Hard to converge for geometric optimizer.

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Hard to converge for geometric optimizer.

Date: 2006/09/19 02:00
Name: Xinyuan Zhang <xzhang@uh.edu>: Dear Prof.
I tried to relax a semiconductor cluster by using DIIS or OPT method. However, in both of the methods, it is extremely hard to converge the minimum MAXforce I can attend is only 0.002 Ha/Bohr. It can't converge further.
Do you have any suggestion on the parameter setting for relax process? Here is my input file.
#
# File Name
#

DATA.PATH /home/x/xzhang/openmx3.0/DFT_DATA

System.CurrrentDirectory ./ # default=./
System.Name a8nm
level.of.stdout 1 # default=1 (1-3)
level.of.fileout 0 # default=1 (1-3)

#
# restart using a restart file, *.rst
#

scf.restart off # on|off,default=off

#
# Definition of Atomic Species
#

Species.Number 2
<Definition.of.Atomic.Species
Si Si6.0-s2p2d1 Si_TM
H H4.0-s2 H_TM
Definition.of.Atomic.Species>

#
# Atoms
#

Atoms.Number 104
Atoms.SpeciesAndCoordinates.Unit Ang # Ang|AU
<Atoms.SpeciesAndCoordinates # Unit=Ang.
1 Si -0.0000 -0.0000 -0.0000 2.0 2.0
2 Si -0.0000 2.7153 2.7153 2.0 2.0
3 Si 2.7153 2.7153 -0.0000 2.0 2.0
4 Si 2.7153 -0.0000 2.7153 2.0 2.0
5 Si 4.0730 1.3577 4.0730 2.0 2.0
6 Si 1.3577 1.3577 1.3577 2.0 2.0
7 Si 1.3577 4.0730 4.0730 2.0 2.0
8 Si 4.0730 4.0730 1.3577 2.0 2.0
9 Si -0.0000 5.4307 5.4307 2.0 2.0
10 Si -0.0000 8.1461 8.1461 2.0 2.0
11 Si 2.7153 8.1461 5.4307 2.0 2.0
12 Si 2.7153 5.4307 8.1461 2.0 2.0
13 Si 4.0730 6.7884 9.5037 2.0 2.0
14 Si 1.3577 6.7884 6.7884 2.0 2.0
15 Si -0.0000 5.4307 -0.0000 2.0 2.0
16 Si -0.0000 8.1461 2.7153 2.0 2.0
17 Si 2.7153 8.1461 -0.0000 2.0 2.0
18 Si 2.7153 5.4307 2.7153 2.0 2.0
19 Si 4.0730 6.7884 4.0730 2.0 2.0
20 Si 1.3577 6.7884 1.3577 2.0 2.0
21 Si -0.0000 -0.0000 5.4307 2.0 2.0
22 Si -0.0000 2.7153 8.1461 2.0 2.0
23 Si 2.7153 2.7153 5.4307 2.0 2.0
24 Si 2.7153 -0.0000 8.1461 2.0 2.0
25 Si 4.0730 1.3577 9.5037 2.0 2.0
26 Si 1.3577 1.3577 6.7884 2.0 2.0
27 Si 1.3577 4.0730 9.5037 2.0 2.0
28 Si 4.0730 4.0730 6.7884 2.0 2.0
29 Si 5.4307 -0.0000 -0.0000 2.0 2.0
30 Si 5.4307 2.7153 2.7153 2.0 2.0
31 Si 6.7884 1.3577 1.3577 2.0 2.0
32 Si 6.7884 4.0730 4.0730 2.0 2.0
33 Si 5.4307 -0.0000 5.4307 2.0 2.0
34 Si 5.4307 2.7153 8.1461 2.0 2.0
35 Si 6.7884 1.3577 6.7884 2.0 2.0
36 Si 6.7884 4.0730 9.5037 2.0 2.0
37 Si 5.4307 5.4307 -0.0000 2.0 2.0
38 Si 5.4307 8.1461 2.7153 2.0 2.0
39 Si 6.7884 6.7884 1.3577 2.0 2.0
40 Si 5.4307 5.4307 5.4307 2.0 2.0
41 Si 5.4307 8.1461 8.1461 2.0 2.0
42 Si 6.7884 6.7884 6.7884 2.0 2.0
43 H -0.8891 0.8891 -0.8891 0.5 0.5
44 H -0.8891 -0.8891 0.8891 0.5 0.5
45 H 0.8891 -0.8891 -0.8891 0.5 0.5
