Function uw12::integrals::transformations::transform_second_index

• Defined in File transformations.hpp

Function Documentation

inline linalg::Mat uw12::integrals::transformations::transform_second_index(const linalg::Mat &J3, const linalg::Mat &C)

Transform second index of a three-index density-fitting integrals object from the ao basis using orbital matrix C.

Transform the second index of the matrix J3 of three-index density-fitting integrals \((p \mu| A)\) for ao index \(\mu\) to the space of orbitals i resulting in a matrix of three-index integrals \((p i | A)\) for df index A.

The density-fitting integrals J3 are in matrix form with n1 * n_ao rows and n3 columns. The orbital coefficient matrix C should be of size n_ao * n_i for number of ao basis functions n_ao and number of i orbitals n_i. The resulting matrix is of size (n1 * n_i) * n3.

No restriction is placed on size of n1 and n3 so may relate to any orbitals space. This function is not compatible with results of mo_transform_one_index_full. Should only be used to transform the second index an asymmetric matrix.

Parameters

• J3 – Three-index density-fitting integrals \((a \mu|A)\)

• C – Orbital coefficients \(C_{\mu i}\)

Returns

Second-index mo transformed df integrals \((a i|A)\)