This paper presents the formulation and implementation of a high performance algorithm to compute the many-body electronic correlation energy via the random-phase approximation within density functional theory. Our approach circumvents computational inefficiencies inherent in direct approaches which exhibit quartic scaling with respect to system size. Our formulation requires solving block linear systems whose coefficient matrices are complex symmetric; these systems are of widely-varying numerical difficulty. We develop a shortterm recurrence block Krylov subspace solver for these systems and leverage a dynamic block size selection to mitigate load imbalances. This selection balances the increased cost per linear solver iteration with a reduction in the number of iterations for slowly-converging systems. Numerical experiments show that our implementation exhibits good parallel scalability, achieves faster solution times than direct approaches on even the smallest chemical system tested, and scales to larger systems and processor counts due to its cubic scaling and greater computational locality.

Exploration of atomic trajectories is fundamental to understanding and characterizing complex chemical systems important in many applications. For instance, any new insight into the mechanisms of ionic migration in catalytic materials could lead to a substantial increase in battery performance. A new statistical measure, called the relative-angle distribution, has been proposed to understand complex motion - whether Brownian, ballistic, or diffusive. The relative-angle distribution can be represented as a collection of 1D histograms, but is currently created in a slow, offline process, making any parameter exploration a tedious and time-consuming task. Furthermore, the resulting plot can hide uncertainty in both the data and the visualization. As a result, once rastered or printed at a fixed resolution, these histograms can be misleading. We present a new analysis tool for the exploration of atomic trajectories that combines an interactive histogram visualization with uncertainty information for both data and plotting errors, and is also linked to an interactive 3D display of trajectories. Our tool enables a holistic exploration of trajectories previously not feasible, with the potential for significant scientific impact. In collaboration with domain experts, we have deployed our tool ta analyze molecular dynamics simulations of lithium-ion diffusion. Users have found that the tool significantly accelerates the exploration process and have used it to validate a number of previously unconfirmed hypotheses.