Training machine-learned force fields for redox reactions
Here we describe the training of [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{2+} }[/math] and [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+} }[/math] ([math]\displaystyle{ \mathrm{Fe}^{2+} }[/math] and [math]\displaystyle{ \mathrm{Fe}^{3+} }[/math] in liquid water) and the training of water with a slab. This is a development of the procedure followed by Jinnouchi et al. [1].
Input files
POSCARs
The following initial structures will be used in this example. Please run the calculations on each structure in a separate directory. The POSCAR files are described on more detail in the redox potential overview page.
Click to reveal the [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{2+} }[/math] POSCAR
Fe_64H2O
1
12.42282200 0.00000000 0.00000000
0.00000000 12.42282200 0.00000000
0.00000000 0.00000000 12.42282200
H O Fe
128 64 1
Direct
0.12743711 0.48760461 0.68402834
0.07224030 0.59099573 0.69720079
0.39623895 0.90251919 -0.68562329
0.52396846 0.89222892 -0.69202626
0.42964083 0.63656491 0.92024856
0.40471536 0.51747508 0.92244566
0.50949529 0.22553243 0.82975356
0.79695561 -0.29210416 -0.14766098
0.00805766 0.01676094 0.93033834
-0.01969191 0.14077136 0.89733509
0.01773692 1.49221026 -0.45662142
-0.09754205 1.45083180 -0.48707747
0.28568895 0.07977712 0.14809775
0.40460027 0.11889958 0.12632577
-0.44823614 -0.23392047 0.91065326
-0.44655395 -0.27382665 1.03236410
0.55758309 0.63486700 0.51461921
0.54015662 1.52364880 0.45450703
0.67045916 0.85136844 0.58289035
0.71164261 0.89435637 0.47626762
1.16684705 0.13193713 0.89590371
0.33871812 0.20748811 0.69296855
0.38041592 0.31864036 0.75378916
-0.26840230 -0.60381695 0.57433173
0.25751301 1.09723808 -0.39131073
0.28561906 1.17135043 -0.49010853
-0.15559770 0.77405954 1.51947552
-0.03350167 0.77676575 1.52339975
0.75237735 1.02309221 1.12180723
0.04826055 0.15234086 0.05862687
-0.09230147 -0.06114088 1.02402855
-0.07779336 -0.14013315 0.92524744
0.68560087 0.63322667 1.36320530
0.79400335 0.69800156 2.34722324
1.01111679 0.16477327 0.53663862
0.98618018 0.28565957 0.49809698
0.20452861 0.81136804 0.83127978
-0.29824646 -0.48415938 0.54811270
0.37502040 1.26549068 0.41257460
1.30154976 0.64025841 0.11667748
1.75290818 0.59403116 0.98316689
1.65052923 0.63412803 0.91547295
0.75375838 0.00138371 -0.37473678
0.76130867 1.05807834 -0.25911110
-0.05696647 -0.29493528 0.76468746
0.02811791 -0.33267590 0.85098776
0.61065413 0.29830310 0.85951557
0.11763966 0.86822584 0.90729729
0.18919114 0.55109134 0.38993918
0.21099928 0.52226945 0.51012484
0.03269714 0.36292005 0.33650725
0.02620788 0.48115860 0.28181401
1.05541232 0.90157404 0.64524915
1.07849658 0.77961507 0.68820380
-0.62352298 1.63205141 0.30877689
0.43788457 1.73907737 0.26620496
0.64515164 -0.84752695 1.12986454
0.64730542 0.18633377 1.26064334
0.19923207 -0.08426170 0.07502044
0.22493320 -0.20749942 0.08281964
0.78950677 1.18291196 0.57758905
0.83466268 1.23338961 0.48038196
1.10490483 1.28683406 0.74494774
0.29928808 0.66864147 -0.17842015
0.69120317 0.84829619 1.11035412
0.67223805 0.75611954 1.18775106
-0.00106366 0.61277354 0.38525072
0.01326608 0.68609575 0.28998127
-0.07137268 0.05723237 0.64512696
0.03262162 0.06902330 0.71661499
0.77907316 0.40440365 0.75246685
0.73437154 0.47097142 0.84530449
0.22165260 0.78128841 0.57222522
0.24873347 0.68762843 0.48624453
0.21948415 0.65300265 -0.26571256
0.79089209 -0.20809083 -0.24704170
1.11107834 0.01381845 0.32957265
1.03239487 0.10538648 0.35890625
-0.22306466 1.43601128 1.11757892
-0.24593929 1.53904148 0.17695298
0.53330947 -0.13832394 0.74775872
0.48380538 -0.08752260 0.84569979
0.33958593 1.05428999 0.90703938
0.29513801 0.93047632 0.90464110
-0.10080201 -0.17071890 0.20726349
0.00812468 -0.20258160 0.13847835
0.08102303 0.64583254 0.03494449
-0.04079584 0.61193214 0.04209357
0.35121443 1.17006312 0.32377652
1.18017291 1.28895470 0.63748305
0.44815316 0.76165600 -0.42603898
0.46425067 0.68605942 -0.32598380
0.26710057 0.21583209 0.85066344
1.08895608 0.13400129 0.17359061
