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A da ase o 175k s able and
me as able ma e ials calcula ed
wi h he PBEsol and SCAN
unc ionals
Jona han Schmid 1, Hai-Chen Wang
1, Tiago F. T. Ce quei a2, Sil ana Bo i
3 &
Miguel A. L. Ma ques
1 ✉
In he pas decade we ha e wi nessed he appea ance o la ge da abases o calcula ed ma e ial
p ope ies. These a e mos o en ob ained wi h he Pe dew-Bu ke-E nze ho (PBE) unc ional o
densi y- unc ional heo y, a well es ablished and eliable echnique ha is by now he s anda d in
ma e ials science. Howe e , he e ha e been ecen heo e ical de elopmen s ha allow o inc eased
accu acy in he calcula ions. He e, we p esen a da ase o calcula ions o 175k c ys alline ma e ials
ob ained wi h wo unc ionals: geome y op imiza ions a e pe o med wi h PBE o solids (PBEsol) ha
yields consis en ly be e geome ies han he PBE unc ional, and ene gies a e ob ained om PBEsol
and om SCAN single-poin calcula ions a he PBEsol geome y. Ou esul s p o ide an accu a e
o e iew o he landscape o s able (and nea ly s able) ma e ials, and as such can be used o eliable
p edic ions o no el compounds. They can also be used o aining machine lea ning models, o e en o
he compa ison and benchma k o PBE, PBEsol, and SCAN.
Backg ound & Summa y
The sea ch o new ma e ials emains one o he mos impo an ques s bu , un o una ely, also one o he g ea
challenges o ma e ials science. Nowadays, da a-d i en sea ching s a egies ha e become he mos cos -e ec i e
me hods o ackle his p oblem, and he as es way o inding new ma e ials o s udy hei p ope ies a e com-
pu a ional high- h oughpu sea ches. A e yea s o da a accumula ion, he e a e millions o calcula ions o
ma e ials a ailable in open da abases1,2 ha a e used as an in aluable ese oi o selec and il e p omising
candida es o u he expe imen al syn hesis and cha ac e iza ion.
These high- h oughpu s udies in solid-s a e ma e ial science3–6 ha e b oadened he explo a ion o he as
chemical space, while plen y o wo ks ha e success ully ound and p edic ed p omising ma e ials o echno-
logical applica ions. Howe e , nea ly all high h oughpu sea ches ely on he use o densi y unc ional heo y
(DFT) wi hin he Pe dew-Bu ke-E nze ho (PBE) app oxima ion o he exchange-co ela ion unc ional7. This
is a well es ablished and eliable app oach ha ea ned i s place as he s anda d echnique in solid-s a e esea ch.
Howe e , he PBE unc ional is now o e 25 yea s old, and mo e ecen (and accu a e) unc ional ha e by now
been p oposed in he li e a u e. Fo example, he A mien o-Ma son 20058 o he PBE o solids9 unc ionals
consis en ly lead o supe io geome ies10,11, while he SCAN me a-gene alized g adien app oxima ion12 yields
o ma ion ene gies ha a e on a e age be e by a ac o o wo han he PBE13. Un o una ely, and in s a k
con as wi h he abundance o PBE da a, he e a e no a ailable compa able la ge scale da ase s calcula ed wi h
hese imp o ed unc ionals.
The e a e a numbe o o he da abases ha use ei he highe accu acy me hods, like G0 W0, o apply
densi y- unc ionals di e en om PBE. Fo example, we can men ion he Compu a ional 2D Ma e ials
Da abase14,15 ha p o ides a da ase o 4000 2D ma e ials calcula ed wi h HSE, G0 W0, RPA and he
1Ins i u ü Physik, Ma in-Lu he -Uni e si ä Halle-Wi enbe g, 06120, Halle (Saale), Ge many. 2CFisUC,
Depa men o Physics, Uni e si y o Coimb a, Rua La ga, 3004-516, Coimb a, Po ugal. 3ins i u ü
Fes kö pe heo ie und -op ik and Eu opean Theo e ical Spec oscopy Facili y, F ied ich-Schille -Uni e si ä Jena,
D-07743, Jena, Ge many. ✉e-mail: [email p o ec ed]
DATA DESC IPTO
OPEN
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Be he-Salpe e equa ion, while JARVIS con ains a la ge numbe o calcula ions wi h dW co ec ions using
Op B88 dW16,17 and pe o med wi h he modi ied Becke-Johnson po en ial18–20.
