quemb.molbe.eri_sparse_DF.contract_with_TA_2nd_to_dense

quemb.molbe.eri_sparse_DF.contract_with_TA_2nd_to_dense(TA, int_mu_i_P)

Contract the first dimension of int_mu_i_P with the first dimension of TA. If the result is known to be symmetric use contract_with_TA_2nd_to_sym_dense() or contract_with_TA_2nd_to_sym_sparse() instead.

Can be used to e.g. compute contractions of mixed fragment-bath integrals.

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

Returns:

A dense 3D tensor \((i a | P)\), which can have different lengths along the first two dimensions, e.g. fragment and bath orbitals. The last dimension is along the auxiliary basis.

Return type:

Tensor3D