0.65188184 1.12136051 0.88104293
0.65005020 0.99400031 0.86041374
0.74276310 0.93357167 0.31617568
0.65193906 1.01050888 0.33337941
0.22155564 -0.06334224 -0.33974479
0.31584241 -0.05457389 -0.25072038
0.46701413 0.39534529 0.33741153
0.37353168 0.43618379 0.40490478
0.88534124 0.31114574 0.85608235
0.90593210 0.27739909 0.97341481
0.39857237 -0.04387750 0.56182123
0.47095275 1.02320312 0.49993905
1.25892990 0.45837652 0.17875477
1.15656687 0.39089427 0.22252886
0.51644837 0.17070272 0.40580457
1.27940834 0.60940694 0.99753791
0.42616197 0.40350440 0.06681017
1.44539498 0.30393771 -0.01376590
0.46562325 1.01534518 0.03284939
0.50319974 0.99064681 0.15470387
0.81037140 0.25082530 0.14657752
0.90914722 0.31376690 1.17885883
0.90887977 0.86774057 1.39942038
0.94187889 0.97203833 1.33441155
0.22890408 0.88765248 0.26506994
0.22943934 0.87502350 1.39740388
0.49252993 0.56873322 1.17531223
0.58322974 0.47973985 1.18073167
1.07353906 0.35801775 -0.07352972
1.10345201 0.46291908 -0.00569576
0.56233028 0.47301291 0.65701182
1.50111441 0.39245196 0.57504212
0.64733050 0.17609466 0.44047892
0.76155406 -0.00064089 0.99805907
0.11696365 0.55392898 0.64536596
0.45665944 0.88787932 -0.73431062
0.37333616 0.58173353 0.89358570
0.83287880 -0.23084103 -0.18836803
0.03157586 0.08326143 0.89500066
-0.01967168 1.44066290 -0.50120574
0.32649692 0.14675159 0.14354441
-0.47815402 -0.28476352 0.96183234
0.58825114 1.58190086 0.46693607
0.73530757 0.86486122 0.54696653
0.36850393 0.23869519 0.76098331
-0.24064441 -0.53169325 0.57977533
0.24867886 1.17176032 -0.42128557
-0.09114394 0.73086170 1.49415350
0.77082046 0.96821649 1.06941593
-0.03834292 -0.10477073 0.98185130
0.72904928 0.67702858 2.31155822
0.98643994 0.21068855 0.47648425
0.18404121 0.88355581 0.86864094
1.08703359 0.18844511 0.11444108
1.71734102 0.59616846 0.90840384
0.79123200 0.05674886 -0.33394462
0.02043659 -0.31156425 0.77570162
0.56069314 0.24338431 0.88537227
0.24569014 0.53057214 0.44182948
0.03448211 0.40131521 0.26357804
1.09819988 0.83512130 0.63612042
-0.60356192 0.67216851 0.24349363
0.68641610 -0.81762609 1.18817124
0.21611881 -0.14120573 0.12450673
0.76919341 1.22245249 0.51393968
1.14696413 1.32734585 0.69656507
0.65811040 0.77819298 1.11522722
0.04903142 0.62925399 0.32627031
0.01260756 0.05983530 0.64228866
0.74653920 0.39814097 0.82582336
0.26593357 0.76215637 0.50729285
0.25423481 0.71079817 -0.23075499
1.04656732 0.05170956 0.30685598
-0.27090311 1.50034802 1.11590884
0.55144479 -0.10997314 0.82138721
0.36595179 0.97842307 0.90355956
-0.04879022 -0.22282940 0.18797022
0.02303649 0.60374665 -0.00064438
0.36248716 1.18806896 0.40233898
0.50553342 0.72818132 -0.38174573
0.23339102 0.17685431 0.91622715
0.69519318 1.05764833 0.86986144
0.66244443 0.93542605 0.32313623
0.29157406 -0.03443908 -0.32197353
0.43576289 0.39304384 0.41288487
0.93290635 0.26807660 0.90192508
0.46947458 -0.04604768 0.53317357
1.23797107 0.38686102 0.19701795
1.24279488 0.62426866 1.06753929
1.39453671 0.36177382 0.00797544
0.49872289 1.04632858 0.09816681
0.86030136 0.31356352 0.11502915
0.87609952 0.92053833 1.35250286
0.23398309 0.92340184 1.33460122
0.50301930 0.49047944 1.17320678
1.13069333 0.39166539 -0.03166013
1.52690177 0.40275423 0.64871882
0.59258213 0.16054156 0.38717393
1.22868038 0.27296875 0.05742047
Click to reveal the [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+} }[/math] POSCAR
Fe_64H2O
1
12.42282200 0.00000000 0.00000000
0.00000000 12.42282200 0.00000000
0.00000000 0.00000000 12.42282200
H O Fe
128 64 1
Direct
-0.38272023 0.47236734 0.69895078
-0.27203601 0.41866794 0.72914269
0.60916541 0.72796225 0.09306829
0.71070494 0.78725068 0.14392771
1.08865564 0.93820602 0.24600432
1.03755512 0.98120737 0.35350048
0.04276558 1.23801733 0.56678300
0.45616640 0.36926572 0.39344586
-0.16977976 0.40716591 0.53863440
-0.25237329 0.38130525 0.44755164
0.44169261 1.14516978 0.14529032
0.37457743 1.13530301 0.24819417
0.18407518 0.25222959 0.06812304
0.09998538 0.14744161 0.06444770
0.27831295 0.57479968 0.31380844
0.29633366 0.45926581 0.36724418