46 H -0.8891 3.6045 1.8262 0.5 0.5
47 H -0.8891 1.8262 3.6045 0.5 0.5
48 H 3.6045 1.8262 -0.8891 0.5 0.5
49 H 1.8262 3.6045 -0.8891 0.5 0.5
50 H 3.6045 -0.8891 1.8262 0.5 0.5
51 H 1.8262 -0.8891 3.6045 0.5 0.5
52 H -0.8891 6.3198 4.5416 0.5 0.5
53 H -0.8891 4.5416 6.3198 0.5 0.5
54 H 0.2964 7.8497 9.6279 0.5 0.5
55 H -1.4819 7.8497 7.8497 0.5 0.5
56 H 0.2964 9.6279 7.8497 0.5 0.5
57 H 1.8262 9.0352 4.5416 0.5 0.5
58 H 3.6045 9.0352 6.3198 0.5 0.5
59 H 3.1839 7.6775 10.3928 0.5 0.5
60 H 4.9621 5.8993 10.3928 0.5 0.5
61 H 0.8891 4.5416 -0.8891 0.5 0.5
62 H -0.8891 6.3198 -0.8891 0.5 0.5
63 H -0.8891 4.5416 0.8891 0.5 0.5
64 H 0.2964 7.8497 4.1972 0.5 0.5
65 H -1.4819 7.8497 2.4190 0.5 0.5
66 H 0.2964 9.6279 2.4190 0.5 0.5
67 H 2.4190 7.8497 -1.4819 0.5 0.5
68 H 4.1972 7.8497 0.2964 0.5 0.5
69 H 2.4190 9.6279 0.2964 0.5 0.5
70 H -0.8891 -0.8891 6.3198 0.5 0.5
71 H 0.8891 -0.8891 4.5416 0.5 0.5
72 H -0.8891 0.8891 4.5416 0.5 0.5
73 H -0.8891 3.6045 7.2569 0.5 0.5
74 H -0.8891 1.8262 9.0352 0.5 0.5
75 H 3.6045 -0.8891 7.2569 0.5 0.5
76 H 1.8262 -0.8891 9.0352 0.5 0.5
77 H 3.1839 2.2468 10.3928 0.5 0.5
78 H 4.9621 0.4686 10.3928 0.5 0.5
79 H 0.4686 4.9621 10.3928 0.5 0.5
80 H 2.2468 3.1839 10.3928 0.5 0.5
81 H 4.5416 -0.8891 0.8891 0.5 0.5
82 H 6.3198 -0.8891 -0.8891 0.5 0.5
83 H 4.5416 0.8891 -0.8891 0.5 0.5
84 H 7.6775 2.2468 0.4686 0.5 0.5
85 H 7.6775 0.4686 2.2468 0.5 0.5
86 H 7.6775 3.1839 4.9621 0.5 0.5
87 H 7.6775 4.9621 3.1839 0.5 0.5
88 H 4.5416 -0.8891 6.3198 0.5 0.5
89 H 6.3198 -0.8891 4.5416 0.5 0.5
90 H 7.6775 2.2468 5.8993 0.5 0.5
91 H 7.6775 0.4686 7.6775 0.5 0.5
92 H 6.4920 3.7767 10.9856 0.5 0.5
93 H 6.4920 5.5549 9.2074 0.5 0.5
94 H 8.2702 3.7767 9.2074 0.5 0.5
95 H 6.3198 4.5416 -0.8891 0.5 0.5
96 H 4.5416 6.3198 -0.8891 0.5 0.5
97 H 6.3198 9.0352 3.6045 0.5 0.5
98 H 4.5416 9.0352 1.8262 0.5 0.5
99 H 7.6775 7.6775 0.4686 0.5 0.5
100 H 7.6775 5.8993 2.2468 0.5 0.5
101 H 6.3198 9.0352 9.0352 0.5 0.5
102 H 4.5416 9.0352 7.2569 0.5 0.5
103 H 7.6775 7.6775 5.8993 0.5 0.5
104 H 7.6775 5.8993 7.6775 0.5 0.5
Atoms.SpeciesAndCoordinates>
Atoms.UnitVectors.Unit Ang # Ang|AU
<Atoms.UnitVectors
30.0 0.0 0.0
0.0 30.0 0.0
0.0 0.0 30.0
Atoms.UnitVectors>
#
# SCF or Electronic System
#
scf.XcType LDA # LDA|LSDA-CA|LSDA-PW|GGA-PBE
scf.SpinPolarization off # On|Off|NC
scf.energycutoff 25.0 # default=150 (Ry)
scf.maxIter 500 # default=40
scf.EigenvalueSolver cluster # DC|GDC|Cluster|Band
scf.Kgrid 1 1 1 # means 4x4x4
scf.Mixing.Type rmm-diis # Simple|Rmm-Diis|Gr-Pulay|Kerker|Rmm-Diisk
scf.Mixing.History 7 # default=5
scf.Mixing.StartPulay 5 # default=6
scf.system.charge 0.0
#
# 1D FFT (using default)
#