In a p e ious wo k21 we combined da a om he AFLOW da abase1, he Ma e ials P ojec 2 and om ou
own g oup o c ea e a a he comple e con ex hull o he modynamic s abili y a he PBE le el. The de ails o
he selec ion o he da ase can be ound in e . 21. Speci ically, we selec ed all ma e ials ha we e calcula ed
wi h he same unc ional, pseudopo en ial, as well as U-pa ame e s used in he Ma e ials P ojec . We emo ed
duplica es, i.e. en ies wi h he same space g oup, composi ion and o al ene gy ( ounded o he 4 h digi ). He e
we de e mined he space g oup using pyma gen wi h he “symp ec” keywo d se o 0.1. F om he AFLOW
da abase we u he emo ed all p o o ypes labeled “_DEVIL_PROTOTYPES_” and all o he combina ions o
p o o ypes and pseudopo en ials ha a e no ed as ill-con e ged in he code o e . 22. As AFLOW is s ill known
o con ain ou lie s22, we also emo ed hem om he calcula ion o he hull ollowing a s a egy simila o he
one explained in e . 22. We used he o al ene gies o all he emaining s uc u es o calcula e he con ex hulls
applying he co ec ions om he ma e ials p ojec wo k low o he ene gies.
F om his da ase 23 we selec ed a ound 175k compounds ha we e ei he s able (i.e., on he con ex hull), o
close o s able (wi hin 100 meV/a om o he hull). These we e hen eop imized wi h PBEsol9. Finally, he o al
ene gies we e ee alua ed wi h SCAN12 o c ea e highly accu a e o ma ion ene gies and con ex hulls.
Me hods
Ou s a ing poin was he da ase used in he machine lea ning s udy o e . 21. This included PBE calcula ions
s emming om he Ma e ials P ojec da abase2, AFLOW1, and ou own calcula ions. These we e hen il e ed o
ob ain a homogeneous se in wha ega ds he calcula ion pa ame e s, leading o a da ase con aining mo e han
wo million compounds. We hen cons uc ed he con ex hull o he modynamic s abili y and ex ac ed en ies
ha we e ei he on he hull o wi hin 0.1 eV/a om24,25. The eason o he choice o his cu o was wo old. Fi s ,
i s alue is s ill below he a e age e o in he o ma ion ene gies calcula ed wi h PBE26,27, bu is la ge han he
es ima ed e o in he dis ances o he con ex hull28,29. As such, he compounds ha we e misiden i ied by he
PBE as he modynamically uns able a e likely o be included in he se . Second, he e a e a numbe o ma e ials
ha a e me as able, bu expe imen ally accessible ( o example o composi ions ha ha e mo e han one pol-
ymo ph). We can easonably expec ha he cu o allows o he inclusion o he majo i y o hese cases. We
also elimina ed ma e ials wi h uni cells ha we e oo la ge o ou compu a ional esou ces, leading o a inal
amoun o ~175k compounds.
All calcula ions we e pe o med using densi y- unc ional heo y, wi hin he p ojec o augmen ed wa e
me hod (PAW)30 as implemen ed in he Vienna ab ini io simula ion package (VASP)31,32. We used he PAW se -
ups shipped wi h e sion 5.4 o asp ha include in o ma ion on he kine ic ene gy densi y o he co e elec ons.
We mos ly ollowed he ecommenda ions o he Ma e ials P ojec o he choice o he pseudopo en ials. The
excep ion was Cs, o which we used an imp o ed pseudopo en ial gene a ed by he asp de elope s, as he s ock
PAW se up o en led o nega i e densi ies du ing he sel -consis en cycle, c ashing he calcula ion. All calcula-
ions we e pe o med aking in o accoun spin-pola iza ion, and s a ed om a e omagne ic con igu a ion (as
in he la ge majo i y o high- h oughpu s udies). This mos likely leads o an inco ec spin con igu a ion o
an i e omagne ic sys ems, esul ing in an ene gy highe han he ue g oud-s a e. Howe e , i is well known
ha in mos cases magne ic exchange ene gies a e a he small, so he e o in he o al ene gy is limi ed o a ew
ens o meV/a om. Me h essel-Pax on o de one smea ing wi h a wid h o 0.2 eV was applied in he in eg a ion
o he B illouin zone.
The s uc u es we e op imized using he PBEsol9 app oxima ion, he “High” p ecision keywo d o asp, and
a Γ-cen e ed k-poin g id wi h 2000 k-poin s pe ecip ocal a om, un il he o ces on he a oms we e below
5 meV/Å. To de ec he s uc u es ha equi ed e-op imiza ion we checked ha he he absolu e alue o he
o ces (in meV/Å) and he indi idual componen s o he s ess enso (in meV/Å3), calcula ed wi h PBEsol
wi h s ic e con e gence c i e ia (520 eV o he wa e- unc ion cu o and 8000 k-poin s pe ecip ocal a om),
emained smalle han 0.05. I i was no he case, we inc eased bo h he ene gy cu o and he numbe o
k-poin s and pe o med again he geome y op imiza ion. A ound 3% o all s uc u es equi ed his u he
calcula ion s ep. We no e ha as we had al eady a easonable s a ing poin , speci ically he PBE geome y, he
geome y op imiza ion equi ed a ela i ely small numbe o s eps in mos cases.
