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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 socalled HellmannFeynman 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 nonselfconsistency (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.
 Winter '12
 Kotakoski

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