0.64763154 -0.53184911 0.87002912
0.63022496 0.40977773 0.99107908
0.47906160 0.58853267 0.63100265
0.59945353 0.62329058 0.64816927
0.87712851 0.41898140 1.07505748
0.26314503 -0.13253460 0.01243951
0.16153170 -0.19745195 0.05804701
0.34412600 -0.01810085 0.81692911
0.14554222 0.77130921 -0.25213594
0.21209078 0.79452634 -0.14442072
0.41500251 0.04461290 0.96837924
0.49008610 0.14359786 0.93019679
0.82125847 0.86254586 1.27147476
0.00873717 0.10267666 0.23211446
0.35980746 0.34237108 0.76169366
0.33485343 0.46345006 0.77046483
0.90320251 0.61221204 0.04264507
0.97690745 0.71802735 1.06017819
0.96030764 0.81465128 0.70019704
1.01749178 0.74674122 0.60432752
0.64007416 0.23981183 0.92947124
0.31788389 -0.12374136 0.74827741
0.99321033 0.93631524 0.55767630
0.15487454 0.51028490 -0.09542554
0.66815917 0.79686891 0.72718580
0.76202793 0.70002522 0.75366280
0.13591369 -0.02901335 0.00566347
0.08957800 1.06396642 -0.07143824
0.53392446 -0.11896063 0.23953882
0.48718378 -0.00799262 0.25860106
-0.07163033 1.26809135 0.50762252
0.67405502 0.12105566 0.95083205
0.74551359 0.62681866 0.34775553
0.66650260 0.64357368 0.25540936
0.38872827 0.12804968 0.55656518
0.33782256 0.21579745 0.49248801
0.92231233 -0.04307885 1.00089073
0.79411522 -0.04854941 1.01531498
-0.40705912 1.12847907 0.48347215
0.65420892 1.23981902 0.47957005
0.84599640 -0.09249550 0.84023452
0.80327236 0.97997213 0.74592535
0.88638541 0.47237368 0.72110537
0.88941805 0.35493190 0.74249811
0.55296221 0.93428417 0.55243420
0.51441228 0.92952738 0.43767406
0.73847683 0.51634987 1.03266322
0.40092134 0.63952229 -0.01737781
0.41176789 0.89134362 1.10615330
0.44444253 0.84405868 0.99393367
0.58073572 0.63347610 -0.04423652
0.60854638 0.72933752 -0.11607112
-0.16580359 0.22001380 0.89963070
-0.04391612 0.21085677 0.85654400
0.40533602 0.50000334 0.11555470
0.34998095 0.38355577 0.10448457
-0.24359234 0.77537730 0.45894937
-0.26614437 0.70560002 0.56106171
0.28303298 0.61126441 0.01597951
0.37578327 0.33380444 0.30290136
0.59618764 0.27699048 1.12423906
0.50319683 0.35108728 1.09799129
0.18989659 0.76741117 1.22566037
0.06153560 0.75549602 0.22936925
0.51785592 0.24354330 0.65223118
0.56708719 0.32005973 0.73245604
0.61206395 0.98022340 0.70759384
0.50678625 0.91620503 0.71723010
0.68602440 0.14707860 0.76412395
0.69294218 0.12172781 0.64036372
0.33488986 0.71525634 0.14956129
0.35814895 0.80854785 0.22920363
0.95945912 1.05245660 0.53679791
0.77994512 0.55222218 1.15138214
0.69626269 0.94689443 0.43758767
0.82244291 0.95270203 0.44158402
-0.08533410 0.30668689 0.99691887
0.88689642 0.15254779 0.21721075
0.96565778 0.66203563 0.74352603
0.91899641 0.64391575 0.86105003
0.60192845 0.32627053 0.34541527
0.54412777 0.22739074 0.29056180
0.33801876 0.24481339 -0.03610605
0.27498242 0.34868783 -0.07124872
0.63970642 0.49240211 0.35877270
0.61552019 0.46892953 0.48438447
0.30584874 0.64699933 -0.22951580
0.42787645 0.64881697 -0.19623458
0.05975532 0.12314654 0.75074831
-0.02832220 1.03112946 0.76086242
1.07382577 0.25251612 0.39457391
1.17074101 0.24004400 0.30909053
0.90882853 0.66787644 0.52270722
0.07399163 0.59412808 0.95304999
0.13906082 0.47905225 0.10518101
1.17121656 0.46180650 0.23562581
0.97971011 0.63429872 0.37278291
0.90631471 0.68858591 0.26904690
0.60516786 0.96463888 0.06395544
0.68233031 1.04347277 1.12012494
0.20897747 0.21380315 0.63498998
0.20507421 0.29490009 0.72649781
0.21069366 1.05104536 -0.68658423
0.27938942 1.09406910 0.40078460
0.70263174 0.14455648 1.25970691
0.75730930 0.04722448 1.29768294
0.91307779 0.40130091 0.34978752
0.94369056 0.50994390 0.28013594
0.08933991 0.43228293 0.60852163
1.17837154 0.48628664 0.53072146
1.00504493 0.58007882 0.54073092
0.86291931 -0.13828811 1.15173275
-0.34491075 0.43621986 0.75416516
0.63900568 0.75492759 0.15829659
1.07199795 1.00257563 0.28363155
0.38420131 0.34485841 0.37967695
-0.17342306 0.37643136 0.46438657
0.45349630 1.14005000 0.22505348
0.11869813 0.21939929 0.09604324
0.23622993 0.50759344 0.33909324
0.64875252 0.47771851 0.95286519
0.55590506 0.57693205 0.60050819
