In mbe_pol, the potential energy is dfined as

\begin{eqnarray*} E = E_\mathrm{MBE(2)} + \kappa E_\mathrm{pol}, \end{eqnarray*}

where $\kappa$ is the scaling factor. $E_\mathrm{MBE(2)}$ is the potential energy of the second-order many-body expansion:

\begin{equation*} E_\mathrm{MBE(2)} = \sum_I \{ E_{I} - E_I^\mathrm{min}\} + \sum_{I > J} \{ E_{IJ} - E_{I} - E_{J}\} \end{equation*}

$E_\mathrm{pol}$ is the polarization energy:

\begin{aligned} E_\mathrm{pol} & = \sum_I E_I^\mathrm{pol} \\ E_I^\mathrm{pol} & = \langle \Psi_{I:Q_I} | \hat{H}_{I:Q_I} | \Psi_{I:Q_I} \rangle - \langle \Psi_I | \hat{H}_{I:Q_I} | \Psi_I \rangle \end{aligned}



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