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

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