0.18736673 -0.15437724 -0.00677806
0.37523088 -0.06818877 0.76435686
0.21811495 0.76245384 -0.22055952
0.42220970 0.12606004 0.96558981
0.85780135 0.81574581 1.21531426
0.30433544 0.39124488 0.77849745
0.95758533 0.65697710 1.00747411
1.03085555 0.79681957 0.66923251
0.69067343 0.18643375 0.90833405
0.96523126 0.16955239 0.22035170
0.68612747 0.72230731 0.74299918
0.08987161 0.03581255 0.00348357
0.46357734 -0.08420990 0.24196675
-0.01222913 1.21468404 0.51335175
0.71162904 0.58691114 0.28804098
0.32268708 0.16090339 0.53975026
0.86234882 -0.08436224 0.98773807
-0.38355188 0.19092778 0.52248232
0.85291582 -0.08281162 0.75894361
0.86323773 0.40597333 0.69118967
0.54292990 0.98123241 0.48667605
0.80728528 0.53397589 1.07560692
0.39528125 0.89790682 1.02768167
0.56047647 0.70886600 -0.05694049
-0.09585039 0.25981162 0.89091800
0.40071565 0.42814971 0.14908255
-0.23238312 0.70278251 0.48864911
0.35169257 0.62880569 0.04279978
0.56212715 0.31299799 1.06345122
0.12066294 0.79773619 1.19966391
0.51154081 0.26173878 0.72839369
0.58450605 0.90652737 0.69203180
0.70957535 0.09399646 0.71195964
0.32002783 0.74390105 0.22241023
0.95247763 0.97831298 0.50380136
0.76168681 0.93342180 0.39565898
-0.07590969 0.35133103 1.07020111
0.90649162 0.63028257 0.78114555
0.61524001 0.25974801 0.30414551
0.30266553 0.31064613 -0.00899828
0.62120647 0.43621160 0.41233540
0.36878355 0.59976322 -0.20951626
0.00592307 0.09406140 0.79582533
1.10947213 0.28743919 0.33114811
0.13898678 0.54360995 0.97023057
1.15168897 0.42574337 0.16437693
0.96099089 0.62982868 0.29120309
0.66514203 1.00695060 0.04564722
0.15635030 0.24896214 0.68388955
0.26078411 1.11001890 0.32632346
0.75255117 0.09346553 1.23417762
0.93550375 0.42521425 0.27361930
1.12555194 0.49730673 0.58995753
0.97951694 0.64650296 0.50479031
1.02535902 0.32276265 0.18627127
Click to reveal the
128H2O_slab POSCARSYSTEM
1
12.50000000 0.00000000 0.00000000
0.00000000 12.50000000 0.00000000
0.00000000 0.00000000 50.00000000
H O
256 128
Direct
-0.15047607 0.45334683 0.32730556
-0.07219808 -0.49010458 0.34403411
0.63805046 0.03123465 0.46999929
0.50838374 0.00754431 0.46372876
0.20742016 -0.23715390 0.31145651
0.21957350 0.63504600 0.31129793
0.49252565 0.97213243 0.52739381
0.46254946 0.86699495 0.51338367
0.46833659 0.30083696 0.47570094
0.56435815 0.28642228 0.46051829
0.73586863 -0.12693724 0.63650708
0.75181963 -0.25406949 0.63203814
0.41854353 0.84406884 0.44927074
0.33515626 0.90054023 0.46728072
0.34479509 0.57962028 0.37911763
0.29762780 -0.47903310 0.40660055
0.15115248 0.54108257 0.49957979
0.08260965 0.53074503 0.52635427
0.89266849 0.40696421 0.52478091
-0.06057907 0.40486920 0.55352216
0.55977900 -0.37296647 0.61748251
0.53858714 -0.26767121 0.59987163
0.71275400 0.42250550 0.56832405
0.78839559 0.34546846 0.58417890
0.67385329 -0.19610180 0.44987464
0.59318198 -0.16624091 0.42828513
0.12312508 0.37123899 0.28937208
0.05023666 0.27675971 0.29997236
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-0.21800579 1.57002107 0.66191007
0.20675683 -0.06108281 0.29221359
0.10312049 -0.09294129 0.30396903
0.20277637 0.06067826 0.60416144
0.19887396 -0.00744650 0.62890026
0.42062864 -0.24439336 0.35497596
0.36814211 -0.33879224 0.34193308
-0.46114333 0.32802380 0.39548517
0.45713828 0.41873416 0.39179412
1.05751346 0.29067408 0.55923161
1.04348507 0.18703047 0.57744764
0.21179010 0.87249263 0.56793233
0.09036024 0.85931851 0.57432053
0.60751605 1.01609789 0.65259722
0.72696147 1.05338974 0.65871807
0.44683747 0.21956247 0.29940199
0.48216169 0.19981749 0.26927194
0.10930269 0.40445023 0.47082959
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1.57461032 1.43827952 0.71246905
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2.02346307 1.41217476 0.66399254
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1.07727341 0.25676911 0.57497686
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0.78587144 0.61673307 0.55124293
0.56011355 0.11309492 0.40567704
1.51701295 1.39737040 0.70673631
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0.65847198 0.61537373 0.40712496
