Comparing two iteration algorithms of Broyden electron density mixing through an atomic electronic structure computation

By performing the electronic structure computation of a Si atom, we compare two iteration algorithms of Broyden electron density mixing in the literature. One was proposed by Johnson and implemented in the well-known VASP code. The other was given by Eyert. We solve the Kohn-Sham equation by using a conventional outward/inward integration of the differential equation and then connect two parts of solutions at the classical turning points, which is different from the method of the matrix eigenvalue solution as used in the VASP code. Compared to Johnson's algorithm, the one proposed by Eyert needs fewer total iteration numbers.