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cp2k/data/MPC_POTENTIALS
Dynamics of Condensed Matter 91e51cab28
Add MPC pseudopotentials (#5188)
2026-05-14 17:10:11 +02:00

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################################################################################
#
# Multipole-conserving (MPC) GTH pseudopotentials
# ------------------------------------------------
#
# Copyright (C) 2025 Andris Gulans, Anders Brakestad, Stig Rune Jensen,
# Luca Frediani, and Stefan Goedecker
#
# Reference:
# A. Gulans, A. Brakestad, S. R. Jensen, L. Frediani, and S. Goedecker,
# "A synthetic pseudopotential benchmark for testing production
# pseudopotentials and constructing pseudopotentials with chemical accuracy"
# (2025).
#
# MPC concept:
# Norm-conserving pseudopotentials conserve the electrostatic monopole of
# the charge inside the core region. MPC extends this idea by fitting also
# the higher multipoles generated by hybridized atomic orbitals, e.g.
#
# psi_b(r) = psi_2s(r) + psi_2px(r)
# psi_a(r) = psi_2s(r) - psi_2px(r)
# rho_b(r) = 2 |psi_b(r)|^2
#
# with charge multipoles
#
# Q_lm[rho] = int rho(r) r^l Y_lm(rhat) d^3r
# = int_0^infty r^(l+2) dr int dOmega rho(r) Y_lm(rhat).
#
# For orbitals that participate in bonding, MPC fits the all-electron (AE)
# and pseudo (PS) moments of orbital products inside a cutoff radius rc:
#
# int_0^rc r^(l+2) R^PS_n1l1(r) R^PS_n2l2(r) dr
# * int dOmega Y_l1m1(rhat) Y_l2m2(rhat) Y_lm(rhat)
# ~= same expression with R^AE instead of R^PS.
#
# The l=0 case is the usual norm/monopole conservation. Matching higher
# multipoles improves the electrostatic interactions of hybridized bonding
# charges, and hence the transferability of the pseudopotential.
#
# Source format: HGH/GTH psppar, PBE (ixc=-101130).
# Potential names use the GTH-MPC-PBE-qX convention to identify the
# multipole-conserving construction. MPC and NLCC are independent concepts:
# MPC denotes the multipole-conserving fit; selected entries additionally
# contain an NLCC core-density correction.
#
# CP2K c_core conversion for entries containing an NLCC block:
#
# c_core = qcore * 4*pi*(Z-Zion)/(sqrt(2*pi)*r_core)^3
#
# Entries intentionally omit a generic GTH-MPC-PBE alias so each potential is
# selected explicitly by its qX valence charge.
#
################################################################################
# PBE functional
#
# source: psppar.H; zatom=1; zion=1; date=20200603; pspcod=10; ixc=-101130
H GTH-MPC-PBE-q1
1
0.15000000000000 2 -5.21038103601596 0.83228852908393
0
#
# source: psppar.Li; zatom=3; zion=3; date=20200622; pspcod=10; ixc=-101130
Li GTH-MPC-PBE-q3
3
0.12911182006012 2 -20.60396614785263 3.48845388100792
1
0.20809331048684 1 0.06607910617214
#
# source: psppar.Be; zatom=4; zion=4; date=20200622; pspcod=10; ixc=-101130
Be GTH-MPC-PBE-q4
4
0.15757532815614 2 -24.78078699284349 4.64339750649381
1
0.22139501435505 2 -0.91115250424055 0.85275009149707
-0.74957083455713
#
# source: psppar.B; zatom=5; zion=5; date=20200514; pspcod=10; ixc=-101130
B GTH-MPC-PBE-q5
4 1
0.10454903445746 1 -42.84494121716708
2
0.11035981316993 2 1.13521516825078 0.82583265578722
1.17469554290255
