Ab initioWannier-function-based many-body approach to Born charges of crystalline insulators

Abstract

In this paper we present an approach aimed at performing many-body calculations of Born-effective charges of crystalline insulators by including the electron-correlation effects. The scheme is implemented entirely in the real space, using Wannier functions as single-particle orbitals. Correlation effects are computed by including virtual excitations from the Hartree-Fock mean field, and the excitations are organized as per a BetheGoldstone-like many-body hierarchy. The results of our calculations suggest that the approach presented here is promising. The Born effective charge (BEC) of a periodic solid is an important phenomenological quantity which connects the electronic structure of the system to its phononic properties. 1Of late, in the context of ferroelectric materials and their phase transitions, BEC has generated tremendous amount of interest.2 Using BEC, one can also describe the lattice dynamics, and its coupling to infrared radiation, in a simple intuitive manner. 3 Most of the modern calculations of BECs are based upon the Berry-phase-based theory of macroscopic polarization developed by King-Smith and Vanderbilt. 4 The aforesaid formalism is based upon single-particle orbitals, and, therefore, can be implemented in a straightforward manner within ab initio density-functional theory (DFT), 2,3 or the Hartree-Fock (HF) framework.5 As far as many-body calculations of polarization properties are concerned, Martin and co-workers have proposed several approaches which, to the best of our knowledge, have not been implemented within an ab initio methodology. 6,7 Filippetti and Spaldin have recently implemented an ab initio method aimed at including correlation effects by using a self-interaction-corrected (SIC) density-functional approach. 8 Recently, we have developed a wave-function-based ab initio methodology aimed at performing electronic structure calculations on crystalline insulators. [9][10][11][12] The approach uses Wannier functions as single-particle orbitals obtained at the Hartree-Fock level, which can subsequently be used to include the electron correlation effects, if needed. The approach has been applied to calculate ground state geometries, cohesive energies, and elastic properties of crystalline insulators at the Hartree-Fock level, 9,10 as well as at the correlated level. 11,12 Moreover, within the Berry-phase formalism of King-Smith and Vanderbilt, 4 we have also used our approach to compute the BECs of several ionic insulators at the HF level. 13 The purpose behind the present work is to use our Wannier-function-based methodology to perform correlated calculations of the BEC's of insulators. Since ours is a real-space approach, we start with the following expression for the electronic contribution to the polarization per unit cell (P e ) valid for insulators: 14where is a parameter governing the state of crystal (for the present case, it represents atomic displacements), ⍀ is the volume of the unit cell, q e is the electronic charge, N͑→ϱ͒, represents the total number of unit cells in th...

Ab initioWannier-function-based correlated calculations of Born effective charges of crystallineLi2Oand LiCl

“…15,16 We follow the same truncation scheme here as well, with the method of correlation calculation being the full-configuration interaction as in our previous works, where other technical details related to the approach are also described. 4,5,15,16 …”

“…We avoid this by using the finite-field approach whereby the expectation values of various components of dipole operator can be obtained by performing both the HF and correlated calculations in the presence of a small electric field in that direction and then computing the first derivative of the computed total energy with respect to the applied electric field. 4,5 This approach of computing expectation values derives its legitimacy from the generalized Hellman-Feynman theorem, and it is called "finite-field method" in quantum chemistry literature. 11 Therefore, the present set of HF and correlated calculations are distinct from our previous ones [12][13][14][15][16] in that the present calculations have been performed in the presence of an external electric field.…”

“…For details related to our Wannier-function-based HF methodology, in the presence of external electric fields, we refer the reader to our earlier papers. 4,5 Correlation contributions to the energy per unit cell E corr , even in the presence of external electric fields, were computed according to the incremental scheme of Stoll, 17…”

“…Recently, we have proposed an approach which allows computation of various polarization properties of crystalline insulators within a many-body framework. 4,5 The approach utilizes a Wannier-function-based real-space methodology, coupled with a finite-field approach, to perform correlated calculations using a Bethe-Goldstone-like many-body hierarchy. Its successful implementation was demonstrated by performing ab initio many-body calculations of the Born charges, 4 and optical dielectric constants, 5 of various insulating crystals.…”

“…4,5 The approach utilizes a Wannier-function-based real-space methodology, coupled with a finite-field approach, to perform correlated calculations using a Bethe-Goldstone-like many-body hierarchy. Its successful implementation was demonstrated by performing ab initio many-body calculations of the Born charges, 4 and optical dielectric constants, 5 of various insulating crystals. We note that an ab initio wave-functional-based real-space correlated approach has recently been successfully demonstrated by Hozoi et al 6 to compute the quasiparticle band structure of crystalline MgO.…”