Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based $Ab$ $Initio$ Molecular Dynamics I: Theory, Algorithm, and Performance

Abstract

By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semi-local density functional theory (DFT), and thereby furnish a more accurate and reliable description of the electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we have devised a linear-scaling yet formally exact approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions, MLWFs) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems at the hybrid DFT level. We provide a comprehensive description of the exx algorithm, which is currently implemented in the Quantum ESPRESSO program and employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize high-performance computing (HPC) resources. This is followed by a critical assessment of the accuracy and parallel performance of this approach when performing AIMD simulations of liquid water in the canonical ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT based AIMD simulations of condensed-phase systems containing 500-1000 atoms with a walltime cost that is comparable to semi-local DFT. In doing so, exx takes us closer to routinely performing AIMD simulations of large-scale condensed-phase systems for sufficiently long timescales at the hybrid DFT level of theory.

34 pages and 10 figures

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Cited by in corpus (10)

• Efficient All-electron Hybrid Density Functionals for Atomistic Simulations Beyond 10,000 Atoms
• Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based $Ab$ $Initio$ Molecular Dynamics II: Extensions to the Isobaric-Isoenthalpic and Isobaric-Isothermal Ensembles
• Nonlocal Machine-Learned Exchange Functional for Molecules and Solids
• Structural and Dynamic Properties of Solvated Hydroxide and Hydronium Ions in Water from Ab Initio Modeling
• Faster Exact Exchange in Periodic Systems using Single-precision Arithmetic
• High-Throughput Condensed-Phase Hybrid Density Functional Theory for Large-Scale Finite-Gap Systems: The SeA Approach
• Speeding-up Hybrid Functional based Ab Initio Molecular Dynamics using Multiple Time-stepping and Resonance Free Thermostat
• Efficient Computation of the Long-Range Exact Exchange using an Extended Screening Function
• Many-body perturbation theory with hybrid density functional theory starting points accelerated by adaptively compressed exchange
• Achieving an Order of Magnitude Speed-up in Hybrid Functional and Plane Wave based Ab Initio Molecular Dynamics: Applications to Proton Transfer Reactions in Enzymes and in Solution