{"term":{"metadata":{"id":"07072","doi":"10.1351\/goldbook.MT07072","code":"MT07072","status":"current","longtitle":"IUPAC Gold Book - Monte Carlo (MC), method of","title":"Monte Carlo (MC), method of","contexts":[],"abbrevs":["MC"],"index":null,"version":"2.3.3","lastupdated":"2014-02-24"},"definitions":{"definition":[{"id":"1","text":"In mathematics, a method originally used for calculating multiple integrals by means of a random sample. The method is used for numerical modelling of many-particle chemical systems, in particular liquids; it is based on the equilibrium statistical mechanics theory. Observables A are calculated as mean values over a great number (≅105 – 106) of instant configurations as determined by coordinates of the particles. ≅10^5-10^6 where < A > = 1\/N (i=1)∑(N) A{ri} is the number of configurations. At the first stage, various configurations are randomly generated and then those energetically unrealizable eliminated. An efficient search for the most probable configurations to be entered into the above expression is provided by the Metropolis algorithm based on the principle of Markov's chain theory. While being elaborated for the study of equilibrium chemical systems, MC method is also applied to studies of the dynamics of chemical reactions.","contexts":{"in":[],"of":[]},"chemicals":[],"links":[{"type":"goldify","url":"http:\/\/dev.goldbook.iupac.org\/terms\/view\/R05129"}],"math":[{"meaning":"Monte Carlo Equation","type":"equation","latex":"< A >\\ = \\frac{1}{N}\\sum _{i=1}^{N}A\\{r_{i}\\}"},{"meaning":"Number of configurations","type":"symbol","latex":"N"},{"meaning":"Observables calculation range","type":"numeric value","latex":"\\cong\\text{10}^{\\text{5}}-\\text{10}^{\\text{6}}"}],"sources":["PAC, 1999, *71<\/em>, 1919. 'Glossary of terms used in theoretical organic chemistry' on page 1952 (https:\/\/doi.org\/10.1351\/pac199971101919)"]}]},"referencedin":[{"title":0,"url":"https:\/\/it.wikipedia.org\/w\/index.php?title=Metodo_Monte_Carlo&oldid=88266974","source":"wikipedia"}],"links":{"html":"http:\/\/dev.goldbook.iupac.org\/terms\/view\/MT07072\/html","json":"http:\/\/dev.goldbook.iupac.org\/terms\/view\/MT07072\/json","xml":"http:\/\/dev.goldbook.iupac.org\/terms\/view\/MT07072\/xml","plain":"http:\/\/dev.goldbook.iupac.org\/terms\/view\/MT07072\/plain","pdf":"http:\/\/dev.goldbook.iupac.org\/terms\/view\/MT07072\/pdf","originalpdf":"http:\/\/iupac.org\/goldbook\/MT07072.pdf"},"citeas":"IUPAC. Compendium of Chemical Terminology, 2nd ed. (the \"Gold Book\"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http:\/\/goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. https:\/\/doi.org\/10.1351\/goldbook.","license":"Licensed under Creative Commons Attribution-NoDerivatives (CC-BY-ND) 4.0 International (https:\/\/creativecommons.org\/licenses\/by-nd\/4.0\/)","disclaimer":"The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.","accessed":"2022-05-26T02:56:48+00:00"}}*