0.11919729897286 1 3.35320424605834
#
# source: psppar.C; zatom=6; zion=6; date=20200603; pspcod=10; ixc=-101130
C GTH-MPC-PBE-q6
4 2
0.10442926427019 1 -53.59126100299123
2
0.10564388844992 2 -0.31569041006470 1.97864614582159
1.46126942201952
0.11172118378821 1 5.54281105784130
#
# source: psppar.N; zatom=7; zion=7; date=20210605; pspcod=10; ixc=-101130
N GTH-MPC-PBE-q7
4 3
0.11242621264024 1 -62.57195769099587
2
0.10759186342789 2 -2.19055984867820 3.62944727292246
1.54647966059246
0.11098059093681 1 9.08933712180711
#
# source: psppar.O; zatom=8; zion=8; date=20210608; pspcod=10; ixc=-101130
O GTH-MPC-PBE-q8
4 4
0.11500000000015 1 -69.16126397188863
2
0.09376144007671 2 -6.15865550189914 -1.43502477505964
13.92040510531785
0.11281705134658 1 10.18567031314194
#
# source: psppar.F; zatom=9; zion=9; date=20210608; pspcod=10; ixc=-101130
F GTH-MPC-PBE-q9
4 5
0.11023852953561 1 -74.26457978288656
2
0.13175930842657 2 -5.69938083542675 7.93330656747557
-6.38574869374265
0.10815313158517 1 10.70620830176562
#
# source: psppar.Na; zatom=11; zion=9; date=20200703; pspcod=12; ixc=-101130
Na GTH-MPC-PBE-q9
3 6
0.19629640089675 2 29.19070512573715 -5.18950946243615
NLCC 1
0.18781308469565 1 218.13155327060389
2
0.33413547556373 3 4.52895581080606 3.00817674630974 -3.90590742941645
-9.55991114228038 6.28649288367896
-3.21756572448228
0.17834139891211 2 -27.70521938139951 8.09927840536277
-0.97270516662278
#
# source: psppar.Mg; zatom=12; zion=10; date=20200703; pspcod=12; ixc=-101130
Mg GTH-MPC-PBE-q10
4 6
0.20161386811616 2 29.29180556655679 -5.45718102194242
NLCC 1
0.18937938473644 1 211.47576167474958
2
0.29267478513464 3 4.06562767494408 3.18783427608112 -3.76531865795533
-9.70271086996774 6.00340336421860
-2.88453954469412
0.19033372194496 2 -27.88419783666498 8.18527889954318
-0.48178252147845
#
# source: psppar.Al; zatom=13; zion=11; date=20200727; pspcod=12; ixc=-101130
Al GTH-MPC-PBE-q11
4 7
0.29132308902740 1 -7.66470685557861
NLCC 1
0.16000000000000 1 352.84586365026308
2
0.24202268683465 3 10.44426391448928 1.54008069340948 -2.28688914089353
-4.44280472488722 -0.53183708311948
2.96389772966515
0.16794287908325 2 -13.50255150699894 -3.80790785591445
9.24813001340789
#
# source: psppar.Si; zatom=14; zion=12; date=20200620; pspcod=12; ixc=-101130
Si GTH-MPC-PBE-q12
4 8
0.26906401643720 1 -8.24939363614006
NLCC 1
0.16291874700232 1 275.34367537929251
2
0.26147974553052 3 2.69418163994313 7.34684002281998 -2.07995295987211
-6.89289445751254 -4.57648945396954
8.23490939060111
0.25071335550345 2 -21.27271068265838 12.42714629689383
-7.92728515844077
#
# source: psppar.P; zatom=15; zion=13; date=20200701; pspcod=12; ixc=-101130
P GTH-MPC-PBE-q13
4 9
0.27035740926636 1 -10.19557516287410
NLCC 1
0.18107738804300 1 259.68818673855907
2
0.32630393543026 3 9.65091440788825 -3.19365097210689 2.62441416534746
-10.04476734443697 2.08069624233179
3.63732298025215
0.26786764816966 2 -21.09926796819445 13.38897119782337
-9.59342829852228
#
# source: psppar.S; zatom=16; zion=14; date=20200702; pspcod=12; ixc=-101130
S GTH-MPC-PBE-q14
4 10
0.22308116828748 1 -11.88690307704700
NLCC 1
0.14360502299267 1 419.56213533779686
2
