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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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