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Training machine-learned force fields for redox reactions

From VASP Wiki

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.

Initial structures

The following initial structures will be used in this example. Please run the calculations on each structure in a separate directory.

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
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      0.51154081       0.26173878       0.72839369
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      0.95247763       0.97831298       0.50380136
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      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
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      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 POSCAR
SYSTEM
1
     12.50000000       0.00000000       0.00000000
      0.00000000      12.50000000       0.00000000
      0.00000000       0.00000000      50.00000000
H  O
  256   128
Direct
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      0.43147580      -0.68083095       0.32528778
      0.81926513       0.85574301       0.56746752
      1.25134221      -0.39325035       0.56126973
      0.87947711       1.14636757       0.70571444
      0.62353030       0.97359658       0.59258366
      0.91315731       0.79159814       0.67046472
      1.00887481      -0.51613717       0.38007575
      0.71990656       0.52980508       0.69520722
      0.42715157       0.93815001       0.61949356
      1.22065693       1.25957506       0.70894987
      0.68302181       0.25679220       0.67873356
      1.04556333       1.22974551       0.74538666
      0.05950376       0.17484591       0.65818294
     -0.25231321       1.76973735       0.70816158
      0.45404841       0.29350534       0.51621152
      0.47580393      -0.01885257       0.68583286
      0.31607039       1.37827042       0.60641490
      0.13921945       1.47529964       0.65395905
     -0.24949740       1.04980313       0.38476573
      1.02198254       0.77527198       0.51809412
     -0.13269955      -0.63172943       0.26362895
     -0.01665243       1.05122555       0.57819040
      0.34830926       0.86183449       0.73481007
      0.08547124       0.49199314       0.59517301
     -0.22931968       0.07879046       0.47296684
      1.15374394       0.51400513       0.30712860
     -0.02575549       0.24426930       0.46122795
      0.33910288       0.28875076       0.42031444
      0.89222545       1.42242644       0.72114703
      0.45112644       0.49752204       0.57217511
      0.78732813       0.24777689       0.30076703
      0.17546728       1.17137686       0.45167807
      0.60114018       1.43939441       0.60809185
      1.96388141       1.37112395       0.67251971
      0.13553192      -0.02618932       0.70064801
      1.23640886       0.39518318       0.34779401
      0.01704024       0.84626979       0.45444055
      0.34009588       0.83637329       0.57759905
      0.44929940      -0.11284502       0.35947285
      0.58008850       0.46021347       0.52387715
      0.65101061       0.61092524       0.34954978
      0.79285789      -0.22059881       0.33571374

Other files

Use the following KPOINTS file in all three examples:

Gamma-point only
 0
Monkhorst Pack
 1 1 1
 0 0 0

The INCAR files are provided in each of the examples separately. Finally, standard POTCAR files are used throughout: PAW_PBE H 15Jun2001, PAW_PBE O 08Apr2002, and PAW_PBE Fe_sv 23Jul2007.

Input files

POSCARs

The following initial structures will be used in this example. Please run the calculations on each structure in a separate directory.

