@article {26624,
	title = {   Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory},
	journal = {Journal of Computational Physics},
	volume = {245},
	year = {2013},
	pages = {205-217},
	abstract = {We present for the first time an efficient iterative method to directly\&nbsp;solve the four-component Dirac-Kohn-Sham (DKS) density functional theory.\&nbsp;Due to the existence of the negative energy continuum in the DKS\&nbsp;operator, the existing iterative techniques for solving the Kohn-Sham\&nbsp;systems cannot be efficiently applied to solve the DKS\&nbsp;systems.\&nbsp; The key component of our method is a novel filtering step (F)\&nbsp;which acts as a preconditioner in the framework of the locally optimal\&nbsp;block preconditioned conjugate gradient (LOBPCG) method.\&nbsp; The resulting\&nbsp;method, dubbed the LOBPCG-F method, is able to compute the desired\&nbsp;eigenvalues and eigenvectors in the positive energy band without\&nbsp;computing any state in the negative energy band.\&nbsp; The LOBPCG-F method\&nbsp;introduces mild extra cost compared to the standard LOBPCG method and\&nbsp;can be easily implemented.\&nbsp; We demonstrate our method in the\&nbsp;pseudopotential framework with a planewave basis set which naturally\&nbsp;satisfies the kinetic balance prescription.\&nbsp; Numerical results for\&nbsp;Pt$_{2}$, Au$_{2}$, TlF, and Bi$_{2}$Se$_{3}$ indicate that the LOBPCG-F\&nbsp;method is a robust and efficient method for investigating the\&nbsp;relativistic effect in systems containing heavy elements.\&nbsp;},
	url = {http://dx.doi.org/10.1016/j.jcp.2013.03.030},
	author = {Lin Lin and Sihong Shao and Weinan E}
}
