Spin contamination
= Spin contamination
{title2=$\langle\hat S^2\rangle-S(S+1)\hbar^2$}
A <wavefunction> intended for a specified total-spin state contains components of other total spins. For an unrestricted <determinant> with one alpha and one beta orbital, $\langle S^2\rangle=1-|\langle\phi_\alpha|\phi_\beta\rangle|^2$ in units of $\hbar^2$.