Towards an Accurate and Efficient Order-<i>N</i> Framework for Real-Space Condensed-Phase Hybrid Density Functional Theory

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 chemistry, physics, and materials science. However, the high computational cost associated with hybrid DFT limits its applicability when treating large-scale and complex condensed-phase systems. To overcome this limitation, we have devised a highly accurate and linear-scaling (order-N) approach based on a local (MLWF) representation of the occupied space that exploits sparsity when evaluating the EXX interaction in real space [1]. In this work, we present a detailed description of the theoretical and algorithmic advances that are needed to perform hybrid DFT based ab initio molecular dynamics (AIMD) simulations of large-scale finite-gap condensed-phase systems using this approach. This is followed by a critical assessment of the accuracy and parallel performance of the exx algorithm when performing AIMD simulations of liquid water and several ice phases in the canonical (NVT) and isobaric-isothermal (NpT) ensembles. With access to high-performance computing (HPC) resources, we demonstrate that exx enables hybrid DFT based AIMD simulations of systems containing 500-1000 atoms with a wall time cost comparable to semi-local DFT. In the strong-scaling limit, this cost is split evenly between computation, communication, and processor idling; as such, we also discuss a three-pronged strategy that directly attacks each of these contributions and reduces the overall wall time cost by approximately an order of magnitude for large-scale heterogeneous systems. With these developments, this work takes us one step closer to routinely performing AIMD simulations of large-scale condensed-phase systems for sufficiently long timescales at the hybrid DFT level.

[1] J Chem Theory Comput 16, 3757 (2020).