Function uw12::three_el::calculate_xab

• Defined in File direct_utils.hpp

Function Documentation

utils::MatVec uw12::three_el::calculate_xab(const integrals::Integrals &W, const integrals::Integrals &V, const ri::ABSProjectors &abs_projectors)

Calculate matrices \(X_{AB}^{\sigma}\) given by:

\[X_{AB} = \sum_{j \mu'} (A | w_{12} | j \mu') \sum_{\nu'} [ S^{-1} ]_{\mu' \nu'} (\nu' j | r_{12}^{-1} | B) \]

for (active) occupied orbitals \(j\), ri orbitals \(\mu', \nu'\), and density-fitting indices \(A, B\). The ri indices run over the ao and auxilliary ri basis sets.

Parameters

• W – Integrals for \(w_{12}\)

• V – Integrals for \(r_{12}^{-1}\)

• abs_projectors – RI projectors \(S^{-1}\)

Returns

Matrices \(X_{AB}^{\sigma}\)