{"id":159,"date":"2018-06-12T09:29:04","date_gmt":"2018-06-12T09:29:04","guid":{"rendered":"http:\/\/bifi.es\/~acastro\/?p=159"},"modified":"2018-06-12T09:29:04","modified_gmt":"2018-06-12T09:29:04","slug":"propagators-for-the-time-dependent-kohn%e2%88%92sham-equations-multistep-runge%e2%88%92kutta-exponential-runge%e2%88%92kutta-and-commutator-free-magnus-methods","status":"publish","type":"post","link":"https:\/\/personal.unizar.es\/acastro\/?p=159","title":{"rendered":"Propagators for the Time-Dependent Kohn\u2212Sham Equations: Multistep, Runge\u2212Kutta, Exponential Runge\u2212Kutta, and Commutator Free Magnus Methods"},"content":{"rendered":"<p>Adri\u00e1n G\u00f3mez Pueyo, Miguel A. L. Marques, Angel Rubio, and Alberto Castro,\u00a0<a href=\"http:\/\/dx.doi.org\/10.1021\/acs.jctc.8b00197\" target=\"_blank\">J. Chem. Thelr. Comp. 14, 3040 (2018)<\/a><\/p>\n<p>We examine various integration schemes for the time-dependent Kohn\u2212Sham equations. Contrary to the time-dependent Schro\u0308dinger\u2019s equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge\u2212Kutta, exponential Runge\u2212Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth- order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.<\/p>\n<p><a href=\"http:\/\/bifi.es\/~acastro\/wp-content\/uploads\/2018\/06\/ct-2018-00197j_0010.gif\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-160\" src=\"http:\/\/bifi.es\/~acastro\/wp-content\/uploads\/2018\/06\/ct-2018-00197j_0010-300x202.gif\" alt=\"ct-2018-00197j_0010\" width=\"300\" height=\"202\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Adri\u00e1n G\u00f3mez Pueyo, Miguel A. L. Marques, Angel Rubio, and Alberto Castro,\u00a0J. Chem. Thelr. Comp. 14, 3040 (2018) We examine various integration schemes for the time-dependent Kohn\u2212Sham equations. Contrary to the time-dependent Schro\u0308dinger\u2019s equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-159","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/posts\/159"}],"collection":[{"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=159"}],"version-history":[{"count":1,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/posts\/159\/revisions"}],"predecessor-version":[{"id":161,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/posts\/159\/revisions\/161"}],"wp:attachment":[{"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=159"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=159"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}