  Ab initio molecular dynamics (AIMD) with hybrid density functionals and plane
wave basis is computationally expensive due to the high computational cost of
exact exchange energy evaluation. Recently, we proposed a strategy to combine
adaptively compressed exchange (ACE) operator formulation and multiple time
step (MTS) integration scheme to reduce the computational cost significantly
[J. Chem. Phys. 151, 151102 (2019)]. However, it was found that the
construction of the ACE operator, which has to be done at least once in every
MD time step, is computationally expensive. In the present work, systematic
improvements are introduced to further speed-up by employing localized orbitals
for the construction of the ACE operator. By this, we could achieve a
computational speed-up of an order of magnitude for a periodic system
containing 32-water molecules. Benchmark calculations were carried out to show
the accuracy and efficiency of the method in predicting the structural and
dynamical properties of bulk water. To demonstrate the applicability,
computationally intensive free energy computations at the level of hybrid
density functional theory were performed to investigate (a) methyl formate
hydrolysis reaction in neutral aqueous medium and (b) proton transfer reaction
within the active site residues of class-C $\beta$-lactamase enzyme.
