Hybrid density functional theory (DFT) represents a quite favorable balance between accuracy and computational cost, and has therefore become the de facto method in quantum chemistry. However, the cubic scaling computational cost associated with the reciprocal-space evaluation of the exact-exchange energy and potential hinders its widespread use in the condensed phase. By utilizing maximally localized Wannier functions (MLWFs) to represent the occupied space, we have developed a linear scaling algorithm that computes the exact-exchange energy and potential by solving the Poisson equation in real space for all overlapping orbital pairs with the conjugate gradient (CG) method. In this work, we present a novel preconditioning technique to further accelerate CG convergence. Our preconditioner reduces the number of CG iterations by a factor of 8 and the time to solution by a factor of 4. For moderate system sizes that contain 500K grid points, our preconditioned conjugate gradient method is 50% faster than multigrid. With the ability to compute the exact-exchange potential for (H2O)256 in &lt;0.2 s, this algorithm takes us one step closer to routine hybrid DFT-based ab initio molecular dynamics simulations of sufficient duration in large-scale condensed-phase systems.

Attacking the strong scaling limit in linear scaling hybrid density functional theory

256th National Meeting (2018)

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