Department of Chemistry and Chemical Biology

Machine precision

If the energy is the same for the first hundred steps or so, and (if the numbers are not close to 0) diverge only by on the order of 1 in the 3rd significant figure after 1000 steps, the results are exactly the same, modulo machine precision; slight differences in the ordering of operations by compilers and different roundoff procedures used by different hardware lead to slight differences accumulated over many cycles.

This ordinarily leads to different numbers of steps before convergence in energy minimization.

If the numbers are small, this effect can be exaggerated, but average properties (in dynamics) are likely to agree better.

Example: final state of energy minimization.

 NSTEP       ENERGY          RMS            GMAX      NAME    NUMBER
  13013         542.823         0.000         0.001     C5      396

 BOND    =        874.5219  ANGLE   =        108.3989  DIHED =        177.3000
 VDWAALS =        177.8272  ELECT   =        358.5989  HBOND =         -4.0348
 1-4 NB  =         80.8837  1-4 ELEC=      -1230.6732  CONST =          0.0000
 
---

 NSTEP       ENERGY          RMS            GMAX      NAME    NUMBER
  12009         542.823         0.000         0.001     C13      94

 BOND    =        874.5233  ANGLE   =        108.4039  DIHED =        177.2966
 VDWAALS =        177.8211  ELECT   =        358.6016  HBOND =         -4.0350
 1-4 NB  =         80.8840  1-4 ELEC=      -1230.6729  CONST =          0.0000

Department of Chemistry and Chemical Biology, 102 Hurtig Hall, 360 Huntington Ave., Boston, MA 02115
Tel: 617-373-2822 Fax: 617-373-8795

Send mail to e.chudin@neu.edu with questions or comments about this web site.
Last modified: Tuesday, April 01, 2003