KM 1.5

KM 1.5 - Limitations of MD: Classical description of atomic...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei One indicator of the validity of the replacement is the de Broglie wavelength Λ . Quantum effects are expected to become significant when Λ is much larger that inter- particle distance. For thermal motion we can use the thermal de Broglie wavelength: Limitations of MD: Classical description of atomic motions T mk h B th π 2 = Λ For T = 300 K we have Λ th = 1 Å for a H atom (m H = 1 amu) Λ th = 0.19 Å for a Si atom (m Si = 28 amu) Λ th = 0.07 Å for a Au atom (m Au = 197 amu) Typical interatomic spacing in solid-state materials is d ~ 1-3 Å. Therefore: ¾ All atoms, except for the lightest ones such as H, He, Ne, can be considered as “point” particles at sufficiently high temperature (d >> Λ ) and classical mechanics can be used to describe their motion. 2. Classical description of atomic motion ¾ In classical MD we replace Schrödinger equation for nuclei with classical Newton equation.
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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Limitations of the MD technique • The classical approximation is rather poor for light elements (e.g. H, He) and quantum corrections are often superimposed on the classical description of motion.
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This note was uploaded on 02/14/2012 for the course MSE 4270 taught by Professor Zhigilei during the Fall '11 term at UVA.

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KM 1.5 - Limitations of MD: Classical description of atomic...

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