Phonon non-analytical term correction

The non-analytical term correction (NAC) corrects the dynamical matrices using (Baroni, 2001, p527; Zhang et al., 2022),

$\tilde{D}_{\kappa \alpha, \kappa^{\prime} \beta}^{\mathrm{NA}}(\boldsymbol{q})=\frac{4 \pi}{\Omega \sqrt{M_{\kappa} M_{\kappa^{\prime}}}} \frac{\left(\sum_{\gamma} q_{\gamma} Z_{\kappa, \gamma \alpha}^{*}\right)\left(\sum_{\gamma^{\prime}} q_{\gamma^{\prime}} Z_{\kappa^{\prime}, \gamma^{\prime} \beta}^{*}\right)}{\sum_{\alpha \beta} q_{\alpha} \epsilon_{\alpha \beta}^{\infty} q_{\beta}}$

where the $Z^*$ denotes the Born effective charge and $\epsilon^\infty$ denotes the dielectric constant.

In phonopy, this is achieved by performing a separate VASP run with LEPSILON = .TRUE. and a denser $k$ -mesh to calculate the $Z^*$ and $\epsilon^\infty$ , then use phonopy-vasp-born to post-process and create a BORN file.

References

Formulations — Phonopy v.2.15.0
Setting tags — Phonopy v.2.15.0
Auxiliary tools — Phonopy v.2.15.0
VASP & phonopy calculation — Phonopy v.2.15.0
LEPSILON - Vaspwiki
Ionic contributions to the frequency dependent dielectric function of NaCl - Vaspwiki
Phonons & Phonopy: Pro Tips - J. M. Skelton
Baroni, S., de Gironcoli, S., Dal Corso, A., & Giannozzi, P. (2001). Phonons and related crystal properties from density-functional perturbation theory. Reviews of Modern Physics, 73(2), 515–562. https://doi.org/10.1103/RevModPhys.73.515
Zhang, L., Wang, H., Muniz, M. C., Panagiotopoulos, A. Z., Car, R., & E, W. (2022). A deep potential model with long-range electrostatic interactions. The Journal of Chemical Physics, 156(12), 124107. https://doi.org/10.1063/5.0083669