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1.27220645 1.14795719 0.57873009
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0.14376608 0.06922992 0.53329165
1.27850839 0.03499489 0.35317314
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1.20665739 1.51259035 0.71454551
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1.10461724 0.26953014 0.36735832
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1.25134221 -0.39325035 0.56126973
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0.62353030 0.97359658 0.59258366
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1.00887481 -0.51613717 0.38007575
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1.22065693 1.25957506 0.70894987
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1.04556333 1.22974551 0.74538666
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0.47580393 -0.01885257 0.68583286
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0.13921945 1.47529964 0.65395905
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1.02198254 0.77527198 0.51809412
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1.15374394 0.51400513 0.30712860
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0.79285789 -0.22059881 0.33571374
INCAR
The INCAR files are shown here for reference; each is reproduced and discussed in the step that uses it.
Click to reveal the on-the-fly training INCAR for [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{2+} }[/math]
NELECT = 526 # Electronic parameters ENCUT = 520.0 EDIFF = 1E-5 GGA = RP IVDW = 11 ISMEAR = 0 SIGMA = 0.10 PREC = Normal LREAL = A NELMIN = 4 ALGO = All NELM = 200 ISPIN = 2 MAGMOM = 128*0 64*0 1*4 NUPDOWN = 4 IWAVPR = 0 AMIX = 0.2 # MD paramters IBRION = 0 ISYM = 0 NSW = 20000 POTIM = 1.0 TEBEG = 300 TEEND = 500 MDALGO = 3 ISIF = 2 LANGEVIN_GAMMA = 10.0 10.0 10.0 LCHARG = .FALSE. LWAVE = .FALSE. # Machine learning ML_LMLFF = .TRUE. # switches on machine learning ML_MODE = train ML_MB = 6000 ML_RCUT1 = 6.0 ML_RCUT2 = 4.0 # Parallelization for electronic calculation (depends on number of cores) NCORE = 4 # Increase mass of hydrogen POMASS = 8.0 16.0 55.847 # Set constant threshold for the Bayesian errors ML_ICRITERIA = 0 ML_CTIFOR = 0.07
Click to reveal the refit INCAR
Click to reveal the on-the-fly training INCAR for [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+} }[/math]
NELECT = 525 # Electronic parameters ENCUT = 520.0 EDIFF = 1E-5 GGA = RP IVDW = 11 ISMEAR = 0 SIGMA = 0.10 PREC = Normal LREAL = A NELMIN = 4 ALGO = All NELM = 200 ISPIN = 2 MAGMOM = 128*0 64*0 1*5 NUPDOWN = 5 IWAVPR = 0 AMIX = 0.2 # MD paramters IBRION = 0 ISYM = 0 NSW = 20000 POTIM = 1.0 TEBEG = 300 TEEND = 500 MDALGO = 3 ISIF = 2 LANGEVIN_GAMMA = 10.0 10.0 10.0 LCHARG = .FALSE. LWAVE = .FALSE. # Machine learning ML_LMLFF = .TRUE. # switches on machine learning ML_MODE = train ML_MB = 6000 ML_RCUT1 = 6.0 ML_RCUT2 = 4.0 # Parallelization for electronic calculation (depends on number of cores) NCORE = 4 # Increase mass of hydrogen POMASS = 8.0 16.0 55.847 # Set constant threshold for the Bayesian errors ML_ICRITERIA = 0 ML_CTIFOR = 0.07
Click to reveal the water-slab training INCAR
ENCUT = 520.0 EDIFF = 1E-5 GGA = RP IVDW = 11 ISMEAR = 0 SIGMA = 0.10 PREC = Normal LREAL = A NELMIN = 4 ALGO = Normal IBRION = 0 ISYM = 0 NSW = 50000 POTIM = 1.0 TEBEG = 300 TEEND = 600 MDALGO = 3 ISIF = 2 LANGEVIN_GAMMA = 10.0 10.0 10.0 LCHARG = .FALSE. LWAVE = .FALSE. ML_LMLFF = .TRUE. # switches on machine learning ML_MODE = train ML_MB = 6000 ML_RCUT1 = 6.0 ML_RCUT2 = 4.0 NCORE = 4 POMASS = 8.0 16.0 55.847
KPOINTS
The Gamma-point only is used for the KPOINTS file:
Gamma-point only 0 Monkhorst Pack 1 1 1 0 0 0
POTCAR
Standard POTCAR files are used throughout:
PAW_PBE H 15Jun2001PAW_PBE O 08Apr2002PAW_PBE Fe_sv 23Jul2007
Step-by-step instructions
Training of [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{2+} }[/math]
Step 0: Preparing the calculation
Use the POSCAR for [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{2+} }[/math], KPOINTS, INCAR and POTCAR from this example.