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
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     -0.34491075       0.43621986       0.75416516
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     -0.01222913       1.21468404       0.51335175
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      0.56047647       0.70886600      -0.05694049
     -0.09585039       0.25981162       0.89091800
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     -0.23238312       0.70278251       0.48864911
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      0.12066294       0.79773619       1.19966391
      0.51154081       0.26173878       0.72839369
      0.58450605       0.90652737       0.69203180
      0.70957535       0.09399646       0.71195964
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      0.95247763       0.97831298       0.50380136
      0.76168681       0.93342180       0.39565898
     -0.07590969       0.35133103       1.07020111
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      0.30266553       0.31064613      -0.00899828
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      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
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      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 POSCAR
SYSTEM
1
     12.50000000       0.00000000       0.00000000
      0.00000000      12.50000000       0.00000000
      0.00000000       0.00000000      50.00000000
H  O
  256   128
Direct
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      0.58336683       0.13133194       0.42359675
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      0.88557936       0.66337125       0.74776712
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     -0.21783861       0.90704975       0.72268493
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      0.89172292       0.88245064       0.51170593
      1.21360535       1.19956259       0.58314768
      1.23188220       0.10388812       0.56520461
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     -0.50295222       0.92300366       0.74813821
     -0.38930037       0.97841032       0.74266531
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     -0.02910081      -0.04303719       0.33290797
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     -0.17158886       0.30160650       0.40269399
     -0.07101085       0.26515881       0.38366272
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     -0.11186987       0.94149530       0.65599853
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     -0.12458051       0.56502080       0.45311411
     -0.04730932       0.59270705       0.47590220
     -0.26829199       0.80830572       0.49363371
     -0.21717255       0.70457633       0.48040899
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     -0.03231861       0.12955620       0.32499376
     -0.09853097       0.23584383       0.32218754
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      0.12508520       0.09293059       0.39933758
      0.43296574       0.12732681       0.64290755
      0.09700574       1.67696831       0.67957377
     -0.02662689      -0.02348385       0.31412699
      0.44363826      -0.24009345       0.42143376
      0.25025628       1.24855748       0.64562073
      0.79823150       1.08209822       0.60445310
      0.24357641       1.08550799       0.29686686
      0.84487510       0.54791453       0.42274978
      1.20665739       1.51259035       0.71454551
     -0.14852600       0.27439958       0.38483199
      0.79875463       1.36570466       0.63635127
      0.20013661      -0.05770220       0.48695782
     -0.08803369       1.01243312       0.64786941
      0.60681036       0.21343304       0.60836199
      0.96760512       0.18267756       0.51744002
      1.01869709      -0.36164031       0.72861865
      0.89279549       0.03025280       0.42811891
     -0.12190623       0.58173239       0.47257350
     -0.28364610       0.74658147       0.48027041
      0.35461305       0.69479199       0.69387913
      0.17636099       0.75539076       0.63132326
      0.64567772       0.08234767       0.30555919
      0.74693252       0.15345949       0.54261621
     -0.02750156       0.20761939       0.32607759
      1.27987775      -0.43232854       0.43958099
      0.00284833      -0.07336365       0.37560644
      0.13403374      -0.30077764       0.37038742
      0.98462893       0.81761037       0.60965656
      0.51924082       0.63814697       0.49321682
      0.28461449       0.88126714       0.66475622
     -0.20914894       0.44302019       0.50652580
      0.58914466       0.74769132       0.56398020
      0.41471483       1.19061656       0.72530883
     -0.12231266       0.52176874       0.60092233
      0.26021422       1.34539425       0.53435665
      1.56662855       1.77066279       0.67736079
      1.10461724       0.26953014       0.36735832
      0.72369042       0.35764108       0.34663600
      0.43147580      -0.68083095       0.32528778
      0.81926513       0.85574301       0.56746752
      1.25134221      -0.39325035       0.56126973
      0.87947711       1.14636757       0.70571444
      0.62353030       0.97359658       0.59258366
      0.91315731       0.79159814       0.67046472
      1.00887481      -0.51613717       0.38007575
      0.71990656       0.52980508       0.69520722
      0.42715157       0.93815001       0.61949356
      1.22065693       1.25957506       0.70894987
      0.68302181       0.25679220       0.67873356
      1.04556333       1.22974551       0.74538666
      0.05950376       0.17484591       0.65818294
     -0.25231321       1.76973735       0.70816158
      0.45404841       0.29350534       0.51621152
      0.47580393      -0.01885257       0.68583286
      0.31607039       1.37827042       0.60641490
      0.13921945       1.47529964       0.65395905
     -0.24949740       1.04980313       0.38476573
      1.02198254       0.77527198       0.51809412
     -0.13269955      -0.63172943       0.26362895
     -0.01665243       1.05122555       0.57819040
      0.34830926       0.86183449       0.73481007
      0.08547124       0.49199314       0.59517301
     -0.22931968       0.07879046       0.47296684
      1.15374394       0.51400513       0.30712860
     -0.02575549       0.24426930       0.46122795
      0.33910288       0.28875076       0.42031444
      0.89222545       1.42242644       0.72114703
      0.45112644       0.49752204       0.57217511
      0.78732813       0.24777689       0.30076703
      0.17546728       1.17137686       0.45167807
      0.60114018       1.43939441       0.60809185
      1.96388141       1.37112395       0.67251971
      0.13553192      -0.02618932       0.70064801
      1.23640886       0.39518318       0.34779401
      0.01704024       0.84626979       0.45444055
      0.34009588       0.83637329       0.57759905
      0.44929940      -0.11284502       0.35947285
      0.58008850       0.46021347       0.52387715
      0.65101061       0.61092524       0.34954978
      0.79285789      -0.22059881       0.33571374

INCAR

The INCAR files are provided in each of the examples separately.

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 15Jun2001
  • PAW_PBE O 08Apr2002
  • PAW_PBE Fe_sv 23Jul2007


Training procedures

Training of [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{2+} }[/math]

Step 0 Prepare 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 Determine 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: Run 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 unfavourable 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. 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.

Step 3: Continue on-the-fly training with 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

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

Training of [math]\displaystyle{ [\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+} }[/math]

Step 0 Prepare 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 Determine 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: Run 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 paramters
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: Continue on-the-fly training with 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 reproducable, 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 Prepare calculation

Use the POSCAR for 128H2O_slab, KPOINTS, INCAR and POTCAR from this example.

Step 1 Run 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 explicitely, 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 reproducable, 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

Related tags and articles

How-tos
Theory
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References


References