{"id":127,"date":"2013-11-20T17:25:17","date_gmt":"2013-11-20T17:25:17","guid":{"rendered":"https:\/\/vallico.net\/casinoqmc\/?page_id=127"},"modified":"2026-10-27T02:42:48","modified_gmt":"2026-10-27T02:42:48","slug":"introductory-and-review-material","status":"publish","type":"page","link":"https:\/\/vallico.net\/casinoqmc\/introductory-and-review-material\/","title":{"rendered":"Introductory and review material"},"content":{"rendered":"<p>The best way to learn quantum Monte Carlo is to do a calculation, and the <a href=\"https:\/\/casinoqmc.net\/casino_manual_dir\/casino_manual.pdf\">CASINO manual<\/a> is now written for that: its first chapter says what a calculation computes, how the two principal methods work, what limits the accuracy of their results and what a calculation costs, for a reader who knows the Schr&ouml;dinger equation and has met Hartree-Fock or density functional theory but has not used quantum Monte Carlo; a later chapter works through a first calculation from trial wave function to diffusion Monte Carlo; and the methods are then derived in full. The <a href=\"https:\/\/vallico.net\/casinoqmc\/summer-schools\/\">summer schools<\/a> held at Vallico Sotto taught the same material over a week, with more than twenty hours of lectures.<\/p>\n<h3>Reviews<\/h3>\n<ul>\n<li>W. M. C. Foulkes, L. Mitas, R. J. Needs and G. Rajagopal, <em>Quantum Monte Carlo simulations of solids<\/em>, Rev. Mod. Phys. <b>73<\/b>, 33 (2001). The standard review of variational and diffusion Monte Carlo, and still the place to start.<\/li>\n<li>R. J. Needs, M. D. Towler, N. D. Drummond and P. L&oacute;pez R&iacute;os, <em>Continuum variational and diffusion quantum Monte Carlo calculations<\/em>, J. Phys.: Condens. Matter <b>22<\/b>, 023201 (2010) [<a href=\"https:\/\/casinoqmc.net\/papers\/qmc_review.pdf\">PDF<\/a>]. The methods as CASINO implements them.<\/li>\n<li>R. J. Needs, M. D. Towler, N. D. Drummond, P. L&oacute;pez R&iacute;os and J. R. Trail, <em>Variational and diffusion quantum Monte Carlo calculations with the CASINO code<\/em>, J. Chem. Phys. <b>152<\/b>, 154106 (2020) [<a href=\"https:\/\/doi.org\/10.1063\/1.5144288\">link<\/a>]. The paper that describes the program, and the one to cite for results obtained with it.<\/li>\n<li>M. D. Towler, <em>Quantum Monte Carlo, or, how to solve the many-particle Schr&ouml;dinger equation accurately whilst retaining favourable scaling with system size<\/em> [<a href=\"https:\/\/casinoqmc.net\/papers\/towler_review.pdf\">PDF<\/a>], the preprint of his chapter in <em>Computational Methods for Large Systems<\/em>, edited by J. R. Reimers (Wiley, 2011) [<a href=\"https:\/\/doi.org\/10.1002\/9780470930779.ch4\">link<\/a>]. An introduction for chemists and physicists who are new to the method.<\/li>\n<li>M. D. Towler, <em>The quantum Monte Carlo method<\/em>, Phys. Status Solidi B <b>243<\/b>, 2573 (2006) [<a href=\"https:\/\/doi.org\/10.1002\/pssb.200642125\">link<\/a>].<\/li>\n<li>M. J. Gillan, M. D. Towler and D. Alf&egrave;, <em>Petascale computing opens new vistas for quantum Monte Carlo<\/em>, Psi-k Scientific Highlight of the Month, No. 103 (2011) [<a href=\"https:\/\/casinoqmc.net\/papers\/petascale_psik.pdf\">PDF<\/a>]. What quantum Monte Carlo does with a hundred thousand cores.<\/li>\n<li>J. Koloren\u010d and L. Mitas, <em>Applications of quantum Monte Carlo methods in condensed systems<\/em>, Rep. Prog. Phys. <b>74<\/b>, 026502 (2011) [<a href=\"https:\/\/doi.org\/10.1088\/0034-4885\/74\/2\/026502\">link<\/a>].<\/li>\n<li>B. M. Austin, D. Yu. Zubarev and W. A. Lester Jr., <em>Quantum Monte Carlo and related approaches<\/em>, Chem. Rev. <b>112<\/b>, 263 (2012) [<a href=\"https:\/\/doi.org\/10.1021\/cr2001564\">link<\/a>].<\/li>\n<li>W. A. Lester Jr., L. Mitas and B. Hammond, <em>Quantum Monte Carlo for atoms, molecules and solids<\/em>, Chem. Phys. Lett. <b>478<\/b>, 1 (2009) [<a href=\"https:\/\/doi.org\/10.1016\/j.cplett.2009.06.095\">link<\/a>].<\/li>\n<\/ul>\n<h3>Books<\/h3>\n<ul>\n<li>B. L. Hammond, W. A. Lester Jr. and P. J. Reynolds, <em>Monte Carlo Methods in Ab Initio Quantum Chemistry<\/em> (World Scientific, 1994) [<a href=\"https:\/\/doi.org\/10.1142\/1170\">link<\/a>]. Old, and still the right first book for a beginner.<\/li>\n<li>W. Schattke and R. D&iacute;ez Mui&ntilde;o, <em>Quantum Monte Carlo Programming for Atoms, Molecules, Clusters and Solids<\/em> (Wiley-VCH, 2013) [<a href=\"https:\/\/doi.org\/10.1002\/9783527676729\">link<\/a>]. Teaches the method by writing the programs.<\/li>\n<li>F. Becca and S. Sorella, <em>Quantum Monte Carlo Approaches for Correlated Systems<\/em> (Cambridge University Press, 2017). The methods for lattice models as well as continuum systems, with reptation Monte Carlo among them.<\/li>\n<\/ul>\n<h3>Lectures<\/h3>\n<p>Slides from the summer schools and from talks on quantum Monte Carlo and CASINO are collected in the <a href=\"https:\/\/vallico.net\/casinoqmc\/talk-archive\/\">talk archive<\/a>. For what the random walks of quantum Monte Carlo have, and have not, to do with the trajectories of pilot-wave theory, see <a href=\"https:\/\/vallico.net\/casinoqmc\/debb\/\">the de Broglie-Bohm page<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The best way to learn quantum Monte Carlo is to do a calculation, and the CASINO manual is now written for that: its first chapter says what a calculation computes, how the two principal methods work, what limits the accuracy of their results and what a calculation costs, for a reader who knows the Schr&ouml;dinger &hellip; <a href=\"https:\/\/vallico.net\/casinoqmc\/introductory-and-review-material\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Introductory and review material<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"footnotes":""},"class_list":["post-127","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Introductory and review material - Quantum Monte Carlo<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/vallico.net\/casinoqmc\/introductory-and-review-material\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Introductory and review material - Quantum Monte Carlo\" \/>\n<meta property=\"og:description\" content=\"The best way to learn quantum Monte Carlo is to do a calculation, and the CASINO manual is now written for that: its first chapter says what a calculation computes, how the two principal methods work, what limits the accuracy of their results and what a calculation costs, for a reader who knows the Schr&ouml;dinger &hellip; 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