Function uw12::integrals::transformations::mo_transform_one_index_full

Function Documentation

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

Transform one index of the three-index density-fitting integrals from the ao basis to mo orbitals using orbital matrix C.

Transform one index of the matrix J3 of three-index density-fitting integrals \((\mu\nu | A)\) for ao indices \(\mu, \nu\) to the space of orbitals k resulting in a matrix of three-index integrals \((\mu k | A)\) for df index A.

The density-fitting integrals J3 are in matrix form with n_ao * (n_ao + 1) /2 rows and nA columns. The orbital coefficient matrix C should be of size n_ao * n_occ for number of ao basis functions n_ao and number of occupied orbitals n_occ. The resulting matrix is of size (n_ao * n_occ) * nA.

Parameters

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

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

Returns

One-index transformed df integrals \((\mu k|A)\)