[CPMD-list] Gauss-Hermite vs Kleinman-Bylander, VDW-CELL
Robert Williams
bob at bob.usuhs.mil
Sun Mar 27 23:31:03 CEST 2005
Dear list,
Following up on my "serial and parallel gradients differ" question:
Ari P Seitsonen wrote:
> 'GEOMETRY STEP NR. 2284' - wow! The geometry of the system should have
> converged MUCH, MUCH earlier. Maybe the reason is that you use the
> Gauss-Hermite integration, did you check (e.g. in small molecules) that
> the default values and pseudos are adequate? Especially the number of grid
> points (the default value has been changed to '20' in the up-coming
> versions of CPMD). The convergence 1.0e-6 is very tight for the ions, and
> thus it has not been reached. My experience is also that the 'LBFGS'
> algorithm (in section '&CPMD') converges usually very fast to the ground
> state.
I'm running an LBFGS tests now, one is reported here.
Thanks to Axel and Ari.
Earlier tests of this SAME unit cell reached full convergence
(E-7) in only 11 geometry steps, instead of 2284, using symmetry
and GAUSS-HERMITE integration:
*** TOTAL STEP NR. 114 GEOMETRY STEP NR. 11 ***
*** GNMAX= 7.496937E-07 [7.90E-05] ETOT= -189.120551 ***
*** GNORM= 2.829654E-07 DETOT= -8.373E-10 ***
*** CNSTR= 0.000000E+00 TCPU= 286.87 ***
Here are the final results for the same input using KLEINMAN-BYLANDER:
*** TOTAL STEP NR. 696 GEOMETRY STEP NR. 59 ***
*** GNMAX= 6.085330E-07 [6.30E-05] ETOT= -189.039472 ***
*** GNORM= 1.387942E-07 DETOT= -2.646E-09 ***
*** CNSTR= 0.000000E+00 TCPU= 172.41 ***
Here are final results using GAUSS-HERMITE and LBFGS:
*** TOTAL STEP NR. 59 GEOMETRY STEP NR. 5 ***
*** GNMAX= 4.302331E-07 [1.93E-06] ETOT= -189.120551 ***
*** GNORM= 1.282000E-07 DETOT= -6.168E-12 ***
*** CNSTR= 0.000000E+00 TCPU= 154.82 ***
WOW!
I'm running a test of KLEINMAN-BYLANDER with LBFGS, but at this
point it is taking more steps than the GAUSS-HERMITE with LBFGS.
I'm sure there are cases where KLEINMAN-BYLANDER is faster than
GAUSS-HERMITE, but in this case, on an organic crystal using
symmetry, G-H appears to be significantly faster, and the energy
is lower. It would be useful to know where to draw the line
with respect to integration of the non-local part.
I don't know if the use of VDW here is a factor.
Symmetry was turned off in the present tests (2284 steps) to see what
values are required for VDW-CELL. When using VDW with VDW-CELL left
at the default of 0 0 0, VDW corrections are applied only to one cell.
This essentially creates a "defect" in the crystal at that cell.
Using symmetry forces the geometry of that cell to look more
like the geometry of the cells with no VDW correction.
With symmetry turned off the molecules in this cell become badly
distorted with respect to the neutron diffraction structure.
Application of VDW correction to several layers of cells
surrounding the cell of interest corrects this behavior.
It's still not clear to me how many layers are sufficient,
but the VDW calculation is so inexpensive, 4 4 4 (9 layers
in all directions) appears to be at least adequate.
To explain: VDW-CELL is followed on the next line by three
numbers indicating how many layers to add in x, y, and z.
1 1 1 indicates -1, 0, and +1 along each axis, and so on.
I'm running a parallel LBFGS test on this case (no symmetry)
right now.
>
> Anyway, coming back to your actual question: The serial calculation has
> been stopped because the default number of electronic iterations, 10000,
> has been reached. So many steps shouldn't been necessary, it's usually a
> sign of a problem during the calculation. Also the second calculation has
> finished before all your convergence criterion for the forces has been
> finished - I don't know why, but also here there is most likely some
> problem in the input (if you send us the output we could give a look,
> however 1400 geometry steps is MUCH too much also). If you definitely
> want so accurate forces (of course very welcome e.g. when heading for
> vibrational spectra), you could first check the Gauss-Hermit integration,
> then try 'LBFGS'; but reaching 1.0e-6 might still be impossible.
>
> Greetings from rainy Paris,
>
> apsi
>
> On Sat, 26 Mar 2005, Robert Williams wrote:
>
>> Dear CPMDers,
>>
>> Results from my serial and parallel optimizations
>> using cpmd3.9.1 differ significantly, starting from
>> identical input files (attached) using tight
>> convergence criteria. Below are parts
>> of the final results for serial and parallel runs
>> on P4 linux systems. Of particular interest to me,
>> why are the gradients zero in the serial results,
>> and near the GNORM in the parallel results?
>> This is reflected also in the GEOMETRY.xyz files.
>> (Compile time optimizations for each version differ
>> a little.)
>>
>> Serial 3.9.1:
>> *** TOTAL STEP NR. 9999 GEOMETRY STEP NR. 2284 ***
>> *** GNMAX= 1.182878E-03 [5.35E-05] ETOT= -189.032981 ***
>> *** GNORM= 2.870398E-04 DETOT= 1.005E-09 ***
>> *** CNSTR= 0.000000E+00 TCPU= 80.58 ***
>> ...
>> = END OF GEOMETRY OPTIMIZATION =
>> * FINAL RESULTS *
>> ...
>> ATOM COORDINATES GRADIENTS (-FORCES)
>> 1 O 5.1224 2.8573 3.3944 0.000E+00 0.000E+00 0.000E+00
>> 2 O 4.1231 8.7555 10.3710 0.000E+00 0.000E+00 0.000E+00
>> 3 O 14.3880 2.7858 3.3105 0.000E+00 0.000E+00 0.000E+00
>> 4 O 13.4023 8.7048 10.1629 0.000E+00 0.000E+00 0.000E+00
>> ..................................................................
>>
>> Parallel 3.9.1:
>> *** TOTAL STEP NR. 6604 GEOMETRY STEP NR. 1400 ***
>> *** GNMAX= 1.825868E-03 [8.65E-09] ETOT= -189.032988 ***
>> *** GNORM= 4.655294E-04 DETOT= -2.749E-10 ***
>> *** CNSTR= 0.000000E+00 TCPU= 18.64 ***
>> ...
>> = END OF GEOMETRY OPTIMIZATION =
>> * FINAL RESULTS *
>> ...
>> ATOM COORDINATES GRADIENTS (-FORCES)
>> 1 O 5.1271 2.8813 3.4124 -7.567E-04 9.170E-05 -4.731E-04
>> 2 O 4.1229 8.6424 10.2943 6.352E-04 -9.080E-06 1.336E-04
>> 3 O 14.4179 2.8784 3.3640 1.826E-03 -1.309E-04 3.528E-04
>> 4 O 13.3743 8.6440 10.2220 -1.175E-03 -2.027E-04 2.011E-04
>> ..................................................................
>>
>>
>> Bob
>>
>>
>
--
Dr. Robert Williams
Department of Biomedical Informatics
Uniformed Services University
4301 Jones Bridge Road
Bethesda, MD 20814
301-295-3568
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