  Graph-based linear scaling electronic structure theory for quantum-mechanical
molecular dynamics simulations is adapted to the most recent shadow potential
formulations of extended Lagrangian Born-Oppenheimer molecular dynamics,
including fractional molecular-orbital occupation numbers, which enables stable
simulations of sensitive complex chemical systems with unsteady charge
solutions. The proposed formulation includes a preconditioned Krylov subspace
approximation for the integration of the extended electronic degrees of
freedom, which requires quantum response calculations for electronic states
with fractional occupation numbers. For the response calculations we introduce
a graph-based canonical quantum perturbation theory that can be performed with
the same natural parallelism and linear scaling complexity as the graph-based
electronic structure calculations for the unperturbed ground state. The
proposed techniques are particularly well-suited for semi-empirical electronic
structure theory and the methods are demonstrated using self-consistent charge
density-functional tight-binding (SCC-DFTB) theory, both for the acceleration
of self-consistent field calculations and for quantum molecular dynamics
simulations. The graph-based techniques combined with the semi-empirical theory
enable stable simulations of large, complex chemical systems, including
tens-of-thousands of atoms.
