Marzari_AIMD_Part_Two - AB-INITIO MOLECULAR DYNAMICS (THE...

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AB-INITIO MOLECULAR DYNAMICS (THE END) Nicola Marzari, DMSE, MIT DFT total energy
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Evaluating H ψ
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It’s really kinetic + (SCF) potential ) ( 2 1 ˆ 2 r V H G + = = = G G G r G i iGr dr G G , 2 2 2 2 1 ) exp( 2 1 ) exp( 2 1 δ ( ) exp( ) ( )exp( ) ( ) GV r G dr iGrV r iGr V G G ′′ =− = Total energy (non-SCF, sort of) 2 1 2 nn n n n EV εψ ψ == + ∑∑ ) exp( ) ( r G i c r G n G n G G G G G = 2 2 , 1 () 2 n GG G n G Ec G c c V G G ⎛⎞ =+ ⎜⎟ ⎝⎠ G G G G
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Dynamical evolution of c’s We need the “force” }] [{ i E E ψ = i i i E F δψ δ }] [{ = i H ˆ =
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Skiing down a valley () ii i FH µ ψψ == ±± i ψ ± “Damped” dynamics skiing
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SD or CG skiing Hellmann-Feynman theorem ˆ ˆˆ i ii dH dE F dR dR dH dV dR dR ΨΨ =− = =Ψ− Ψ=Ψ− Ψ G GG
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Born-Oppenheimer Molecular Dynamics ˆ ii i i dV mR F dR == Ψ Ψ GG ±± G Lots of Skiing if Atoms Move
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Lots of Skiing if Atoms Move The extended CP Lagrangian
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Equations of motion Equations of motion (II)
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This note was uploaded on 12/07/2011 for the course CHEM 350 taught by Professor Duanejohnson during the Summer '06 term at University of Illinois, Urbana Champaign.

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Marzari_AIMD_Part_Two - AB-INITIO MOLECULAR DYNAMICS (THE...

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