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Quantum-based molecular dynamics (QMD) is a highly accurate and transferablemethod for material science simulations. However, the time scales and systemsizes accessible to QMD are typically limited to picoseconds and a few hundredatoms. These constraints arise due to expensive self-consistent ground-stateelectronic structure calculations that can often scale cubically with thenumber of atoms. Linearly scaling methods depend on computing the densitymatrix P from the Hamiltonian matrix H by exploiting the sparsity in bothmatrices. The second-order spectral projection (SP2) algorithm is an O(N)algorithm that computes P with a sequence of 40-50 matrix-matrixmultiplications. In this paper, we present task-based implementations of arecently developed data-parallel graph-based approach to the SP2 algorithm,G-SP2. We represent the density matrix P as an undirected graph and use graphpartitioning techniques to divide the computation into smaller independenttasks. The partitions thus obtained are generally not of equal size and giverise to undesirable load imbalances in standard MPI-based implementations. Thisload-balancing challenge can be mitigated by dynamically scheduling parallelcomputations at runtime using task-based programming models. We developtask-based implementations of the data-parallel G-SP2 algorithm using bothIntel's Concurrent Collections (CnC) as well as the Charm++ programming modeland evaluate these implementations for future use. Scaling and performanceresults of our implementations are investigated for representative segments ofQMD simulations for solvated protein systems containing more than 10,000 atoms.

Task-based Parallel Computation of the Density Matrix in Quantum-based Molecular Dynamics using Graph Partitioning