuB1u + B2uB1 + B2EuA1' + A2'A1 + A2EB2u + B3uB1u + B2uB1 + B2A1 + B1A1 + B22BuAu + Bu2A'A' + A"
ΓgE2gE2A1g + A2gE'EA1 + A2Ag + B1gAg + B3gA1 + A2A1 + B1A1 + B22AgAg + Bg2A'A' + A"
ΓuE2uE2A1u + A2uE"EB1 + B2Au + B1uAu + B3uA1 + A2A2 + B2A2 + B12AuAu + Bu2A"A' + A"

a 对于C∞v，D6，D4，和C2，去掉下角标g和u。
b 对于D3，去掉'和"。
c 对于D3d去掉'和"，加上与D∞h一致的g和u。

来源：Herzberg, Molecular Spectra and Molecular Structure III, 表59。