Algorithm 3.

“1permutation-abcijk” algorithm.

Rijba = Tijab
for c = 1, nv
for $b\ge c$
for $a\ge b$
$w_{ijk}={\mathcal{I}}_{i,d}^{ab}{\left(T_{jk,d}^c\right)}^{†}+T_{ij,d}^b{\left({\mathcal{I}}_{k,d}^{ca}\right)}^{†}+{\mathcal{I}}_{i,d}^{ac}{{\left(R_{jk,d}^b\right)}^{†}+R_{ij,d}^a\left({\mathcal{I}}_{k,d}^{cb}\right)}^{†}$
$v_{kij}=T_{ki,d}^a{\left({\mathcal{I}}_{j,d}^{bc}\right)}^{†}+R_{ki,d}^c{\left({\mathcal{I}}_{j,d}^{ba}\right)}^{†}$
$w_{ijk}\leftarrow T_{i,l}^{ac}{\mathcal{I}}_{l,jk}^b+{\mathcal{I}}_{ij,l}^b{T}_{l,k}^{ac}+T_{i,l}^{ab}{\left({\mathcal{I}}_{jk,l}^c\right)}^{†}$
$v_{kij}\leftarrow {\left({\mathcal{I}}_{l,ki}^c\right)}^{†}{T}_{l,j}^{ab}+{\mathcal{I}}_{ki,l}^a{T}_{l,j}^{cb}+T_{k,l}^{cb}{\mathcal{I}}_{l,ij}^a$
$w_{ijk}\leftarrow v_{kij}$
$v_{ijk}=w_{ijk}+V_{jk}^{bc}{T}_i^a+V_{ik}^{ac}{T}_j^b+V_{ij}^{ab}{T}_k^c$
Calculate energy contribution according to Eq. (A1)
end for
end for
end for