UHF Spin Information

Spin Information:
  N(alpha): 2
  N(beta):  1
  <S²>:     0.750000 (ideal: 0.750000)

Fields

FieldDescription
N(alpha)Number of α electrons
N(beta)Number of β electrons
⟨S²⟩Expectation value of spin-squared operator
idealIdeal value for pure spin state: S(S+1)

Spin Contamination

For a pure spin state, ⟨S²⟩ = S(S+1) where S = (N_α - N_β)/2.

MultiplicitySIdeal ⟨S²⟩
Singlet (1)00.0
Doublet (2)1/20.75
Triplet (3)12.0
Quartet (4)3/23.75

Significant deviation from the ideal value indicates spin contamination (the determinant is not a pure spin eigenfunction). OpenQuantum reports ⟨S²⟩ for every UHF calculation.

Notes

  • RHF/ROHF always have ⟨S²⟩ = ideal value (spin-pure)
  • UHF may show spin contamination, especially for stretched bonds or transition metals
  • ROHF is spin-pure but has a more complex Fock matrix construction