#
# Orbital Optimization
#

orbitalOpt.Method off # Off|Unrestricted|Restricted

#
# output of contracted orbitals
#

CntOrb.fileout off # on|off, default=off

#
# SCF Order-N
#
orderN.HoppingRanges 6 # default=5.0 (Ang)
orderN.NumHoppings 2 # default=2

#
# MD or Geometry Optimization
#

MD.Type diis # Nomd|Constant_Energy_MD|Opt
MD.Opt.DIIS.History 8
MD.Opt.StartDIIS 5 # default=5
MD.maxIter 500 # default=1
MD.TimeStep 1.0
MD.Opt.criterion 4.0e-4 # default=1.0e-4 (Hartree/bohr)

#
# Band dispersion
#
# if <Band.KPath.UnitCell does not exist,
# the reciprical lattice vector is employed.

Band.dispersion off # on|off, default=off

#
# MO output
#

MO.fileout off # on|off
num.HOMOs 1 # default=1
num.LUMOs 1 # default=1
MO.Nkpoint 1 # default=1
<MO.kpoint
0.0 0.0 0.0
MO.kpoint>

#
# DOS and PDOS
#

Dos.fileout off # on|off, default=off

Page: [1]

Re: Hard to converge for geometric optimizer. ( No.1 )

Date: 2006/09/19 15:23
Name: Xinyuan Zhang <xzhang@uh.edu>

Dear Prof.
It seems I have figure out what the problem is. The energy cutoff I set is 25 Ry, which is too small. I set it to 100, and the geometric optimization converges very fast.
However, I am still a little puzzled. What's the difference between th energy cutoffs of openmx and other plane wave based program, like VASP and PWSCF? Because, in those softwares, the cutoff is usually around 30Ry.
Thank you very much.

XZ

Re: openmx runtime questions ( No.2 )

Date: 2006/09/19 15:42
Name: T.Ozaki

Hi,

scf.energycutoff is used for integrations of constructing
Hamiltonian associated with exchange-correlation potential and
difference charge Hartree potential. In addition, the same grid
is used to solve Poisson' equation.

Thus, if one wants to find any correspondence, it can be regarded
that this cutoff energy corresponds to the cutoff energy of
solving Poisson's equation in PW codes.

The cutoff energy of 30 Ryd you referred is usually used for the basis
function expansion of PW. In that case, the cutoff energy of solving
Poisson's equation in PW codes becomes 30 times 4 = 120 Ryd, which
is a similar vaule to 100 Ryd you used in OpenMX.

Although the force calculated by OpenMX is always consistent
with the total energy without depending the scf.energycutoff,
provided that the SCF is well converged and the gap is large enough,
a too small scf.energycutoff leads an energy surface with ripple
which makes the convergence difficult (see PRB 72, 045121 (2005)).

Thus, the value of scf.energycutoff should be increased as long as
the computational time and resource are permitted, while the proper
value is usually determined by considering a balance between accuracy
and computational efficiency.

Regards,

TO

Re: Hard to converge for geometric optimizer. ( No.3 )

Date: 2006/09/20 10:50
Name: jessK

Dear Dr. Ozaki,

Nevertheless, the geometry optimization which implemented in openmx, is really very slow. For example, more than 300 steps is needed for relaxation of nanotube, 20-atoms in unit cell, 150 Ry cutoff. In contrast, only 20 steps is needed when plane-wave code is used (bfgs method). Is there a way to improve geometry optimization method?

JK

Re: Hard to converge for geometric optimizer. ( No.4 )

Date: 2006/09/20 11:34
Name: Xinyuan Zhang <xzhang@uh.edu>

Dear Jessk:
I am not sure about your problem. I am relaxing a semiconductor cluster. DIIS takes around 70 steps to converge around 4e-4Ha/Bohr. You said it takes 300 steps? Did you set your convergence criterior too small?
Actually, I still think it is problem dependent. I also used bfgs method in plane-wave based code. It takes around 50 steps to converge. I didn't see too much difference. However, I still hope bfgs method can be implemented in the next release of openmx. At least, we can have one more option. :)

Xinyuan

Re: Hard to converge for geometric optimizer. ( No.5 )

Date: 2006/09/20 22:37
Name: TO

Dear Dr. JessK,

In my experiences, the DIIS in OpenMX converges very quickly for bulk systems
(I mean dense structures).
But the convergence speed becomes very slow for open systems like molecules.
I am not so sure why it is. LBFGS can be one of options for such a case, however,
I think that there is no definite reason that LBFGS should be much faster than DIIS.

