Title: Monte Carlo method
Long Title: IUPAC Gold Book - Monte Carlo method
DOI: 10.1351/goldbook.MT07072
Status: current

Definition
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 (\(\cong\rm{10}^{\rm{5}}-\rm{10}^{\rm{6}}\)) of instant configurations as determined by coordinates of the particles. \[< A >\ = \frac{1}{N}\sum _{i=1}^{N}A\{r_{i}\}\] where \(N\) 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.

Related Term
- random sample: https://goldbook.iupac.org//terms/view/R05129

Source
- PAC, 1999, 71, 1919. 'Glossary of terms used in theoretical organic chemistry' on page 1952 (https://doi.org/10.1351/pac199971101919)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/MT07072/html
- json: https://goldbook.iupac.org/terms/view/MT07072/json
- xml: https://goldbook.iupac.org/terms/view/MT07072/xml

Citation: Citation: 'Monte Carlo method' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.MT07072
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Accessed: 2026-05-28T09:49:46+00:00