Linear Algebra and Charge Self-consistent Tight-binding Method for Large-scale Electronic Structure Calculations

Abstract

We review our recently developed electronic structure calculation methods for the dynamics of large-scale solids, liquids or soft materials with an efficient algorithm of linear algebra. The Hamiltonian of electronic structures is based on the 'atomic superposition and electron delocalization molecular orbitals theory' (ASED), using the Mulliken charge density. Very crucial algorithms of the linear algebra are the generalized Lanczos method and the generalized shifted COCG (conjugate orthogonal conjugate gradient) method for general eigen-value problems. The shift equation and the seed switching method are essential for the shifted COCG method and reduce the computational cost much. We, then, present some applications to electronic structure calculations with MD simulation, such as the fracture propagation in nano-scale Si crystals and the proton transfer in water.