A inal ene gy e alua ion wi h he SCAN me a-GGA unc ional was pe o med wi h a cu o o 520 eV, 8000
k-poin s pe ecip ocal a om, and including he non-sphe ical con ibu ions om he g adien co ec ions
inside he PAW sphe es. As expec ed, SCAN calcula ions we e much mo e uns able han PBEsol, due o he
well known nume ical ins abili ies o his unc ional33,34, which led o a much lowe a e age con e gence a e.
In any case, we succeeded in con e ging nea ly all calcula ions. In o al, he calcula ions p esen ed he e equi ed
a ound 10 million CPU hou s.
Da a eco ds
The ou pu iles o asp we e collec ed and p ocessed wi h he pyma gen lib a y35. Each inal da a eco d con-
sis ed o a Compu edS uc u eEn y ha included he chemical composi ion, he o al ene gy, and he de ailed
c ys al s uc u e o he en y. Two iles, con aining all en ies o each unc ional, can be eely downloaded om
he Ma e ials Cloud eposi o y36 and can be loaded i ially using he json module o py hon. Fo con enience,
we also p o ide a summa y o he da a in abula ed o m, ha include he ields lis ed in Table1.
In panel a o Fig.1 we plo he his og am o he numbe o di e en chemical elemen s in ou ma e ials.
We can clea ly see ha he da ase is domina ed by e na y compounds, ollowed by bina y and qua e na y.
Rela i ely ew mul ina y ma e ials wi h mo e han 4 di e en chemical elemen s a e p esen . We can unde s and
his dis ibu ion by conside ing ha he numbe o pe mu a ions inc eases e y apidly wi h he numbe o
chemical elemen s, explaining, e.g., why we ha e many mo e bina ies han elemen a y subs ances o e na y
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han bina y compounds. Howe e , we ha e o keep in mind ha he complexi y o he uni cells also inc eases
and ha mos o he sys ema ic high- h oughpu DFT s udies we e pe o med o e na y sys ems37–42. This can
also be seen in panel (b) o Fig.1 whe e we show a his og am o he numbe o a oms in he p imi i e uni cell.
The dis ibu ion is domina ed by a peak cen e ed a ound i e a oms pe uni cell, a ising om he ma e ials
s emming om he high- h oughpu s udies o AFLOW1 and om ou g oup3,37,38. Ob iously, we do no expec
ha he ue dis ibu ion o all possible he modynamically s able and me as able ma e ials ollows he beha io
depic ed in Fig.1. Finally, in panels (c) and (d) o he same igu e, we plo an his og am o he numbe o ma e-
ials as a unc ion o he space g oup index and o he c ys al sys em. We see ha he mos ep esen ed sys ems
a e he igonal and o ho hombic, while he e agonal and iclinic a e he leas ep esen ed.
In Fig.2 we show he dis ibu ion o chemical elemen s o he calcula ed s uc u es. We conside ed all
elemen s excep noble gases up o bismu h as well as mos lan hanides, and ac inides up o plu onium. We can
obse e some ob ious ends. No su p isingly, he mos common elemen is oxygen due o he abundance o
Composi ion Chemical composi ion o each ma e ial.
Numbe o si es Numbe o a oms in he uni cell.
EPBE To al ene gy pe a om calcula ed wi h PBE (ex ac ed om he p ima y da ase )
EPBEsol To al ene gy pe a om calcula ed wi h PBEsol.
ESCAN To al ene gy pe a om calcula ed wi h SCAN.
VPBE Volume pe a om o he PBE uni cell (ex ac ed om he p ima y da ase ).
VPBEsol Volume pe a om o hePBEsol uni cell.
GapPBEsol Band gap calcula ed wi h PBEsol.
GapSCAN Band gap calcula ed wi h SCAN.
MPBEsol To al magne ic momen pe a om calcula ed wi h PBEsol.
MSCAN To al magne ic momen pe a om calcula ed wi h SCAN.
SSCAN The diagonal elemen s o he s ess enso calcula ed wi h SCAN.
Table 1. Fields included in he summa y o he da a in abula ed o m.
Fig. 1 Dis ibu ion o (a) numbe o di e en chemical elemen s pe uni cell, (b) numbe o a oms pe uni cell,
(c) index o space g oups, and (d) c ys al sys ems o all he ma e ials in ou da ase .
