ffsim.contract.contract_diag_coulomb

ffsim.contract.contract_diag_coulomb(vec, mat, norb, nelec, *, z_representation=False)[source]

Contract a diagonal Coulomb operator with a vector.

A diagonal Coulomb operator has the form

\[\begin{split}\sum_{\substack{ij \\ \sigma \tau}} Z^{(\sigma \tau)}_{ij} n_{i\sigma} n_{j\tau} / 2\end{split}\]

where \(n_{i\sigma}\) denotes the number operator on orbital \(i\) with spin \(\sigma\) and \(Z^{(\sigma \tau)}\) is a real-valued matrix

Parameters:

  • vec (ndarray) – The state vector to be transformed.

  • mat (ndarray | tuple[ndarray | None, ndarray | None, ndarray | None]) – The diagonal Coulomb matrix \(Z\). You can pass either a single Numpy array specifying the coefficients to use for all spin interactions, or you can pass a tuple of three Numpy arrays specifying independent coefficients for alpha-alpha, alpha-beta, and beta-beta interactions (in that order). If passing a tuple, you can set a tuple element to None to indicate the absence of interactions of that type.

  • norb (int) – The number of spatial orbitals.

  • nelec (tuple[int, int]) – The number of alpha and beta electrons.

  • z_representation (bool) – Whether the input matrices are in the “Z” representation.

Return type:

ndarray

Returns:

The result of applying the diagonal Coulomb operator on the input state vector.