quemb.molbe.eri_sparse_DF.contract_with_TA_2nd_to_sym_dense

quemb.molbe.eri_sparse_DF.contract_with_TA_2nd_to_sym_dense(TA, int_mu_i_P)

Contract the first dimension of int_mu_i_P with the first dimension of TA. We assume the result to be symmetric in the first two dimensions.

If the result is known to be non-symmetric use contract_with_TA_2nd_to_dense() instead.

Can be used to e.g. compute contractions to purely fragment, or purely bath integrals.

\[\begin{split}(i j | P) = \sum_{\mu} T_{\mu,i} (\mu j | P) \\ (a b | P) = \sum_{\mu} T_{\mu,a} (\mu b | P)\end{split}\]
Returns:

A dense 3D tensor \((i j | P)\), symmetric in the first two (MO) dimensions. The last dimension is along the auxiliary basis.

Return type:

Tensor3D