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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
Billiardball 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 LennardJones
LennardJones 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.
 Winter '12
 Kotakoski

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