Step 1: Determining the number of electrons of the neutral system
Execute the following command:
mpirun -np 1 vasp_executable --dry-run
Using the --dry--run argument, VASP executes most of the setup routines but bypasses the computationally heavy tasks. Besides testing the input, running VASP with this option is an easy way to determine system-dependent default values for parameters such as NBANDS, etc. In this example, we will use this run to determine the number of electrons NELECT of the system. For that type:
grep NELECT OUTCAR
You should get an output like:
NELECT = 528.0000 total number of electrons
So the number of electrons in the system is 528. We will use this value as a starting point for the INCAR.
Step 2: Running the on-the-fly training
First we will train for NSW=50000 steps with a 1 femtosecond stepsize (POTIM=1.0). Please run the calculation with the following INCAR file:
NELECT = 526 # Electronic parameters ENCUT = 520.0 EDIFF = 1E-5 GGA = RP IVDW = 11 ISMEAR = 0 SIGMA = 0.10 PREC = Normal LREAL = A NELMIN = 4 ALGO = All NELM = 200 ISPIN = 2 MAGMOM = 128*0 64*0 1*4 NUPDOWN = 4 IWAVPR = 0 AMIX = 0.2 # MD paramters IBRION = 0 ISYM = 0 NSW = 20000 POTIM = 1.0 TEBEG = 300 TEEND = 500 MDALGO = 3 ISIF = 2 LANGEVIN_GAMMA = 10.0 10.0 10.0 LCHARG = .FALSE. LWAVE = .FALSE. # Machine learning ML_LMLFF = .TRUE. # switches on machine learning ML_MODE = train ML_MB = 6000 ML_RCUT1 = 6.0 ML_RCUT2 = 4.0 # Parallelization for electronic calculation (depends on number of cores) NCORE = 4 # Increase mass of hydrogen POMASS = 8.0 16.0 55.847 # Set constant threshold for the Bayesian errors ML_ICRITERIA = 0 ML_CTIFOR = 0.07
Since there are so many tags, we give a brief description of them below in the context of this system:
- NELECT: In the previous step, we determined that the system has 528 electrons. To simulate [math]\displaystyle{ Fe_{2+} }[/math] in liquid water, we decrease the number of electrons in the system by setting NELECT=526 (the two electrons are put in the background to remain charge neutral in the SCF calculations).
- IVDW: For water, we need to use van der Waals interactions.
- ALGO=ALL: We need an "exact" solution of the electronic states, since this system is set up as magnetic and, as with many of the magnetic systems, it can be hard to find global minima.
- NUPDOWN: Using this tag is absolutely necessary, since otherwise the magnetic states would strongly fluctuate, leading to very unfavorable configurations that cannot be converged electronically.
- MDALGO=3: We use a Langevin thermostat.
- ISIF=2: We run the calculation in the NVT ensemble.
- ML_MB=6000: We select 6000 local reference configurations (4000 would likely also be sufficient). A larger number of local reference configurations leads to a higher accuracy of the force field but requires more computational resources and is potentially less stable.
- ML_RCUT1=6.0, ML_RCUT2=4.0: These are empirical settings for liquid water that lead to improved accuracy.
- POMASS: The mass of hydrogen is increased by a factor of 8. This is needed so that we can use larger timesteps.
- ML_ICRITERIA=0: For complex systems, the automatic determination of the threshold for on-the-fly learning (ML_ICRITERIA = 1) can fail, so we would like to use a constant threshold (ML_ICRITERIA = 0). Unfortunately, the threshold (ML_CTIFOR) is system-dependent, so it needs to be determined by the user via test calculations.