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oxides in ou plane and hei s abili y in ou oxygen- ich a mosphe e. The emaining chalcogens (S, Se, Te) a e
all equally ep esen ed, which is p obably an indica ion o hei chemical simila i y. Fo he halogen amily we
see a dec easing numbe o ma e ials ollowing he dec ease o he elec onega i i y, wi h iodine compounds
being hal as abundan as luo ides. Fo he pnic ogens we wi ness exac ly he opposi e beha io , wi h much
ewe ni ides han compounds con aining an imony. This can be unde s ood om he high chemical s abili y
o he N2 molecule and he a he high nominal oxida ion s a e o ni ogen (−3) ha hinde s he syn hesis o
ni ides. Finally ca bon-con aining ma e ials a e a he sca ce due o he absence o o ganic compounds in ou
da ase .
F om he me als, he wo wi h he highes numbe o compounds a e aluminum and li hium. The o me is
wi hin a clus e o highly ep esen ed chemical elemen s (such as nickel, coppe , zinc, o indium). The excep ion
in his egion o he pe iodic able is gallium, in spi e o i s impo ance in many semiconduc o s used in elec-
onics and op oelec onics. Li hium compounds, on he o he hand, a e much mo e common in ou da ase
han ma e ials con aining any o he alkali elemen , which migh be explained by he popula i y o s udies in li h-
ium compounds in iew o hei applica ion in ba e y echnologies. In e es ingly, in con as o he o he alkali
ea h elemen s, be yllium appea s in ela i ely ew compounds, p obably due o i s high oxici y. Ano he egion
ha exhibi s ela i ely ew compounds is he one cen e ed in anadium and ha includes henium, ha nium,
niobium, e c. We can obse e a con inui y in he alues in his egion ha migh indica e ha hese chemical ele-
men s, o en exhibi ing he e y high oxida ion numbe s o +4, +5 o +6, ha e mo e di icul y p oducing s able
compounds han o he me als wi h lowe oxida ion numbe s. Finally, he leas ep esen ed g oups a e unsu p is-
ingly he lan hanides and he ac inides, showing how li le we know he chemis y o hese chemical elemen s
ha a e essen ial in a mul i ude o echnologies, such as in ha d magne s o in he s o age o nuclea was e.
I is also in e es ing o look a he s uc u al di e si y in ou da ase . Wi h ha objec i e, we used pyma gen
o di ide ou s uc u es in o g oups acco ding o s uc u al simila i y. In o al, ou da a u ned ou o con ain
24706 p o o ypes o 4557 di e en gene ic composi ions. Howe e , and as expec ed, he dis ibu ion o com-
pounds among hese p o o ypes was a he unbalanced. Fo example, 15399 p o o ypes only appea ed once in
he da ase and 2412 only wice. On he o he hand, mos ma e ials belong o jus a ew p o o ypes. The mos
common was by a he Heusle amily o compounds, wi h almos 12 000 composi ions, ollowed by he double
pe o ski e amily wi h mo e han 5000 elemen s. O cou se, hese numbe s e lec no only he chemical s abili y
and size o each one o he amilies, bu also he in e es o he communi y o hese compounds.
Technical Valida ion
In he le panel o Fig.3 we plo he dis ibu ion o he olumes pe a om wi h he PBE (ob ained om he
p ima y da a) and PBEsol. Bo h cu es look simila , wi h a peak a a ound 15 Å3 and skewed owa ds la ge ol-
umes. We can also obse e ha he PBE da a is shi ed owa d la ge olumes wi h espec o PBEsol. This is due
o he well known unde binding o he PBE43 ha leads o la ice cons an s ha a e la ge han hei expe imen-
al alues by 2–3% (and consequen ly olumes ha a e o e es ima ed by ~10%). This unde binding is almos
o ally co ec ed by PBEsol, yielding smalle olumes in much be e ag eemen wi h expe imen . In he igh
panel o he same igu e we plo a his og am o he h ee diagonal componen s o he s ess enso calcula ed
wi h SCAN a he PBEsol geome y. We can see ha he calcula ions yield a he small s esses, showing ha he
s uc u es a e close o mechanical equilib ium. This is expec ed because SCAN, like PBEsol, yields high quali y
geome ies in good ag eemen wi h expe imen 10,44. This also alida es ou p agma ic app oach o using a single
poin SCAN calcula ion a he PBEsol geome ies.
