md2011-06-note_Part_7

md2011-06-note_Part_7 - O F AIMD I In principle, the forces...

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Unformatted text preview: O F AIMD I In principle, the forces can be numerically calculated from F I = - I h |H e | i . (27) I Unfortunately this is both too slow and too inaccurate for the MD calculations. I Instead, analytical estimation of the forces is required I h |H e | i = h | I H e | i + h I |H e | i + h |H e | I i (28) I When the wave function is an exact eigenfunction of the H e , the contributions vanish exactly (this is the so-called Hellmann-Feynman Theorem ). Notes I Hence, we are in theory left with F HFT I = h | I H e | i . (29) I In reality, however, the incomplete basis set used to construct the wave function requires a correction (IBS) which corresponds to the wave function force or Pulay force. I Another source for error results from non-self-consistency (NSC) which is due to approximate potential. I Hence, the total force in AIMD is a combination of these three terms F I = F HFT I + F IBS I + F NSC I . (30) Notes I...
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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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md2011-06-note_Part_7 - O F AIMD I In principle, the forces...

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