In the original publication1 the expression for elements of the A and B matrices, Eq. (A1) in the Appendix, is mistaken. The correct form reads

\begin{eqnarray*}\forall _{\scriptsize\begin{array}{c}p\ne q\\r\ne s\end{array}}\quad B_{pq,rs} &=&A_{pq,sr} =(n_{p}-n_{q})(\delta _{ps}h_{qr}-\delta _{qr}h_{ps})\nonumber \\&&+\,(c_{p}c_{s}\delta _{I_{p}I_{s}}+c_{q}c_{r}\delta _{I_{q}I_{r}})(\left\langle pq|rs\right\rangle +\left\langle pq|sr\right\rangle )\nonumber \\&&+\,[n_{p}n_{s}(1-\delta _{I_{p}I_{s}})+n_{q}n_{r}(1-\delta _{I_{q}I_{r}} )-n_{p}n_{r}(1-\delta _{I_{p}I_{r}})-n_{q}n_{s}(1-\delta _{I_{q}I_{s} })]\left\langle pr||qs\right\rangle \nonumber \\&&-\,\delta _{qr}c_{p}\sum _{t}\delta _{I_{p}I_{t}}c_{t}\left\langle ps|tt\right\rangle -\delta _{ps}c_{q}\sum _{t}\delta _{I_{q}I_{t}}c_{t} \left\langle qr|tt\right\rangle -\delta _{pr}c_{r}\sum _{t}\delta _{I_{r}I_{t} }c_{t}\left\langle qs|tt\right\rangle -\delta _{qs}c_{s}\sum _{t}\delta _{I_{s}I_{t}}c_{t}\left\langle pr|tt\right\rangle \nonumber \\&&+\,\delta _{ps}\sum _{t}n_{t}[n_{p}(1-\delta _{I_{p}I_{t}})-n_{q}(1-\delta _{I_{q}I_{t}})]\left\langle qt||rt\right\rangle -\delta _{qr}\sum _{t} n_{t}[n_{p}(1-\delta _{I_{p}I_{t}})-n_{q}(1-\delta _{I_{q}I_{t}})]\left\langle pt||st\right\rangle,\end{eqnarray*}
$∀p≠qr≠sBpq,rs=Apq,sr=(np−nq)(δpshqr−δqrhps)+(cpcsδIpIs+cqcrδIqIr)(pq|rs+pq|sr)+[npns(1−δIpIs)+nqnr(1−δIqIr)−npnr(1−δIpIr)−nqns(1−δIqIs)]pr‖qs−δqrcp∑tδIpItctps|tt−δpscq∑tδIqItctqr|tt−δprcr∑tδIrItctqs|tt−δqscs∑tδIsItctpr|tt+δps∑tnt[np(1−δIpIt)−nq(1−δIqIt)]qt‖rt−δqr∑tnt[np(1−δIpIt)−nq(1−δIqIt)]pt‖st,$

where

\begin{equation*}\left\langle pq||rs\right\rangle =2\left\langle pq|rs\right\rangle -\left\langle pq|sr\right\rangle .\end{equation*}
$pq‖rs=2pq|rs−pq|sr.$
1.
K.
Pernal
,
K.
Chatterjee
, and
P. H.
Kowalski
,
J. Chem. Phys.
140
,
014101
(
2014
).