$\mathrm{1\; <mo>\; :\; </mo>2\; <mo>\; :\; </mo>5\; <mo>\; :\; </mo>6\; <mo>\; :\; </mo>7}$

$\to \langle V{P}^{5}V\rangle \Delta E_1\Delta E_3{\left(\Delta E_1\right)}^2$

$\to S_1{S}_3{S}_1^2=\left(2\right)$

$\mathrm{1\; <mo>\; :\; </mo>3\; <mo>\; :\; </mo>4\; <mo>\; :\; </mo>5\; <mo>\; :\; </mo>7}$

$\to \langle V{P}^{5}V\rangle \Delta E_2{\left(\Delta E_1\right)}^2\Delta E_2$

$\to S_2{S}_1^3{S}_2=\left(1\right)$

$\mathrm{1\; <mo>\; :\; </mo>3\; <mo>\; :\; </mo>4\; <mo>\; :\; </mo>6\; <mo>\; :\; </mo>7}$

$\to \langle V{P}^{5}V\rangle \Delta E_2\Delta E_1\Delta E_2\Delta E_1$

$\to S_2{S}_1{S}_2{S}_1=\left(1\right)$

$\mathrm{1\; <mo>\; :\; </mo>3\; <mo>\; :\; </mo>5\; <mo>\; :\; </mo>6\; <mo>\; :\; </mo>7}$

$\to \langle V{P}^{5}V\rangle {\left(\Delta E_2\right)}^2{\left(\Delta E_1\right)}^2$

$\to S_2^2{S}_1^2=\left(1\right)$

$\mathrm{1\; <mo>\; :\; </mo>4\; <mo>\; :\; </mo>5\; <mo>\; :\; </mo>6\; <mo>\; :\; </mo>7}$

$\to \langle V{P}^{5}V\rangle \Delta E_3{\left(\Delta E_1\right)}^3$

$\to S_3{S}_1^3=\left(2\right)$

$\mathrm{1\; <mo>\; :\; </mo>2\; <mo>\; :\; </mo>3\; <mo>\; :\; </mo>4\; <mo>\; :\; </mo>5\; <mo>\; :\; </mo>7}$

$\to -\langle V{P}^{6}V\rangle {\left(\Delta E_1\right)}^4\Delta E_2$

$\to S_1^4{S}_2=\left(1\right)$

$\mathrm{1\; <mo>\; :\; </mo>2\; <mo>\; :\; </mo>3\; <mo>\; :\; </mo>4\; <mo>\; :\; </mo>6\; <mo>\; :\; </mo>7}$

$\to -\langle V{P}^{6}V\rangle {\left(\Delta E_1\right)}^3\Delta E_2\Delta E_1$

$\to S_1^3{S}_2{S}_1=\left(1\right)$

$\mathrm{1\; <mo>\; :\; </mo>2\; <mo>\; :\; </mo>3\; <mo>\; :\; </mo>5\; <mo>\; :\; </mo>6\; <mo>\; :\; </mo>7}$

$\to -\langle V{P}^{6}V\rangle {\left(\Delta E_1\right)}^2\Delta E_2{\left(\Delta E_1\right)}^2$

$\to S_1^2{S}_2{S}_1^2=\left(1\right)$

$\mathrm{1\; <mo>\; :\; </mo>2\; <mo>\; :\; </mo>4\; <mo>\; :\; </mo>5\; <mo>\; :\; </mo>6\; <mo>\; :\; </mo>7}$

$\to -\langle V{P}^{6}V\rangle \Delta E_1\Delta E_2{\left(\Delta E_1\right)}^3$

$\to S_1{S}_2{S}_1^3=\left(1\right)$

$\mathrm{1\; <mo>\; :\; </mo>3\; <mo>\; :\; </mo>4\; <mo>\; :\; </mo>5\; <mo>\; :\; </mo>6\; <mo>\; :\; </mo>7}$

$\to -\langle V{P}^{6}V\rangle \Delta E_2{\left(\Delta E_1\right)}^4$

$\to S_2{S}_1^4=\left(1\right)$

$\mathrm{1\; <mo>\; :\; </mo>2\; <mo>\; :\; </mo>3\; <mo>\; :\; </mo>4\; <mo>\; :\; </mo>5\; <mo>\; :\; </mo>6\; <mo>\; :\; </mo>7}$

$\to \langle V{P}^{7}V\rangle {\left(\Delta E_1\right)}^6$

$\to S_1^6=\left(1\right)$