- ML_CTIFOR=0.07: For this example we have predetermined this value from shorter (NSW = 5000-10000) test calculations where we guessed ML_CTIFOR with ML_ICRITERIA=0.
Step 3: Continuing the training with a smaller threshold
Here we will continue to train for another NSW=50000 steps with a 1 femtosecond step size (POTIM=1.0). Open a new folder in which you will continue the calculation; copy ML_ABN and CONTCAR from the previous folder to ML_AB and POSCAR in the new folder, respectively. Also copy the POTCAR, POSCAR and INCAR file to the new directory.
To further increase the sampling rate and the stability of the force field, decrease the threshold for learning in the INCAR file from 0.07 to 0.03:
ML_CTIFOR = 0.03
After running the force field, obtain the errors of the force field on the training data by typing:
grep ERR ML_LOGFILE
The exact errors are never fully reproducible, but one should have an error close to the following:
# ERR ###################################################################### # ERR This line contains the RMSEs of the predictions with respect to ab initio results for the training data. # ERR # ERR nstep ......... MD time step or input structure counter # ERR rmse_energy ... RMSE of energies (eV atom^-1) # ERR rmse_force .... RMSE of forces (eV Angst^-1) # ERR rmse_stress ... RMSE of stress (kB) # ERR ###################################################################### # ERR nstep rmse_energy rmse_force rmse_stress # ERR 2 3 4 5 # ERR ###################################################################### ... ... ... ... ... ERR 24182 3.34379956E-04 4.21034293E-02 3.25574507E-01 ERR 45641 3.52798835E-04 4.30397061E-02 3.24044663E-01 ERR 49316 3.72327940E-04 4.37625524E-02 3.18168785E-01
Typically a few percent deviation is expected, since the trajectories of the training runs cannot be reproduced if run in parallel (due to a random order of summation in MPI together with limited floating point accuracy). Since we will train and run our production calculations in the NVT ensemble low errors for energy and forces are more important than for the stress. Low errors in forces are required to have a stable force field which gives a physically correct trajectory. Later we want to apply this force field to thermodynamic integration where the energy is the key quantity. So we also need low errors in the energy. Here we are satisfied with an accuracy of <0.5 meV/atom for the energy.
Step 4: Refitting
Refit the ML_ABN from the previous step and obtain the final ML_FF file. For that use the following INCAR file that uses empirically optimized tags:
ML_LMLFF = .TRUE. ML_MODE = REFIT ML_RCUT1 = 6 ML_RCUT2 = 4 ML_MRB1 = 8 ML_MRB2 = 6 ML_W1 = 0.5
The final five tags have been empirically optimized for water. The most important change is the reduction of the cutoff radii: ML_RCUT1 is lowered from its default value of 8 Å to 6 Å, and ML_RCUT2 from 5 Å to 4 Å. Because a smaller cutoff radius also reduces the required descriptor space, the maximum numbers of radial basis functions, ML_MRB1 and ML_MRB2, can be reduced accordingly. Collectively, these adjustments reduce overfitting, which is one reason this parameter set improves accuracy. The radial and angular descriptor mixing parameter ML_W1 has only a minor effect on force-field accuracy and is therefore not discussed here.
Training of [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+} }[/math]
Step 0: Preparing the calculation
Use the POSCAR for [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+} }[/math], KPOINTS, INCAR and POTCAR from this example.
Step 1: Determining the number of electrons of the neutral system
This step is analogous to [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{2+} }[/math].
Step 2: Running the on-the-fly training
The INCAR is very similar to the one of [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{2+} }[/math]:
NELECT = 525 # Electronic parameters ENCUT = 520.0 EDIFF = 1E-5 GGA = RP IVDW = 11 ISMEAR = 0 SIGMA = 0.10 PREC = Normal LREAL = A NELMIN = 4 ALGO = All NELM = 200 ISPIN = 2 MAGMOM = 128*0 64*0 1*5 NUPDOWN = 5 IWAVPR = 0 AMIX = 0.2 # MD paramters IBRION = 0 ISYM = 0 NSW = 20000 POTIM = 1.0 TEBEG = 300 TEEND = 500 MDALGO = 3 ISIF = 2 LANGEVIN_GAMMA = 10.0 10.0 10.0 LCHARG = .FALSE. LWAVE = .FALSE. # Machine learning ML_LMLFF = .TRUE. # switches on machine learning ML_MODE = train ML_MB = 6000 ML_RCUT1 = 6.0 ML_RCUT2 = 4.0 # Parallelization for electronic calculation (depends on number of cores) NCORE = 4 # Increase mass of hydrogen POMASS = 8.0 16.0 55.847 # Set constant threshold for the Bayesian errors ML_ICRITERIA = 0 ML_CTIFOR = 0.07
Step 3: Continuing the training with a smaller threshold
Here we will continue to train for another NSW=50000 steps with a 1 femtosecond stepsize (POTIM=1.0). Open a new folder in which you will continue the calculation; copy ML_ABN and CONTCAR from the previous folder to ML_AB and POSCAR in the new folder, respectively. Also copy the POTCAR, POSCAR and INCAR file to the new directory.
