eQE: An open‐source density functional embedding theory code for the condensed phase

Abstract

In this work, we present the main features and algorithmic details of a novel implementation of the frozen density embedding (FDE) formulation of subsystem density functional theory (DFT) that is specifically designed to enable ab initio molecular dynamics (AIMD) simulations of largescale condensed-phase systems containing 1000s of atoms. This code (available at http://eqe. rutgers.edu) has been given the moniker of embedded Quantum ESPRESSO (eQE) as it is a generalization of the open-source Quantum ESPRESSO (QE) suite of programs. The strengths of eQE reside in a hierarchical parallelization scheme that allows for an efficient and fully self-consistent treatment of the electronic structure (via the addition of an additional DIIS extrapolation layer) while simultaneously exploiting the inherent symmetries and periodicities in the system (via sampling of subsystem-specific first Brillouin zones and utilization of subsystem-specific basis sets).While bulk liquids and molecular crystals are two classes of systems that exemplify the utility of the FDE approach (as these systems can be partitioned into weakly interacting subunits), we show that eQE has significantly extended this regime of applicability by outperforming standard semilocal Kohn-Sham DFT (KS-DFT) for large-scale heterogeneous catalysts with quite different layerspecific electronic structure and intrinsic periodicities. eQE features very favorable strong parallel scaling for a model system of bulk liquid water composed of 256 water molecules, which allows for a significant decrease in the overall time to solution when compared to KS-DFT. We show that eQE achieves speedups greater than one order of magnitude (>103) when performing AIMD simulations of such large-scale condensed-phase systems as: (1) | I N T R O D U C T I O NThe Kohn-Sham (KS) formulation of density functional theory (DFT) [1] is currently the most widely employed electronic structure method in the fields of chemistry, physics, and materials science. This is largely due to the fact that KS-DFT employing semilocal exchange-correlation (xc) functionals produces models of remarkable accuracy and predictive capability [2] with a relatively low associated computational cost (that in general Int J Quantum Chem. 2017;117:e25401.

Cooperation and Environment Characterize the Low-Lying Optical Spectrum of Liquid Water

“…While we do not expect that subsystem electron density localization be a generally beneficial feature of the model, it is beneficial in the limit of simulating systems composed of noncovalently bound subunits. Such as molecular liquids, crystals, and layered periodic systems [20]. Simulations were carried out with the package embedded Quantum-ESPRESSO (eQE) [20], employing the PBE xc functional and ultrasoft pseudopotentials (O.pbe-rrkjus.UPF/H.pbe-rrkjus.UPF from the Quantum-ESPRESSO PP Library [21]).…”

“…Such as molecular liquids, crystals, and layered periodic systems [20]. Simulations were carried out with the package embedded Quantum-ESPRESSO (eQE) [20], employing the PBE xc functional and ultrasoft pseudopotentials (O.pbe-rrkjus.UPF/H.pbe-rrkjus.UPF from the Quantum-ESPRESSO PP Library [21]). We employ plane wave kinetic energy cutoffs of 50 and 500 Ry for the waves and charge densities, respectively.…”

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

“…Good ideas to solve these problems are divide-and-conquer, subsystem DFT, and fragment molecular-orbital approaches (Gordon et al 2012;He and Jr 2010;Andermatt et al 2016) combined with the special sampling techniques. As an example of these new approaches, Genova and co-workers have implemented and reported a speedup of 40x for simulation of (GLY)6 solvated by 395 water molecules (1230 atoms) using a frozen density embedding (FDE) formulation of subsystem DFT (1462 s for subsystem DFT against 56,405 s for conventional DFT, both carrying out ten steps of ab initio MD) (Genova et al 2017).…”

Subsystem density-functional theory as an effective tool for modeling ground and excited states, their dynamics and many-body interactions

“…[82,89] The FDE implementation is added as a higher level of parallellization to the existing code using the popular Message Passing Interface (MPI) libraries. To the best of our knowledge, ours is the most comprehensive implementation of subsystem DFT in a PW basis.…”

“…Efforts in our group to fill this gap are ongoing [82] and involve the implementation of FDE in the plane wave (PW) code Quantum-Espresso (QE) [89,124]. Using PW allows for a very accurate and efficient calculation of the Hartree energies and potentials in reciprocal space.…”