0.18709427968593 3 9.42562973909626 8.64023950300721 -5.50898084997528
-3.38496766911945 -4.73204201433474
7.40163684882062
0.20647194591090 2 -29.65044715348547 17.19288601193370
-10.75061412402404
#
# source: psppar.Cl; zatom=17; zion=15; date=20200606; pspcod=12; ixc=-101130
Cl GTH-MPC-PBE-q15
4 11
0.13591022143832 1 -0.73327853213339
NLCC 1
0.13496699202782 1 635.81525790638693
2
0.15422702713177 3 31.97210832838817 6.74642814822497 -13.67161294738851
-3.30752293122772 0.39206109861280
5.58447606436170
0.21785526757594 2 -20.48075831702418 13.35333552466377
-9.90623734666835
#
# source: psppar.K; zatom=19; zion=9; date=20210501; pspcod=12; ixc=-101130
K GTH-MPC-PBE-q9
3 6
0.21411637556325 2 -8.08262244072304 -2.98403510393556
NLCC 1
0.17613336318145 1 1460.20952833853266
2
0.23284626216003 3 18.25498034458694 0.92967730737392 -3.28789684967476
2.47629149211555 2.26503823455225
4.69493410146714
0.27547146370751 3 10.54759199626624 0.79987074459018 -0.23916032510183
-1.11155775526364 -0.46434416076029
1.30115589130906
#
# source: psppar.Ca; zatom=20; zion=10; date=20210430; pspcod=12; ixc=-101130
Ca GTH-MPC-PBE-q10
4 6
0.18032325728140 2 -7.96295967995462 -1.72731639619400
NLCC 1
0.25338210772958 1 490.46975106882593
2
0.21745627530885 3 18.28839233874969 -0.59261536060746 -2.27636541660219
3.37191948393712 2.95496594817167
5.02188736623509
0.25886862426616 3 10.69899508726989 1.39222081402185 -0.15630641383213
-0.79855408514500 -0.61901648381288
1.16544921004311
#
# source: psppar.Sc; zatom=21; zion=11; date=20210213; pspcod=12; ixc=-101130
Sc GTH-MPC-PBE-q11
4 6 1
0.34237268077427 1 -0.02293405214969
NLCC 1
0.18503524965681 1 1259.43758659863283
3
0.32109802903114 3 13.52669258942180 3.87705165479189 -5.50226146754139
1.42797573971435 -1.14877248169009
2.45569072811122
0.33274847786536 3 6.04021170603947 3.47202869062425 -0.26391704933151
-11.30597371094451 1.98599563479157
0.41051302716976
0.21219454821407 2 -3.62833637033709 -1.73312778942658
0.99548104418498
#
# source: psppar.Ti; zatom=22; zion=20; date=20210126; pspcod=12; ixc=-101130
Ti GTH-MPC-PBE-q20
6 12 2
0.10744537000000 0
NLCC 1
0.10750863981019 1 1284.22155612663664
3
0.21940184433913 2 24.67538494091689 -11.74146458918433
21.07722799394976
0.21361599720771 2 -22.10332600372438 16.26985604825476
-18.66330480798636
0.25066325060363 1 0.00546616027201
#
# source: psppar.V; zatom=23; zion=13; date=20210411; pspcod=12; ixc=-101130
V GTH-MPC-PBE-q13
4 6 3
0.27517762000000 0
NLCC 1
0.17440528903176 1 1504.04596097193348
3
0.29315386949600 3 13.65507143313891 7.39817991776004 -6.85347929414602
0.80397349111609 -2.29230107911158
3.97042497279931
0.27405177075026 3 9.98260189340021 2.69104382867149 -0.09448998925349
-8.38272779921355 0.03829939059226
1.74126054303488
0.18635407577995 2 -8.70767875939882 -0.39536690855737
1.59939395044204
#
# source: psppar.Cr; zatom=24; zion=14; date=20210403; pspcod=12; ixc=-101130
Cr GTH-MPC-PBE-q14
3 6 5
0.27895002000000 0
NLCC 1
0.17086385561345 1 1599.51919048950549
3
0.28351164582959 3 14.28343127428783 7.37037472199635 -6.53058693746250
-0.11123777581237 -2.20254445537591
3.92826828597909
0.27194885278611 3 10.01463987601001 2.26485215053604 -0.84731507827282
