A Filon-like integration strategy for calculating exact exchange in periodic boundary conditions: a plane-wave DFT implementation

Eric J Bylaska,Eric D Hermes,Judit Zádor,Kevin M Rosso,Kevin Waters

doi:10.1186/s41313-020-00019-9

Abstract

An efficient and accurate approach for calculating exact exchange and other two-electron integrals has been developed for periodic electronic structure methods. Traditional approaches used for integrating over the Brillouin zone in band structure calculations, e.g. trapezoidal or Monkhorst-Pack, are not accurate enough for two-electron integrals. This is because their integrands contain multiple singularities over the double integration of the Brillouin zone, which with simple integration methods lead to very inaccurate results. A common approach to this problem has been to replace the Coulomb interaction with a screened Coulomb interaction that removes singularities from the integrands in the two-electron integrals, albeit at the inelegance of having to introduce a screening factor which must precomputed or guessed. Instead of introducing screened Coulomb interactions in an ad hoc way, the method developed in this work derives an effective screened potential using a Filon-like integration approach that is based only on the lattice parameters. This approach overcomes the limitations of traditionally defined screened Coulomb interactions for calculating two-electron integrals, and makes chemistry many-body calculations tractable in periodic boundary conditions. This method has been applied to several systems for which conventional DFT methods do not work well, including the reaction pathways for the addition of H2 to phenol and Au_{20}^{-} nanoparticle, and the electron transfer of a charge trapped state in the Fe(II) containing mica, annite.

Highlights

One of the more computationally demanding and important scientific simulations for materials and chemistry is the ab initio Molecular Dynamics (AIMD) method (Car and Parrinello 1985; Remler and Madden 1990; Payne et al 1992; Marx and Hutter 2009; Bylaska et al 2011b; Bylaska 2017) in which the motions of the atoms are simulated using Newton’s laws where the forces on the atoms are obtained using the plane-wave DFT (2020) 4:3 methods
With large scale high-performance computers these methods are capable of performing ab initio molecular dynamics efficiently enough to carry out standard rare event simulations with ground-state adiabatic surfaces to find adiabatic electron transfer (ET) rates, while at the same time being accurate enough to model ET rates and transmission factors, κel Conclusion In summary, we have developed a new method for accurately calculating exact change integrals in periodic systems that is based on a Filon-like integration approach in which an effective screened potential is defined using a narrow integration that accounts for the singularity in the two-electron Coulomb integrand
The technique developed can readily be employed in plane-wave DFT programs, and it is applicable to both confined and extended systems, as well as AIMD simulations and periodic electron transfer calculations

Summary

Introduction

One of the more computationally demanding and important scientific simulations for materials and chemistry is the ab initio Molecular Dynamics (AIMD) method (Car and Parrinello 1985; Remler and Madden 1990; Payne et al 1992; Marx and Hutter 2009; Bylaska et al 2011b; Bylaska 2017) in which the motions of the atoms are simulated using Newton’s laws where the forces on the atoms are obtained using the plane-wave DFT (2020) 4:3 methods. We present an efficient and accurate approach for calculating exact exchange and other two-electron integrals in periodic electronic structure methods.

Results

Conclusion