<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Lin Lin</style></author><author><style face="normal" font="default" size="100%">Sihong Shao</style></author><author><style face="normal" font="default" size="100%">Weinan E</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">   Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Computational Physics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dx.doi.org/10.1016/j.jcp.2013.03.030</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">245</style></volume><pages><style face="normal" font="default" size="100%">205-217</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">We present for the first time an efficient iterative method to directly&amp;nbsp;solve the four-component Dirac-Kohn-Sham (DKS) density functional theory.&amp;nbsp;Due to the existence of the negative energy continuum in the DKS&amp;nbsp;operator, the existing iterative techniques for solving the Kohn-Sham&amp;nbsp;systems cannot be efficiently applied to solve the DKS&amp;nbsp;systems.&amp;nbsp; The key component of our method is a novel filtering step (F)&amp;nbsp;which acts as a preconditioner in the framework of the locally optimal&amp;nbsp;block preconditioned conjugate gradient (LOBPCG) method.&amp;nbsp; The resulting&amp;nbsp;method, dubbed the LOBPCG-F method, is able to compute the desired&amp;nbsp;eigenvalues and eigenvectors in the positive energy band without&amp;nbsp;computing any state in the negative energy band.&amp;nbsp; The LOBPCG-F method&amp;nbsp;introduces mild extra cost compared to the standard LOBPCG method and&amp;nbsp;can be easily implemented.&amp;nbsp; We demonstrate our method in the&amp;nbsp;pseudopotential framework with a planewave basis set which naturally&amp;nbsp;satisfies the kinetic balance prescription.&amp;nbsp; Numerical results for&amp;nbsp;Pt$_{2}$, Au$_{2}$, TlF, and Bi$_{2}$Se$_{3}$ indicate that the LOBPCG-F&amp;nbsp;method is a robust and efficient method for investigating the&amp;nbsp;relativistic effect in systems containing heavy elements.&amp;nbsp;</style></abstract></record></records></xml>