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md2011-04-note_Part_3

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

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D I P Pair potentials : U ( r ) = U 0 + i , j U 2 ( r i , r j ) Pair functionals : U [ F , r ] = i , j U 2 ( r i , r j ) + i F j g 2 ( r i , r j ) Cluster potentials : U ( r ) = U 0 + i , j U 2 ( r i , r j )+ i , j , k U 3 ( r i , r j , r k ) Cluster functionals : U [ F , r ] = i , j U 2 ( r i , r j )+ i F j g 2 ( r i , r j ) , j , k g 3 ( r i , r j , r k ) Real potentials are often combinations of the above. Notes

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I P P I Idealistic potentials can serve as the first approximation. Hard Sphere Potential U HS ( r ) = , r < σ 0 , r > σ (3) I First ever MD potential I Billiard-ball physics I Works for packing problems Notes
Square Well Potential U SW ( r ) = , r < σ 1 - ε , σ 1 6 r < σ 2 0 , r > σ 2 (4) Notes

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Soft Sphere Potentials U SS ( r ) = ε h σ r i ν (5) ν = 1 ν = 12 Notes
M R P P Lennard-Jones I 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
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