Function uw12::three_el::calculate_xab_dttilde

Function Documentation

linalg::Mat uw12::three_el::calculate_xab_dttilde(const linalg::Mat &W3idx_one_trans, const linalg::Mat &V3idx_one_trans, const linalg::Mat &xab, const linalg::Vec &W_vals, const linalg::Vec &V_vals, size_t n_active, size_t n_ao)

Fock contribution from the derivative of \(\tilde{t}_{AB}^{\sigma}\)

Calculates the direct three-electron fock contribution corresponding to the derivative of \(\tilde{t}_{AB}^{\sigma}\) with matrix \(X_{AB}^{\sigma'}\), given by:

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

Parameters

  • W3idx_one_trans – Integrals \((j \rho | w_{12} |A)\)

  • V3idx_one_trans – Integrals \((j \rho | r_{12}^{-1} |A)\)

  • xab – Matrix \(X_{AB}^{\sigma'}\)

  • W_vals – Vector of df eigenvalues for \((A| w_{12} |B)\)

  • V_vals – Vector of df eigenvalues for \((A| r_{12}^{-1} |B)\)

  • n_active – Number of active orbitals

  • n_ao – Number of atomic orbital basis functions

Returns

Fock matrix contribution