DeltaIntegrals

Table of Contents

1. Brief description

\begin{equation} \langle pq \mid \delta(r_{12}) \mid rs \rangle = \int \int d\mathbf{r}_1 d\mathbf{r}_2 \psi_p^*(\mathbf{r}_1) \psi_q^*(\mathbf{r}_2) \delta(r_{12}) \psi_r (\mathbf{r}_1) \psi_s (\mathbf{r}_2) \end{equation}

with the one-dimensional Dirac delta function \(\delta(r)\) and the interelectronic distance \(r_{12}=|\mathbf{r}_1-\mathbf{r}_2|\). The delta-integrals have to be provided and cannot be evaluated within Cc4s. The integrals are needed by the BasisSetCorrection algorithm.

Only two slices of the DeltaIntegrals are currently needed by the BasisSetCorrection algorithm: DeltaIntegralsPPHH (\(\langle ab \mid \delta(r_{12}) \mid ij \rangle\)) and DeltaIntegralsHH (\(\langle ij \mid \delta(r_{12}) \mid ij \rangle\)).

2. Literature

Created: 2022-09-19 Mon 15:00