Problem with geometry optimization using LS_SCF

[Torstein Fjermestad]

Dear all, 

First some background for my question:

I got computing hours on a cluster with GPUs. I did some tests with single point calculations, and I found that linear scaling SCF ran about 5 times faster than "normal" SCF for my system on that cluster. The total energy between SCF and LS_SCF differed only by about 0.04 kJ mol-1; and I therefore found the results encouraging. 

I then went on to compare LS_SCF and "normal" SCF for geometry optimizations on a machine without GPUs. I did three tests:

Test 1: Single point calculation

Test 2: Geometry optimization starting from the geometry in Test 1

Test 3: Geometry optimization starting from the optimized geometry in Test 2

I used the following keywords in the LS_SCF section. 

&LS_SCF

  EPS_FILTER 1.0E-7

  EPS_SCF    1.0E-7

&END

At the beginning of the attached output files the complete input is echoed. 

I now describe the results of the tests.

Test 1: Single point calculation. The total energy differs by 0.05 kJ mol-1

entry	Total energy/ Ha	wall time / s	LS_SCF?
1	-3499.00767	309	yes
2	-3499.00768	380	no

Test 2: Geometry optimization starting from the geometry in Test 1. SCF_GUESS ATOMIC is used 

entry	Total energy, first geom / Ha	max. grad of first step	# geometry steps	Total energy, optim geom / Ha	wall time, s	wall time / geom. step, s	LS_SCF?
1	-3499.00767	0.03493	54	Did not converge within the requested wall time	7260 a	134	yes
2	-3499.00769	0.03613	123	-3499.11153	4386	36	no

^a Requested wall time in submit script

In Test 2, the wall time per geometry step is much longer when LS_SCF is used than when "normal" SCF is used. This is in spite of Test 1 showing that LS_SCF is notably faster for a single point calculation. 

Am I doing something wrong here?
Is the start guess of the wavefunction at each geometry step perhaps not adequate in the case of LS_SCF?

How should I change the LS_SCF parameters in order to improve the calculation?

Test 3: Re-optimization of the optimized structure in Test 2 (entry 2). SCF_GUESS ATOMIC is used 

 

entry	Total energy, first geom / Ha	max.grad of first step	# geometry steps	Total energy, optim geom / Ha	wall time	wall time / geom step	LS_SCF?
1	-3499.11150	0.00016	1	-3499.11153	396	396	no
2	-3499.11147	0.00183	19	Did not converge within the requested wall time	7260a	382	yes

^a Requested wall time in submit script

Not unexpectedly, in Test 3,  the geometry optimization with "normal" SCF converges after 1 geometry step. 

However, the geometry optimization with LS_SCF did not converge within two hours and took only 19 geometry steps.

I see that the max. gradient of the first geometry step is much higher in the case of LS_SCF than in the case of "normal" SCF. 

Are there some LS_SCF parameters I should adjust to check if the gradient has converged?

I would really appreciate help in this matter, because in the current situation, I am not able to use LS_SCF for geometry optimizations. 

Thanks and regards,

Torstein Fjermestad

  

 

[Thomas Kühne]

Dear Torstein, 

apparently you are not exploiting the WF guess in your LS_SCF run, as you have guessed. 

Without an input I can only speculate, but by default EXTRAPOLATION_ORDER is 4 within 

LS_SCF and 3 for all other methods. Regarding test 3, did you also restart the Hessian matrix? 

Cheers, 

Thomas

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==============================

Thomas D. Kühne

Dynamics of Condensed Matter

Chair of Theoretical Chemistry

University of Paderborn

Warburger Str. 100

D-33098 Paderborn

Germany

tdku...@mail.upb.de

+49/(0)5251/60-5726

[Torstein Fjermestad]

Dear Thomas,

Thanks for your fast reply.

I did not restart the Hessian matrix in test 3.

The LS_SCF section with all default made explicit, you can see here:

The complete input file is attached.

Thanks

Regards,

Torstein

     &LS_SCF

       LS_DIIS  F

       INI_DIIS  2

       MAX_DIIS  4

       NMIXING  2

       EPS_DIIS     1.0000000000000001E-01

       MAX_SCF  20

       EPS_SCF     9.9999999999999995E-08

       MIXING_FRACTION     4.5000000000000001E-01

       EPS_FILTER     9.9999999999999995E-08

       EPS_LANCZOS     1.0000000000000000E-03

       MAX_ITER_LANCZOS  128

       MU    -1.0000000000000001E-01

       FIXED_MU  F

       EXTRAPOLATION_ORDER  4

       S_PRECONDITIONER  ATOMIC

       PURIFICATION_METHOD  SIGN_MATRIX

       DYNAMIC_THRESHOLD  F

       NON_MONOTONIC  T

       MATRIX_CLUSTER_TYPE  ATOMIC

       SINGLE_PRECISION_MATRICES  F

       RESTART_WRITE  F

       RESTART_READ  F

       S_INVERSION  SIGN_SQRT

       SIGN_SQRT_ORDER  3

       REPORT_ALL_SPARSITIES  T

       PERFORM_MU_SCAN  F

       CHECK_S_INV  F

     &END LS_SCF

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[Fabian Ducry]