In Fig.4 we show he dis ibu ion o (indi ec ) band gaps calcula ed wi h bo h PBEsol and SCAN. As
expec ed, he cu es decay mono onically wi h he alue o he gap, and exhibi a a ail ha ex ends beyond
10 eV. I is known ha PBEsol, as well as PBE, s ongly unde es ima e he alue o he band gaps by essen ially
a ac o o wo, leading o mean absolu e pe cen age e o s bo de ing he 50%45,46 wi h espec o expe imen .
This is o some ex en co ec ed by SCAN, ha inc eases consis en ly he band gaps leading o a mean absolu e
pe cen age e o o a ound 40%45,46. This inc ease is e iden om Fig.4, whe e he SCAN band gap dis ibu ion
is shi ed o he igh wi h espec o PBEsol.
Fig. 2 Pe iodic able depic ing he chemical elemen s p esen in ou da ase . The numbe benea h he chemical
symbol is he numbe o ma e ials p esen in he da ase ha con ain he gi en elemen .
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Finally, we pe o med an analysis o he con ex hulls ob ained wi h PBE, PBEsol, and SCAN. The hulls
con ained 36985, 40246 and 38692 ma e ials espec i ely. These di e ences a e expec ed, and mos ly s em om
ela i ely small changes in he o ma ion ene gy o compounds ha we e close o he hull. The dis ibu ions
o he dis ances o he con ex hull o he modynamic s abili y a e plo ed in he igh panel o Fig.4. Fo his
plo , we always emo ed he compound unde s udy om he hull, allowing he e o e o nega i e dis ances.
Al hough his allows o a be e in e p e a ion o he esul s, we should emembe ha echnically speaking all
compounds wi h nega i e dis ances should be placed s ic ly a ze o. Bo h dis ibu ions g ow as o nega i e
dis ances o he hull, ha ing a ma ked peak a ze o. The main con ibu o s o his beha io a e he expe imen al
compounds. The numbe o ma e ials wi h posi i e dis ance o he hull is ela i ely cons an , un il eaching ou
cu o a ±0.2 eV/a om. This cu o is ob iously smea ed o he PBEsol and SCAN calcula ions.
As an illus a ion, we plo in Fig.5 he e na y phase diag ams o Li–Al–Cu and Mg–Sc–Zn. We see ha he
h ee unc ionals ag ee o a la ge ex en on which a e he s able ma e ials. Howe e , some di e ences a e also
clea . Fo example, MgZn is s able wi h he PBE unc ional bu no wi h PBEsol o SCAN, o LiAl3 is uns able
wi h SCAN bu s able wi h he o he wo unc ionals. In any case, compounds ha a e s able wi h one unc ional
do appea s able, o a leas me as able wi h he o he unc ionals. O cou se, SCAN is he mos accu a e o he
Fig. 3 Le : Dis ibu ion and sca e plo s o olumes pe a om calcula ed wi h PBE ( om he p ima y da a) and
PBEsol unc ionals. The wid h o he bins is 0.35 Å3/a om. Righ : dis ibu ion and sca e plo s o he diagonal
componen s o he s ess enso calcula ed wi h PBEsol and SCAN a PBEsol geome ies. The wid h o he bins
is 0.6 meV/Å3.
Fig. 4 Le : Dis ibu ion and sca e plo s o he (in)di ec band gaps calcula ed wi h PBEsol and SCAN a he
PBEsol geome y. The wid h o he bins is 0.1 eV. Righ : Dis ibu ion and sca e plo s o he dis ances o he
con ex hull calcula ed wi h PBEsol and SCAN a PBEsol geome ies. The co esponding hulls con ain 40246
and 38692 ma e ials. The wid h o he bins is 2 meV/a om.

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h ee unc ionals in wha conce ns o ma ion ene gies and dis ances o he con ex hull, so he SCAN diag ams
should on a e age ha e he highes accu acy.
Usage No es
The da a can be downloaded om he Ma e ials Cloud eposi o y36. The ene gies, composi ions, and s uc-
u es o each ma e ial a e o ma ed as Compu edS uc u eEn ies and s o ed as comp essed json iles. They can
he e o e be i ially loaded in py hon and analyzed wi h pyma gen. We no e ha we used e sion 2019.10.2 o
pyma gen, bu he da a should be compa ible wi h o he e sions.
Code a ailabili y
All da a can be easily p ocessed wi h publicly a ailable ools such as json and pyma gen35. An example usage is
p o ided wi h he da a. The da ase was gene a ed wi h VASP, he bash and py hon sc ip s o gene a e inpu iles
o manage he ou pu iles can be downloaded om gi hub eposi o y: h ps://gi hub.com/hyllios/u ils/ ee/main/
h _pd_scan.
