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We can compute the Born charges from the electric-field response in either finite or periodic systems (as a complementary approach to using the vibrational response):  \begin{align}  Z^{*}_{i j \alpha} = -\frac{\partial^2 E}{\partial \mathcal{E}_i \partial R_{j \alpha}} = \frac{\partial F_{j \alpha}}{\partial \mathcal{E}_i} \\ \nonumber  = Z_\alpha \delta_ij} \delta_{ij}  - \sum_n^{\rm occ} \left[ \left< \varphi_n \left| \frac{\partial V_{\alpha}}{\partial r_i} \right| \frac{\partial \varphi_n}{\partial \mathcal{E}_j} \right> + {\rm cc.} \right] \end{align}  This expression can be evaluated with the same approach as for the dynamical matrix elements, and is easily generalized to non-zero frequency too.  We can also make the previous expression Eq. \ref{eq:Born} for Born charges from the vibrational perturbation usable in a periodic system with the replacement $\vec{r} \varphi \rightarrow -i \partial \varphi/\partial k$.