spin_contamination

sisl.physics.electron.spin_contamination(state_alpha, state_beta, S=None, sum=True)

Calculate the spin contamination value between two spin states

This calculation only makes sense for spin-polarized calculations.

The contamination value is calculated using the following formula:

$$\begin{array}{rl}{S}_{\alpha ,i}^2& =\sum _j|⟨{\psi }_j^{\beta }|\mathbf{S}|{\psi }_i^{\alpha }⟩{|}^2\\ S_{\beta ,j}^2& =\sum _i|⟨{\psi }_i^{\alpha }|\mathbf{S}|{\psi }_j^{\beta }⟩{|}^2\end{array}$$

where $\alpha$ and $\beta$ are different spin-components.

The arrays $S_{\alpha }^2$ and $S_{\beta }^2$ are returned.

Parameters:

• state_alpha (ndarray) – vectors describing the electronic states of spin-channel $\alpha$, 2nd dimension contains the states

• state_beta (ndarray) – vectors describing the electronic states of spin-channel $\beta$, 2nd dimension contains the states

• S (ndarray, optional) – overlap matrix used in the $⟨\psi |\mathbf{S}|\psi ⟩$ calculation. If None the identity matrix is assumed. The overlap matrix should correspond to the system and $\mathbf{k}$ point the eigenvectors have been evaluated at.

• sum (bool) – whether the spin-contamination should be summed for all states (a single number returned). If sum, a spin-contamination per state per spin-channel will be returned.

Return type:

oplist

Notes

state_alpha and state_beta need not have the same number of states.

Returns:

spin squared expectation value per spin channel $\alpha$ and $\beta$. If sum is true, only a single number is returned (not a oplist, otherwise a list for each state.

Return type:

oplist

Parameters:

sum (bool)