Editing Molecular dynamics (section)

{{Short description|Computer simulations to discover and understand chemical properties}}
{{Use American English|date = February 2019}}
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[[File:Cudeposition.gif|thumb|upright=1.35|Example of a molecular dynamics simulation in a simple system: deposition of one [[copper]] (Cu) [[atom]] on a cold crystal of copper ([[Miller index]] (001) [[Surface science|surface]]). Each circle represents the position of one atom. The kinetic energy of the atom approaching from the top is redistributed among the other atoms, so instead of bouncing off it remains attached due to attractive forces between the atoms.]]
[[File:MD water.gif|thumb|upright=1.35|Molecular dynamics simulations are often used to study biophysical systems. Depicted here is a 100 ps simulation of water.]]
[[File:Molecular dynamics algorithm.png|thumb|upright=1.8|A simplified description of the standard molecular dynamics simulation algorithm, when a predictor-corrector-type integrator is used. The forces may come either from classical [[interatomic potential]]s (described mathematically as <math> F= - \nabla V(\vec r) </math>) or quantum mechanical (described mathematically as <math> F=F( \Psi(\vec r) ) </math>) methods. Large differences exist between different integrators; some do not have exactly the same highest-order terms as indicated in the flow chart, many also use higher-order time derivatives, and some use both the current and prior time step in variable-time step schemes.]]

'''Molecular dynamics''' ('''MD''') is a [[computer simulation]] method for analyzing the [[Motion (physics)|physical movements]] of [[atoms]] and [[molecules]]. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the [[dynamics (mechanics)|dynamic]] "evolution" of the system. In the most common version, the [[trajectory|trajectories]] of atoms and molecules are determined by [[Numerical integration|numerically solving]] [[Newton's laws of motion|Newton's equations of motion]] for a system of interacting particles, where [[Force (physics)|forces]] between the particles and their [[potential energy|potential energies]] are often calculated using [[interatomic potential]]s or [[molecular mechanics|molecular mechanical]] [[Force field (chemistry)|force fields]]. The method is applied mostly in [[chemical physics]], [[materials science]], and [[biophysics]].

Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such [[complex systems]] analytically; MD simulation circumvents this problem by using [[Numerical analysis|numerical]] methods. However, long MD simulations are mathematically [[condition number|ill-conditioned]], generating cumulative errors in numerical integration that can be minimized with proper selection of algorithms and parameters, but not eliminated.

For systems that obey the [[ergodic hypothesis]], the evolution of one molecular dynamics simulation may be used to determine the macroscopic [[thermodynamic]] properties of the system: the time averages of an ergodic system correspond to [[microcanonical ensemble]] averages. MD has also been termed "[[statistical mechanics]] by numbers" and "[[Laplace]]'s vision of [[Newtonian mechanics]]" of predicting the future by animating nature's forces<ref>{{cite book |doi=10.1007/978-1-4612-4066-2_13 |chapter=Pursuing Laplace's Vision on Modern Computers |title=Mathematical Approaches to Biomolecular Structure and Dynamics |series=The IMA Volumes in Mathematics and its Applications |year=1996 | vauthors = Schlick T |volume=82 |pages=219–247 |isbn=978-0-387-94838-6 }}</ref> and allowing insight into molecular motion on an atomic scale.