Application of the Recursive Projection Method to Electronic Structure Calculation

In this work, we focus on the mixing scheme used during the Self-Consistent (SC) process of solving the Kohn-Sham (KS) equations. The two most common mixing schemes used in practice are the “Simple Mixing” and the “Modified Broyden Mixing”, the former is a fixed point method while the latter is a Quasi-Newton method. A characterization of the former method is that it takes less computation time per iteration but required a lot of iterations to converge; the latter gives quadratic convergence hence fewer iteration but takes more computational time per iteration. It can be shown that Simple Mixing converges if the eigen-values of the Jacobian lie within some ellipse. Thus even if only a few eigen-values lie outside the ellipse, Simple Mixing will not converge. We proposed the “Recursive Projection Method” (RPM) modified for electronic structure calculation, where we estimate the subspace spanned by the eigen-vectors whose eigen-values lie within the ellipse, call this the “stable-subspace”. We perform Simple Mixing on the stable-subspace and Modified Broyden on the complementary subspace. We expect that this method will improve convergence for systems of large size.