md2011-04-note_Part_3

md2011-04-note_Part_3 - D I P Pair potentials: U(r) = Pair...

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Unformatted text preview: D I P Pair potentials: U(r) = Pair functionals: U[F , r] = Cluster potentials: U(r) = U0 + i ,j U2 (ri , rj ) + U0 + i ,j ,k Cluster functionals: U[F , r] = i ,j i U2 (ri , rj ) i ,j i F j U2 (ri , rj )+ i ,j U3 (ri , rj , rk ) U2 (ri , rj )+ F j g2 (ri , rj ), j ,k Real potentials are often combinations of the above. Notes g2 (ri , rj ) g3 (ri , rj , rk ) I P P Idealistic potentials can serve as the first approximation. Hard Sphere Potential UHS (r ) = ∞, 0, r<σ rσ First ever MD potential Billiard-ball physics Works for packing problems Notes (3) Square Well Potential ∞, SW −ε, U (r ) = 0, r < σ1 σ1 r < σ2 r σ2 (4) Notes Soft Sphere Potentials USS (r ) = ε ν=1 Notes σ r ν (5) ν = 12 M R P P Lennard-Jones Lennard-Jones potential [Proc. R. Soc. Lond. A 106 (1924) 463] is perhaps the best known pair potential which can be used in realistic simulations (although only for certain specific structures). It was developed to describe dipole interactions. Let’s have a look at how to figure out a functional from for such a potential [following Kittel, Introduction to Solid State Physics, 8th ed., Wiley, p. 53]. When we have a system of two indentical inert gas atoms, what holds them together to form a dimer? If the charge distributions of the atoms would be rigid, the cohesive energy would be zero. However, the atoms induce dipole moments in each other, and the induced moments cause an attractive interaction. Notes ...
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This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.

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md2011-04-note_Part_3 - D I P Pair potentials: U(r) = Pair...

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