Recei ed: 16 Ap il 2021; Accep ed: 25 Janua y 2022;
Published: xx xx xxxx
e e ences
1. Cu a olo, S. e al. AFLOW: An au oma ic amewo k o high- h oughpu ma e ials disco e y. Compu . Ma e . Sci. 58, 218–226,
h ps://doi.o g/10.1016/j.comma sci.2012.02.005 (2012).
2. Jain, A. e al. Commen a y: The ma e ials p ojec : A ma e ials genome app oach o accele a ing ma e ials inno a ion. APL Ma e . 1,
011002, h ps://doi.o g/10.1063/1.4812323 (2013).
3. Kö bel, S., Ma ques, M. A. L. & Bo i, S. S able hyb id o ganic–ino ganic halide pe o ski es o pho o ol aics om ab ini io high-
h oughpu calcula ions. J. Ma e . Chem. A 6, 6463–6475, h ps://doi.o g/10.1039/c7 a08992a (2018).
4. G aužiny ė, M., Bo i, S., Ma ques, M. A. L., Goedecke , S. & Flo es-Li as, J. A. Compu a ional accele a ion o p ospec i e dopan
disco e y in cup ous iodide. Phys. Chem. Chem. Phys. 21, 18839–18849, h ps://doi.o g/10.1039/c9cp02711d (2019).
5. Flo es-Li as, J. A., Sa mien o-Pé ez, R., Bo i, S., Goedecke , S. & Ma ques, M. A. L. Ra e-ea h magne ic ni ide pe o ski es. JPhys
Ma e . 2, 025003, h ps://doi.o g/10.1088/2515-7639/ab083e (2019).
6. Wang, H.-C., Pis o , P., Ma ques, M. A. L. & Bo i, S. Double pe o ski es as p- ype conduc ing anspa en semiconduc o s: a high-
h oughpu sea ch. J. Ma e . Chem. A 7, 14705–14711, h ps://doi.o g/10.1039/c9 a01456j (2019).
7. Pe dew, J. P., Bu ke, K. & E nze ho , M. Gene alized g adien app oxima ion made simple. Phys. Re . Le . 77, 3865, h ps://doi.
o g/10.1103/PhysRe Le .77.3865 (1996).
8. A mien o, R. & Ma sson, A. E. Func ional designed o include su ace e ec s in sel -consis en densi y unc ional heo y. Phys. Re .
B 72, 085108, h ps://doi.o g/10.1103/PhysRe B.72.085108 (2005).
9. Pe dew, J. P. e al. Res o ing he densi y-g adien expansion o exchange in solids and su aces. Phys. Re . Le . 100, 136406, h ps://
doi.o g/10.1103/PhysRe Le .100.136406 (2008).
10. Csonka, G. I. e al. Assessing he pe o mance o ecen densi y unc ionals o bulk solids. Phys. Re . B 79, 155107, h ps://doi.
o g/10.1103/PhysRe B.79.155107 (2009).
11. T an, F., S elzl, J. & Blaha, P. Rungs 1 o 4 o DFT Jacob’s ladde : Ex ensi e es on he la ice cons an , bulk modulus, and cohesi e
ene gy o solids. J. Chem. Phys. 144, 204120, h ps://doi.o g/10.1063/1.4948636 (2016).
Fig. 5 Te na y phase diag ams o he Li–Al–Cu (uppe panel) and Mg–Sc–Zn (lowe panel) sys ems, calcula ed
wi h he PBE (le ), PBEsol (middle) and SCAN ( igh ). The blue poin s indica e composi ions on he con ex
hull, while ed poin s deno e ma e ials ha a e wi hin 50 meV/a om om he hull.
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Scien i ic Da a | (2022) 9:64 | h ps://doi.o g/10.1038/s41597-022-01177-w
www.na u e.com/scien i icda a
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12. Sun, J., Ruzsinszky, A. & Pe dew, J. P. S ongly cons ained and app op ia ely no med semilocal densi y unc ional. Phys. Re . Le .
115, 036402, h ps://doi.o g/10.1103/PhysRe Le .115.036402 (2015).
13. Zhang, Y. e al. E icien i s -p inciples p edic ion o solid s abili y: Towa ds chemical accu acy. Npj Compu . Ma e . 4, h ps://doi.
o g/10.1038/s41524-018-0065-z (2018).
14. Haas up, S. e al. The compu a ional 2D ma e ials da abase: high- h oughpu modeling and disco e y o a omically hin c ys als.
2D Ma e ials 5, 042002, h ps://doi.o g/10.1088/2053-1583/aac c1 (2018).
15. Gje ding, M. N. e al. Recen p og ess o he compu a ional 2d ma e ials da abase (c2db). 2D Ma e ials 8, 044002, h ps://doi.
o g/10.1088/2053-1583/ac1059 (2021).