-7.15591757337656 -0.01156571729768
1.88773279547146
0.18942130379947 2 -8.72294925753834 -0.85654721074104
2.18375390737332
#
# source: psppar.Mn; zatom=25; zion=15; date=20210411; pspcod=12; ixc=-101130
Mn GTH-MPC-PBE-q15
4 6 5
0.25554276000000 0
NLCC 1
0.15737534603508 1 2047.05714928897532
3
0.27532719401740 3 14.99984084032039 8.42929716332426 -7.65091732459534
0.09817583700791 -2.48023431412042
4.51676214379425
0.24048877889181 3 11.54261543108316 1.81242783754854 -0.03487642204098
-7.17834722363293 0.80722564629020
0.33480556021210
0.16636714114343 2 -8.69749186029548 -2.48338513199224
3.09737537357712
#
# source: psppar.Fe; zatom=26; zion=16; date=20210413; pspcod=12; ixc=-101130
Fe GTH-MPC-PBE-q16
4 6 6
0.26127724000000 0
NLCC 1
0.15499643385455 1 2142.76697005388360
3
0.26773083677267 3 15.18234703557230 8.88256185473846 -7.74303309328161
-0.92103607273864 -2.63953890529492
4.99718450639144
0.24568744491923 3 14.20583200007404 -0.13298181220702 -0.49476289827896
-6.29411742659549 0.37496754356789
1.31758314521080
0.16927529907025 2 -9.65830128106300 -2.21377434733804
2.98125114584934
#
# source: psppar.Co; zatom=27; zion=17; date=20210417; pspcod=12; ixc=-101130
Co GTH-MPC-PBE-q17
4 6 7
0.30879754000000 0
NLCC 1
0.15902512829840 1 1984.00516121086525
3
0.26904897371224 3 11.69871673202627 7.83530529788853 -6.75183434071066
-2.43581701839808 -1.79828604433429
4.05283080113709
0.29398953679109 3 5.93413004574420 0.23526631512157 0.57111981187369
-5.31181266082947 -0.33776466614481
1.48931286767601
0.17123347834299 2 -6.05685914126775 -3.28851295382212
-0.40116375630101
#
# source: psppar.Ni; zatom=28; zion=18; date=20210416; pspcod=12; ixc=-101130
Ni GTH-MPC-PBE-q18
4 6 8
0.29207407000000 0
NLCC 1
0.15109180613969 1 2313.22204900856968
3
0.24753987876535 3 13.50331185001111 10.21219439965361 -8.32017053374250
-3.06896895340399 -2.04783736451083
4.70699507834514
0.23526821311672 3 7.95062879978143 1.23883242014503 0.48979661022862
-5.48079318664226 -1.30404268147426
2.09978034193113
0.16202238323462 2 -5.12764996453382 -4.57195664493410
-0.02454477867206
#
# source: psppar.Cu; zatom=29; zion=19; date=20210215; pspcod=12; ixc=-101130
Cu GTH-MPC-PBE-q19
3 6 10
0.29769235000000 0
NLCC 1
0.15046986929661 1 2342.02448042044671
3
0.25375807187669 3 12.04098194507405 8.67969492212623 -6.97478873314255
-4.25164005686857 -1.70750639871733
4.31838633416375
0.30564069644288 3 3.85656937867876 -0.01514768335563 -0.56812494830060
-3.15251119251863 0.53824672201123
0.61737126969946
0.16443747002543 2 -6.50229648278565 -4.75001337873628
0.40559430828437
#
# source: psppar.Zn; zatom=30; zion=20; date=20210202; pspcod=12; ixc=-101130
Zn GTH-MPC-PBE-q20
4 6 10
0.21554424762735 1 20.19788806953730
NLCC 1
0.17970160066474 1 504.08277867717561
3
0.24276988366102 3 13.95384905901293 7.01056198147370 -9.02303054359064
3.17588196438396 -2.87782901754981
5.00471854778930
0.21262217231359 3 2.48576151867546 4.13819055221568 -4.72802477449156
3.40204021140976 -2.48306853350061
3.17570603685731
0.13957620276779 2 -11.68503818834517 -2.98567704364368
-3.96556814856214
#
# source: psppar.Ga; zatom=31; zion=21; date=20210528; pspcod=12; ixc=-101130
Ga GTH-MPC-PBE-q21