Dear Torstein,

On Test 2:

I am no expert on LS_SCF but my understanding ist that PURIFICATION_METHOD SIGN should only be used if the chemical potential is know and set using MU. This is useful for AIMD where MU is known and does not fluctuate too much. Switching PURIFICATION_METHOD to TRS4 and enabling DYNAMIC_THRESHOLD will improve convergence if you do not know MU beforehand. I assume that the reason for the long walltime/step for LS_SCF is because of poor convergence originating in the purification.

On Test 3:

As OT and LS_SCF are numerical methods they will not result in identical densies, similar but not the same. So you can expect the forces to be slightely different too. If I run your input with tighter settings EPS_SCF 1.0e-8 and EPS_FILTER 1.0e-8 the max. force at step 126 (starting val 123) is already below the convergence threshold:

 --------  Informations at step =   126 ------------
  Optimization Method        =                 BFGS
  Total Energy               =     -3498.3787056930
  Real energy change         =        -0.0000126132
  Predicted change in energy =        -0.0000107671
  Scaling factor             =         0.0000000000
  Step size                  =         0.0038980052
  Trust radius               =         0.4724315332
  Decrease in energy         =                  YES
  Used time                  =               49.665

  Convergence check :
  Max. step size             =         0.0038980052
  Conv. limit for step size  =         0.0030000000
  Convergence in step size   =                   NO
  RMS step size              =         0.0004691139
  Conv. limit for RMS step   =         0.0015000000
  Convergence in RMS step    =                  YES
  Max. gradient              =         0.0004187196
  Conv. limit for gradients  =         0.0004500000
  Conv. in gradients         =                  YES
  RMS gradient               =         0.0000483787
  Conv. limit for RMS grad.  =         0.0003000000
  Conv. in RMS gradients     =                  YES
 ---------------------------------------------------

Best,

Fabian

[Thomas Kühne]

Dear Torstein, 

beside the advice by Fabian to reduce the numerical noise within the forces to improve 

the convergence of the geometry optimization, set EXTRAPOLATION_ORDER to 3 for 

consistency. Since the sign-method is an alternative to diagonalization, which is at variance 

to OT that is a direct minimization method (inspite the fact that the minimization steps 

are also called SCF iterations within CP2K!), the largest difference is due to the rather 

simplistic mixing. You may try to use DIIS acceleration (LS_DIIS T together with appropriate 

values for INI_DIIS & NMIXING) or BROYDEN_MIXING inside RHO_MIXING. 

Cheers, 

Thomas

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<input-explicit.inp>

[Torstein Fjermestad]

Dear Fabian and Thomas,

Thanks a lot for your useful feedback.

I thought I should give you an update to clarify a confusion I might have caused.

When I said "normal" SCF, I meant orbital transformation (OT). Sorry for the sloppy terminology.

I completely confused myself (and probably also you) when I reported the wall time for a single point / geometry step.

When I look at the wall time per SCF iteration, the OT method is significantly faster than LS_SCF both for the CPU and GPU machine, see table below. 

I think the wall time per SCF iteration is a more relevant quantity to look at because for the OT method, the number of SCF iterations is reduced significantly when the start guess can be read from the previous geometry of a geometry optimization.

Entry	Total energy/ Ha	machine	nodes	tasks-per-node	tasks-per-socket	cpus-per-task	gpus-per-node	threads	wall time	# SCF steps	wall time/ SCF step	Method	purification method	EPS_SCF	dynamic threshold
1	-3499.007666	cpu - MPI	3	36	-	-	-	-	309.3	8	38.7	LS_SCF	sign	1.0E-07	FALSE
2	-3499.00768	cpu - MPI	3	36	-	-	-	-	380.0	86	4.4	OT	-	1.0E-06	-
3	-3499.00769	gpu -MPI/OMP	4	4	2	32	4	16	67.5	11	6.1	LS_SCF	trs4	1.0E-06	TRUE
4	-3499.00768	gpu -MPI/OMP	4	4	2	32	4	16	361.7	86	4.2	OT	-	1.0E-06	-

Entry 1 and 2 are the same calculations as shown in Test 1 at the start of this thread. 

Best regards,

Torstein

Cheers, 

Thomas

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<input-explicit.inp>