I guess that some subtle control of the optimizer, which depends on the problem
under consideration, may be needed to improve the convergence. Such development
in OpenMX will be a future work.

Anyway, thank you for pointing it out.

TO

Re: Hard to converge for geometric optimizer. ( No.6 )

Date: 2006/09/20 12:11
Name: jessK

Dear Xinyuan,

Unfortunately, I didn't find the exact numbers, so I could be wrong. But I clearly remember that difference was huge.

The system i tested - is BN nanotube, large band gap semiconductor. There are no problem to reach the SCF convergence and relaxation is very simple. Even SIESTA (LCAO) with conjugate gradient method relaxes this material very fast. In case of OpenMX, it took much more time.

As another example, I tested this nanotube with applied electric field. with siesta, I relaxed the structure during ~ 1 hour, 4 cpus. With OpenMX, I was unable to get relaxed structure, it took 4days*200 geom. steps and I aborted the calculations. You can see the relaxation history:

***********************************************************
***********************************************************
History of geometry optimization
***********************************************************
***********************************************************

MD_iter SD_scaling |Maximum force| Utot
(Hartree/Bohr) (Hartree)

1 9.30797663 0.02197065 -132.64687333
2 9.30797663 0.02145252 -132.65276043
3 9.30797663 0.02064926 -132.65862297
4 9.30797663 0.01985557 -132.66446138
5 9.30797663 0.01977825 -132.67028853
6 9.30797663 0.02013174 -132.67405128
7 9.30797663 0.02241399 -132.61098877
8 9.30797663 0.02357071 -132.58116026
9 9.30797663 0.02415250 -132.64733098
10 9.30797663 0.03276165 -133.03728808
11 9.30797663 0.02570220 -132.97949091
12 9.30797663 0.02256132 -132.24066978
13 9.30797663 0.02315663 -132.20677233
14 9.30797663 0.02761036 -134.32308919
15 9.30797663 0.02756749 -133.76465454
16 9.30797663 0.02438147 -133.77080470
17 9.30797663 0.02445360 -133.77678258
18 9.30797663 0.02444201 -133.78269535
19 9.30797663 0.02410570 -133.78857994
20 9.30797663 0.02331311 -133.79445200
21 9.30797663 0.02270091 -133.79823230
22 9.30797663 0.02162058 -133.80585924
23 9.30797663 0.02359062 -133.78985488
24 9.30797663 0.03002973 -133.75251843
25 9.30797663 0.02459928 -133.82001915
26 9.30797663 0.03100769 -133.63978259
27 9.30797663 0.03395454 -133.90019888
28 9.30797663 0.02423437 -133.73979940
29 9.30797663 0.02189136 -133.76571380
30 9.30797663 0.02170732 -133.76156455
31 9.30797663 0.02190546 -133.76755288
32 9.30797663 0.02234673 -133.77350782
33 9.30797663 0.02259680 -133.77942227
34 9.30797663 0.02247975 -133.78529277
35 9.30797663 0.02192682 -133.79112793
36 9.30797663 0.02147870 -133.79487444
37 9.30797663 0.02189250 -133.81961375
38 9.30797663 0.02221760 -133.77661006
39 9.30797663 0.02592658 -133.67233324
40 9.30797663 0.02482809 -133.61670021
41 9.30797663 0.02159366 -133.87473653
42 9.30797663 0.02697263 -134.17930085
43 9.30797663 0.02196968 -133.96302923
44 9.30797663 0.02178490 -133.95345230
45 9.30797663 0.02145672 -133.90566359
46 9.30797663 0.02047087 -133.91156351
47 9.30797663 0.02082911 -133.91739190
48 9.30797663 0.02119024 -133.92318177
49 9.30797663 0.02129926 -133.92896788
50 9.30797663 0.02102021 -133.93478152
51 9.30797663 0.02070365 -133.93855572
52 9.30797663 0.02584953 -133.79930082
53 9.30797663 0.02759281 -133.78276163
54 9.30797663 0.03859741 -134.19220581
55 9.30797663 0.03721584 -134.18927366
56 9.30797663 0.04718647 -134.50154978
