Spectral representation analysis of dielectric screening in solids and molecules

We propose a new approach to identifying and rationalizing the contribution of core electron polarization to dielectric screening, based on ab initio calculations of the dielectric matrix in its eigenpotential basis. We also present calculations of phonon frequencies, dielectric constants, and quasiparticle energies of several systems, and we discuss the quantitative effect of including core polarization. Our findings illustrate efficient ways of approximating the spectral decomposition of dielectric matrices used, e.g., in many-body perturbation theory and dielectric constant calculations, with substantial computational gains for large systems composed of heavy atoms.

Figure 1

Lowest 15 bands of the dielectric band structure (DBS) for fcc crystal NaH obtained by using core valence partitions with (a) one valence electron (VE) and (b) nine VEs (SC) for Na (see text). The (colored) circles in (a) and (b) show the magnitude of the projections $\langle {\zeta }_m^{\mathrm{SC}}\left({\mathbf{q}}_{\mathbf{o}}\right)|{\zeta }_j^{\mathrm{VE}}\left(\mathbf{q}\right)\rangle$ and $\langle {\zeta }_m^{\mathrm{SC}}\left({\mathbf{q}}_{\mathbf{o}}\right)|{\zeta }_j^{\mathrm{SC}}\left(\mathbf{q}\right)\rangle$ of the eigenpotentials of ${\left({\tilde{\epsilon }}^{\mathrm{SC}}\right)}^{-1}$, $|{\zeta }_m^{\mathrm{SC}}\left({\mathbf{q}}_{\mathbf{o}}\right)\rangle$ at a ${\mathbf{q}}_{\mathbf{o}}$ point near $\mathbf{q}=0$ onto the eigenpotentials of ${\left({\tilde{\epsilon }}^{\mathrm{VE}}\right)}^{-1}$ and ${\left({\tilde{\epsilon }}^{\mathrm{SC}}\right)}^{-1}$, respectively. (c) Inverse participation ratio (IPR) of the DM eigenpotentials of the SC and VE partitions at the $\Gamma$ point. (d) IPR; the circle size is the projection ($1-F_m$) as defined in Eq. (10) for the SC eigenpotentials at the $\Gamma$ point. The color code used for the arrows is the same as that used for the eigenpotentials in (a) and (b).

Figure 2

Density of states of the dielectric matrix $g\left({\lambda }^{-1}\right)={\sum }_m\delta ({\lambda }^{-1}-{\lambda }_m^{-1})·w_m·(1-{\lambda }^{-1})$ as a function of the eigenvalue $\lambda$ for the Rb${}_2$ dimer, KCl molecule, and SrO molecule, where the weight $w_m$ is defined in Eq. (10). (a–c) Density of states of ${\left({\tilde{\epsilon }}^{\mathrm{SC}}\right)}^{-1}$ [red; see Eq. (7)] and ${\left({\tilde{\epsilon }}^{\mathrm{VE}}\right)}^{-1}$ [black; see Eq. (8)] for $w_m=1$. (d–f) Density of states of ${\left({\tilde{\epsilon }}^{\mathrm{SC}}\right)}^{-1}$ for $w_m=1$ [red; the same as reported in (a–c)] and $w_m=F_m$ [blue; see Eq. (10)].

Figure 3

Inverse participation ratio (IPR) as a function of the eigenvalues $\lambda$ of ${\left({\tilde{\epsilon }}^{\mathrm{SC}}\right)}^{-1}$; the circle size is the projection ($1-F_m$) [see Eq. (10)] for (a) alkali dimers, (b) alkali halides, and (c) alkaline earth oxides. The log scale on the abscissa is chosen to better distinguish the eigenvalues near 1, where they would become very dense on a linear scale.