Linear-scaling Quantum Molecular Dynamics for Reactive Systems

Abstract: The purpose of this thesis is to demonstrate linear-scaling, energy stable, propagation of the electronic degrees of freedom in finite temperature ExtendedLagrangian Born-Oppenheimer Molecular Dynamics for reactive systems in aself-consistent charge density-functional tight-binding formulation. The inverse Jacobian kernel matrix in the electronic equation of motion is approximated using alow-rank combination of directional derivatives of the ground state residual function. For accurate and efficient kernel calculation in the simulation of reactive systems, the derivative direction vectors are chosen from a pre-conditioned Krylov subspace. The full Jacobian inverse pre-conditioning matrix can be represented in sparse form with a constant number of non-zeros per row independently of matrix size, which is a major result of this work as this allows linear-scaling, pre-conditioned kernel calculation in each molecular dynamics time step. Density matrix perturbation response evaluation from an implicit, recursive expansion of the Fermi-Dirac function is used to find the directional derivatives. The auxiliary matrix inverses computed in the implicit,Fermi-Dirac density matrix expansion are stored and reused for efficient response calculations.