Function uw12::four_el::calculate_ttilde(const integrals::Integrals&, const integrals::Integrals&, const utils::MatVec&)

• Defined in File four_electron_utils.hpp

Function Documentation

utils::MatVec uw12::four_el::calculate_ttilde(const integrals::Integrals &W, const integrals::Integrals &V, const utils::MatVec &tab)

Calculate matrices \(\tilde{t}_{AB}^{\sigma}\) given by:

\[\tilde{t}_{AB} = \sum_{j k} (\tilde{A} | w_{12} | k j) (j k | r_{12}^{-1} | \tilde{B}) = w_A t_{AB} v_{B} \]

for (active) occupied orbitals \(j\), occupied orbitals \(k\), and density-fitting indices \(A, B\).

Transformed integrals are given by:

\[(\tilde{A} | w_{12} | k j) = w_A (A | w_{12} | kj ) \]

where \(w_A\) are the density-fitting eigenvalues of \((A|w_{12}|B)\), and similarly for \(v_B\).

Parameters

• W – Integrals for \(w_{12}\)

• V – Integrals for \(r_{12}^{-1}\)

• tab – \(\sum_{j k} (A | w_{12} | k j) (j k | r_{12}^{-1} | B)\)

Returns

Matrices \(\tilde{t}_{AB}^{\sigma}\) {