Function uw12::three_el::calculate_ttilde_dxab

Function Documentation

linalg::Mat uw12::three_el::calculate_ttilde_dxab(const integrals::Integrals &W, const integrals::Integrals &V, const linalg::Mat &ttilde, const ri::ABSProjectors &abs_projectors)

Fock contribution from the derivative of \(X_{AB}^{\sigma}\)

Calculates the direct three-electron fock contribution corresponding to the derivative of \(X_{AB}^{\sigma}\) with matrix \(\tilde{t}_{AB}^{\sigma}\), given by:

\[F_{\alpha\beta}^{\sigma\sigma'} = \sum_{AB} \tilde{t}_{AB}^{\sigma'} \frac{d X_{AB}^{\sigma}}{d D_{\alpha_\beta}} \]

Parameters

  • W – Integrals for \(w_{12}\)

  • V – Integrals for \(r_{12}^{-1}\)

  • ttilde – Matrix \(\tilde{t}_{AB}^{\sigma'}\)

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

Returns

Fock matrix contribution