Quantum-based molecular dynamics (QMD) is a highly accurate and transferable method for material science simulations. However, the time scales and system sizes accessible to QMD are typically limited to picoseconds and a few hundred atoms. These constraints arise due to expensive self-consistent ground-state electronic structure calcu lations that can often scale cubically with the number of atoms. Linearly scaling methods depend on c omputing the density matrix P from the Hamiltonian matrix H by exploiting the sparsity in both matrices. The second-order spectral projection (SP2) algorithm is an O(N) algorithm that computes P with a sequence of 40--50 matrixmatrix multiplications. In this paper, we present task-based imp lementations of a recently developed data-parallel graph-based approach to the SP2 algorithm, G-SP2. We represent the density matrix P as an undirected graph and use graph partitioning techniq ues to divide the computation into smaller independent tasks. The partitions thus obtained are generally not of equal size and give rise to undesirable load imbalances in standard MPI-based implementations. This load-balancing challenge can be mitigated by dynamically scheduling parallel computations at runtime using taskbased programming models. We develop task-based implementations of the data-parallel G-SP2 algorithm using both Intel's Concurrent Collections (CnC) as well as the Charm++ programming model and evaluate these implementations for future use. Sca ling and performance results of our implementations are investigated for representative segments of QMD simulations for solvated protein systems containing more than 10,000 atoms. [ABSTRACT FROM AUTHOR]