57 9.30797663 0.02392354 -133.71281184
58 9.30797663 0.02550873 -133.70084194
59 9.30797663 0.02176464 -133.72960079
60 9.30797663 0.02386478 -133.77071066
61 9.30797663 0.02302093 -133.77683705
62 9.30797663 0.02205432 -133.78283121
63 9.30797663 0.02108444 -133.78871002
64 9.30797663 0.02054105 -133.79449874
65 9.30797663 0.02097819 -133.80024576
66 9.30797663 0.02124354 -133.80395443
67 9.30797663 0.03150436 -133.62946266
68 9.30797663 0.04573399 -133.36079221
69 9.30797663 0.04463750 -133.37046333
70 9.30797663 0.02466560 -133.74306683
71 9.30797663 0.03498671 -133.70491629
72 9.30797663 0.02496894 -133.85992432
73 9.30797663 0.02280401 -133.88640985
74 9.30797663 0.02851026 -133.31994870
75 9.30797663 0.03172489 -132.95966429
76 9.30797663 0.02738792 -132.96618241
77 9.30797663 0.02613051 -132.97233264
78 9.30797663 0.02595023 -132.97840499
79 9.30797663 0.02614248 -132.98450671
80 9.30797663 0.02545145 -132.99067568
81 9.30797663 0.02540712 -132.99468441
82 9.30797663 0.02660395 -132.96502309
83 9.30797663 0.02890728 -132.91854956
84 9.30797663 0.02898357 -133.01427976
85 9.30797663 0.02571749 -133.03626397
86 9.30797663 0.02255966 -133.12773730
87 9.30797663 0.02354591 -133.16177327
88 9.30797663 0.02278014 -133.06225987
89 9.30797663 0.02423647 -133.07450723
90 9.30797663 0.02346100 -133.11610403
91 9.30797663 0.02177290 -133.12205689
92 9.30797663 0.02141257 -133.12795273
93 9.30797663 0.02111751 -133.13383743
94 9.30797663 0.02111017 -133.13973090
95 9.30797663 0.02149041 -133.14565316
96 9.30797663 0.02159532 -133.14948555
97 9.30797663 0.02398750 -133.10830757
98 9.30797663 0.02397391 -133.10849695
99 9.30797663 0.02494061 -133.09053534
100 9.30797663 0.02887842 -133.16093541
101 9.30797663 0.02414730 -133.12747964
102 9.30797663 0.02599571 -133.00253932
103 9.30797663 0.02321235 -133.33366556
104 9.30797663 0.03140513 -132.87856435
105 9.30797663 0.02934975 -133.35485183
106 9.30797663 0.02265887 -133.36087797
107 9.30797663 0.02157519 -133.36669047
108 9.30797663 0.02154246 -133.37247548
109 9.30797663 0.02168855 -133.37829034
110 9.30797663 0.02164087 -133.38416412
111 9.30797663 0.02144234 -133.38798715
112 9.30797663 0.03948405 -133.10372352
113 9.30797663 0.03912256 -133.09113125
114 9.30797663 0.04272725 -133.03374289
115 9.30797663 0.02949344 -133.17490892
116 9.30797663 0.03099392 -133.06349996
117 9.30797663 0.02118986 -133.53573143
118 9.30797663 0.02079006 -133.56237323
119 9.30797663 0.02064962 -133.46617181
120 9.30797663 0.02644971 -133.63438464
121 9.30797663 0.02307512 -133.64034140
122 9.30797663 0.02182445 -133.64626999
123 9.30797663 0.02200790 -133.65217890
124 9.30797663 0.02193168 -133.65807642
125 9.30797663 0.02149207 -133.66395942
126 9.30797663 0.02102844 -133.66774452
127 9.30797663 0.02130413 -133.69349513
128 9.30797663 0.02143085 -133.69546718
129 9.30797663 0.02431362 -133.51143975
130 9.30797663 0.02366149 -133.52112817
131 9.30797663 0.02770383 -133.39491422
132 9.30797663 0.02098401 -133.77652187
133 9.30797663 0.02320749 -133.73859751
134 9.30797663 0.02161926 -133.63099707
135 9.30797663 0.02171984 -133.63947058
136 9.30797663 0.02177625 -133.64535258

You see, the forces change very slow. But, of course, I could make mistake.

JK

Re: Hard to converge for geometric optimizer. ( No.7 )

Date: 2006/09/21 16:56
Name: Xinyuan <xzhang@uh.edu>

Hi jessK,
I am not sure about your problem. But I suggest you can try LDA only and turn off the spin polarization. I found it converges much better than GGA-PBE.

XZ

Page: [1]