16. Thonhause , T. e al. Van de waals densi y unc ional: Sel -consis en po en ial and he na u e o he an de waals bond. Phys. Re .
B 76, 125112, h ps://doi.o g/10.1103/PhysRe B.76.125112 (2007).
17. Klimeš, J. C. V., Bowle , D. R. & Michaelides, A. Van de waals densi y unc ionals applied o solids. Phys. Re . B 83, 195131, h ps://
doi.o g/10.1103/PhysRe B.83.195131 (2011).
18. Choudha y, K. e al. The join au oma ed eposi o y o a ious in eg a ed simula ions (JARVIS) o da a-d i en ma e ials design.
npj Compu a ional Ma e ials 6, h ps://doi.o g/10.1038/s41524-020-00440-1 (2020).
19. Choudha y, K. e al. Compu a ional sc eening o high-pe o mance op oelec onic ma e ials using Op B88 dw and TB-mBJ
o malisms. Scien i ic Da a 5, h ps://doi.o g/10.1038/sda a.2018.82 (2018).
20. Choudha y, K., Cheon, G., Reed, E. & Ta azza, F. Elas ic p ope ies o bulk and low-dimensional ma e ials using an de Waals
densi y unc ional. Phys. Re . B 98, 014107, h ps://doi.o g/10.1103/PhysRe B.98.014107 (2018).
21. Schmid , J., Pe e sson, L., Ve dozzi, C., Bo i, S. & Ma ques, M. A. L. C ys al g aph a en ion ne wo ks o he p edic ion o s able
ma e ials. Science Ad ances 7, eabi7948, h ps://doi.o g/10.1126/sciad .abi7948 (2021).
22. Oses, C. e al. A low-chull: Cloud-o ien ed pla o m o au onomous phase s abili y analysis. J. Chem. In . Model. 58(12), 2477–2490,
h ps://doi.o g/10.1021/acs.jcim.8b00393 (2018).
23. Schmid , J. & Pe e sson, L. C ys al-g aph a en ion ne wo ks o he p edic ion o s able ma e ials. Ma e ials Cloud h ps://a chi e.
ma e ialscloud.o g/ eco d/2021.222 (2021).
24. Eme y, A. A. & Wol e on, C. High- h oughpu DFT calcula ions o o ma ion ene gy, s abili y and oxygen acancy o ma ion
ene gy o ABO3 pe o ski es. Sci. Da a 4, h ps://doi.o g/10.1038/sda a.2017.153 (2017).
25. Sun, W. e al. The he modynamic scale o ino ganic c ys alline me as abili y. Sci. Ad . 2, e1600225, h ps://doi.o g/10.1126/
sciad .1600225 (2016).
26. Sa mien o-Pé ez, R., Bo i, S. & Ma ques, M. A. L. Op imized exchange and co ela ion semilocal unc ional o he calcula ion o
ene gies o o ma ion. J. Chem. Theo y Compu . 11, 3844–3850, h ps://doi.o g/10.1021/acs.jc c.5b00529 (2015).
27. S e ano ić, V., Lany, S., Zhang, X. & Zunge , A. Co ec ing densi y unc ional heo y o accu a e p edic ions o compound
en halpies o o ma ion: Fi ed elemen al-phase e e ence ene gies. Phys. Re . B 85, 115104, h ps://doi.o g/10.1103/
PhysRe B.85.115104 (2012).
28. Hau ie , G., Ong, S. P., Jain, A., Moo e, C. J. & Cede , G. Accu acy o densi y unc ional heo y in p edic ing o ma ion ene gies o
e na y oxides om bina y oxides and i s implica ion on phase s abili y. Phys. Re . B 85, 155208, h ps://doi.o g/10.1103/
PhysRe B.85.155208 (2012).
29. Ba el, C. J., Weime , A. W., Lany, S., Musg a e, C. B. & Holde , A. M. The ole o decomposi ion eac ions in assessing i s -
p inciples p edic ions o solid s abili y. Npj Compu . Ma e . 5, 1–9, h ps://doi.o g/10.1038/s41524-018-0143-2 (2019).
30. Blöchl, P. E. P ojec o augmen ed-wa e me hod. Phys. Re . B 50, 17953–17979, h ps://doi.o g/10.1103/PhysRe B.50.17953 (1994).
31. K esse, G. & Fu hmülle , J. E iciency o ab-ini io o al ene gy calcula ions o me als and semiconduc o s using a plane-wa e basis
se . Compu . Ma e . Sci. 6, 15–50, h ps://doi.o g/10.1016/0927-0256(96)00008-0 (1996).
