原子球形群与各种点群子群的对应关系

球形群Oh (O a)TdD∞h (C∞v a)D6h (D6 a, C6v b)D4h (D4 a, C4v b)D3h (D3d c, D3 d, C3h e)C3vD2dD2h (D2 a)C2vCs
SgA1gA1Σg+A1gA1gA1'A1A1AgA1A'
SuA1uA2Σu-A1uA1uA1"A2B1AuA2A"
PgF1gF1Σg- + ΠgA2g + E1gA2g + EgA2' + E"A2 + EA2 + EB1g + B2g + B3gA2 + B1 + B2A' + 2A"
PuF1uF2Σu+ + ΠuA2u + E1uA2u + EuA2" + E'A1 + EB2 + EB1u + B2u + B3uA1 + B1 + B22A' + A"
DgEg + F2gE + F2Σg+ + Πg + ΔgA1g + E1g + E2gA1g + B1g + B2g + EgA1' + E' + E"A1 + 2EA1 + B1 + B2 + E2Ag + B1g + B2g + B3g2A1 + A2 + B1 + B23A' + 2A"
DuEu + F2uE + F1Σu- + Πu + ΔuA1u + E1u + E2uA1u + B1u + B2u + EuA1" + E' + E"A2 + 2EA1 + A2 + B1 + E2Au + B1u + B2u + B3uA1 + 2A2 + B1 + B22A' + 3A"
FgA2g + F1g + F2gA2 + F1 + F2Σg- + Πg + Δg + ΦgA2g + B1g + B2g + E1g + E2gA2g + B1g + B2g + 2EgA1" + A2' + A2" + E' + E"A1 + 2A2 + 2EA2 + B1 + B2 + 2EAg + 2B1g + 2B2g + 2B3gA1 + 2A2 + 2B1 + 2B23A' + 4A"
FuA2u + F1u + F2uA1 + F1 + F2Σu+ + Πu + Δu + ΦuA2u + B1u + B2u + E1u + E2uA2u + B1u + B2u + 2EuA1' + A2' + A2" + E' + E"2A1 + A2 + 2EA1 + A2 + B2 + 2EAu + 2B1u + 2B2u + 2B3u2A1 + A2 + 2B1 + 2B24A' + 3A"
GgA1g + Eg + F1g + F2gA1 + E + F1 + F2Σg+ + Πg + Δg + Φg + ΓgA1g + B1g + B2g + E1g + 2E2g2A1g + A2g + B1g + B2g + 2EgA1' + A1" + A2" + 2E' + E"2A1 + A2 + 3E2A1 + A2 + B1 + B2 + 2E3Ag + 2B1g + 2B2g + 2B3g3A1 + 2A2 + 2B1 + 2B25A' + 4A"
GuA1u + Eu + F1u + F2uA2 + E + F1 + F2Σu- + Πu + Δu + Φu + ΓuA1u + B1u + B2u + E1u + 2E2u2A1u + A2u + B1u + B2u + 2EuA1' + A1" + A2' + E' + 2E"A1 + 2A2 + 3EA1 + A2 + 2B1 + B2 + 2E3Au + 2B1u + 2B2u + 2B3u2A1 + 3A2 + 2B1 + 2B24A' + 5A"

a 这些点群要去掉下角标g和u。
b A1g和A2u改为A1，A2g和A1u改为A2，其余的不可约表示去掉下角标g和u。
c 去掉'和"，加上与球形群一致的g和u。
d 去掉'和"。
e 不再区分A1和A2。

来源：Herzberg, Molecular Spectra and Molecular Structure III, 表58。