Molecular Dynamics with 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 underlying electronic structure in systems throughout chemistry, physics, and materials science. However, the high computational cost associated with hybrid DFT has limited its applicability when treating large-scale condensed-phase systems. To overcome this limitation, we have devised a linear-scaling yet formally exact approach that utilizes a local representation of the occupied orbitals to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. Here, we present a detailed description of the theoretical and algorithmic advances required to perform ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems with hybrid DFT. We focus our theoretical discussion on integrating this approach into the framework of Car-Parrinello AIMD, and provide a comprehensive description of our algorithm, which is implemented in the open-source Quantum ESPRESSO program and employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the high-performance computing (HPC) resources available on supercomputer architectures. This is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when performing AIMD simulations of liquid water in the canonical (NVT) and isobaric-isothermal (NpT) ensembles. With access to HPC resources, we demonstrate that our algorithm enables hybrid DFT based AIMD simulations of condensed-phase systems containing ~1000 atoms with a wall-time cost that is comparable to semi-local DFT. In doing so, 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 of theory.