32. K esse, G. & Fu hmülle , J. E icien i e a i e schemes o ab ini io o al-ene gy calcula ions using a plane-wa e basis se . Phys. Re .
B 54, 11169–11186, h ps://doi.o g/10.1103/PhysRe B.54.11169 (1996).
33. Ba ók, A. P. & Ya es, J. R. Regula ized SCAN unc ional. J. Chem. Phys. 150, 161101, h ps://doi.o g/10.1063/1.5094646 (2019).
34. Fu ness, J. W., Kaplan, A. D., Ning, J., Pe dew, J. P. & Sun, J. Accu a e and nume ically e icien 2SCAN me a-gene alized g adien
app oxima ion. J. Phys. Chem. Le . 11, 8208–8215, h ps://doi.o g/10.1021/acs.jpcle .0c02405 (2020).
35. Ong, S. P. e al. Py hon ma e ials genomics (pyma gen): A obus , open-sou ce py hon lib a y o ma e ials analysis. Compu . Ma e .
Sci. 68, 314–319, h ps://doi.o g/10.1016/j.comma sci.2012.10.028 (2013).
36. Schmid , J., Wang, H.-C., Ce quei a, T. F. T., Bo i, S. & Ma ques, M. A. L. A new da ase o 175k s able and me as able ma e ials
calcula ed wi h he PBEsol and SCAN unc ionals. Ma e ials Cloud h ps://a chi e.ma e ialscloud.o g/ eco d/2021.164 (2021).
37. S chmid , J. e al. P edic ing he he modynamic s abili y o solids combining densi y unc ional heo y and machine lea ning. Chem.
Ma e . 29, 5090–5103, h ps://doi.o g/10.1021/acs.chemma e .7b00156 (2017).
38. Schmid , J., Chen, L., Bo i, S. & Ma ques, M. A. L. P edic ing he s abili y o e na y in e me allics wi h densi y unc ional heo y
and machine lea ning. J. Chem. Phys. 148, 241728, h ps://doi.o g/10.1063/1.5020223 (2018).
39. Saal, J. E., Ki klin, S., Aykol, M., Me edig, B. & Wol e on, C. Ma e ials design and disco e y wi h high- h oughpu densi y unc ional
heo y: The open quan um ma e ials da abase (OQMD). JOM 65, 1501–1509, h ps://doi.o g/10.1007/s11837-013-0755-4 (2013).
40. Hau ie , G., Fische , C. C., Jain, A., Muelle , T. & Cede , G. Finding na u e’s missing e na y oxide compounds using machine
lea ning and densi y unc ional heo y. Chem. Ma e . 22, 3762–3767, h ps://doi.o g/10.1021/cm100795d (2010).
41. Shi, J. e al. High- h oughpu sea ch o e na y chalcogenides o p- ype anspa en elec odes. Sci. Rep. 7, h ps://doi.o g/10.1038/
s ep43179 (2017).
42. Oliynyk, A. O. e al. High- h oughpu machine-lea ning-d i en syn hesis o ull-heusle compounds. Chem. Ma e . 28, 7324–7331,
h ps://doi.o g/10.1021/acs.chemma e .6b02724 (2016).
43. Haas, P., T an, F. & Blaha, P. Calcula ion o he la ice cons an o solids wi h semilocal unc ionals. Phys. Re . B 79, h ps://doi.
o g/10.1103/phys e b.79.085104 (2009).
44. Isaacs, E. B. & Wol e on, C. Pe o mance o he s ongly cons ained and app op ia ely no med densi y unc ional o solid-s a e
ma e ials. Phys. Re . Ma e . 2, 063801, h ps://doi.o g/10.1103/PhysRe Ma e ials.2.063801 (2018).
45. B o lido, P. e al. Exchange-co ela ion unc ionals o band gaps o solids: benchma k, epa ame iza ion and machine lea ning. Npj
Compu . Ma e . 6, h ps://doi.o g/10.1038/s41524-020-00360-0 (2020).
46. Bo lido, P. e al. La ge-scale benchma k o exchange-co ela ion unc ionals o he de e mina ion o elec onic band gaps o solids.
J. Chem. Theo y Compu . 15, 5069–5079, h ps://doi.o g/10.1021/acs.jc c.9b00322 (2019).
Acknowledgemen s
The au ho s g a e ully acknowledge he Gauss Cen e o Supe compu ing e.V. (www.gauss-cen e.eu) o
unding his p ojec by p o iding compu ing ime on he GCS Supe compu e Supe MUC-NG a he Leibniz
Supe compu ing Cen e unde he p ojec pn68wa. We would also like o hank Geo g K esse o p o iding us
wi h an imp o ed PAW se up o Cs.
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