TABLE II.

Working equations and their scaling for the evaluation of MP2 density matrices.

Step	Scaling
1 Assemble (ai|bj) list
$(ai|bj)={\sum }_Q{J}_{ai}^Q{J}_{bj}^Q$	$n_{\mathrm{occ}}^2{n}_{\mathrm{virt}}^2{n}_{\mathrm{aux}}$
2 Compute $T_{ij}^{ab}$
$T_{ij}^{ab}=(ai|bj)/D_{ij}^{ab}$	$n_{\mathrm{occ}}^2{n}_{\mathrm{virt}}^2$
3 Compute intermediate $X_{ij}^{ab}$
$X_{ij}^{ab}=2T_{ij}^{ab}-T_{ij}^{ba}$	$n_{\mathrm{occ}}^2{n}_{\mathrm{virt}}^2$
4 Compute density matrices
${\overline{D}}_{ij}^{\mathrm{MP2}}={\sum }_{kab}{T}_{ik}^{ab}{X}_{jk}^{ab}$	$n_{\mathrm{occ}}^3{n}_{\mathrm{virt}}^2$
$D_{ab}^{\mathrm{MP2}}={\sum }_{ijc}{T}_{ij}^{ca}{X}_{ij}^{cb}$	$n_{\mathrm{occ}}^2{n}_{\mathrm{virt}}^3$