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# lecture10 - Chapter 9 Molecular-dynamics Integrate...

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Chapter 9: Molecular-dynamics Integrate equations of motion-- classical! Discrete form of Newton’s second law Forces from interaction potential For a simple pair potential, we get ρ F i = - r Ñ i U r r 1 , r r 2 ,..., r r N ( ) U r r 1 ,..., r r N ( ) = 1 2 u ( ij å r ij )

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Integrating equations of motion F i , x = m i dv i , x dt F i , y = m i dv i , y dt F i , z = m i dv i , z dt dv i , x dt = d 2 x i dt 2 » x i ( n +1) - 2 x i ( n ) + x i ( n - 1) D t 2 x i ( n +1) = 2 x i ( n ) - x i ( n - 1) + F i , x m i D t 2 This works out to give the Verlet algorithm,
Lennard-Jones potential for noble gas V r ( ) = 4 e s r ae è ç ö ø ÷ 12 - s r ae è ç ö ø ÷ 6 é ë ê ù û ú QuickTimeª and a TIFF (LZW) decompressor are needed to see this picture.

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Placing atoms on fcc lattice… non-primitive basis ! start with non-primitive fcc basis r1(1)=0.0d0 r2(1)=0.0d0 r3(1)=0.0d0 r1(2)=0.5d0 r2(2)=0.5d0 r3(2)=0.0d0 r1(3)=0.5d0 r2(3)=0.0d0 r3(3)=0.5d0 r1(4)=0.0d0 r2(4)=0.5d0 r3(4)=0.5d0
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lecture10 - Chapter 9 Molecular-dynamics Integrate...

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