Partition

$$S_p$$

Schrödinger energy term(s)

1 1 1 1 1 1 1

1

$$\langle VPVPVPVPVPVPV\rangle$$

2 1 1 1 1 1

1

$$-\Delta E_1\langle V{P}^{2}VPVPVPVPVPV\rangle$$

1 2 1 1 1 1

1

$$-\Delta E_1\langle VPV{P}^{2}VPVPVPVPV\rangle$$

1 1 2 1 1 1

1

$$-\Delta E_1\langle VPVPV{P}^{2}VPVPVPV\rangle$$

1 1 1 2 1 1

1

$$-\Delta E_1\langle VPVPVPV{P}^{2}VPVPV\rangle$$

1 1 1 1 2 1

1

$$-\Delta E_1\langle VPVPVPVPV{P}^{2}VPV\rangle$$

1 1 1 1 1 2

1

$$-\Delta E_1\langle VPVPVPVPVPV{P}^{2}V\rangle$$

2 2 1 1 1

1

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

1 2 2 1 1

1

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

1 1 2 2 1

1

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

1 1 1 2 2

1

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

2 1 2 1 1

1

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

2 1 1 2 1

1

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

1 2 1 1 2

1

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

2 1 1 1 2

1

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

1 2 1 2 1

1

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

1 1 2 1 2

1

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

2 2 2 1

1

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

2 2 1 2

1

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

2 1 2 2

1

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

1 2 2 2

1

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

3 2 1 1

2

$$\Delta E_2\Delta E_1\langle V{P}^{2}V{P}^{2}VPVPV\rangle$$

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

3 1 2 1

2

$$\Delta E_2\Delta E_1\langle V{P}^{2}VPV{P}^{2}VPV\rangle$$

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

3 1 1 2

2

$$\Delta E_2\Delta E_1\langle V{P}^{2}VPVPV{P}^{2}V\rangle$$

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

2 3 1 1

2

$$\Delta E_1\Delta E_2\langle V{P}^{2}V{P}^{2}VPVPV\rangle$$

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

1 3 2 1

2

$$\Delta E_2\Delta E_1\langle VPV{P}^{2}V{P}^{2}VPV\rangle$$

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

1 3 1 2

2

$$\Delta E_2\Delta E_1\langle VPV{P}^{2}VPV{P}^{2}V\rangle$$

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