A dataset of 175k stable and metastable materials calculated with the PBEsol and SCAN functionals

1 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 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 2 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 www.na u e.com/scien i icda a/ 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 3 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 www.na u e.com/scien i icda a/ 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 . 4 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 www.na u e.com/scien i icda a/ 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 . 5 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 www.na u e.com/scien i icda a/ 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. 6 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 www.na u e.com/scien i icda a/ 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. 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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. 8 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 www.na u e.com/scien i icda a/ Au ho con ibu ions J.S., H.W. and M.A.L.M. pe o med he calcula ions. 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