1 3 1 2

$S_1^2{S}_3{S}_2=2\to \langle VPV{P}^{2}VPV{P}^{2}V\rangle \Delta E_1\Delta E_2$

(2)

$\to -\langle VPV{P}^{3}VPV{P}^{2}V\rangle {\left(\Delta E_1\right)}^3$

2 1 1 3

$S_2{S}_1^2{S}_3=2\to \langle V{P}^{2}VPVPV{P}^{2}V\rangle \Delta E_1\Delta E_2$

(2)

$\to -\langle V{P}^{2}VPVPV{P}^{3}V\rangle {\left(\Delta E_1\right)}^3$

3 1 1 2

$S_3{S}_1^2{S}_2=2\to \langle V{P}^{2}VPVPV{P}^{2}V\rangle \Delta E_2\Delta E_1$

(2)

$\to -\langle V{P}^{3}VPVPV{P}^{2}V\rangle {\left(\Delta E_1\right)}^3$

3 2 2

$S_3{S}_2^2=2\to -\langle V{P}^{2}V{P}^{2}V{P}^{2}V\rangle \Delta E_2{\left(\Delta E_1\right)}^2$

(2)

$\to \langle V{P}^{3}V{P}^{2}V{P}^{2}V\rangle {\left(\Delta E_1\right)}^4$

2 3 2

$S_2^2{S}_3=2\to -\langle V{P}^{2}V{P}^{2}V{P}^{2}V\rangle \Delta E_1\Delta E_2\Delta E_1$

(2)

$\to \langle V{P}^{2}V{P}^{3}V{P}^{2}V\rangle {\left(\Delta E_1\right)}^4$

2 2 3

$S_2^2{S}_3=2\to -\langle V{P}^{2}V{P}^{2}V{P}^{2}V\rangle {\left(\Delta E_1\right)}^2\Delta E_2$

(2)

$\to \langle V{P}^{2}V{P}^{2}V{P}^{3}V\rangle {\left(\Delta E_1\right)}^4$

3 3 1

$S_3^2{S}_1=4\to \langle V{P}^{2}V{P}^{2}VPV\rangle {\left(\Delta E_2\right)}^2$

(4)

$\to -\langle V{P}^{3}V{P}^{2}VPV\rangle {\left(\Delta E_1\right)}^2\Delta E_2$

$\to -\langle V{P}^{2}V{P}^{3}VPV\rangle \Delta E_2{\left(\Delta E_1\right)}^2$

$\to \langle V{P}^{3}V{P}^{3}VPV\rangle {\left(\Delta E_1\right)}^4$

3 1 3

$S_3^2{S}_1=4\to \langle V{P}^{2}VPV{P}^{2}V\rangle {\left(\Delta E_2\right)}^2$

(4)

$\to -\langle V{P}^{3}VPV{P}^{2}V\rangle {\left(\Delta E_1\right)}^2\Delta E_2$

$\to \langle -V{P}^{2}VPV{P}^{3}V\rangle \Delta E_2{\left(\Delta E_1\right)}^2$

$\to \langle V{P}^{3}VPV{P}^{3}V\rangle {\left(\Delta E_1\right)}^4$

1 3 3

$S_1{S}_3^2=4\to \langle VPV{P}^{2}V{P}^{2}V\rangle {\left(\Delta E_2\right)}^2$

(4)

$\to -\langle VPV{P}^{3}V{P}^{2}V\rangle {\left(\Delta E_1\right)}^2\Delta E_2$

$\to -\langle VPV{P}^{2}V{P}^{3}V\rangle \Delta E_2{\left(\Delta E_1\right)}^2$

$\to \langle VPV{P}^{3}V{P}^{3}V\rangle {\left(\Delta E_1\right)}^4$

4 1 1 1

$S_4{S}_1^3=5\to -\langle V{P}^{2}VPVPVPV\rangle \Delta E_3$

(2)

$\to \langle V{P}^{3}VPVPVPV\rangle \Delta E_1\Delta E_2$

(1)

$\to \langle V{P}^{3}VPVPVPV\rangle \Delta E_2\Delta E_1$

(1)

$\to -\langle V{P}^{4}VPVPVPV\rangle {\left(\Delta E_1\right)}^3$

(1)

1 4 1 1

$S_1^3{S}_4=5\to -\langle VPV{P}^{2}VPVPV\rangle \Delta E_3$

(2)

$\to \langle VPV{P}^{3}VPVPV\rangle \Delta E_1\Delta E_2$

(1)