Another potential issue of this hemi-density approach is that the Cholesky decomposition is only possible for Hermitian, positive-semidefinite matrices (i.e. matrices with only real eigenvalues greater than or equal to 0). While the response matrix is always Hermitian, it is only required to be positive-definite in the static limit . This method would also require extensive updates to the typical linear response implementation, as generally the response matrix is not formed explicitly, but rather the perturbed density is formed through an iterative process. Therefore, we implemented it only as an external Python script.