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16Simulating Matter withMolecular DynamicsProblem: Determine whether a collection of argon molecules placed in a box willform an ordered structure at low temperature.You may have seen in your introductory classes that the ideal gas law can be derived fromfirst principles if gas molecules are treated as billiard balls bouncing off the walls but notinteracting with each other. We want to extend this model so that we can solve for themotion of every molecule in a box interacting with every other molecule via a potential. Wepicked argon because it is an inert element with a closed shell of electrons and so can bemodeled as almost-hard spheres.16.1 Molecular Dynamics (Theory)Molecular dynamics (MD) is a powerful simulation technique for studying the physicaland chemical properties of solids, liquids, amorphous materials, and biologicalmolecules. Even though we know that quantum mechanics is the proper theoryfor molecular interactions, MD uses Newton’s laws as the basis of the techniqueand focuses on bulk properties, which do not depend much on small-r behaviors.In 1985 Car and Parrinello showed how MD can be extended to includequantum mechanics by applying density functional theory to calculate the force[C&P 85]. This technique, known as quantum MD, is an active area of researchbut is beyond the realm of the present chapter. 1 For those with more interestin the subject, there are full texts [A&T 87, Rap 95, Hock 88] on MD and gooddiscussions [G,T&C 06, Thij 99, Fos 96], as well as primers [Erco] and codes,[NAMD, Mold, ALCMD] available on-line.MD’s solution of Newton’s laws is conceptually simple, yet when applied to avery large number of particles becomes the “high school physics problem fromhell.” Some approximations must be made in order not to have to solve the10 23 –10 25 equations of motion describing a realistic sample but instead to limit theproblem to ∼10 6 particles for protein simulations and ∼10 8 particles for materialssimulations. If we have some success, then it is a good bet that the model willimprove if we incorporate more particles or more quantum mechanics, somethingthat becomes easier as computing power continues to increase.1 We thank Satoru S. Kano for pointing this out to us.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 424