4 7 10
0.36641431496237 1 -0.88720709408953
NLCC 1
0.22464849797937 1 703.76798069292397
3
0.20806383736519 3 4.71840362535330 5.00465426369649 -1.88349294250463
3.21780611910995 -0.89726445014793
-4.62124436540348
0.25101496231058 2 -7.38778284925241 4.62560209778675
-5.54343715769045
0.19290174061420 1 -17.47814217032260
#
# source: psppar.Ge; zatom=32; zion=22; date=20210602; pspcod=12; ixc=-101130
Ge GTH-MPC-PBE-q22
4 8 10
0.36092490694740 1 -9.36717581275619
NLCC 1
0.19942760929068 1 817.61029726295521
3
0.20006820198874 3 -10.31493347193097 29.33153334510591 -11.16888875201415
-2.56483418172491 -10.86853709701219
11.60125512987251
0.29270514241876 2 2.41372860562653 -2.83595478407880
2.56103160007024
0.14776418400871 1 -27.35168765267485
#
# source: psppar.As; zatom=33; zion=23; date=20210526; pspcod=12; ixc=-101130
As GTH-MPC-PBE-q23
4 9 10
0.38930422494739 1 -8.84402538556668
NLCC 1
0.20338674493058 1 948.35758957238249
3
0.21969584133030 3 8.16569955298836 8.39450965492363 -6.43447712583620
-1.57793799720107 -3.73670282324891
4.55257471384879
0.29708031428311 2 -4.82148073223230 1.16766631335528
-0.27985658684481
0.15761934762306 1 -27.23545239095241
#
# source: psppar.Se; zatom=34; zion=24; date=20210529; pspcod=12; ixc=-101130
Se GTH-MPC-PBE-q24
4 10 10
0.36876605403135 1 -9.88416113558777
NLCC 1
0.19236809988151 1 1120.83296535649879
3
0.19838940151064 3 -0.24993451548854 17.87087629514775 -8.67347292086375
0.05648741654083 -7.90764248989669
7.41225694718136
0.27946762214918 2 -3.53931485976759 0.14830751451718
0.56402138520067
0.14938899638735 1 -29.81887721481769
#
# source: psppar.Br; zatom=35; zion=25; date=20210510; pspcod=12; ixc=-101130
Br GTH-MPC-PBE-q25
4 11 10
0.36575679715774 1 -10.14591893309538
NLCC 1
0.19168691622132 1 1132.82454255810899
3
0.19679162265913 3 -0.03244706442963 17.83621512191033 -10.15593593477214
-3.17388735278819 -4.72524623945969
5.14461715299437
0.27465189083439 2 -6.48767505748851 1.80600056394247
-0.66740298273003
0.14724683817521 1 -32.18275038820432
#
# source: psppar.Y; zatom=39; zion=11; date=20220909; pspcod=12; ixc=-101130
Y GTH-MPC-PBE-q11
4 6 1
0.47818621899480 1 0.94522820897045
NLCC 1
0.31585136867803 1 709.00582516026986
3
0.36090941247571 3 5.29364469700985 6.52807056734071 -5.50226146754139
4.19529003085839 -1.14877248169009
0.99770768778135
0.30732477527299 3 1.63347683351258 1.65706711670668 -0.26391704933151
0.78037093185524 1.98599563479157
-2.50040093394082
0.33350743918317 2 3.20660361117644 -1.48846373028481
1.71135028433087
#
# source: psppar_PBE_NR_MPC.Au; zatom=79; zion=33; date=20231215; pspcod=12; ixc=-101130
Au GTH-MPC-PBE-q33
3 6 10 14
0.28044482859388 1 23.08556154084568
NLCC 1
0.19254387969760 1 4339.21468013634603
4
0.22577773239440 3 14.59410209653008 14.35460885927382 -12.40323679881997
0.32739944796636 2.18375597779117
13.36920610794461
0.21869970156176 3 1.26203418499454 0.96287028296869 1.28926980593834
2.27343967651214 -1.30578795289945
12.02948761032872
0.28825489167728 2 2.99498063324890 2.34638816064647
0.32054529273801
0.21958587704622 1 -16.32282015375762
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