To further increase the sampling rate and the stability of the force field, decrease the threshold for learning in the INCAR file from 0.07 to 0.03:
ML_CTIFOR = 0.03
After running the force field, obtain the errors of the force field on the training data by typing:
grep ERR ML_LOGFILE
The exact errors are never fully reproducible, but one should have an error close to the following:
# ERR ###################################################################### # ERR This line contains the RMSEs of the predictions with respect to ab initio results for the training data. # ERR # ERR nstep ......... MD time step or input structure counter # ERR rmse_energy ... RMSE of energies (eV atom^-1) # ERR rmse_force .... RMSE of forces (eV Angst^-1) # ERR rmse_stress ... RMSE of stress (kB) # ERR ###################################################################### # ERR nstep rmse_energy rmse_force rmse_stress # ERR 2 3 4 5 # ERR ###################################################################### ... ... ... ... ... ERR 48581 5.12372302E-04 4.72631941E-02 3.49022532E-01 ERR 49124 5.10950338E-04 4.73081124E-02 3.50467103E-01 ERR 50000 5.10380095E-04 4.73261876E-02 3.50002289E-01
Step 4: Refitting
Refit the ML_ABN from the previous step and obtain the final ML_FF file using the same INCAR as for [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+} }[/math].
Training of water slab
Step 0: Preparing the calculation
Use the POSCAR for 128H2O_slab, KPOINTS, INCAR and POTCAR from this example.
Step 1: Running the on-the-fly training
The training of the slab works quite fine with an automatic threshold determination, so we will use that in this example. For that, one does not need to set any tag explicitly, since that is the default.
Otherwise, the INCAR file for the water slab is similar to the previous examples:
ENCUT = 520.0 EDIFF = 1E-5 GGA = RP IVDW = 11 ISMEAR = 0 SIGMA = 0.10 PREC = Normal LREAL = A NELMIN = 4 ALGO = Normal IBRION = 0 ISYM = 0 NSW = 50000 POTIM = 1.0 TEBEG = 300 TEEND = 600 MDALGO = 3 ISIF = 2 LANGEVIN_GAMMA = 10.0 10.0 10.0 LCHARG = .FALSE. LWAVE = .FALSE. ML_LMLFF = .TRUE. # switches on machine learning ML_MODE = train ML_MB = 6000 ML_RCUT1 = 6.0 ML_RCUT2 = 4.0 NCORE = 4 POMASS = 8.0 16.0 55.847
For the slab, it is enough to train for 50000 MD steps, but running longer would further ensure the stability of the calculation.
After running the force field, obtain the errors of the force field on the training data by typing:
grep ERR ML_LOGFILE
The exact errors are never fully reproducible, but one should have an error close to the following:
# ERR ###################################################################### # ERR This line contains the RMSEs of the predictions with respect to ab initio results for the training data. # ERR # ERR nstep ......... MD time step or input structure counter # ERR rmse_energy ... RMSE of energies (eV atom^-1) # ERR rmse_force .... RMSE of forces (eV Angst^-1) # ERR rmse_stress ... RMSE of stress (kB) # ERR ###################################################################### # ERR nstep rmse_energy rmse_force rmse_stress # ERR 2 3 4 5 # ERR ###################################################################### ... ... ... ... ... ERR 49240 1.25708895E-03 5.02528627E-02 1.97068357E-01 ERR 49792 1.25205691E-03 5.03152901E-02 1.97839796E-01 ERR 50000 1.25113931E-03 5.03108647E-02 1.98322319E-01
Step 2: Refitting
Refit the ML_ABN from the previous step and obtain the final ML_FF file using the same INCAR as for the previous examples.
Recommendations and advice
- The Bayesian errors and hence also their thresholds are system dependent. To determine ML_CTIFOR one could also first run a calculation with automatically determined thresholds, plot error predictions and thresholds at every MD step and deduce values for ML_CTIFOR from the plot.
- Let it be mentioned here that it is possible to increase the accuracy of the energy. This is achieved by increasing the weight of the energy equations during fitting using ML_WTOTEN (typically increase it to 5, 10 or even more). Of course at the same time forces and stress will become more inaccurate. So one needs to find a good balanced value where the increase in accuracy of the energy is significantly larger than the decrease in accuracy of the rest. The behavior with respect to ML_WTOTEN is unfortunately strongly system dependent. We note that for this example ML_WTOTEN=1 was good enough.
Related tags and articles
- How-tos
- Construction:Thermodynamic integration: redox potential
- Construction:Thermodynamic integration between MLFFs
- Construction:Thermodynamic integration between MLFF and GGAs
- Theory
- Machine learning force field calculations: Basics
- Best practices for machine-learned force fields
- Machine learning force field: Theory
- Files
- Tags
References