  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.
