################################################################################
#
# 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
